Citation
Toughening in Shape Memory Alloy Reinforced Composites

Material Information

Title:
Toughening in Shape Memory Alloy Reinforced Composites
Creator:
Barrie, Fatmata
Place of Publication:
[Gainesville, Fla.]
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (209 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Materials Science and Engineering
Committee Chair:
MYERS,MICHELE V
Committee Co-Chair:
SODANO,HENRY
Committee Members:
MECHOLSKY,JOHN J,JR
PATTERSON,BURTON ROE
VU,LOC QUOC
Graduation Date:
12/13/2013

Subjects

Subjects / Keywords:
Austenite ( jstor )
Composite materials ( jstor )
Fracture strength ( jstor )
J integral ( jstor )
Martensite ( jstor )
Moduli of elasticity ( jstor )
Phase transformations ( jstor )
Retraining ( jstor )
Shape memory alloys ( jstor )
Steels ( jstor )
Materials Science and Engineering -- Dissertations, Academic -- UF
composite -- fracture -- martensite -- toughness
Genre:
Electronic Thesis or Dissertation
born-digital ( sobekcm )
Materials Science and Engineering thesis, Ph.D.

Notes

Abstract:
Materials capable of undergoing martensitic phase transformations have been shown to inherently increase the fracture toughness of monolithic and composite materials, in a process known as transformation toughening.  This toughening behavior via martensitic transformations has been extensively studied in transformation induced plasticity (TRIP) steels, stabilized zirconia, and some titanium alloy systems, however there is a limited amount of data on the effect of the martensitic phase transformation in composites reinforced with un-prestrained shape memory alloys (SMAs). Therefore, the objective of this work was to gain a fundamental understanding of how the constrained SMA martensitic phase transformation affects the fracture toughness of SMA reinforced composites. J-integral fracture toughness testing was performed on nickel titanium (NiTi) SMAs in both epoxy and metal matrices.  In addition to the SMAs, non-transforming aluminum and steel reinforcements were tested for comparative purposes.  Systematic single fiber pullout tests were also performed on epoxy composites embedded with NiTi SMA wires to determine the effect of the martensite phase transformation and variant reorientation processes on composite debonding since the interfacial behavior is known to affect composite fracture toughness.  The NiTi was heat-treated to produce varying stable room temperature phases, elastic moduli, and transformation stresses. This work found that SMA fibers that were deformed in the austenite phase had greater debond loads as compared to SMAs that were deformed in the martensite phase for the tested embedded fiber lengths for the tested embedded lengths.  Moreover, the SMA martensite transformation and variant reorientation did not appear to inherently increase the fracture toughness of a composite for the composite geometry and reinforcement orientation examined.  The driving factor of toughening in SMA fiber reinforced composites may be the mechanical properties, elastic modulus and yield stress.  The conclusions drawn were corroborated through analytical studies. In order to maximize the SMA contribution to fracture toughness, SMAs may likely need to be pre-strained prior to being embedded within a matrix.  Pre-straining results in compressive stresses on the matrix because the SMAs want to retract to recover its original shape.  In this sense the compressive mechanism within the pre-strained SMA and the stress-induced phase transformation in stabilized zirconia are similar. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: MYERS,MICHELE V.
Local:
Co-adviser: SODANO,HENRY.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2014-12-31
Statement of Responsibility:
by Fatmata Barrie.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright by Fatmata Barrie. Permission granted to University of Florida to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
12/31/2014
Resource Identifier:
907646075 ( OCLC )
Classification:
LD1780 2013 ( lcc )

Downloads

This item has the following downloads:


Full Text

PAGE 1

1 TOUGHENING IN SHAPE MEMORY ALLOY REINFORCED COMPOSITES By FATMATA HAJA BARRIE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTO R OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013

PAGE 2

2 2013 Fatmata Barrie

PAGE 3

3 To my mom, dad, and family

PAGE 4

4 ACKNOWLEDGMENTS I would first like to state my sincere appreciation for my mother and father for their cont inued encouragement and support throughout my life. I would also like to acknowledge m y sister and brother for always keeping life entertaining Additionally, I would like to acknowledge m y extended family members that are far too numerous to name thank you. I would also like to thank my committee chair, Dr. Manuel for her continued support, guidance, and encouragement throughout the course of this work and also for giving me the freedom and backing to p ursue and present my research at a number of na tional and international conferences Thanks also go to my committee members, Drs. Mecholsky, Vu Quoc, Sodano, and Patterson for their guidance throughout the course of this research. Thank you Dr s Sinnott and Mecholsky for those helpful discussions reg arding my future endeavors I would also like to th ank Dr. Greenslet and Arthur Gr aziano for assisting me in collecting data surface roughness data. There are a special group of people that I have grown to know during my time in Gainesville that made thos e tough times bearable. Thank you Darina, Alondra, and Derek. You all are amazing. Thanks also go to Shruti, Alison, Peiru, Cas Billy, and Miguel I would like to acknowledge the current Materials Design and Prototyping Laboratory (MDPL) members. I w ould also like to thank the University of Florida South East Alliance for the Graduate Engineering Professoriate ( SEAGEP ) for putting together informative conferences, study abroad trips, and funding. Lastly, I would like to acknowledge the NASA Office o f the Chief Technologist's Space Technology Research Opportunity Early Career Faculty grant number NNX12AQ42G and the University of Central Florida NASA Florida Space Grant

PAGE 5

5 Consortium and the National Science Foundation grant number CMMI 0845868 for the ir financial support.

PAGE 6

6 TABLE OF CONTENTS page ACK NOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ .......... 10 LIST OF FIGURES ................................ ................................ ................................ ........ 12 LIST OF ABBR EVIATIONS ................................ ................................ ........................... 20 ABSTRACT ................................ ................................ ................................ ................... 22 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 24 Motivation ................................ ................................ ................................ ............... 24 Objective ................................ ................................ ................................ ................. 27 Dissertation Guidelines ................................ ................................ ........................... 28 2 BACKGROUND ................................ ................................ ................................ ...... 30 Fracture Toughness ................................ ................................ ................................ 30 Relevant Toughening Mechanisms ................................ ................................ ......... 31 Crack Bridging ................................ ................................ ................................ .. 31 Interfacial Strength ................................ ................................ ........................... 32 Transformation Toughening ................................ ................................ ............. 32 Crack Bo wing ................................ ................................ ................................ ... 34 Microcracking ................................ ................................ ................................ ... 34 Crack Shielding (via plasticity) ................................ ................................ .......... 35 Sha pe Memory Alloys ................................ ................................ ............................. 35 Nickel Titanium (NiTi) Shape Memory Alloys ................................ ................... 37 Energy Dissipation and Absorption in Shape Memory Alloys ........................... 38 3 EQUIPMENT AND EXPERIMENTAL TECHNQUES ................................ .............. 48 Encapsulation/Heat Treatments ................................ ................................ .............. 48 Differential Scanning Calorimetry (DSC) ................................ ................................ 48 X ray Florescence Spectroscopy (XRF) ................................ ................................ .. 49 Optical Profilometer ................................ ................................ ................................ 49 Mechanical Testing ................................ ................................ ................................ 50 Tensile Tests ................................ ................................ ................................ .... 50 Polymer ................................ ................................ ................................ ...... 50 Metal ................................ ................................ ................................ .......... 51 Single Fiber Pullout ................................ ................................ .......................... 51 Epoxy matrix ................................ ................................ .............................. 52

PAGE 7

7 Metal matrix ................................ ................................ ............................... 52 Fracture Toughness ................................ ................................ ......................... 52 Epoxy matrix ................................ ................................ ................................ ..... 53 Metal matrix ................................ ................................ ................................ ...... 54 Optical Microscopy ................................ ................................ ................................ 57 Scanning Electron Microscopy (SEM) ................................ ................................ ..... 58 4 EFFECT OF MARTENSITE TRANSFORMATION AND REORIENTATION ON DEBONDING ................................ ................................ ................................ .......... 65 Materials and Characterization ................................ ................................ ............... 66 Heat Treatment Effect on Shape Memory Alloys ................................ .................... 67 Results and Discussion ................................ ................................ ........................... 69 Effect of Phase Type on Debond Behavior ................................ ....................... 69 Effect of Transformation on Debond Behavior ................................ .................. 71 SMA Surface Roughness Analysis ................................ ................................ ... 72 Pullout Energy ................................ ................................ ................................ .. 73 Summary ................................ ................................ ................................ ................ 74 5 INTRINSIC TOUGHENING IN SHAPE MEMORY ALLOY EMBEDDED COMPOSITES ................................ ................................ ................................ ........ 84 Materials and Methods ................................ ................................ ............................ 84 Materials Selection ................................ ................................ ........................... 84 Materials Characterization ................................ ................................ ................ 86 Single Fiber Pullout Test ................................ ................................ .................. 87 Results and Discussion ................................ ................................ ........................... 87 Fracture Toughnes s ................................ ................................ ......................... 87 Effect of Elastic Modulus and Yield /Transformation Stress on Fracture Toughness ................................ ................................ ................................ .... 88 Evaluating Reinforcement Martensitic Ph ase Transformation through Beam Analysis ................................ ................................ ................................ ......... 89 Single Fiber Pullout ................................ ................................ .......................... 92 Summary ................................ ................................ ................................ ................ 93 6 EXTRINSIC TOUGHENING OF SHAPE MEMORY ALLOY COMPOSITES: EPOXY MATRIX ................................ ................................ ................................ ... 104 Materials and Methods ................................ ................................ .......................... 105 Materials Sel ection ................................ ................................ ......................... 105 Materials Characterization ................................ ................................ .............. 106 Results and Discussion ................................ ................................ ......................... 107 Fracture Toughness ................................ ................................ ....................... 107 Composite Debonding Behavior ................................ ................................ ..... 109 Aluminum debonding behavior ................................ ................................ 109 Shape memory alloy debonding behavior ................................ ................ 110 Single Fiber Pullout ................................ ................................ ........................ 110

PAGE 8

8 Composite Fracture Surfaces ................................ ................................ ......... 112 Analytical Determination of Transformation/Reorientation ............................. 112 Crack Bridging Fracture Toughness Contribution ................................ ........... 114 Aluminum ................................ ................................ ................................ 115 Shape memory alloy (austenite) ................................ .............................. 116 Shape memory alloy (martensite) ................................ ............................ 116 Discussion ................................ ................................ ................................ 117 Summary ................................ ................................ ................................ .............. 117 7 EXTRINSIC TOUGHENING OF SHAPE M EMORY ALLOY COMPOSITES: METAL MATRIX ................................ ................................ ................................ ... 136 Materials and Methods ................................ ................................ .......................... 137 Materials Selection ................................ ................................ ......................... 137 Materials Characterization ................................ ................................ .............. 138 Composite Fabrication Effects on Reinforcements ................................ ............... 139 Fabrication Effect s on Shape Memory Alloy ................................ ................... 139 Fabrication Effects on Steel ................................ ................................ ............ 140 Interface ................................ ................................ ................................ ......... 140 Results and Discussions ................................ ................................ ....................... 141 Single Fiber Pull Out Testing ................................ ................................ .......... 141 J Integral Fracture Toughness ................................ ................................ ....... 143 Fracture Surfaces ................................ ................................ ........................... 143 Summary ................................ ................................ ................................ .............. 145 8 CONCLUSIONS ................................ ................................ ................................ ... 163 Contribution to Field ................................ ................................ .............................. 164 Future Work ................................ ................................ ................................ .......... 165 APPENDIX A DESIGN OF MIXTURES ................................ ................................ ....................... 168 B EXPERIMENTAL DATA ................................ ................................ ........................ 175 Single Fiber Pullout Data ................................ ................................ ...................... 175 Intrinsic Toughening Data ................................ ................................ ..................... 175 Extrinsic Toughening Data ................................ ................................ .................... 176 C DERIVATION OF BENDING STRESS EQUATIONS ................................ ........... 189 Neutral Axis ................................ ................................ ................................ .......... 189 Reinforcement Bending Stress ................................ ................................ ............. 191 D SHAPE MEMORY ALLOY ELECTRICAL RESISITIVITY CHARACTERIZATION 195 LIST OF REFERENCES ................................ ................................ ............................. 197

PAGE 9

9 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 209

PAGE 10

10 LIST OF TABLES Table page 2 1 The table shows elastic modulus and yield (SMA transformation stress) of the NiTi and steel wires. ................................ ................................ ..................... 46 4 1 The table shows relevant prope rties of the reinforcements. Water quenched is represented by WQ. The A and M designations represent the austenite and martensite phases, respectively. ................................ ................................ 76 4 2 The table shows the transformat ion temperatures of the heat treated SMAs. .... 76 5 1 The table shows the mechanical properties and transformation temperatures of the reinforcing elements used in this study. ................................ .................... 96 5 2 The table shows the transformation temperatures of the NiTi and NiTi ht reinforcing elements used in this study. ................................ .............................. 96 6 1 The table lists the m echanical properties of the constituent materials used in the extrinsic toughness, epoxy matrix study. *martensite transformation stress. **martensite variant reorientation stress. ................................ ............. 121 6 2 T he table lists the transformation temperatures of the NiTi SMAs used in the extrinsic toughness, epoxy matrix study. ................................ .......................... 121 6 3 The table shows the values used for the Al, NiTi austenite, and NiT i martensite reinforcements when calculating G using the Spring Model Method. ................................ ................................ ................................ ............ 135 7 1 The table lists relevant mechanical properties of the NiTi, steel, and Zn Al used in the metal matrix stu 148 A 1 The table shows the maximum and minimum compositions of the epoxy mixture. ................................ ................................ ................................ ............. 171 A 2 The table shows the run orders in addition to the mixture component weight ratios. The highlighted rows refer to the runs that were removed when performing the calculations. ................................ ................................ .............. 173 B 1 The table shows the actual embedded fiber length and corresponding debond loads of the sample were embedded at approximately 3 mm. ............. 179 B 2 The table shows the actual embedded fiber lengt h and corresponding debond loads of the sample were embedded at approximately 4 mm. The asterisk indicate the samples that transformed (*) or reoriented (**). ............... 179

PAGE 11

11 B 3 The table shows relevant values used to calculate the J integral of the monolithic epoxy samples. The plots were shown in the Intrinsic Toughening Chapter. ................................ ................................ ................................ ............ 180 B 4 The table shows relevant values used to calculate t he J integral of the aluminum embedded epoxy samples. The plots were shown in the Intrinsic Toughening Chapter. ................................ ................................ ........................ 181 B 5 The table shows relevant values used to calculate the J integral of the steel embedded epoxy samples. The plots were shown in the Intrinsic Toughening Chapter. ................................ ................................ ........................ 182 B 6 The table shows relevant values used to calculate the J integral of the NiTi embedded epoxy sa mples. The plots were shown in the Intrinsic Toughening Chapter. ................................ ................................ ........................ 183 B 7 The table shows relevant values used to calculate the J integral of the NiTi ht embedded epoxy samples. The plots wer e shown in the Intrinsic Toughening Chapter. ................................ ................................ ........................ 184 B 8 The table shows relevant values used to calculate the J integral of the monolithic samples. The plots were shown in the Extrinsic Tougheni ng Chapter. ................................ ................................ ................................ ............ 185 B 9 The table shows relevant values used to calculate the J integral of the aluminum reinforced epoxy samples. ................................ ............................... 186 B 10 The table shows relevant values used to calculate the J integral of the NiTi austenite reinforced epoxy samples. ................................ ................................ 187 B 11 The table shows relevant values used to calculate the J integr al of the NiTi martensite reinforced epoxy samples. ................................ .............................. 188

PAGE 12

12 LIST OF FIGURES Figure page 2 1 The schematic shows crack bridging in the presence of rein forcing elements. .. 41 2 2 The schematic shows an example of the transformation toughening phenomena that can occur in stabilized zirconia. The black particles represent the tetragonal zirconia particles and the red particles near the crack tip indicate a transformed particle. ................................ ............................ 41 2 3 The schematic shows crack bowing in a composites. ................................ ........ 42 2 4 The schematic shows the SMA pseudoelastic behavior. The regions correspond to the austenite elastic deformation, martensite transformation, martensite elastic deformation, and martensite plastic deformation. .................. 43 2 5 The schematic shows the SMA shape memory behavior. After martensite variant reorientation, the SMA must be heated above the AF temperature to recover its original shape. ................................ ................................ ................... 44 2 6 The schematic shows the shape recovery mechanism in shape memory alloys. ................................ ................................ ................................ ................. 45 2 7 The schematic shows how energy is spent in an SMA in the austenite phase, an SMA in the martensite phase, and a non transforming metal. ....................... 46 2 8 The graph shows the pseudoelastic behavior of NiTi SMA wires that were subjected to incremental strains and finally tested to fail ure. When the SMA is deformed within the plateau region, the deformation is recoverable. .............. 47 2 9 The graph shows the deformation behavior of carbon steel 1080 steel wire incrementally loaded a nd unloaded to failure. Cycle 1 corresponded to the steel wire being loaded elastically. ................................ ................................ ..... 47 3 1 The graph shows a representative DSC curve of the SMA transformation temperatures. An example of the extrapolated onset method that was used to calculate the transformation temperatures is also shown. .............................. 59 3 2 The schematic shows the dimensions of the tensile specimens used to perform me chanical testing. ................................ ................................ ................ 59 3 3 The images show representative surface map images. ................................ ... 60 3 4 The schematic shows the parameters require d to calculate the surface roughness, Ra. ................................ ................................ ................................ ... 61 3 5 This schematic shows the single fiber pullout test setup. ................................ ... 61

PAGE 13

13 3 6 The picture sh ows an Oomoo silicon rubber single fiber pullout mold used to make the epoxy matrix single fiber pullout samples. ................................ .......... 62 3 7 The image shows a picture of the graphite crucible. ................................ ........... 62 3 8 The picture shows one of the Oomoo silicon rubber fracture toughness molds used to make the epoxy samples. The molds also had openings for wire placement. ................................ ................................ ................................ .......... 63 3 9 The schematic shows the 3 point bend setup and sample placement. ............... 63 3 10 The schematic shows the unstable crack growth, stable crack growth, and the initial crack region of the epoxy fracture toughness samples. The picture shows an optical microscopy image of an actual fracture surface. ..................... 64 3 11 The picture shows the graphite molds used to make the metal matr ix fracture toughness samples along with the wire placement within the mold. ................... 64 4 1 The graph shows the SMA properties of the wires used in this study with the data point labels explained in t able 1. Each data point represents the averaged results of 5 tested samples. ................................ ................................ 77 4 2 The optical microscopy image shows the as received NiTi microstructure. ........ 77 4 3 The NiTi microstructure of a wire subjected to a 1000 C, 1 hour heat treatment. The optical microscopy image was taken at 50X microstructure. ..... 78 4 4 The si ngle fiber pullout results for all of the single fiber pullout samples. Unfilled data points indicate that the sample experienced the martensitic transformation or reorientation. ................................ ................................ ........ 78 4 5 Th e curve shows a single fiber pullout curve for the M259 sample that had an embedded length of 3.96 mm. At approximately 1.0 mm of extension, the NiTi begins to undergo a martensitic reorientation. ................................ ............ 79 4 6 The graph shows the debond load versus the embedded fiber length for the 3mm embedded fiber lengths. Each data point represents the average of at least 4 tested samples. ................................ ................................ ....................... 79 4 7 T he debond load versus elastic modulus of the austenite 3mm embedded fiber length samples. Each data point represents the average of at least 4 tested samples. ................................ ................................ ................................ .. 80 4 8 Graph illustrating the de bond load versus the embedded fiber length for the 4 mm embedded fiber lengths. The error bars represent the statistical variance ................................ 80

PAGE 14

14 4 9 The debond load versus elastic modulus of the untransformed austenite 4mm embedded fiber lengths. The error bars represent the statistical ............................. 81 4 10 The graph show the average surface roughness measurements for each NiTi SMA wire condition used in the single fiber pullout testing. The standard deviations are also shown. ................................ ................................ ................. 81 4 11 The graph shows the debond load versus the surface roughness for the SMA wires that were embedded at approximately 3 mm. ................................ ........... 82 4 12 The graph shows representative surface roughness profi les of the NiTi SMA wires used to perform the single fiber pullout tests. ................................ ............ 8 2 4 13 The graphs shows pullout work versus the embedded fiber length for the austenite NiTi SMA wires. ................................ ................................ ................... 83 4 14 The graph shows representative single fiber pullout curves for the austenite SMA wires that were embedded to approximately 4 mm. The A347 sample underwent a martensitic phase transformation where as A 416 and A476 did not. The curves are shown until the point of debonding. ................................ ... 83 5 1 The 3 point bend fracture toughness specimen geometry and dimensions. The ruler units are cm. ................................ ................................ ........................ 95 5 2 The graph shows representative stress strain curves of the constituent materials used in this study. ................................ ................................ ............... 95 5 3 The graph shows the repre sentative DSC curves for the NiTi and NiTi ht SMA reinforcements used in this study. ................................ ............................. 97 5 4 The graph shows the fracture toughness results for the monolithic epoxy and NiTi, NiTi ht, aluminum, and steel embedded composites for crack extensions less than 0.35 mm. ................................ ................................ ........... 97 5 5 Fracture toughness results for the monolithic epoxy and NiTi, NiTi ht, and aluminum embedded composites. ................................ ................................ ...... 98 5 6 The figures shows an optical microscope image of a steel reinforced epoxy sample. The sample underwent unstable crack growth during testing as a result of a pore. ................................ ................................ ................................ ... 98 5 7 The graph shows the NiTi bending stresses at the onset of tranformation in rows 1 and 3 with respect to the distance from the neutral axis. ........................ 99 5 8 The graph shows the NiTi ht bending stresses at the onset of transformation in rows 1 and 3 with respect to the distance from the neutral axis. ..................... 99

PAGE 15

15 5 9 The schematics show the locations of where th e bending stress calculations were perfor med. ................................ ................................ ............................. 100 5 10 Graph showing the SMA reinforcement bending stress with respect to the distance from the neutral axis at a 470 N applied load. The sha ded regions refer to the indicated SMA reinforcement placement. The horizontal portion of the bending stress curves indicates that the SMA has undergone transformation. ................................ ................................ ................................ .. 101 5 11 NiTi and NiTi ht SMA stress distribution along the sample length at a 470 N applied load. The L/2 length corresponds to the crack plane. The horizontal portion of the bending stress curves indicates that the SMA has undergone transformation. ................................ ................................ ................................ .. 101 5 12 NiTi fracture toughness sample showing debonding ahead of the crack tip as indicated by the arrow ................................ ................................ ...................... 102 5 13 Representative single fiber pull out te st curve showing the locations of debond load, frictional sliding, and fiber pull out. ................................ .............. 102 5 14 nterfacial shear strength as a function of embedded fiber length for the NiTi, NiTi ht, and alum inum reinforcing elements. ................................ .................... 103 6 1 The stress strain curves of the constituent materials used in the epoxy matrix crack bridging study. The materials were tested to failure. .............................. 119 6 2 The graph shows the extension rate dependence of the epoxy matrix used in this chapter. The epoxy consisted of 64.5wt% Epon 828 and 35.5wt% Jeffamine D 400 as the resin and hardener, respectively. ................................ 119 6 3 The DSC curve shows the glass transition range for the epoxy matrix used in this chapter. ................................ ................................ ................................ ...... 120 6 4 The schematic show the di mensions and placement of the reinforcement wires for the 3 point bend composites. ................................ ............................. 122 6 5. The plot shows representative 3 point bend curves of the samples for the J integral fracture toughne ss tests. Each of the samples had crack growth to approximately 3 mm. ................................ ................................ ........................ 122 6 6 The results of the 3 point bend fracture toughness testing curves. The approximate location of the wires is also indicated in the image. ..................... 123 6 7 The image shows necking that occurred in the SMA embedded epoxy samples. The necking was seen in the monoclinic and Al samples as well. .... 123 6 8 The images show the crack bridging that occurred in epoxy composites ........ 124

PAGE 16

16 6 9 The images show the effect of the recovery behavior of several samples . ...... 125 6 10 The image shows an aluminum reinforced epoxy sample. Rows 1 and 2 show limited interfacial debonding. Debonding is indicated by the white parentheses. ................................ ................................ ................................ ..... 126 6 11 The image shows screen shots of video taken during a 3 point bending test of the NiTi austenite reinforced epoxy samples. The screen shots were taken at specific crosshead extensions as indicated by the black arr ows on the compressive load versus the crosshead extension. The white parentheses indicate the extent of debonding. The black sticker has a width of 2 mm. ................................ ................................ ................................ ........... 127 6 12 The graph shows t he single fiber pullout results for the NiTi austenite, NiTi martensite, and aluminum reinforced epoxy samples. ................................ ...... 131 6 13 The graph shows the interfacial debonding length along the Row 1 of the NiTi austenite and NiTi martensite samples at similar crack extension lengths. ................................ ................................ ................................ ............. 131 6 14 The fracture surfaces of the epoxy composites. The white dotted lines indicate the cr ack arrest line. Images A D were taken at 2 mm and images E H were taken at 3 mm crack extensions. ................................ ...................... 132 6 15 The graph shows the bending stress of the NiTi austenite reinforcements du ring applied loads of 267N, 340N, and 575N. ................................ ............... 133 6 16 The graph shows the bending stress of the NiTi martensite reinforcements during applied loads of 244N, 315N, and 594N. ................................ ............... 133 6 17 The graph shows the bending stress of the Al reinforcements during applied load of 267 N. ................................ ................................ ................................ ... 134 6 18 The graph show s the change in composite neutral axis with respect to the applied load for the SMA reinforced composites. ................................ ............. 134 6 19. The schematic shows relevant terms used to calculate the toughening increment. ................................ ................................ ................................ ...... 135 7 1 The zinc aluminum phase diagram was created using Thermocalc Software The Zn 7wt%Al is indicated by the black dotted line. ................................ ........ 147 7 2 The figure shows the stress strain curve for the as cast Zn 7wt%Al (nomin al) alloy, NiTi, and steel. ................................ ................................ ........................ 148 7 3 The optical microscopy image shows the 93wt%Zn 7wt%Al as cast microstructure ................................ ................................ ................................ .. 149

PAGE 17

17 7 4 The optical microscopy image shows the NiTi 93wt%Zn 7wt%Al as cast composite microstructure. ................................ ................................ ............. 150 7 5 The schematic shows the dimensions and wire placement of the 3 point bend fracture toughness samples. ................................ ................................ ............ 151 7 6 The DSC results show the change i n transformation temperature as a result of the Zn Al casting process. ................................ ................................ ............ 152 7 7 The figure shows the single fiber pullout curves for the steel reinforced Zn Al samples. The steel was embedded at depths of 8, 16, and 32 mm. ................ 152 7 8 The figure shows the single fiber pullout curves for the NiTi reinforced Zn Al samples. ................................ ................................ ................................ ........... 153 7 9 The optical microscopy image shows an example of the fatigue pre crack at 10x magnification. ................................ ................................ ............................. 153 7 10 The graph shows the fracture toughness results f or the monolithic and NiTi and steel reinforced Zn Al composites. ................................ ............................ 154 7 11 The fracture surface of a steel reinforced Zn Al matrix composite shows 3 distinct regions on the fracture s urface. The blue coated, dark gray, and lighter gray regions indicate fatigue, stable, and quick fracture. ....................... 154 7 12 The fracture surface of a NiTi reinforced Zn Al matrix composite s hows 3 distinct regions on the fracture surface. The ruler is in units of mm. ................ 155 7 13 The fracture surface of a monolithic Zn Al composite shows 3 distinct crack growth regions on t he fracture surface. The units are in mm. ......................... 155 7 14 The representative SEM image of the NiTi reinforced Zn Al composites shows the interface between the fatigue and stable crack grow th region. The white arrow indicates the direction of crack growth. The schematic shows the relative position of where the image was taken. ................................ ......... 156 7 15 The SEM image shows the microstr ucture in the fatigue cracked (region A) of the NiTi reinforced Zn Al matrix composites. The schematic shows the relative position of where the image was taken. ................................ ............... 157 7 16 The SEM imag e shows the microstructure of the stable crack growth region (region B) of the NiTi reinforced Zn Al matrix composites. The schematic shows the relative position of where the image was taken. .............................. 158 7 17 The SEM image shows the microstructure of the NiTi reinforced Zn Al reinforced composites in the quick fracture region. The schematic shows the relative position of where the image was taken. ................................ ............... 159

PAGE 18

18 7 18 T he SEM image shows the microstructure in the region surrounding a wire in the NiTi reinforced Zn Al composites. The schematic shows the relative position of where the image was taken. ................................ ............................ 160 7 19 The SEM image shows the stable crack growth region of the NiTi reinforced Zn Al alloy. The schematic shows the relative position of where the image was taken. ................................ ................................ ................................ ........ 161 7 20 The SEM image shows the fatigue cracked region of the monolithic Zn Al alloy at 250x magnification. The schematic shows the relative position of where the image was taken. ................................ ................................ ............. 162 A 1 The plot shows the maximum and minimum compositions used. The compositions were determined by performing an initial set of experiments. The actual compositions of points A, B, and C are listed in Table A 1. ............ 171 A 2 The plot shows the epoxy composition used to perform the design of experiments as determined by Minitab. ................................ ............................ 172 A 3 T he plot shows an example of the variation in the epoxy properties based on composition. ................................ ................................ ................................ ..... 172 A 4 The graph shows the ductility response as a function of composition. ............ 174 A 5 The graph show a 3 D ductility response as a function of composition. ........... 174 B 1 The graphs show representative DSC curves fo r the SMAs used in Chapter 4. ................................ ................................ ................................ ..................... 177 B 2 The graphs show representative stress strain curves f or the SMAs used in Chapter 4. ................................ ................................ ................................ ....... 178 C 1 The schematic shows the 3 point bend sample geometry used to derive the bending stress equations. ................................ ................................ ................. 193 C 2 The schematic shows the cross sectional view of the 3 point bend samples. The 3 7 point towards the reinforcements and 2 points towards the unbroken ligament length matrix area. ................................ ................................ ............. 193 C 3 The schematic shows the relationship between the neutral axis (NA), centroid (D), and height from the neutral axis to the centroid (y). ..................... 194 C 4 The schematic shows the 3 point bend sample and loading parameters. L, W, and P are the roller span, sample width, and applied load, respectively. .... 194 D 1 The graph shows the voltage versus extension curves with the NiTi load curve overlaid on the data. ................................ ................................ ............... 196

PAGE 19

19 D 2 The graph shows the voltage versus extension curves with the NiTi load curve ove rlaid on the data at different extension rates. ................................ .... 196

PAGE 20

20 LIST OF ABBREVIATIONS A F austenite finish temperature Al aluminum A S austenite start temperature Au gold Cd cadmium Co cobalt Cu copper Fe iron Ga gallium Hf hafnium J j oule m meter mm millimeter M F martensite finish temperature Mn manganese Ms martensite start transformation temperature N Newton Ni nickel NiTi nickel titanium Pd palladium Pt platinum SMA shape memory alloy Ti titanium TWSME two way shape memory effect

PAGE 21

21 wt weight Zn zinc Zr zirconium

PAGE 22

22 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy TOUGHENING IN SHAPE MEMORY ALLOY REINF ORCED COMPOSITES By Fatmata Haja Barrie December 2013 Chair: Michele V. M yers Major: Materials Science and Engineering Materials capable of undergoing martensitic phase transformations have been shown to inherently increase the fracture toughness of m onolithic and composite materials, in a process known as transformation toughening. This toughening behavior via martensitic transformation s has been extensively studied in transformation induced plasticity ( TRIP ) steels, stabilized zirconia and some tit anium alloy systems, however there is a limited amount of data on the effect of the martensitic phase transformation in composites reinforced with un prestrained shape memory alloys (SMAs) Therefore, the objective of this work was to gain a fundamental un derstanding of how the constrained SMA martensitic phase transformation affects the fracture toughness of SMA reinforced composites. J integral fracture toughness testing was performed on nickel titanium (NiTi) SMA s in both epoxy and metal matrices In a ddition to the SMAs, non transforming aluminum and steel reinforcements were tested for comparative purposes. Systematic single fiber pullout tests were also performed on epoxy composites embedded with NiTi SMA wires to determine the effect of the martens ite phase transformation and variant reorientation processes on composite debonding since the interfacial behavior is known

PAGE 23

23 to affect composite fracture toughness The NiTi was heat treated to produce varying stable room temperature phases, elastic moduli and transformation stresses. T his work found that SMA fibers that were deformed in the austenite phase had greater debond loads as compared to SMAs that were deformed in the martensite phase for the tested embedded fiber lengths for the tested embedded l engths Moreover, the SMA marte nsite transformation and variant reorientation did not appear to inherently increase the fracture toughness of a composite for the composite geometry and reinforcement orientation examined The driving factor of toughening in SMA fiber reinforced composites may be the mechanical properties, elastic modulus and yield stress. The conclusions drawn were corroborated through analytical studies. In order to maximize the SMA contribution to fracture toughness, SMAs may likely nee d to be pre strained prior to being embedded within a matrix. Pre straining results in compressive stresses on the matrix because the SMAs want to retract to recover its original shape. In this sense the compressive mechanism within the pre strained SMA and the stress induced phase transformation in stabilized zirconia are similar.

PAGE 24

24 CHAPTER 1 INTRODUCTION Motivation Materials capable of undergoing martensitic phase transformations have been shown to inherently increase the fracture toughness of monolithic and composite materials, in a process known as transformation toughening. This toughening behavior via martensitic transformation has been extensively studied for transformation induced plasticity ( TRIP ) steels ( Antolovi, 1971 ; Aranzabal, 1997 ; Jacques, 2001 ) stabilized zirconia ( Evans, 1988 ; Gupta, 1977 ; Lange, 1982a ; Michel, 1983 ; Viswanathan, 1983 ) and some titanium (Ti) alloy systems ( Grujicic, 1997 ) however there is a limited amount of data on the effect of the martensitic phase transformation in composites reinforced with un pre strained shape memory alloys (SMAs) Therefore, a fundamental understanding of the martensitic phase transformation on SMA embedded composites is needed. SMAs are considered a smart material because the SMA can respond in a predeter mined manner to environmental and external stimuli. Notable SMA characteristics include a high damping capacity, 2 sets of distinct material properties dependent upon the SMA operational temperature, large elastic strains, and large recovery stresses that are the result of thermoelastic martensitic phase transformations ( Otsuka and Ren, 2005 ) It is these characteristics that led Rogers et al to use SMAs as reinforcements within m onolithic materials in 1988 ( Rogers, 1988 ) Today, SMA reinforced composites are being increasingly investigated for use in a number of engineering and structural applications specifically for their crack closure, damping, and shape morphing capabilities.

PAGE 25

25 Furuya et al investigated a NiTi SMA aluminum composite for use in structural applications. They showed that the distinct property changes associated with SMAs affects the damping capability of the SMA embedded composite ( Furuya et al., 1993 ) Additionally, Furuya et al noted that use of SMAs w ithin machinery components is ideal since the SMA mechanical properties increase with increasing temperature. Friend et al showed that SMAs could be used to actively change the natural frequency of structures effectively reducing the magnitude of vibratio ns experienced by structures ( Friend and Armstrong, 1997 ) Increasing the SMA reinforcement temperature resulted in a change in the SMA mechanical p roperties which resulted in the composite dampening. Similar results were also seen by several investigators e.g. ( Ju and Shimamoto, 1999 ; Parlinska et al., 2001 ; Rogers, 1990 ) Zhang et al showed that embedding SMA wires within an E glass matrix resulted in increased energy absorption prior to fracture th rough impact testing ( Zhang et al., 2003 ) The increased energy absorption was attributed to the stress hystere sis associated with the SMA psuedoelastic behavior, however the tests did not consider the effect of embedding a reinforcement within a matrix (composite toughening), nor did they compare the results to conventional, non transforming reinforcements. Roger s et al. also saw increased energy absorption, however did not discount fiber debonding and pullout as possible factors for the increased energy absorption ( Paine and Rogers, 1994 ) Several researchers have also i nvestigated using SMAs as actuators to facilitate shape change within a composite ( Baz et al., 2000 ; Kim et al., 20 06 ; Kim et al., 2002 ; Lind and Doumanidis, 2003 ; Song et al., 2000 ; Villanueva et al., 2010 ) The SMAs were

PAGE 26

26 embedded within a monolithic matrix or laminates and activated using temperature changes via the application of a current. Through SMA activation, the composites were able to change int o particular shapes. Pre deformed (prestrained) SMAs have also been studied for their potential to increase composite toughness and facilitate crack closure. The pre deformed SMAs impart a compressive residual stress on the composite that impedes crack gr owth effectively increasing the composite toughness ( Kimura et al., 2006 ; Murasawa et al., 2004b ; Watanabe et al., 2002 ) Self healing polymers have been developed that consist of a polymer matrix embedded with micro capsules filled with a healing agent and a catalyst that is homogenously dispersed thro ughout the matrix. As a crack propagates through the matrix, it comes into contact with the micro capsules, causing them to rupture. When the healing agent comes into contact with the catalyst, a polymerization reaction occurs and the crack is filled in, bonding the crack faces ( White et al., 2001 ) Later re search focused on the use of SMA reinforcements within the polymer to result in smaller crack volumes due to the crack closure associated with SMAs ( Kirkby et al., 2008 ) The smaller crack volume allows the healing agent to more effecti vely fill in the crack volume. Self healing metals are also being investigated. Self healing metals are composite s that consist of a metal matrix reinforced with uni directionally oriented SMA wires. Crack propagation through the stressed matrix causes t he SMA wires to undergo a stress induced martensitic phase transformation (martensite to austenite) Stress removal coupled with increasing the composite temperature results in the SMA

PAGE 27

27 undergoing a reverse transformation, thereby forcing the crack faces i nto contact and allowing the healing process to take place ( Manuel, 2007 ; Manuel and Olson, 2007 ) A commonality of all the previously discussed SMA composite studies is that the composite must resist mechanisms detrimental to t he functioning of the SMA, thereby allowing the SMA to act in its intended use, whether it be for crack closure, damping, shape morphing, etc. As such, an understanding of fracture toughness is critical to the use of the SMA material systems. Mechanisms associated with composite fracture include debonding and pullout in addition to crack growth. However it is important to determine how these fracture mechanisms behave in conjunction with the SMA martensitic phase transformation. Objective Use of SMAs a s reinforcing elements is increasing due to the adaptive nature of the material. It is therefore necessary to understand how SMAs behave as reinforcing elements in order to design effective composites. Additionally, before SMA composites can be widely im plemented, the fracture toughness of the material system must be well understood. A major difficulty in quantifying the martensitic transformation effects in composites is being able to decouple and isolate composite toughening from transformation toughen ing mechanisms. Thus it is important to isolate the individual contributions of these mechanisms to gain a deeper understanding of the role of martensitic phase transformations on toughness. Therefore, the objective of this work is to gain a fundamental understanding of how the constrained SMA martensitic phase transformation affects the fracture toughness of SMA reinforced composites. Of particular interest is the SMA behavior in the un prestrained state to isolate the martensitic phase contribution to the fracture toughness.

PAGE 28

28 Dissertation Guidelines The dissertation is organized into 8 chapters. Chapter 2 begins with a background of relevant topics that will enable the reader to understand the topics/themes discussed in the documents. In the next cha pter (3), all of the experimental techniques and corresponding equipment used in the experimental studies performed in the dissertation work are discussed in detail. Subsequent chapters refer to the techniques detailed in the Equipment and Experimental Te chniques Chapter. In Chapter 4, the debonding behavior of SMA composites were investigated to determine the effect of the SMA martensitic phase transformation and martensite variant reorientation on debonding through a systematic single fiber pullout stud y. Single fiber pullout tests were also performed in each subsequent experimental chapter to determine the specific debonding behavior of the respective matrices and reinforcements on the fracture toughness in the corresponding chapter. The following 3 c hapters, Chapters 5, 6, and 7, investigate the fracture toughness of SMA reinforced composites through J integral studies. Specifically, Chapter 5 focuses on the intrinsic toughening behavior of SMAs on fracture toughness using an epoxy matrix. Chapters 6 and 7 focus on the extrinsic toughening behavior of SMA reinforcements using epoxy and metal matrices, respectively. An epoxy matrix was initially investigated because t he debonding and crack growth can be observed in addition to the ease of sample fabrication and minimal thermo mechanical effects imparted on the SMA reinforcements during composite fabrication Metal matrices are more structurally relevant, however process ing effects can arise that can complicate fracture toughness data interpretation. Therefore, once the extent of transformation toughening was understood in the epoxy

PAGE 29

29 matrix, a metal matrix was used to verify findings in a more complex system. The document concludes with a summary of the conclusions from experimental sections and discusses potential future work.

PAGE 30

30 CHAPTER 2 BACKGROUND Fracture Toughness In 1920, Griffith discovered that the fracture stress of a material was related to the flaws present on the material surface ( Griffith, 1921 ) Cyclical loads within the elastic region of fl a wed surfaces resulted in fracture. Through a mathematical analysis, it was determined that defects increase the local stresses and str ains 2 6 fold dependent upon the flaw shape. As such, the stress intensity factor, K, was introduced by Irwin in 1957 ( Zhu and Joyce, 2012 ) The stress intensity f actor relates the flaw size and stress intensity at the crack tip by the following equation: (2 1) respectively. Equation 2 1 is the governing equation of linear elastic fracture mechanics (LEFM). While the equation is adequate for brittle materials, it is does not accurately capture the fracture toughness behavior of materials that undergo significant inelastic deformation prior to failure. To evaluate materials that do not adhere to LEFM principles, J. Rice developed the J integral method in 1968, which is based on elastic plastic fracture mechanics (EPFM) ( Rice, 1968 ) The J integral method can evaluate the fracture toughness of non linearly deforming materials, as long as the material does not undergo unloading during testing by taking the line integral along a path independent con tour. The J integral is calculated using the following equation: (2 2)

PAGE 31

31 where U D is the strain energy density, y and x refer to the coordinate plane, T i is the stress vector acting outside the con tour, u is the displacement, and s is the arc length along the contour. The J integral is equal to 0 for a closed contour. Mechanisms have been identified that result in increased fracture toughness. The toughening mechanisms can be split up into 2 categ ories: intrinsic and extrinsic ( Ritchie, 1988 1999 ) Intrinsic toughening is associated with mechan isms ahead of the crack front and extrinsic toughening refers to mechanisms in the wake of the crack. Oftentimes the amount of toughening contribution to the fracture toughness is dependent upon the extent of crack growth. The toughness dependency on cra ck growth is known as R curve behavior ( Launey and Ritchie, 2009 ) R curve behavior is an indication that toughening mechanisms are active ( Nagendra and Jayaram, 2000 ) In materials that are capable of plastically deforming, it is often best to represent the fracture toughness as curves with respect to crack growth instead of as a si ngle value to capture the R curve behavior. Crack bridging, interfacial strength, transformation toughening, and crack bowing are all toughening mechanisms that can contribute to R curve behavior ( Ashby et al., 1989 ; Bartolome et al., 2002 ; Evans, 1990 ; N agendra and Jayaram, 2000 ; Raddatz et al., 1998 ; Ritchie, 1999 ) Relevant Toughening Mechanisms Crack Bridging Crack bridging occurs once a crack has passed a reinforcing element leaving the crack faces connected or bridged via grains ( Pezzotti et al., 1998 ; Swanson et al., 1987 ) particles ( Sbaizero and Pezzotti, 2000 ; Zhang et al., 1997 ) or fi bers ( Goto and Kagawa, 1996 ; Raddatz et al., 2000 ) The bridging element imparts a crack closure force on the crack faces that is proportional to the crack mouth opening displacement.

PAGE 32

32 mechanical properties ( Bao and Suo, 1992 ; Kaute et al., 1993 ) The purpose of a crack bridging element is to facilitate energy dissipation through fiber deformation and fracture, which typically results in R curve behavior because the longer the crack, the more particles /fibers that a re available to bridge the crack. A schematic of crack bridging is shown in Figure 2 1 The increased fracture toughness that results from crack bridging is typically followed by pullout, however the pullout is dependent upon the interfacial strength bet ween the matrix and second phase. The interfacial strength between the matrix and fiber is critical in crack bridging and is what determines whether the fiber will survive the crack propagation process. Interfacial Strength The interfacial behavior betw een the matrix and reinforcement strongly influences the behavior of the composite since stress is transferred from the matrix to the reinforcement via the interface ( Albertsen et al., 1995 ; Fu et al., 2008 ) The strength of the interface also dictates how or if a composite will deform, fracture, and pullout. Weakly bonded interfaces promote debonding and fiber pullout ( Chawla et al., 2000 ) whereas a stro ngly bonded interface promotes fiber fracture ( Evans et al., 1991 ) Therefore the interfacial behavior is also correlated to th e composite toughness. Transformation Toughening Some materials, when subjected to an external stimuli (change in temperature, stress, magnetic field), undergo a diffusionless, crystallographic martensitic phase transformation. When the martensitic phase t ransformation is accompanied a volumetric expansion of the transformed material, this can result in an increase in the material fracture toughness. Volume expanding martensitic phase transformations have been

PAGE 33

33 seen in transformation induced plasticity ( TRI P ) steels ( Antolovi, 1971 ; Aranzabal et al., 1992 ; Mei and Morris, 1990 ) stabilized zirconia (ZrO 2 ) ( Evans, 1988 ; Kelly and Rose, 2002 ; Lange, 1982a ; Lange, 1982b ) and titanium ( Grujicic, 1997 ) Stabilized zirconia consists of tetragonal zirconia particles that are stabilized within a monoclinic parent phase. When the tetragonal particles are subjected to a critical stress, the particles transform from the tetragonal phase to the monoclinic phase. The tetragonal to monoclinic phase transformation is irreversible. Since the monoclinic phase is approximately 4% larger in volume as compare to the tetragonal phase ( Green, 1998 ) a compressive residual stress applied to the crack surfaces results. The compressive residual stress reduces the stress intensity at the crack tip which effectively increases the fracture toughness of these types of materials. The stabilized zirconia transformation toughening mechanism is shown in Figure 2 2 The mechanism behind toughening in steels is similar to that described of stabilized zirconia, however in TRIP steels, austenitic and multiphase steels containing the austenite phase when subje cted to a critical deformation will result in the transformation of the austenite phase to martensite. The martensitic phase transformation results in an increase in the local strain hardening rate, thus delaying the onset of necking. Similar to stabiliz ed zirconia, the austenite to martensite transformation is irreversible. The increase in toughness as a result of transformation toughening T, is described by (2 3)

PAGE 34

34 where C, E, V t v h, and are a constant, elastic modulus, volume fraction of transforming zirconia, volumetric transformation strain, transformation zone width, and ( Green, 1998 ; Ruf and Evans, 1983 ) Crack Bowing In the presence of reinforcing elements within a matrix, crack propagation can beco me nonlinear as the crack front tries to pass impenetrable reinforcements ( Xu et al., 1998 ) The re inforcements pin the crack front at the reinforcement locations, however at other positions along the crack that are not affected by the reinforcements continue to grow, resulting in crack bowing ( Lange, 1970 ) The crack bowing process causes the crack front to lengthen. The energy required to lengthen the crack around the reinforcement is what contributes to composite toughening. Crack bowing has also been found to be dependent upon the reinforcement bonding strength to the matrix. The crack bowing phenomena is shown in Figure 2 3 Microcracking In certain brittle materials, such as ceramics and some metals, secondary cracks ahead of the main crack phenomena can occur ( Hutchinson, 1989 ; Nalla et al., 2003 ) These secondary cracks are known as microcracks. Microcracks that form dur ing crack propagation ( Green, 1998 ) and are located in the vicinity of the main crack phenomena ( Pompe et al., 1978 ) can favorable affect the fracture toughness ( i.e. serve as a toughening mechanism). The microcracks can lower the stresses experienced by the crack therefore serving in a stress shielding capacity ( Green, 1998 ; Ritchie, 1988 ) The shielding effect can further improve as the crack continues to propagate.

PAGE 35

35 Crack Shielding (via plasticity) In ductile materials, an inherent mechanism for dissipating energy in the crack tip region is through pl astic deformation ( Cotterell and Reddel, 1977 ; Mai and Cotterell, 1986 ; Ritchie, 1999 ; Wu et al., 1993 ) With continued deformation the plastic zone can grow, further dissipating energy during the crack propagation process. Plastic deformation is theref ore an inherent crack shielding toughening mechanism in materials capable of undergoing plastic deformation A secondary effect of the plastic zone can include crack tip blunting making it more difficult for a crack to advance ( Chan, 1992 ; Kruzic et al., 2003 ) Shape Memory Alloys Shape memory alloys (SMAs) are active materials that can remember their origina l shape after significant deformation. The shape recovery is the result of a reversible thermoelastic martensitic phase transformation that is temperature and stress dependent ( Miyazaki and Otsuka, 1989 ; Mohamed and Washburn, 1976 ; Otsuka and Ren, 2005 ; Sha w and Kyriakides, 1995 ) Common uses for SMAs include medical applications such as braces, stents, etc. ( Duerig et al., 1999 ; Iwabuchi et al., 1975 ) ; actuators ( Kim et al., 2006 ; Otsuka and Kakeshita, 2002 ) ; and da mping applications ( Desroches and Delemont, 2002 ; Graesser and Cozzarelli, 1991 ; Saadat et al., 2001 ; Saadat et al., 2002 ) SMAs consist of a high temperature parent phase with a cubic crystal structure and a low temperature phase with an asymmetric c rystal structure; the phases are known as austenite and martensite, respectively. The symmetry associated with the parent phase allows for multiple variants or orientations to form of the martensite phase ( O tsuka and Kakeshita, 2002 ) The phases have corresponding transformation

PAGE 36

36 temperatures A s A F M s M F where A, M, S, and F are austenite, martensite, start and finish, respectively. The ambient in relation to the transformation temperatures dictate ho w the SMA responds mechanically. There are two properties associated with SMAs, pseudoelasticity and shape memory effect. Pseudoelasticity is the stress dependent property that occurs after a load is removed from a deformed shape memory resulting in s hape recovery. Pseudoelasticity is depicted in Figure 2 4 The SMA pseudoelastic curve is split into several regions. In region 1, the austenite phase elastically deforms. Region 2 shows the propagation and nucleation of the stress induced martensite p hase. The transformation requires no additional stress to produce elongation. In region 3, the martensite phase is elastically deformed. While theoretically the SMA is only elastically deforming in region 3, because of dislocation motion associated with the movement of the austenite martensite interface, plastic deformation is often seen in region 3 ( Simon et al., 2010 ) Additionally, residual pockets of the austenite phase transforms to the martensite phase. Region 4 indicates the onset of permanent deformation. If the SMA is unloaded in region 2, the strain is fully recovered as shown by curve 1 via the reverse transformation from martensite to austenite. However, in region 4 the onset of plastic deformation begins, as shown by the residual stain in curve 2. Hence the usefulness of these alloys lies in their utilization withi n their extended elastic region, region 2. Shape memory effect occurs due to shape recovery by heating the material above the transformation temperature. The shape memory property is shown in Figure 2 5 For shape memory, the SMA beings in the martensite phase. Region 1 indicates the elastic deformation of the self accommodating martensite. Region 2 indicates the

PAGE 37

37 martensite variant reorientation. Martensite reorientation refers to the growth one martensite variant at the expense of others ( Lagoudas, 2008 ) In region 3, the reoriented martensite phase elastically deforms. Finally in region 4 plastic deformation occurs. When unloading occurs in any region beyond region 1, a residual strain remains as shown in t he unloading curve in Figure 2 5 For shape recovery to take place, unloading must occur in region 2 an d the SMA must subsequently be heated above the austenite transfo rmation temperature. Figure 2 6 shows a schematic of the microstructural changes associated with pseudoelasticity and shape memory effect. Nickel Titanium (NiTi) Shape Memory Alloys The most commonly researched shape memory alloy is nickel titanium (NiTi). It displays recoverable strains upwards of 10% ( Sehitoglu et al., 2003 ) Compositions that display shape recovery are the near equi atomic. Research has shown that the behavior of NiTi i s highly dependent on composition, processing, and microstructure. Aging nickel rich NiTi results in the formation of Ni 4 Ti 3 precipitates ( Otsuka and Ren, 1999 ) which depletes Ni from the matrix. This in turn increases the transformation temperatures of the shape memory alloy. A number of SMA systems exist. Tertiary elements are can be added to NiTi to achieve specific microstructures and mechanical behavior. The tertiary elements include Au, Cu, Fe, Hf Pd, Pt, and Zr. Other SMA systems include AgCd, CoNiAl, CoNiGa, FeMn, NiMnGa, NiAl, NiAlFe, and copper based SMAs among others. Use of the different SMA systems and processing within SMA systems results in differences in the following thermo mechanical properties: strength, ductility, fracture toughness, cyclic behavior, temperature region the SMA can be used in without degradation, transformation temperatures, temperature hysteresis, and dimensional stability.

PAGE 38

38 Energy Dissipation and Absorption in Sha pe Memory Alloys A number of studies have been performed that investigated the implementation of SMAs as reinforcements within matrices ( Ju and Shimamoto, 1999 ; Paine and Rogers, 1994 ; Zhang et al., 2006 ) and structural members ( Ben Mekki and Auricchio, 2011 ; Birman, 2008 ; Desroches and Delemont, 2002 ; Graesser and Cozzarelli, 1991 ; Mccormick et al., 2006 ; Saadat et al., 2001 ; Saadat et al., 2002 ; Van Humbeeck and Liu, 2000 ) In these studies, the SMA elements are subjected to loads that are within associat ed with the SMA martensitic phase transformation is exploited to dissipate energy being supplied to the systems via mechanical deformation. After deformation, the SMA composites/structures sustain minimal residual plastic strains. The reverse martensitic a result, these systems are better able to maintain their mechanical integrity. and SMA composites. T his term simply refers to the energy dissipation. The energy is said to be absorbed because upon unloading the energy is lost, or absorbed, without any mechani cal effect on the SMA. Figures 2 7 A and B show the energetic breakdown of SMAs that display ps eudoelastic and shape memory effect behavior, respectively. For pseudoelastic SMAs, when looking at the stress strain loop, the area enclosed by the curve corresponds to the energy dissipated or permanently lost during deformation. The energy is dissipat ed through frictional losses associated with the movement of the phase transformation interface, martensite variant growth and reduction, and reorientation ( Gil and G uilemany, 1997 ; Hamilton et al., 2004 ; Kato and Miura, 1995 ) It is the dissipated energy that gives rise to the stress hysteresis. The other ener gy

PAGE 39

39 component is the stored elastic energy which is represented by the energy under the reverse martensitic transformation curve. The stored elastic energy facilitates the reverse martensitic phase transformation. The dissipated and stored elastic energy a re shown in Figure 2 7 A Energetically, the SMA shape memory effect behavior is quite different from that of the pseudoelastic SMA. In fact it is similar to that of conventional, non transforming metals, however the mechanism behind the deformation is d ifferent. For SMAs that exhibit shape memory effect and non transforming metals, the dissipated energy is that enclosed by the stress strain loop, as shown in Figure s 2 7 B and C respectively. For the SMA, the primary cause of the dissipated energy is t he reorientation of martensite variants. The shape change is recoverable only by increasing the SMA temperature above the austenite transformation temperature. Therefore, work (via heat) must be put into the SMA system to enable shape recovery. In non t ransforming, conventional metals, the energy dissipated is the result of dislocation motion. The shape of conventional materials is typically irrecoverable once plastic deformation has taken place. The stress strain curve for a conventiona l metal is show n in Figure 2 7 C To illustrate the energy absorption benefit of SMAs, NiTi SMAs in the austenite phase and carbon steel wires are considered. The elastic modulus and yield stress (NiTi martensite transformation stress) are given in Table 2 1. The NiTi and steel have vastly different mechanical properties. Figures 2 8 and 2 9 show the stress strain curves of actual pseudoelastic NiTi and carbon steel 1080 wires, respectively. Not accounting for the mechanical properties, if one were to estimate the tou ghness of the SMA and steel wire by calculating the area under the stress strain curves during

PAGE 40

40 successive load and unloading, for one deformation cycle, steel has the higher toughness as compared to the NiTi SMA, 8.9 J/m 3 and 5.6 J/m 3 respectively. The s teel and NiTi were strained to 2.1% and 2.4%, respectively. The SMA recovers the 5.6 J/m 3 With successive deformation cycles where the materials are deformed past their yield/martensite transformation stresses, the same behavior is repeated for the NiTi and steel. Because the SMA is able to recover its shape repeatedly when loaded within the martensite transformation plateau region, the energy absorbed by the SMA during the deformation process, in totality, is higher than that of the steel, because a re sidual plastic strain remains due to slip. If fatigue in the SMA were not considered then the SMA would be able to sustain shape recovery cyclical behavior indefinitely, however for the steel failure will occur once the material is loaded past a critical stress, a s shown in cycle 6 of Figure 2 9 giving rise to the notion that SMAs are good at dissipating energy. In the case of no unloading, both of the materials behave the same macroscopically and the SMA would eventually fracture as well, as shown in Fi g ure 2 8 It is through the unloading process that the stored elastic energy in the SMA is able to return the SMA to the austenite phase. It is now evident how the SMA martensitic phase transformation is responsible for dissipating energy during the loa d unload cycle. Namely as a result of the extended elastic region that SMAs undergo as a result of the martensitic phase transformation.

PAGE 41

41 Figure 2 1 The schematic shows crack bridging in the presence of reinforcing elements. Figure 2 2 The schema tic shows an example of the transformation toughening phenomena that can occur in stabilized zirconia. The black particles represent the tetragonal zirconia particles and the red particles near the crack tip indicate a transformed particle.

PAGE 42

42 Figure 2 3 The schematic shows crack bowing in a composites.

PAGE 43

43 Figure 2 4 The schematic shows the SMA pseudoelastic behavior. The regions correspond to the austenite elastic deformation, martensite transformation, martensite elastic deformation, and marten site plastic deformation.

PAGE 44

44 Figure 2 5. The schematic shows the SMA shape memory behavior. After martensite variant reorientation, the SMA must be heated above the AF temperature to recover its original shape.

PAGE 45

45 Figure 2 6 The schematic shows the shape recovery mechanism in shape memory alloys.

PAGE 46

46 Figure 2 7 The schematic shows how energy is spent in an SMA in the austenite phase, an SMA in the martensite phase, and a non transforming metal. Table 2 1. The table shows elastic modulus and y ield (SMA transformation stress) of the NiTi and steel wires. Material E (GPa) Yield/ Trans. Stress NiTi 67.9 491 MPa Steel 165 1.98 GPa

PAGE 47

47 Figure 2 8 The graph shows the pseudoelastic behavior of NiTi SMA wires that were subjected to incre mental strains and finally tested to failure. When the SMA is deformed within the plateau region, the deformation is recoverable. Figure 2 9 The graph shows the deformation behavior of carbon steel 1080 steel wire incrementally loaded and unloaded to failure. Cycle 1 corresponded to the steel wire being loaded elastically.

PAGE 48

48 CHAPTER 3 EQUIPMENT AND EXPERIMENTAL TECHNQUE S A number of experimental techniques were used to obtain the experimental results shown and discussed in the following chapters. T h e experimental techniques and the corresponding equipment are described i n the following sections and will be referred to throughout the document. Encapsulation/Heat Treatments To prevent oxidation during heat treatments, samples were encapsulated in tubes For heat treatments below 600C P yrex Borosilicate glass tubes were used. Since Pyrex has a softening point of approximately 820C ( Science s, 2008 ) quartz tubes were used for samples that required heat treatments greater than 600C. The samples were wrapped in stainless steel foil to prevent the samples from coming in contact with the tube s during the heat treatment The tubes were pulle d under a vacuum and back filled with argon 3 times. While sealing the tube, a 30 millitorr vacuum was pulled. After encapsulation, the samples were heated treated in Thermo Scientific model F48025 or F62735 bench top muffle furnaces T he sample tempera tures were externally monitored using type k thermocouples that were positioned close to the sample location Upon completion of the heat treatment, the samples were quenched into a room temperature water bath to retain their high temperature microstructu re Differential Scanning Calorimetry (DSC) Differential scanning calorimetry (DSC) was used to determine relevant thermodynamic characteristics, such as sample transformation, melting, and solidification temperatures. A Perkin Elmer DSC 8000 was used to perform tests. Th e

PAGE 49

49 machine had a n operating temperature range of to Measurements were made in a nitrogen atmosphere using a To determine the critical temperatures, the extrapolated onset method was used ( Inczdy et al., 1998 ) An example of this method is shown in F igure 3 1 to find the SMA austenite and martensite phase transformation temperatures. X ray Florescence Spectroscopy ( XRF ) X ray Florescence Spectrosc opy (XRF) was used t o determine the composition of cast metal samples An Eagle III Probe from E DAX Inc. was used to perform the measurements under vacuum The XRF machine used a 80 mm 2 l ithium drifted s ilicon crystal detector with a and 20 kV vol tage to collect data Vision 32 S oftware was used to identify the characteristic peaks and their relative phase fractions. Optical Profilometer T o determine the surface roughness of the SMA fibers used in this dissertation, a Zygo NewView model 7200 non c ontact optical probe profilometer was used The samples were ultrasonicated in ethanol for 3 minutes to remove any surface contaminants. A 20x objective lens was used to perform the profile measureme nts scan length MetroPro Software was used to analyze the data To account for the curvature associated with the wire surface, a cylinder was subtracted from the data Figure 3 2 shows the representative surface plots with and without the cur vature removed. T he surface roughness was compared by using the Ra value The R a value is a measure of the width between peaks P and valley, V, as shown in Figure 3 3. Equation 3 1 shows the equation used to calculate R a Surface profiles were also g enerated which plot the relative height with respect to position on the sample surface.

PAGE 50

50 3 1 Mechanical Testing All mechanical testing was performed on an Instron 5582 servo driven mechanical testing machine except where indicated The mechanical testing machine had a 100 kN load cell with a resolution of 1 N. The data acquisition system (DAQ) was capable of recordi ng extension and load. M echanical testing experiments performed at an elevated temperature, were conducte d using an Instron Series 3119 Environmental Chamber. The environmental chamber had an operating temperature of ambient to 350C. Specific mechanical testing techniques are described below for polymer and metal matrices. Tensile Tests Tensile tests were performed to determine the mechanical properties of the materials used in this dissertation. Wedge grips were used to run the tensile tests at selected displacement rates. To measure strain, an Epsilon clip on extensometer with a 1 inch gage length was u sed. Stress and strain were plotted to determine relevant mechanical properties. Two families of materials were used: polymer and metal. The sample preparation for the material families is described below. Polymer Dog bone shaped tensile samples were cr eated using an OOMOO silicon rubber mold. The samples dimensions are shown in Figure 3 4 and are based on recommended dimensions from ASTM Standard E 8m 04 ( International, 2004 )

PAGE 51

51 Metal Dog bone shaped tensile samples were created using the graphite mold shown in Figure 3 5 and are based on recommended dimensions from ASTM Standard E 8m 04 ( International, 2004 ) The graphite mold was coated with a thin layer of boron nitride spray to prevent the molten metal from stick ing to the mold. The mold had two slots for casting samples, tensile and bar shaped. The removable ends of the graphite mold had openings for wires to be placed. Single Fiber Pullout Single fiber pullout testing was performed to analyze the interfacial strength between the matrix and fiber. The confined end of the wires w ere ground down to remove the deformed region introduced during the cutting process. After the wires had been subjected to necessary heat treatments, the wires were cleaned with ethan ol and water. A metal fixture was secured in mechanical vice grips to perform the single fiber pullout experiments consistent with the restrained matrix top loading method ( Zhou et al., 1992 ) The metal fixture had an opening of approximately 4.5 times the diameter of the wires allowing for free deformation and pullout of the wire. The grips secured the fixture and the free wire. The t est setup is shown in Figure 3 6. The single fiber pullout samples were tested at 0.5 mm/minute extension rate which is consistent with the fracture toughness extension rates The mechanical testing machine deformed the reinforcement at a constant exten sion rate at room temperature until the wire had completely debonded or fractured. The load and extension were measure d and used to determine the debond load or average interfacial shear strength, The following equation was used to determine the average interfacial shear strength ( Chawla, 2006 ) :

PAGE 52

52 ( 3 2) where P, d, and l e are the debond load, fiber diameter, and embedded fiber length. Equation 3 2 assumes a uniform interfacial shear stress. The sample preparation for the material families are described below. Two families of materials were used: polymer and metal. Epo xy m atrix The epoxy matrix samples were prepared by using molds made of G 1000 silicon or Oomoo silicon rubber as shown in Figure 3 6 The molds had an opening for the wires to be passed through The wires were fed through the opening to pre determined l engths with the ground embedded within the epoxy. The epoxy mixture was then mixed together and poured into the mold cavity. Metal m atrix The bar portion of a graphite mold was used to p repare the metal matrix samples T he graphite mold is shown in Fig ure 3 7 The graphite mold had openings for wires which allowed for the wires to be embedded to different lengths. The metal matrix, after having the appropriate raw materials measure d out, were melted using a bench top muffle furnace in a crucible that was coated with boron nitride. When the metal was molten and well combined the melt was poured into the graphite mold. Fracture Toughness Three point bend fracture toughness tests were performed to measure the fracture toughness properties of composi te samples. The fracture toughness methods are described below for the epoxy and metal matrix composites.

PAGE 53

53 Epoxy m atrix Oomoo silicon rubber molds shown in Figure 3 8, were molds were created from 2 machined aluminum samples such that identical samples co uld be created. One aluminum blank had a notch and the other did not. Additionally, the aluminum blanks had slots through which wire reinforcements could be fed through and aligned. An Epon 828 epoxy mixture was used in one of 2 compositions. A razor blade was tapped into the notch to create a starter crack. The 3 point bend setup had a roller span 70 mm. The test setup is shown in Figure 3 9 ( D6068 96, 2002 ) A 0.5 mm/m in extension rate was used to deform the composite because this facilitated slow stable crack growth. Load and crosshead extension were measured. Aft er incremental growth, the test was stopped at progressive crack extensions. The samples were cooled to below 0 C and placed back on the 3 point bend fixture. The cross head was jogged down quickly to differentiate the region between stable and unstable crack growth. A representative sample fracture surface is shown in Figure 3 10. To measure crack growth, an optical microscope was used. The crack was measured at 5 positions of the crack as shown in Figure 3 10 and averaged to determine the crack extens ion. In addition to testing the notched samples, an indentation sample (the un notched three point bend sample) was tested allow s for the removal of pin/fixture effects from the results. The energy absorbed by the indentation samples were subtracted from the energy absorbed by the notched three point bend samples The J integral was calculated using the following equation ( D6068 96, 2002 ) : ( 3 3 )

PAGE 54

54 o are the dimensional factor, energy absorbed during deformation, sample thickness, sample width and pre crack length, respectively ( D6068 96, 2002 ) The indentation and pin effects were subtracted from the total energy a bsorbed by each sample (U total ) and the resulting energy term was used to calculate the J integral. The indentation and pin effect energies (U indent ) corresponding to specific crack growth lengths were determined by running a sample identical to the respe ctive tested fracture toughness composite, except that it did not contain a notch or crack. The aforementioned sample is also known as an indentation sample ( D6068 96, 2002 ) The 3 point bend roller span was minimized and the load and load line displacement were measured. An Olympus PME3 optical microscope was used to meas ure the crack growth along five points along the crack front. The five points were then averaged plotted to produce the fracture toughness curves. Metal m atrix A graphite mold, as shown in Figure 3 11, was used to cast the metal matrix fracture toughness samples. The mold had openings for wires to be fed through and was modified with a custom graphite end piece in order to fabricate sample half the length of the mold. The mold was not used in its entirety as the molten metal caused the wires to bunch together towards the center of the mold. Raw materials were measured out according the matrix composition using a Denver Instrument digital scale with an accuracy of 0.1 mg The measured raw materials were put into a graphite crucible that was coated with boron nitride and melted in a Thermo Scientific model F62735 bench top muffle furnace. During the melting process, the molten metal was

PAGE 55

55 stirred several times with a graphit e rod to ensure that the materials were well incorporated and then cast into the graphite mold. The samples were cast into a graphite crucible with openings for wires. Once the samples were cast a mill was used to machine the samples to the appropriate dimensions as d escribed in ASTM Standard E813 ( Astm, 1989 ) To create the notch a mill was used to drill a hole into sample at the intended tip of the notch with a 5 /64" drill bit A low speed cutting lubricant was applied to the drill bit in order to prevent the drill bit from breaking. A cut off saw was then used to cut a notch to the drilled hole. Fatigue pre cracks were creat ed using a hydraulic model 312.21 MTS machine that was operated using a MTS 407 Controller The maximum applied load was determined by using the following equation ( Astm, 1989 ) : ( 3 4 ) B, b o y and S are the sample thickness, initial uncrack ed ligament length after pre cracking, yield stress, and span, respectively. T he pre crack was grown to approximately 1.3 mm. A uni paint oil based paint marker made by Mitsubishi Pencil was used to coat the fatigue crac ked fracture surface to enable delineation between the fatigue and stable crack growth region. 5 samples were prepared for each composite system. The multiple specimen technique was used instead of the single specimen method to avoid n on linear unloading and to develop an R curve. In the multiple specimen method the samples are loaded to different displacements. Prior to testing relevant dimension were measured (width and thickness). Un notched

PAGE 56

56 samples were also fabricat ed to determine the compliance in the test setup. The un notched samples were loaded to 125% of the maximum load sustained by the samples during the 3 point bend tests. The load load line displacement curves were measured and used to calculate the compli ance. The sample load line displacement of the load load line displacement curves were then adjusted using the calculated compliance. The samples were loaded at an extension rate of 0. 1 mm/min to specific predetermined displacements of 0.48, 0.61, 0.74, 0.91, and 1.18 mm and unloaded. Following testing, crack growth was marked by coating the stable crack growth region with iodine solution that contained 2wt% iodine, 2.4wt% sodium iodine, 47wt% alcohol, and 48.6wt% purified water The sample was then br oken using a 400 mm/min extension rate and the crack growth was measured. Equations 3 5 3 9 are used to calculate the J integral for each sample according to ASTM Standard E813 ( Astm, 1989 ) The governing equation used to calculate the J integral fracture toughness is given in Equation 3 5: ( 3 5 ) where J el and J pl are the elastic and plastic components of the J integral, respectively. J el is ( 3 6 ) where ( 3 7 )

PAGE 57

57 i W, and a o crack length, respectively. The function is a dimensional factor that can be calculated using the following equation: ( 3 8 ) The J integral plastic component is ( 3 9 ) where A pl(i) and b o are the area enclosed by the load load line curve, and unbroken ligament length respectively. The J integral fracture toughness for each sample was then plo tted with respect to the amount of crack growth to produce R curves for the different materials tested Optical Microscopy To look at the microstructure of the metal samples, an Olympus PME3 optical microscope was used The microscope was capable of 10x 50x, 100x, 200x, and 500x magnification. Samples were set in an epoxy base to make the grinding/polishing process easier. To prepare the samples for optical microscopy, the sample surfaces were mechanically polished using successively finer SiC polishin g pap er and alumina

PAGE 58

58 To etch the NiTi SMA samples, a 3 HNO 3 + 2 H 2 O + 1 HF, in part s solution was used to etch the NiTi SMA wires. A Nita l solution that consisted of 2 % nitric acid and 98 % ethanol by volume wa s used to etch the ZnAl metal matrix samples. Scanning Electron Microscopy (SEM) Scanning Electron Microscopy (SEM) was performed using a J EOL 6400 SEM to take secondary electron images of the fracture surfaces. The samples were mounted on a metal puck using double sided carbon tape.

PAGE 59

59 Figure 3 1 The graph shows a representative DSC curve of the SMA transformation temperatures. An example of the extrapolated onset method that was used to calculate the transformation temperatures is also shown. Fi gure 3 2. The schematic shows the dimensions of the tensile specimens used to perform mechanical testing.

PAGE 60

60 Figure 3 3. The images show representative surface map images. a) the uncorrected wire surface map and b) the wire surface map that was corre cted to account for the wire curvature. a) b )

PAGE 61

61 Figure 3 4. The schematic shows the parameters required to calculate the surface roughness, Ra. Figure 3 5 This schematic shows the single fiber pullout test setup.

PAGE 62

62 Figure 3 6. The picture shows an Oomoo silicon rubber single fiber pullout mold used to make the epoxy matrix single fiber pullout samples. Figure 3 7 Th e image shows a picture of the graphite crucible. a) graphite mold was used to cast tensile specimens (dog bone shape slot: top) and the single fiber pullout samples (bar shaped slot: bottom) and b) the graphite mold end pieces with the wire slots. a) b )

PAGE 63

63 Figure 3 8 The picture shows one of the O omoo si licon rubber fracture toughness molds used to make the ep oxy samples. The molds also had openings for wire placement. Figure 3 9 The schematic shows the 3 point bend setup and sample placement.

PAGE 64

64 Figure 3 10. The schematic shows the unstable crack growth, stable crack growth, and the initial crack region of the epoxy fracture toughness samples The picture shows an optical microscopy image of an actual fracture surface. Figure 3 11. The picture shows the graphite molds used to make the metal matrix fracture toughness samples along with the wir e placement within the mold.

PAGE 65

65 CHAPTER 4 EFFECT OF MARTENSITE TRANSFORMATION AND REORIENTATION ON DEBONDING a composite, particularly fracture toughness, it is important to u nderstand the role that the martensitic phase transformation and martensite variant reorientation deformation mechanisms play on the debonding behavior of SMA embedded composites. Payandeh et al. and Murasawa et al. suggested that when SMA wires in the au stenite phase at room temperature are embedded within an epoxy matrix, the stress induced martensitic phase transformation resulted in debonding in tensile samples ( Murasawa et al., 2004a ; Payandeh et al., 2012 ) In another study, Payendeh et al. found that the SMA martensitic phase transformation and variant reorientation affected the composite debond beha vior ( Payandeh et al., 2010 ) As with most composi tes, a strong interfacial bond between the matrix and fiber is essential to facilitate load transfer and dictates how a composit e respon ds to deformation. In order for the active SMA behavior to translate to the matrix, the matrix reinforcement interfacia l strength must be strong enough to withstand the stresses associated with transformation ( Bagwell and Wetherhold, 2005 ; Feldhoff et al., 1997 ; Naslain, 1998 ; Pothan et al., 1997 ) A widely accepted method used to analyze composite interfacial strength is single fiber pullout testing ( Brahmakumar et al., 2005 ; Jang and Kishi, 2005 ; Pommet et al., 2008 ; Redon et al., 2001 ; Shannag et al., 1997 ; Yue a nd Padmanabhan, 1999 ) However, transforming materials pose an additional complexity that is often not accounted for in traditional pullout testing models. This is especially true regarding the interfacial strength, since the martensitic phase transfor mation is often accompanied by ( Hatcher et al., 2009 ;

PAGE 66

66 Qiu et al., 2011 ; Spinner and Rozner, 1966 ) and elastic modulus ( Brill et al., 1991 ; Liang et al., 1991 ) However, SMAs offer a unique opportunity to systematically investigate the effect of phase transformations on composite debonding behavior independent of surface chemistry since these alloys c an be processed in the austenite or martensite phase with a singular chemistry. Materials and Characterization Pseudoelastic NiTi wires with a nominal composition of 50.7at%Ni Ti and a 0.87 mm diameter were purchased from Memry Corporation. The wires were used in the as received and heat treated conditions. Heat treatments were used to change the thermo mechanical properties wires. These heat treatments included a series of high temperature annealing steps followed by a water quench (WQ). A Perkin Elmer 8000 DSC was used to determine the transformation temperatures of the wires tested in this study through the extrapolated onset method, as described in Chapter 3. An epoxy mixture that consisted of 71.43 wt% Epon 828, 17.46 wt% Diethylenetriamine, and 11. 11 wt% benzyl alcohol was used to create the matrix. The epoxy mixture was cured in air at 58C for 2 hours followed by room temperature for 1 hour. An Instron 5582 was used to perform tensile tests to measure the elastic modulus and plateau/reorientatio n stress of the SMA wires. The strain was measured using clip on Epsilon extensometer with a 1 inch gage length. Table 4 1 and 4 2 summarize the thermo mechanical behavior of all of the wires used in this investigation with a corresponding alphanumeric d esignation. With regards to the designation, A and M designations refer to the room temperature phase, austenite or martensite, respectively. The number that follows the designation is correlated to the SMA transformation stress or reorientation stress, as denoted in Table 4 1. The elastic

PAGE 67

67 modulus of the epoxy is also given in the table. Figure 4 1 shows relevant mechanical properties of the wires used in the study with each experimental data point representing the averaged results of 5 tested samples. The standard deviations of the elastic modulus and transformation stresses are also included in the graph. Minitab, a statistical analysis software program, was used to perform an analysis of variance (ANOVA) to determine the level of statistical signifi cance between the mechanical properties of the M341 and M321 and A347 and 416 heat treated SMAs, respectively. It was found to a 95% confidence level that the elastic moduli were the same, but the transformation/reorientation stresses were different. Heat Treatment Effect on Shape Memory Alloys While the previous processing history of the SMA wires used in this study is proprietary, the general effects of heat treatments and cold working on the SMAs will be discussed. The heat treatments performed in this study can be characterized into 2 groups, aging (for lower heat treatment temperatures) and solution treatments (for higher heat treatment temperatures). During the aging process, precipitate formation occurs. In NiTi, the precipitate evolution when ag ing below 680C is as follows, Ni 4 Ti 3 Ni 3 Ti 2 Ni 3 Ti ( Nishida et al., 1986 ; Otsuka and Wayman, 1998 ) as a function of time. When precipitation occurs, the matrix composition is altered ( Yang et al., 2005 ) In NiTi, the Ni composition is known to directly influence the austenite and martensite transformation temperatures, where aging results in an increase in transformation temperatures ( Khalil Allafi et al., 2002 ; Otsuka and Ren, 2005 ; Pelton et al., 2000 ) The change in transformation temperatures is also accompanied by a change in martensite transformation stress ( Adharapurapu and Vecchio, 2007 ; Pelto n et al., 2000 ) since the plateau stress is directly correlated to the test temperature.

PAGE 68

68 Solution treatments are typically performed to remove secondary phases from a microstructure, including precipitates. As a result, aged NiTi SMAs typically have a higher martensite transformation temperature as compared to solution treated NiTi SMAs. Cold working of SMAs, as with non transforming metals, increases the dislocation density within the SMA microstructure. The dislocations in turn suppresses the marte nsitic phase transformation ( Kurita et al., 2004 ; Legresy et al., 1991 ; Nakayama et al., 2001 ) by inhibiting propagation of the austenite martensite phase front ( Treppmann and Hornbogen, 1997 ) Since cold wo rking suppresses the martensitic phase transformation, a subsequent solution treatment is typically performed that results in the recovery of transformation and with time, recrystallization where dislocation free, un textured grains form and grow ( Miller and Lagoudas, 2001 ; T. Todoroki and Tamura, 1987 ) Therefore, heat treatments can counteract the ef fects of cold working. The final microstructure and mechanical behavior after solution and aging treatments is dependent upon the SMA composition and thermo mechanical history. However, generally speaking, the martensite transformation stress is greater than the martensite reorientation stress because less energy is required to move the martensite interface as compared to form the martensite phase ( Gall et al., 1999 ) Additionally, the magnitude of the transformation stress is related to the grain size ( Otsuka and Ren, 2005 ; Waitz et al., 2007 ) which impedes the martensitic phase transformation front growth ( Gall et al., 1999 ) In regards to the specific heat treatments performed in this study, the M341 and M321 SMAs were aged, likely resulting in the formation of the Ni 4 Ti 3 precipitate which

PAGE 69

69 inc reased the martensite transformation temperatures. The A347 and A416 samples were likely solution treated, which is why the as received sample, A476, had a higher martensite transformation stress as compared to solution treated samples, A416 and A347. An d why these samples remained in the austenite phase at room temperature. M259 was initially solution treated followed by aging and the likely formed Ni 4 Ti 3 precipitates. Figure 4 2 and 4 3 shows optical microscopy images of an as received SMA and an SMA h eat treated at 1000C for 1 hour. Figure 4 2 and 4 3 suggest that there was grain growth in the SMA heat treated at 1000C. Results and Discussion Effect o f Phase Type on Debond Behavior Figure 4 4 shows the results of the SMA reinforcement single fiber pullout tests performed in this study. Samples that underwent the martensitic phase transformation or reorientation process as a result of deformation during testing are shown as unfilled data points. During testing, the free portion of the wire initiall y deforms elastically. Continued deformation results in either debonding or the martensitic transformation/reorientation followed by debonding and frictional sliding as shown in Figure 4 5 In general, the magnitude of the debond load appears to be corre lated to the embedded fiber length as is expected as the longer fiber lengths constitute a greater interfacial area. Additionally, the austenite SMA wires consistently experienced greater debond loads as compared to the martensite SMA wires, regardless o f whether or not the SMA underwent a martensitic phase transformation/reorientation. Since there is a correlation between mechanical properties and embedded length ( Takaku and Arridge, 1973 ) the 3 and 4mm embedded fiber lengths will be analyzed independently. The brackets indicate the data points that were included as a part of the

PAGE 70

70 3 and 4 mm analysis. For all the compar isons, a 95% confidence interval was used for the ANOVA analysis. Figure 4 6 shows the single fiber pullout results for the 3 mm embedded fiber lengths. None of the samples underwent transformation or reorientation. It was determined that the debond load s of the martensite samples (M259, M341, and M321) were statistically the same through an ANOVA analysis, however, this was not the case for the austenite samples (A416, A347, and A476). From the statistical analysis, A416 and A347 had the same debond l oad, as well as A347 and A476. However, A416 and A476 were different and these results were compared. To determine a possible relationship between the debond load and SMA mechanical properties, the debond loads of the austenite 3 mm embedded fiber length samples were plotted with respect to the elastic modulus of the respective SMA wires, Figure 4 7 These results suggest that the SMA fiber elastic modulus may affect the debond behavior of the composites. The SMA fibers with higher elastic moduli, have l ower debond loads. This behavior is likely related to the elastic mismatch between the matrix and reinforcement ( Klingbeil and Beuth, 2000 ; Ona et al., 2013 ) From Table 4 1 the elastic modulus of the epoxy matrix was found to be 2.1 GPa. It has been established that the main differences between the SMA austenite and and elastic modulus, as shown in Table 4 1 and in ( Hatcher et al., 2009 ; Qiu et al., 2011 ; Stebner et al., 2011 ) Since the elastic mismatch behavior is not followed when comparing the austenite and martensite debond loads Reported values f 1.77 ( Hatcher et

PAGE 71

71 al., 2009 ; Qiu et al., 2011 ; Spinner and Rozner, 1966 ) for austenite and 0.31 0.44 ( Hatcher et al., 2009 ; Qiu et al., 2011 ; Stebner et al., 2011 ) for martensite. The high for the austenite phase is gene rally greater as compared to the martensite phase. A martensite phase is le ss than that of the austenite phase, the differences in the Figure 4 8 shows the single fiber pullout results for the 4 mm embedded fiber lengths. The samples that und erwent a martensitic transformation or reorientation are shown as separate data points and will be discussed in the following section. Similar to the 3 mm embedded fiber lengths, analysis of M341 and M321 shows that the samples had statistically the same d ebond load. Additionally, the A416 and A476 debond loads are statistically similar As expected, the debond behavior follows the same trend described previously with the greater elastic modulus corresponding to a lesser debond load, Figure 4 9 Effect of Transformation on Debond Behavior Figure 4 4 shows the single fiber pullout results for the samples that underwent martensite transformation or reorientation (illustrated by the unfilled symbols) Figure 4 4 show s that the transformation/reorientation oc curred at the higher embedded fiber lengths. Following transformation or reorientation, the wires are debonded in the plateau region of the SMA. As shown in Figure 4 5 the load remains relatively constant during the martensitic transformation/reorientat ion. Further extension results in the

PAGE 72

72 continuation of the martensitic transformation/reorientation, which is accompanied by significant elongation. Figure 4 8 indicates the samples that transformed, A347, and reoriented, M259 and M321. The debond loadi ng curve is directly correlated to the SMA material response to deformation. The debond loads experienced by transforming or reorienting martensite variants reach a relative maximum within the martensite transformation/ reorientation plateau. First consid ering the martensite samples, the debond loads are statistically different with M321 having a higher debond load as compared to M259. The martensite reorientation loads that correspond to the stresses, given in Table 4 1 are 154 N and 191 N for the M259 and M321 wires, respectively. The actual debond load for M259 reoriented and M321 reoriented is 163 N and 192 N respectively. Therefore, the debond load is correlated to the transformation/reorientation stress of the SMA reinforcement. This pattern is c onsistent for the A347 transformed sample where the transformation and debond load s are 206 N and 205 N, respectively. Because the samples did not debond immediately upon experiencing the martensitic transformation /reorientation, as see n in Figure 4 5 it is thought that it is not the physical action of the transformation/ reorientation process that results in debonding but rather secondary effects associated with sustained elongation and changes in material properties that cause debonding at the tested emb edded lengths. The secondary effects include a change in material properties for the austenite SMA, and extensive elongation for both the austenite and martensite SMA that may accelerate debonding. SMA Surface Roughness Analysis To characterize the effect of the heat treatment process on the SMA wires, the surface roughness was measured using a noncontact optical profilometer, as described

PAGE 73

73 in Chapter 4: Equipment and Experimental Techniques. The results, shown in Figure 4 10, show that the higher the heat treatment temperature the rougher the SMA wire surface. Accordingly, the A476 (as received) SMA had the lowest surface roughness and the A416 SMA had the highest surface roughness. The surface roughness changes that resulted from the heat treatment, app ears not to have affected the single fiber pullout results. Had the heat treatments affected the magnitude of the debond loads, the SMA with the roughest surface (A416) would have had the highest debond load due to mechanical locking at the 3 mm embedded length; t his was not the case, since A416 actually had the lowest debond load. Figure 4 11 shows the debond loads plotted with respect to the surface roughness of the 3 mm embedded lengths for the austenite and martensite phases. The 4 mm embedded length results are not shown in Figure 4 11 because of the additional transformation and reorientation mechanisms taking place at the 4 mm embedded lengths. A representative surface profile is shown in Figure 4 1 2 for each of the SMA wires used in the study. Pu llout Energy The pullout energy corresponds to the work required to debond and pullout the fiber from the matrix. Figure 4 1 3 shows a comparison of the work required to pullout the SMA wires from the matrix for the austenite phase wires. Since the load wa s approximately 0, after debonding, as shown in Figure 4 5, the pullout energy was calculated using the area under the single fiber pullout curves to the point of debonding. Figure 4 14 shows representative debonding curves of A476, A416, and A347 that we re embedded at approximately 4 mm. From the results, it is clear that the SMAs that underwent a martensitic phase transformation, A347 open data points, had the higher

PAGE 74

74 displaye d the higher pullout energy had the statistically the same debond load as A476. The reason for the higher pullout energy is attributed to the strain associated with the martensitic phase transformation that enabled the extended strain prior to debonding. Summary The effect of the thermo mechanical properties of NiTi SMA wires were investigated to understand their effects on debonding behavior on samples with 3 mm and 4 mm embedded lengths. NiTi SMA wires were heat treated to produce wires with varying t hermo mechanical properties (room temperature phase, elastic modulus, and martensite transformation/reorientation stress). The wires that were in the austenite phase displayed greater debond loads as compared to the wires that were in the martensite phase By comparing the austenite samples, A347, A416 and A476, the results suggest that the greater the elastic modulus, the lesser the debond load. The reader can refer to Figure 4 5 and Figure 4 7 for a reminder of the sample debond load statistical relati onships. For the SMA wires that did undergo a martensitic phase transformation or reorientation, the debond loads corresponded to the SMA transformation/reorientation plateau loads. Debonding did not occur immediately upon the SMA undergoing the martensi tic phase transformation/reorientation. Therefore, the transformation/reorientation behavior in itself does not result in debonding. Instead the substantial elongation associated with transformation/reorientation may lead to a significant lateral contrac tion that facilitates the debonding process. Lastly, the surface roughness of the wires were also investigated and it was determined that while the heat treatments did change the surface roughness of the SMA wires, the heat treatment effect on surface rou

PAGE 75

75 While the load displacement curves can be used as an indication of the energy absorbed by a reinforcing element during deformation, it does not directly correlate to the increase in fracture toughn ess due to the addition of reinforcements to a matrix. In the following chapters, the fracture toughness of SMA embedded composites will be investigated.

PAGE 76

76 Table 4 1. The table shows relevant properties of the reinforcements. Water quenched is represente d by WQ. The A and M designations represent the austenite and martensite phases, respectively. Designation Heat Treatment Room Temp. Phase Elastic Modulus (GPa) Transformation/ Reorientation Stress (M P a) A476 As received A 72.4 476.6 A3 47 650C 1hr WQ A 82.7 347.3 A416 1000C 1hr WQ A 85.5 416.5 M341 400C 1 hr WQ M 56.9 341.9 M321 450C 1hr WQ M 56.5 321.2 M259 900C 1hr 350C 8 hr WQ M 46.8 259.4 Epoxy 2.1 Table 4 2. The table shows the transformation temperatures of the heat treated SMAs. Designation A s (C) A f (C) M s (C) M f (C) A476 3.9 0.24 14.2 2.1 4.7 0.56 14.5 1.6 A347 8.8 0.81 3.4 2.0 31.8 0.41 45.5 1.8 A416 6.0 0.90 5.1 2.1 24.7 0.75 37 0.57 M341 40.8 0.6 48.7 0.9 2 38.9 0.31 29.5 0.31 M321 3 5 0 0.38 41.9 1.0 32.4 0.77 24.4 1.0 M259 50.6 0.61 57.0 0.93 47.9 1.3 38.8 0.62

PAGE 77

77 Figure 4 1. The graph shows the SMA properties of the wires used in this study with t he data point labels explained in table 1. Each data point represents the averaged results of 5 tested samples. Figure 4 2. The optical microscopy image shows the as received NiTi microstructure.

PAGE 78

78 Figure 4 3. The NiTi microstructure of a wire subjected to a 1000 C, 1 hour h eat treatment. The optical microscopy image was taken at 50X microstructure. Figure 4 4. The single fiber pullout results for all of the single fiber pullout samples. Unfilled data points indicate that the sample experienced the martensitic transform ation or reorientation.

PAGE 79

79 Figure 4 5. The curve shows a single fiber pullout curve for the M259 sample that had an embedded length of 3.96 mm. At approximately 1.0 mm of extension, the NiTi begins to undergo a martensitic reorientation. Figure 4 6 The graph shows the debond load versus the embedded fiber length for the 3mm embedded fiber lengths. Each data point represents the average of at least 4 tested samples.

PAGE 80

80 Figure 4 7. The d ebond load versus elastic modulus of the austenite 3mm emb edded fiber length samples. Each data point represents the average of at least 4 tested samples. Figure 4 8. Graph illustrating the debond load versus the embedded fiber length for the 4 mm embedded fiber lengths. The error bars represent the stat istical

PAGE 81

81 Figure 4 9. The debond load versus elastic modulus of the untransformed austenite 4mm embedded fiber lengths. The error bars represent the statistical debond load and elastic modulus. Figure 4 10. The graph show the average surface roughness measurements for each NiTi SMA wire condition used in the single fiber pullout testing. The standard deviations are also shown. Austenite Martensite

PAGE 82

82 Figure 4 11. The gra ph shows the debond load versus the surface roughness for the SMA wires that were embedded at approximately 3 mm. Figure 4 12. The graph shows representative surface roughness profiles of the NiTi SMA wires used to perform the single fiber pullout test s.

PAGE 83

83 Figure 4 13. The graphs shows pullout work versus the embedded fiber length for the austenite NiTi SMA wires. Figure 4 14. The graph shows representative single fiber pullout curves for the austenite SMA wires that were embedded to approximatel y 4 mm. The A347 sample underwent a martensitic phase transformation whereas A 416 and A476 did not. The curves are shown until the point of debonding.

PAGE 84

84 CHAPTER 5 INTRINSIC TOUGHENING IN S HAPE MEMORY ALLOY EMBEDDED COMPOSITES This chapter seeks to explor e the contribution of the SMA martensitic phase transformation on the intrinsic fracture toughness of SMA embedded composites. Of particular interest is the effect of the martensitic phase transformation on the crack tip shielding mechanics ahead of the advancing crack front. A J integral fracture toughness study was performed to quantify the toughening increment and specific contribution of the martensitic phase transformation in SMA reinforced epoxy composites Non transforming aluminum (Al) and stee l reinforcements were also examined for comparative purposes. Due to the difficulty in determining whether the martensitic phase transformation took place during fracture toughness testing, analytical models that estimate the internal bending stress with in the SMA reinforcements were performed. Since the fracture toughness of composites has been shown to be dependent upon the constituent material interfacial interactions ( Deve, 1992 ; Kim, 1991 ) single fiber pullout tests were also performed to characterize the reinforcement interfacial shear strengths for the SMA reinforced epoxy composites. These results will be used to analyze the overall fracture toughness behavior of this class of materials and discuss the efficacy of SMA reinforcements as an intrinsic toughening mechanism for brittle matrix composites. Materials and Methods Materials Selection Epoxy matrix c omposites were created using alloy BB superelastic SMA wires with a nominal composition of 50.7at%Ni Ti from Memry Corporation, hereafter referred

PAGE 85

85 to as NiTi. The NiTi was received in the fully pseudoelastic state. In addition to being used in the as re ceived condition, the NiTi was also heat treated to alter the microstructure to produce stress induced martensite in pseudoelastic SMAs ( Melton, 1990 ; Zhang et al., 1999 ) The heat treated NiTi (NiTi ht) was solution treated at 1000C for 1 hour and then water quenched. These samples were then encapsulated in an evacuated quartz tube that was back filled with argon to prevent oxidation. Aluminum alloy 1100 (Al) and carbon steel 1080 (steel) purchased from McMaster Carr were also used as reinforcing element s The Al was used in the as received condition and was chosen due to its similar elastic modulus to t he NiTi austenite phase. This was to remove the effect of stiffness mismatch between the selected reinforcements from changes in fracture energy and to isolate the contributions from the martensitic phase transformation. Additionally, previous research ha s shown that the difference between the elastic modulus of the matrix and reinforcement does affect the composite debonding characteristics ( Kim, 1991 ) This effect would increase the complexity of the analysis and is reserved for a separate study. The steel was heat treated at 768C for 1 hour, furnace cooled to 666C, and then taken out of the furnace and allowed to cool to room temperature. The steel heat treatment resulted in the wires having a similar yield stress to the NiT i transformation stress. The epoxy matrix consisted of 71.4 wt% Epon 828, 17. 5 wt% diethylenetriamine, and 11.1 wt% benzyl alcohol, as the resin, hardener and plasticizer, respectively. A design of mixtures experiment was performed to determine a ductile epoxy composition for use in the study. The design of mixtures experimental setup and results are described in Appendix A.

PAGE 86

86 during testing so that debonding and crack growth can be observed. A schematic of the 3 point bend fracture toughness samples and a picture of an actual sample are shown in Figure 5 1A and B, respectively. Materials Characterization determined usi ng the procedure described in Chapter 3 using a cross head extension rate of 0.25 mm/min. The 0.25 mm/min extension rate was selected because the extension rate was slow enough to stop the J integral fracture toughness test at various amounts of crack ex tension. Each material was tested until the sample showed evidence of inelastic deformation. Representative tensile stress strain curves are shown in Figure 5 2 Thermal analysis using a Perkin Elmer 8000 differential scanning calorimeter (DSC) machin e was performed to characterize the transformation behavior of the NiTi and NiTi ht SMA reinforcements. Representative DSC curves are shown in Figure 5 3. Relevant thermo mechanical properties of the SMAs, Al, steel and epoxy are summarized in Tables 5 1 and 5 2 T able 5 1 includes elastic modulus, yield strength, stress induced martensite transformation stress and transformation temperatures. It is noted that there was a change in the SMA elastic modulus between the NiTi and NiTi ht samples that can be attributed to the reduction of texture induced from prior processing during the heat treatment ( Gao G, 2003 ; Liu, 1997 ) Table 5 2 lists the SMA transformation temperat ures. The reinforcement wires had diameters of 0.87, 0.87 and 0.78 mm for the NiTi, NiTi ht and Al, respectively, and were oriented perpendicular to the crack plane. A 2 sample t test was performed using Minitab, a statistical analysis software, to valida te

PAGE 87

87 the statistical significance between the stress to induce martensite (plateau stress) in the NiTi and NiTi ht reinforcements. It was found that the two SMA reinforcement types were statistically different from each other within a 95% confidence interva l. The NiTi and NiTi ht DSC results indicate that both SMAs are in the austenite phase at room temperature. All experiments were performed at room temperature. Single Fiber Pullout Test NiTi, NiTi ht and Al embedded epoxy matrix single fiber pullout sam ples were prepared using the epoxy single fiber pullout method described in Chapter 3 SMA reinforcement embedded wire lengths between 20 30 mm were tested since the debond load has been shown to vary with embedded fiber length ( Difrancia, 1996 ; Wetherhold, 2000 ) Results and Discussion Fracture Toughness Figure 5 4 shows the fracture toughness results for the monolithic epoxy and the Al, steel, NiTi and NiTi ht embedded epoxy samples for crack extens ion lengths below 0.35 mm. Each sample showed an increasing J integral value with progressive crack growth. The steel reinforced samples displayed the greatest fracture toughness. The remaining samples had virtually indistinguishable fracture toughness behavior indicating that the crack minimally interacts with the reinforcements at these crack lengths. Figure 5 5 shows the extended crack growth results for the monolithic epoxy, and the Al, NiTi, and NiTi ht embedded epoxy samples. Above 0.35 mm of cr ack growth, there were significant differences in the fracture toughness behavior. The results indicate that the NiTi ht samples displayed the greatest fracture toughness, followed by the NiTi, Al and lastly monolithic epoxy samples. The overall contribu tion of the Al

PAGE 88

88 reinforcement was not significant, in that the Al reinforced samples only minimally increased the fracture toughness over the monolithic samples. A few samples experienced unstable crack growth. The monolithic epoxy samples fractured compl etely, whereas all of the reinforced samples underwent partial matrix fracture to the second or third row of wires thus avoiding complete catastrophic failure. A likely reason for the unstable crack growth in some samples could be attributed to the prese nce of microstructural defects such as pores. An image of such a pore can be found in Figure 5 6. The NiTi and NiTi ht embedded fracture toughness samples showed debonding ahead of the crack tip. Debonding was apparent when the epoxy lost transparency. The NiTi and NiTi ht embedded samples also showed debonding along the third row of wires, farthest away from the pre crack, as indicated in Figure 5 1A During loading t he debonded region grew circumferentially around the reinforcement and down the length of the reinforcement. Previous research has shown that in pseudoelastic SMA composites, debonding was found to occur during the SMA martensitic transformation ( Murasawa et al., 2004b ) which could explain the debonding nature of the SMA embedded composites investigated in the study. The Al reinforced epoxy fracture toughness samples also showed debonding but only when the crack tip was near the rei nforcing element or in the samples with substantial crack growth. Effect of Elastic Modulus and Yield /Transformation Stress on Fracture Toughness The previously discussed results show that the reinforcing elements have varying effects on the composite f racture toughness behavior. When considering composite reinforcements with similar elastic moduli but different yield strengths (or transformation

PAGE 89

89 stresses in the case of the SMA reinforcements), the reinforcement with the larger yield strength will produc e a higher fracture toughness. This was shown in Figure 5 5 when comparing the Al and NiTi reinforced composites. Alternatively, when considering composite reinforcements with a similar yield strength or transformation stress, but different elastic modu li, the reinforcement with the greater elastic modulus will produce the greater fracture toughness. This is shown in Figure 5 4 with the steel and NiTi reinforced epoxy samples. The yield strength and elastic modulus observations help to explain the fract ure toughness behavior of the NiTi and NiTi ht reinforced composites where it appears that the elastic modulus differences have a more pronounced effect than the transformation stress. Evaluating Reinforcement Martensitic Phase Transformation through Bea m Analysis Since the fracture toughness testing described in this study cannot directly identify initiation and formation of stress induced martensite in the NiTi and NiTi ht SMA reinforcements during testing, an analytical model based on beam theory is pr oposed. j within the reinforcements was calculated using the following equation ( Sun, 2007 ) : ( 5 1 ) M, E, I, and y are the bending moment, elastic modulus, second moment of inertia and distance from the composite neutral axis to the component centroid, respectively. The subscripts j and i both refer to the component numbe r as defined in Figure 5 1A T he bending moment, M, was defined by M=PL/4, where P and L

PAGE 90

90 represent the applied load and roller span, respectively. The NA location was derived using the following equation, 0 = i E i y i A i to satisfy static equilibrium Therefore, ( 5 2 ) where B, H, A and D are the sample thickness, unbroken ligament height, area and component centroid height, respectively. The subscripts m and r refer to the matrix and reinforcement. These calculations assume that the matrix and reinforcement experience tension compression symmetry, the NA location remains constant, the matrix and reinforcement are perfectly bonded and the constituent materials behave as elastic plastic materials. Crack e xtension was not accounted for in the calculations. The NiTi and NiTi ht composite NA s w ere located at 12.50 and 12.53 mm, respectively from the bottom of the sample. A complete derivation of the equations used to calculate the bending stresses within t he reinforcements is given in Appendix B. The applied loads to initiate transf ormation were 33 6 and 2 72 N for the NiTi and NiTi ht SMAs, respectively, in row 3. Upon further loading the SMAs in row 1 begin to transform at 410 and 322 N for the NiTi and Ni Ti ht SMAs, respectively. Figures 5 7 and 5 8 show the reinforcement bending stress at the critical applied loads to induce transformation in the wires for the NiTi and NiTi ht SMAs, respectively. The calculation in Figures 5 7 and 5 8 were performed at the sample center, in the crack plane, as shown in Figure 5 9A. The horizontal portions of the bending stress curves indicate that the SMAs have reached the martensitic phase transformation stress. Figure 5 10 shows the SMA stress evolution with respect to the distance from the neutral axis at a 470 N applied load. The 470 N applied load was the average maximum load experienced by the 3 point bend SMA reinforced composites. The difference in the

PAGE 91

91 bending stress curve slopes occurs due to the larger elast ic modulus of the NiTi ht relative to NiTi reinforcements. The larger elastic modulus and lower martensite transformation stress causes the NiTi ht SMA to reach its martensitic transformation stress at a lower stress level than the NiTi reinforcement. It can be seen from the bending stress calculations, that the martensitic phase transformation occurred in the row 3 and 1 wires, in the crack plane, effectively resulting in a mixed phase reinforcement that contained both the martensite and austenite phases The transformation locations were expected because the bending stress is proportional to the distance from the NA The larger the distance from the NA the greater the bending stress. S ince rows 3 and 1 are the farthest away, transformation can be expe cted to occur there first. Figure 5 11 shows the stress profile along the center of the reinforcement diameter. The sample length, L, is shown in Figure 5 1A Figure 5 9B shows the plane sample plane where the calculations were performed. Since the be nding stress is symmetric about the sample midpoint, L/2, the stress was only plotted to the midpoint. Results from rows 1 and 3 are not symmetric as a function of the internal bending stress of the SMAs because the NA was not located in the sample center The elastic energy contribution of the SMA appears to dominate over the martensiti c transformation contribution. During the analytical examination of the reinforcement bending stress, several assumptions were made. The implications of the assumptions are addressed below. Crack growth and the associated plastic zone were not considered in the calculations. This assumption would actually increase the bending stress experienced in the

PAGE 92

92 reinforcement and as such require a smaller applied load to result i n transformation. Perfect interfacial bonding between the matrix and reinforcement was not necessarily the case as debonding did occur in the SMA composites, as shown in Figure 5 12. Debonding reduces the stress transfer efficiency across the interface, therefore decreasing the stress experienced by the SMA reinforcement in the debonded region. The results from the fracture toughness tests and beam analysis suggest that Rows 1 and 3 experienced transformation, however the primary contribution to the com posite fracture toughness were the reinforcement mechanical properties. This suggests that the SMA reinforcements may be used more effectively in a crack bridging capacity with sufficient interfacial shear strength to facilitate the stress induced martens ite transformation since the SMA can sustain more deformation prior to plastically deforming as compared to a non transforming reinforcement and upon load removal can absorb sufficient energy dependent on the amount of deformation. Single Fiber Pullout S ince debonding occurred in the SMA reinforced composites, as shown in Figure 5 12, t he interfacial bonding characteristics were studied to examine the role of interfacial properties on toughening. Figure 5 13 shows representative single fiber pullout curv es for the SMA and Al reinforced samples. The results show that the Al samples plastically deformed, even at small embedded fiber lengths. This indicates that the interfacial shear strength was sufficiently high enough to promote yielding in the Al wires It should be noted that each sample the Al fiber plastically deformed followed by fracture. Because no transformation took place during the single fiber pullout experimentation, the average interfacial shear strength was calculated using Equation

PAGE 93

93 3 2 Figure 5 14 shows the average interfacial shear strength plotted with respect to the embedded fiber length for each of the SMA tested samples. The average calculated values were 1.4 0.1 and 1.4 0.3 MPa for the NiTi and NiTi ht embedded samples, res pectively. The average interfacial shear strength values indicate that the NiTi ht surface properties appear not to have been affected by the heat treatment. T he reinforcement surface roughness and wettability of the epoxy on the reinforcement has been s hown to contribute to the interfacial behavior ( Chawla, 2006 ) Based on the surface roughness results discussed in t he previous chapter, heat treatments of the NiTi SMA at 1000C resulted in an increased surface roughness, but the extent of the increase did not appear to affect the debond behavior. Therefore, interfacial toughness does not appear to contribute to the i ncreased toughness behavior of the NiTi ht composite relative to the NiTi composite. Summary A comparative fracture toughness study was performed using the J integral methodology. The results appear to suggest that below 0.35 mm of crack extension, th e steel embedded samples displayed a greater fracture toughness as compared to the NiTi, NiTi ht, and Al embedded samples. Above 0.35 mm, when the steel reinforcement was removed from the analysis, the NiTi ht embedded epoxy samples produced the greatest fracture toughness when compared to monolithic, Al and NiTi embedded epoxy composites. For the sample geometry and reinforcement orientation used in the study, t he results may suggest that when considering two composites with an identical matrix, if the r einforcements have the same modulus, then the magnitude of the yield/transformation stress dominates the fracture toughness behavior. Similarly, if the composites have the same yield/transformation stress, then the magnitude of the elastic

PAGE 94

94 modulus dominat es the fracture toughness behavior. Analytical bending stress calculations were performed to verify formation of stress induced martensite in the SMA during crack propagation. The results show that the onset of the martensitic phase transformation was c omputed to first occur in the NiTi ht samples at a 270 N applied load. In the NiTi reinforcement, the martensitic transformation began at a higher applied load of 336 N. The differences bet ween the SMA toughness behaviors may be attributed to the magnit ude of the reinforcement elastic moduli. Lastly, single fiber pullout tests were performed to study the interfacial characteristics between the reinforcement and epoxy matrix and its role in increasing the toughness of the composite. The NiTi and NiTi ht reinforcements were found to have equivalent interfacial shear strength values and thus interfacial toughness was determined not to be the primary factor in the fracture toughness differences seen in the J integral tests. Therefore, the results may sugge st that the SMA elastic properties are behind the NiTi ht embedded epoxy samples displaying the highest fracture toughness behavior with the elastic deformation contribution do minating the toughness behavior Now that the effect of the stress induced martensitic transformation on the intrinsic composite fracture toughness has been examined, the extrinsic effect will be explored to understand the effect of the SMA martensitic transformation and reorientation process on fracture toughness.

PAGE 95

95 Figure 5 1 The 3 point bend fracture toughness specimen geometry and dimensions. The ruler units are cm. Figure 5 2. The graph shows r epresentative stress strain curves of the constituent materials used in this study

PAGE 96

96 Table 5 1. The table shows the m echanical properties and transformation temperatures of the reinforcing elements used in this study. Table 5 2. The table shows the transformation temperatures of the NiTi and NiTi ht reinforcing elements used in this study.

PAGE 97

97 Figure 5 3. The grap h shows the representative DSC curves for the NiTi and NiTi ht SMA reinforcements used in this study. Figure 5 4. The graph shows the f racture toughness results for the monolithic epoxy and NiTi, NiTi ht, aluminum, and steel embedded composites for c rack extensions less than 0.35 mm

PAGE 98

98 Figure 5 5. Fracture toughness results for the monolithic epoxy and NiTi, NiTi ht, and aluminum embedded composites. Figure 5 6. The figures shows an o ptical microscope image of a steel reinforced epoxy sample. The sample underwent unstable crack growth during testing as a result of a pore

PAGE 99

99 Figure 5 7. The graph shows the NiTi bending stresses at the onset of tranformation in rows 1 and 3 with respect to the distance from the neutral axis. Figure 5 8. T he graph shows the NiTi ht bending stresses at the onset of transformation in rows 1 and 3 with respect to the distance from the neutral axis.

PAGE 100

100 Figure 5 9. The schematics show the locations of where the bending stress calculations were performed. A) in the y z plane at the sample center, B) in the x y plane. A) B)

PAGE 101

101 Figure 5 10. Graph showing the SMA reinforcement bending stress with respect to the distance from the neutral axis at a 470 N applied load. The shaded regions refer to the indicated SM A reinforcement placement. The horizontal portion of the bending stress curves indicates that the SMA has undergone transformation. Figure 5 11. NiTi and NiTi ht SMA stress distribution along the sample length at a 470 N applied load. The L/2 length corresponds to the crack plane. The horizontal portion of the bending stress curves indicates that the SMA has undergone transformation.

PAGE 102

102 Figure 5 12. NiTi fracture toughness sample showing debonding ahead of the crack tip as indicated by the arrow Figure 5 13. Representative single fiber pull out test curve showing the locations of debond load, frictional sliding, and fiber pull out.

PAGE 103

103 Figure 5 14. Interfacial shear strength as a function of embedded fiber length for the NiTi, NiTi ht, and aluminum reinforcing elements.

PAGE 104

104 CHAPTER 6 EXTRINSIC TOUGHENING OF SHAPE MEMORY ALLOY COMPOSITES : EPOXY MATRIX Crack bridging is an excellent source of toughening in composites and has been shown to greatly increase the toughness of b rittle ceramic ( Bartolome et al., 2002 ; Budiansky et al., 1988 ; Sbaizero et al., 1998 ) metal ( Mendiratta et al., 1991 ) polymer ( Cardwell and Yee, 1998 ) and natural material matrices ( Nalla et al., 2003 ; Peterlik et al., 2006 ) The use of a ductile second phase enables a reinforcement to undergo deformation beyond the elastic regime, thereby increasing the reinforcement contribution to fracture toughness w hen serving in a crack bridging capacity ( Sun and Yeomans, 1996 ) This extended deformation due to plastic deformation can lead to enhanced toughness as long as complete interfacial debonding does not occur, since debonding has been iden tified as a factor that can limit the work output of ductile reinforcing members ( Wetherhold, 2000 ; Zhu and Beyerlein, 2002 ) Increased toughness resulting from the use of ductile reinforcing elements is also compounded by toughening mechanisms associated w ith crack shielding. The high ductility, high strength characteristics of SMAs may make the material an ideal candidate for crack bridging reinforcing elements for increased toughening, because SMAs are able to sustain a large amount of deformation prior to experiencing plastic deformation. Additionally, there is the added benefit of inherent crack closure upon load removal and/or increasing the SMA operating temperature. The Extrinsic Toughening of Shape Memory Alloy Composites study is divided into 2 c hapters that separately focus on polymers and metal matrices. Chapter 6 considers an epoxy matrix that was chosen due to its simplicity in manufacturing and transparency, which facilitates efficient analysis and visual inspection of the composite

PAGE 105

105 debondi ng behavior. Additionally, the epoxy low curing temperature prevented thermo mechanical changes in the SMA reinforcement, while the low mechanical properties of the epoxy, exaggerated the effects of the reinforcements. Chapter 7 considers a Zn Al metal m atrix that was chosen due to its brittle nature, relative ease of castability in air, interfacial properties which enabled embedded SMA reinforcements to undergo martensitic phase transformations. Each matrix is address ed separately as they display mechan isms that are different from each other, which could play a significant contribution in the overall toughness behavior. NiTi SMA wires in either the martensite or austenite phase at room temperature were used as reinforcements to distinguish the effect o f the stress induced martensite phase transformation and martensite variant reorientation phenomena on the composite fracture toughness. The SMAs were used in their un prestrained state to isolate the transformation and reorientation effect from other kno wn SMA toughening mechanisms. Materials and Methods Materials Selection Epoxy matrix composites were created using alloy BB superelastic SMA wires with a nominal composition of 50.7at%Ni Ti from Memry Corporation, hereafter referred to as NiTi austenite. The NiTi was received in the pseudoelastic state. In addition to being used in the as received condition, the NiTi was also heat treated to alter the room temperature phase of the SMA from austenite to martensite in order to investigate the effect of m artensite reorientation on composite fracture toughness. The heat treated NiTi (NiTi martensite) was heat treated at 400C for 1 hour and then water quenched. These samples were then encapsulated in an evacuated quartz tube that was back

PAGE 106

106 filled with argon to prevent oxidation. The encapsulation procedure is described in further detail in Chapter 3. Aluminum alloy 1100 (Al), purchased from McMaster Carr, was also used as a reinforcing element. The Al was used in the as received condition and was chosen d ue to its similar elastic modulus to the NiTi austenite phase. Similar to the previous chapter, this was to deconvolute the elastic modulus influence from changes in fracture energy in order to isolate the contributions from the SMA reinforcement deformat ion. The epoxy matrix consisted of 64.5wt% Epon 828 and 35.5wt% Jeffamine D 400 as the resin and hardener, respectively. The resin was cured at 80C for 2 hours, 125C for 3 hours, room temperature for 1 hour and then immediately tested. It is worth no ting that the epoxy used in this chapter was different from the one used in the previous chapter. A different hardener and curing schedule was used. Materials Characterization det ermined using the tensile testing method described in Chapter 3. Figure 6 2 shows the extension rate dependence of the epoxy. A cross head extension rate of 0.25 mm/min was used since it is the s ame used during the fracture toughness tests. Each sample was tested to failure. Representative tensile stress strain curves for the constituent materials are shown in F igure 6 1, where the strain was measured using an extensometer. DSC was performed using the method described in Chapter 3 to characterize the t ransformation behavior of the NiTi and NiTi ht SMA reinforcements. Additionally, through DSC, the epoxy glass transition range was determined to be 29 41C. The DSC plots for the SMA wires and epoxy matrix are shown in Figures 6 3 A and B respectively. Relevant thermo mechanical properties of the SMAs, Al, and epoxy

PAGE 107

107 are summarized in T able 6 1. The table includes the elastic modulus, yield strength, stress induced martensite transformation stress, and martensite reorientation stress Table 6 2 shows t he SMA transformation temperatures. The reinforcement wires had diameters of 0.87, 0.87 and 0.78 mm for the NiTi austenite, NiTi martensite, and Al, respectively, and were oriented perpendicular to the crack plane. A schematic of the composite showing di mensions and reinforcement placement is presented in Figure 6 4. All experiments were performed at room temperature. Results and Discussion Fracture Toughness Figure 6 5 shows representative 3 point bend curves for the monolithic, Al, NiTi austenite, and NiTi martensite samples that were used to calculate the J integral fracture toughness values. The curves correspond to the samples that had crack extensions of approximately 3 mm. For each sample in Figure 6 5 stable crack growth occurred, however in the NiTi martensite sample a slight drop in load, approximately 25 N, occurred and corresponds to abrupt interfacial debonding. The abrupt load drop in the NiTi martensite sample is seen at approximately 5 mm of compressive extension. After the maximum loa d is achieved in the compressive load compressive extension curves, the load slowly decreased. The Figure 6 5 shows that for samples with approximately the same crack extension, the energy absorbed (energy under the compressive load compressive extension curves) was greatest in the NiTi austenite followed by the NiTi martensite, Al, and lastly the monolithic sample. Figure 6 6 shows the J integral fracture toughness results for the monolithic and NiTi austenite, NiTi martensite, and Al reinforced samples The fracture toughness

PAGE 108

108 curves show that all of the samples including the monolithic epoxy samples displayed R curve behavior. In the monolithic sample, the R curve behavior is likely due to the increasing plastic zone surrounding the crack tip, similar to the composite shown in Figure 6 7. The monolithic and Al samples behaved similarly, with the Al showing only a minimally increase over the fracture toughness of the monolithic samples. This is likely in part due to the limited debonding that took pla ce that allowed for only a small, localized region of the Al to plastically deform in addition to the low yield strength of the reinforcement relative to the SMA samples. The Al debonding behavior is different from the SMA debonding behavior that experien ced more substantial debonding. The debonding behavior will be discussed in further detail in the following section. Crack bridging was seen in the Al, NiTi austenite, and NiTi martensite samples, as shown in Figure s 6 8 A and B. In the Al composites, at greater crack extensions, the Al fibers in Row 1 necked and then fractured. The NiTi SMA fibers, however, experienced uniform deformation throughout the entirety of the test. During the deformation of the composites, the NiTi austenite SMA appears to h ave sustained minimal if any permanent plastic deformation since upon removal of the 3 point bend deformation load, the crack faces returned back together as shown in Figure 6 9 A This occurred for all of the NiTi austenite samples. Alternatively, the Ni Ti martensite composite crack faces did not return together after the 3 point bend applied load was removed, as shown in Figure 6 9 B Shape recovery did not occur in the NiTi martensite samples because the martensite reorientation does not allow for recov ery without added heat.

PAGE 109

109 The resistance to stable crack growth can be expressed as or the slope of the J integral crack extension graphs. In looking at the Figure 6 6, of the monolithic samples remain constant as the crack length increases meaning that there is no change in the resistance to stable crack growth. The Al samples behaved in a similar manner to the monolithic samples below 4 mm of crack extension, further indicating the fact that as the crack front passed the Al wires, the Al wires only minimally enhanced the fracture toughness of the composite. Above 4 mm, the begins to decrease. The reason for the change in of the Al samples is likely attributed to the Al reinforcements necking and fracturing at greater crack extensions. of the NiTi martensite also remained relatively constant until after the crack passed the second row of wires, after which there was an increase in was higher for the NiTi martensite as compared to the Al reinforced samples. The NiTi austenite embedded composites behaved differently from the monolithic, Al, and NiTi martensite samples. Since the amount of debonding, dictates the extent to which the bridging element can assist in toughening, an understanding of the debonding behavior is necessary. Composite Debonding Behavior The NiTi SMAs and Al debonding behavior were evaluated to understand its effect on the composite toughening behavior. First, observations were made about the NiTi SMAs and Al debonding during composite deformation. Then the single fiber pullout results will be discussed for the SMAs and Al reinforced composites. Aluminum debonding b ehavior The Al embedded epoxy samples sustained minimal debonding during deformation. Figure 6 10 shows the extent of debonding. The white parentheses

PAGE 110

110 indicate the debonding length. During deformation, d ebonding did not occur ahead of the crack tip. The crack tip encountering the Al reinforcement is what facilitated debonding. The debonding that occurred was not substantial and was centered on the crack area. With continued crack growth, debonding then occurred in the 2 nd row again with limited debonding. It is evident that it was more energetically favorable for the Al reinforcement to yield instead of debond. Shape m emory a lloy debonding b ehavior Figure 6 11 A H shows the debonding behavior of the Ni Ti austenite SMAs embedded epoxy composites during 3 point bend testing. The images are video stills taken at various stages during the test. The white parentheses in the image s indicate the debonding length along the SMA wires. Additionally, the corres ponding load load line displacement curves are included on the upper left hand corner of each image. With increased load, debonding initially occurs in the 1 st row of wires ahead of the crack tip. With progressive deformation, the crack tip reaches and s ubsequently passes the 1 st row of wires. During this time the debonding length along the first row of wires grows. The 2 nd row of wires then debonds as the load continues to increase. Debonding often occurred asymmetrically, along the fiber reinforcemen ts. Both NiTi SMA reinforcements behaved in this manner. Single Fiber Pullout To evaluate the interfacial debonding behavior and determine whether the interfacial strength was strong enough to withstand transformation or reorientation, single fiber pullou t tests were performed. Figure 6 12 shows the single fiber pullout results for the NiTi austenite, NiTi martensite, and Al reinforced epoxy samples. The Al sample was embedded at 1.62 mm. At this small embedded length, the Al fiber

PAGE 111

111 plastically deformed prior to fracturing. No debonding or pullout was observed. The SMA reinforcements were embedded at nominal lengths of 8 and 14 mm. The actual lengths were 7.73 mm and 12.9 mm for the NiTi austenite SMAs and 8.81 mm and 15.2 mm for the NiTi martensite SMAs. The smaller Al embedded length was selected because previous research has shown that it is more favorable for the aluminum to plastically deform instead of debond and pullout. Both the NiTi austenite and NiTi martensite samples were able to undergo a martensitic phase transformation and reorientation, respectively, and debonded in the transformation/reorientation regions. For the SMAs, the longer the embedded length, the more deformation the samples were able to withstand prior to debonding. The N iTi austenite samples were able to absorb a higher amount of energy due to the higher transformation stress as compared to the NiTi martensite samples that had a lower martensite reorientation stress. The surface roughness results from Chapter 4 indicated that differences between the as received and wire treated at 400C for 1 hour were statistically insignificant and therefore did not contribute to the debond behavior. Since the NiTi martensite samples had a lower debond load because of the lower reorie martensite sample would have more pronounced debonding. Therefore, the debonding in Row 1 of the NiTi austenite and NiTi martensite 3 point bend fracture toughness samples were compared at similar crack extensions in Figure 6 13. Figure 6 13 shows that at the smaller crack extensions, the difference between the interfacial debonding lengths is minimal, however at greater crack extensions, the interfacial debonding lengths in the NiTi mar tensite samples are higher than the NiTi austenite samples.

PAGE 112

112 Composite Fracture Surfaces Figure 6 14 shows the fracture surfaces of selected 3 point bend fracture toughness samples tested at approximately 2 mm and 3 mm of crack growth. As an aside, the cor responding 3 point bend curves are shown in Figure 6 5 for the 3 mm crack extension. The monolithic and Al reinforced samples did not show crack bowing, which was expected for the monolithic sample because there were no impediments to the crack front grow th. For the Al sample the lack of crack bowing is an indication that the wires did not interact with the crack. Both of the SMA samples showed crack bowing indicating that the SMA reinforcements did affect crack growth. Since the crack lengthening assoc iated with crack bowing is also a source of toughening, this also contributes to the enhanced toughness in the Al samples as compared to the SMA embedded samples. Analytical Determination of Transformation/Reorientation There have been indications that th e NiTi austenite SMA has undergone the martensitic phase transformation, such as the recovery of the deformation induced during the 3 point bend testing (Figure 6 9). However to assess the extent of transformation within the reinforcements, the bending st ress of the reinforcements was determined. Similar to the analysis performed in the previous chapter, the bending stress corresponds to the distance from the neutral axis. The neutral axis location was determined using Equation 5 2, with the appropriate geometrical dimensions used from Figure 6 2. The bending stress within the constituent materials was determined using Equation 5 1. The calculation of the reinforcement bending stress was an iterative process that consisted of increasing the applied lo ad, P, and checking to see if the

PAGE 113

113 bending stress surpassed the yielding stress of the reinforcement or matrix. If yielding did occur, the yielded area was removed from the calculations, since an elastic plastic assumption was made (recall that once a mate rial yielded, no further increasing load was necessary to deform the material). The neutral axis was then recalculated to account for the removed area. The bending stress was calculated using the following assumptions: the constituent materials behave e lastic plastically, perfect bonding, the constituent materials have tension compression symmetry and the neutral axis location is not constant. The crack growth was not accounted for. Additionally, the plastic stress associated with crack growth was als o not included. Figures 6 15 and 6 16, show the evolution of martensite transformation and reorientation with respect to the applied load for the NiTi austenite and NiTi martensite SMA reinforcements, respectively, at the sample center (in the crack plan e) where the loads are at their maximum value. The loads were selected because the maximum average load for the NiTi austenite composites were 594N and the maximum average loads for the NiTi martensite composites were 575N. The horizontal line indicates that the reinforcement has undergone the martensitic transformation or reorientation. The neutral axis shifts towards the row 1 fibers because more epoxy material at the top of the sample is increasingly yielding. The figures show the martensite phase fr action of the wires increases with increasing applied load. At an applied load of 267N and 244N for the NiTi austenite and NiTi martensite composites the SMA reinforcements have not yet begun to yield, however this contrasts with the Al reinforced samples where rows 1 and 3 are fully yielded and row 2 is partially yielded due to the low yield strength. A graph of the aluminum reinforcement bending stress is shown in Figure 6 17, at a 267 N

PAGE 114

114 applied load. The 267 N and 244 N applied loads, for the NiTi a ustenite and NiTi martensite SMAs respectively, were examined because at these loads neither of the SMA reinforcements had undergone transformation or reorientation. Since the Al reinforcement has a high ductility and limited debonding, it is able to rea dily deform to failure. Additionally, for the NiTi austenite samples, at the max loads applied to the composite rows 1 and 3 fully transformed. For the NiTi martensite samples, rows 1, 3, and part of 2 had fully transformed. The previous observations ap ply to the area in the crack plane. Figures 6 15 and 6 16 show that as the applied load and amount of yielded material increases, the neutral axis changes position. The change in neutral axis with applied load is shown in Figure 6 18 as calculated for th e SMA reinforced composites. As the applied load increases the neutral axis shifts towards the bottom of the sample. Crack Bridging Fracture Toughness Contribution Crack bridging is likely the dominant toughening mechanism during the previously described fracture toughness experiments (Figure 6 6). To determine the relative contribution of crack bridging and to further confirm that transformation toughening does not contribute to the fracture toughness of un prestrained SMA reinforced composites, the toug hening increment ass ociated with fracture toughness was calculated for the Al, NiTi (austenite), and NiTi (martensite) reinforcing elements. The Law of Superposition ( Green, 1998 ) can be applied when estimating the fracture toughness of a material. Once various toughening mechanisms are identified taking place during crack extension previously determined models can be added together to determine the increase in the fracture toughness due to the various mechanisms. First we apply current crack bridging models to see if they can account for the fracture

PAGE 115

115 toughness behavior seen in the SMA reinforcements. Equation 6 1, based on the spring model system shown in Fi gure 6 19a, describes the work needed to deform and fracture reinforcement elements that bridge two crack surfaces ( Ashby et al., 1989 ) (6 1) intercepted by the crack, crack opening displacement, and stress within the reinforcement, and crack opening displacement, respectively. Aluminum T he increase in fractu re toughness due to the addition of non transforming Al reinforcement within the epoxy matrix will be evaluated. A regression fit in Excel, where R 2 was found to be 0.65, was determined as a function of displacement, based on representative Al stress stra in curves. Equation 6 2 shows the Al stress strain equation: (6 2) writing the strain in an alternate form: (6 3) o are the change in crack opening displacement and the initial crack opening displacement, respectively. Substituting Equation 6 3 into Equation 6 2 yields: (6 4) u o was assumed to be 4.7 mm, which corresponds to the razor blade thickness. u max was determined to be 1.8 mm. f was calculated using the following equation:

PAGE 116

116 (6 5) Therefore, using E quat ion 6 aluminum =7.95 kJ/m 2 From the actual experimental data, the increase in toughness over the monolithic epoxy was calculated to be 6.37 kJ/m 2 Shape m emory a lloy ( a ustenite) Equation 6 6 shows a representative curve for the NiTi austenite SMA: (6 6) Equation 6 6 was determined using a regression fit in Excel, where R 2 was found to be 0.99. Since the NiTi austenite wires did not undergo plastic deformation during testing, Equation 6 6 only accounts for the region until the end of stress induced martensitic phase transformation. Due to the debonding between the matrix and interface, the initial gage length is no longer represented as u o To account for the debonding, u o is taken to be the summation of the razor blade t hickness and the debonding length. Through an analysis of video/pictures that were taken during the 3 point bend fracture toughness test, u* was determined to be 2.86 mm. When loading NiTi austenite =60.2 kJ/m 2 From the actual data, the increase in toughness over the monolithic epoxy was calculated to be 68.5 kJ/m 2 Shape m emory a lloy ( m artensite) Equation 6 7 shows the representative curve for the NiTi martensite SMA: ( 6 7) Equation 6 7 was determined using a regression fit in Excel, where R 2 was found to be 0.96. Through an analysis of pictures that were taken during the 3 point bend

PAGE 117

117 fracture toughness test, u* was determined to be 2.1 mm. Similar to the austenite analysis, u o was taken to be the summation of the razor blade thickness and debonding NiTi martensite =31.3 kJ/m 2 From the actual data, the increase in toughness over the monolithic epoxy was calculated to be 27 kJ/m 2 Discussion A summary of the result s (Al, SMA austenite, and SMA martensite) is shown in Table 6 3 Therefore, this is a furth er indication that the martensitic phase transformation in itself plays a minimal role in increasing the composite fracture toughness since the crack bridging model accounts for the crack toughening increase. Summary A comparative J integral fracture tou ghness study was performed within an epoxy matrix to systematically study the effect of transformation on the crack bridging capacity of phase transforming composites. NiTi wires in the austenite and martensite phase were used as reinforcements in addition to a non transforming Al reinforcement. The monolithic and Al reinforced epoxy composites behaved similarly with J integral values that were very close in magnitude. The NiTi austenite and NiTi martensite SMA reinforced epoxy composites had J integral v alues that were larger than the Al and monolithic samples. The difference in fracture toughness between the Al and monolithic samples and NiTi SMA samples increased with increasing crack growth. The resistance to stable crack growth, was also considered and it was determined that at higher crack extensions, began to decrease due to the diminishing contribution of the Al reinforcement wires after they necked and subsequently fractured.

PAGE 118

118 Single fiber pullout testing showe d that the interfacial strength was high enough to withstand the martensitic phase transformation and reorientation in the NiTi austenite and NiTi martensite SMA reinforcements. Because of the strong interfacial bonding between the epoxy and the Al, only a limited amount of the fiber reinforcement length was able to deform, therefore only consuming a small amount of energy during the composite deformation process. Analytical results suggests that the SMA reinforcements underwent a martensitic phase tran sformation or reorientation however, the agreement between the already established crack bridging spring model that was used to calculate the fracture toughening increment may suggest that the SMA transformation and reorientation mechanisms do not signific antly affect the fracture toughness for the geometry and wire orientation of the composites used in this study

PAGE 119

119 Figure 6 1. The stress strain curves of the constituent materials used in the epoxy matrix crack bridging study. The materials were t ested to failure. Figure 6 2. The graph shows the extension rate dependence of the epoxy matrix used in this chapter. The epoxy consisted of 64.5wt% Epon 828 and 35.5wt% Jeffamine D 400 as the resin and hardener, respectively.

PAGE 120

120 Figure 6 3. The DSC curve shows the glass transition range for the epoxy matrix used in this chapter. A ) B ) NiTi (austenite) NiTi ( martensite )

PAGE 121

121 Table 6 1. The table lists the mechanical properties of the constituent materials used in the extrinsic toughness, epoxy matrix study. *martensite transformatio n stress. **martensite variant reorientation stress. Material Elastic Modulus Yield Stress Epoxy 2.5 GPa 26.8 MPa NiTi (Austenite) 67.9 GPa 459 MPa* NiTi (Martensite) 59.4 GPa 354 MPa** Aluminum 1100 67.8 GPa 68.5 MPa Table 6 2. The table lists th e transformation temperatures of the NiTi SMAs used in the extrinsic toughness, epoxy matrix study. Material A s (C) A f (C) M s (C) M f (C) NiTi (Austenite) 6.1 11.1 2.5 13.6 NiTi (Martensite) 41.1 49.6 38.1 28.3

PAGE 122

122 Figure 6 4. The schematic show the dimensions and placement of the reinforcement wires for the 3 point bend composites. Figure 6 5. The plot shows representative 3 point bend curves of the samples for the J integral fracture toughness tests. Each of the sample s had crack growth to approximately 3 mm.

PAGE 123

123 Figure 6 6. The results of the 3 point bend fracture toughness testing curves. The approximate location of the wires is also indicated in the image. Figure 6 7. The image shows necking that occurred in the SMA embedded epoxy samples. The necking was seen in the monoclinic and Al samples as well.

PAGE 124

124 Figure 6 8. The images show the crack bridging that occurred in the epo xy composites. A) the SMA reinforced composite samples and B) the aluminum reinforced composite samples. A ) B )

PAGE 125

125 Figure 6 9. The images show the effect of the recovery behavior of several samples. A) NiTi austenite samples and B) NiTi martensite samples. The NiTi austenite samples resulted in crack closure because of the martensitic phase transformation where as the NiTi martensite samples have a residual plastic deformation. A ) B )

PAGE 126

126 Figure 6 10. The image shows an aluminum reinforced epoxy sample. Rows 1 and 2 show limited interfacial debonding. Debonding is indicated by the white parentheses. ) ( ) (

PAGE 127

127 Figure 6 11. The image shows screen shots of video taken during a 3 point bending test of the NiTi austenite reinforced epoxy samples. The screen shots were taken at specific crosshead extensions as indicated by the black arrows on the compress ive load versus the crosshead extension. The white parentheses indicate the extent of debonding. The black sticker has a width of 2 mm. A ) B )

PAGE 128

128 Figure 6 11. Continued. C ) D)

PAGE 129

129 Figure 6 11. Continued. F ) E )

PAGE 130

130 Figure 6 11. Co ntinued. G) H )

PAGE 131

131 Figure 6 12. The graph shows the single fiber pullout results for the NiTi austenite, NiTi martensite, and aluminum reinforced epoxy samples. Figure 6 13. The graph shows the interfacial debonding length along the Row 1 of the NiTi austen ite and NiTi martensite samples at similar crack extension lengths.

PAGE 132

132 Figure 6 14. The fracture surfaces of the epoxy composites. The white dotted lines indicate the crack arrest line. Images A D were taken at 2 mm and images E H were taken at 3 mm crack extensions A) B ) G ) F ) E ) D ) C ) H )

PAGE 133

133 Figure 6 15. The graph shows the bending stress of the NiTi austenite reinforcements during applied loads of 267N, 340N, and 575N. Figure 6 16. The graph shows the bending stress of the NiTi martensite reinforcements dur ing applied loads of 244N, 315N, and 594N. a

PAGE 134

134 Figure 6 17. The graph shows the bending stress of the Al reinforcements during applied load of 267 N. Figure 6 18. The graph shows the change in composite neutral axis with respect to the applied load for the SMA reinforced composites.

PAGE 135

135 Table 6 3 The table shows the values used for the Al, NiTi austenite, and NiTi martensite reinforcements when calculating G using the Spring Model Method. Aluminum NiTi (austenite) NiTi (martensite) f 0.0537 0.0779 0.0581 u* (mm) 1.8 2.86 2.1 uo (mm) 4.73 28.2 36.2 Crack Extension (mm) 4.2 3.59 3.01 (kJ/m 2 ) Calculated 7.95 60.2 31.3 Actual 6.365 68.5 27 Fi gure 6 19. The schematic shows relevant terms used to calculate the toughening increment. a) T he premise behind the spring model theory and b) relevant geometrical parameters. A) B )

PAGE 136

136 CHAPTER 7 EXTRINSIC TOUGHENING OF SHAPE MEMORY ALLOY COMPOSITES: METAL MA TRIX As stated in the previous chapter, the current chapter is a continuation into the investigation of extrinsic toughening mechanisms associated with SMA reinforcing elements embedded, however this chapter focuses on metal matrix composites that contain SMA reinforcements. Metal matrices are of interest because of their extensive use in structural applications. Moreover, the effects of a ductile reinforcement within a metal matrix will not be as pronounced due to the greater mechanical properties of a me tal as compared to an epoxy matrix. Non transforming reinforcements were also used for comparative purposes. When using a metal matrix, secondary effects arise as the result of the metal matrix composite fabrication process that can complicate computatio n of fracture toughness. These effects can include a change in thermo mechanical properties of reinforcements due to high fabrication temperatures associated with a molten metal matrix. Differences in coefficients of thermal expansion can induce stress w ithin the matrix that also must be accounted for. Because the matrix is no longer transparent, debonding is not easily discernable. Lastly, determining crack arrest features on the fracture surface is not as straightforward. Therefore, having determine d the effect of embedding SMAs within an epoxy matrix in the previous chapters on the composite fracture toughness, a metal matrix was used to ensure that the fracture toughness behavior of the SMA reinforced metal matrix composites were consistent between different families of matrices and to understand the consequences of the previously mentioned effects on the fracture toughness behavior

PAGE 137

137 Materials and Methods Materials Selection A Zn 7wt% Al alloy was chosen for this study due to the following reasons : 1) the alloy matrix adhered to the reinforcement, 2) was able to result in the martensite transformation of the SMA reinforcement, 3) the matrix was brittle, similar to that of the epoxy study, and 4) was easily cast in air. An off eutectic compositi on was used to reduce microstructural effects on the mechanical properties of the as cast sample. The phase diagram of the Zn Al material system is shown in Figure 7 1 with the dotted line indicating the composition used in this study. The phase diagram was created using Thermo Calc Software Database SSOL2. NiTi and carbon steel 1080 (steel) wires were used as reinforcing elements within the Zn Al matrix. The reinforcements were both used in the as received condition and had diameters of 0.87 and 0.78 mm for the NiTi and steel, respectively. The NiTi SMA wires, purchased from Memry Corporation, had a nominal composition of 50.7at%Ni Ti. The NiTi SMA was in the austenite phase at room temperature and used because the material is capable of undergoing a stress induced martensitic phase transformation. Carbon steel was selected because of the increased elastic modulus and yield strength as compared to the NiTi SMA reinforcement. The NiTi and steel reinforcements were used because results from Chapters 5 and 6 suggest that transformation toughening does not contribute to the fracture toughness of SMA embedded composites in the current composite geometry As such, it is expected that the steel reinforced Zn Al composites will have a greater fracture toughn ess as compared to the NiTi reinforced Zn Al composites because steel has greater mechanical properties than NiTi.

PAGE 138

138 Materials Characterization Tensile mechanical tests were performed on the composite constituent materials according to the method described i n Chapter 3 using a 0.5 mm/min extension rate and dog bone shaped tensile samples Representative stress strain curves are shown for the constituent composite materials in Figure 7 2. The elastic modulus and yield stress were determined from tensile stre ss strain curves and are given in Table 7 3. The composites were used in the as cast condition because a solution heat treatment was found to alter the stable SMA room temperature phase from austenite to martensite. To verify the matrix composition, XR F was performed. The XRF procedure is described in Chapter 3. The results of the XRF show that that the actual average composition was 91.2 0.6 wt%Zn 8.8 0.6 wt%Al. Through DSC, the temperatures at the onset of melting and solidification were determ ined to be 394.7 1.5C and 388.4 1.3C, respectively. Optical microscopy images of the Zn Al matrix were taken to determine the as cast microstructure of the Zn Al matrix. The optical images are shown in Figures 7 3 A and B The images show a dendri tic microstructure. Representative optical images the interface between the Zn Al matrix and SMA reinforcement is shown in Figure 7 4. From the optical microscopy images, it is not apparent that chemical bonding took place. A schematic of the 3 point ben d fracture toughness sample is shown in Figure 7 5. The wire placements were selected to maximize the volume fraction of wires within the composite while also allowing the molten metal Zn Al matrix to fill the space between the wires without leaving areas of porosity within the sample. The reinforced composites contained a reinforcement volume fraction of approximately 2.6% and 2.1%

PAGE 139

1 39 for the NiTi and steel, respectively. The J integral fracture toughness, single fiber pullout, optical microscopy and SEM m ethodologies and corresponding equipment used to perform these tests are described in detail in Chapter 3. Composite Fabrication Effects on Reinforcements The composite fabrication process could have an effect on the NiTi and steel reinforcement wires. This is because the wires are subjected to elevated temperatures of approximately 625C as a result of the molten Zn Al matrix surrounding the wires during casting. The following section s discuss the effect of the casting process on the wire reinforcemen ts. Fabrication Effects on Shape Memory Alloy The casting process can affect the inherent shape memory properties of SMA reinforcing elements especially when being cast from a relatively high cast temperature, 625C. Over sustained periods, the SMA can age ( Khalil Allafi et al., 2002 ; Otsuka and Ren, 2005 ; Treppmann and Hornbogen, 1997 ) The surface temperature of the cast composite was found to cool from 625C to approximately 92C in less than 2 mins. However, since NiTi SMAs can undergo aging between 300C 600C ( Otsuka and Ren, 2005 ) it is important to understand the effect of casting on the SMA thermo mechanical properties. The transformation temperatures of the NiTi SMA were measured before and after the Zn Al matr ix casting process using the DSC method described in Chapter 3 for a single sample. The results are shown in Figure 7 6. The figure shows that in the short time that the NiTi wire was surrounded by the molten/hot metal matrix, the transformation temperat ures changed slightly. The martensite transformation temperatures, M s and M F decreased by 5.8C and 4.4C, respectively. The austenite

PAGE 140

140 transformation temperatures, A s and A f decreased by 2.8C and 0.8C, respectively. The mechanical properties of 2 wi res were tested after they had been subjected to the casting process. The elastic modulus and martensite transformat ion stress were determined to be 69.3 0.6 GPa and 444.1 9 MPa, respectively. Comparing the after cast mechanical properties to the vir gin mechanical properties in Table 7 1 confirm minimal changes. Therefore the casting process appears to have a minimal effect on the NiTi transformation temperatures and that the room temperature phase remains in the austenite phase. Fabrication Effect s on Steel The mechanical properties of 2 wires were mechanically tested after they had been subjected to the Zn Al casting process. Similar to the previous section the mechanical properties of the steel wire were determined through tensile tests. The el astic modulus and yield stress of the steel were 223 5 GPa and 1804 29 MPa respectively While the elastic modulus was unaffected by the casting process, the yield stress did decrease by approximately 500 MPa. Even with the decrease in yield stress however, the yield stress still remains greater than the transformation stress of the NiTi. Interface To determine whether chemical bonding took place during composite fabrication, optical microscopy images were taken of the Zn Al NiTi composites, Figures 7 4 A and B The figures show that the matrix reinforcement interface remains intact with a clear line separating the matrix from the fiber. Figure 7 4 B shows a magnified image of Figure 7 4 A The dark areas near the interface are defects introduced during the polishing process.

PAGE 141

141 Results and Discussions Single Fiber Pull Out Testing Single fiber pullout testing was performed on the steel and NiTi reinforcements as shown in Figures 7 7 and 7 8, respectively. The steel wires were embedded at lengths of 8, 16, and 32 mm and each sample was tested until the wire had completely pulled out of the matrix. Upon inspection of the steel wire after pullout, the wire surface was no longer smooth, however, it show ed little evidence of chemical bonding. During the steel single fiber pullout tests, there was no distinguishable characteristic load drop to indicate the onset of debonding or subsequent slip stick behavior. Figure 7 7 shows that the steel single fiber pullout samples initially followed the same elastic loading path. However after some stress value, the steel wire began to inelastically deform. The steel single fiber pullout samples were able to keep a sustained load during the test until complete pullout took place, however the sustained load varied b etween samples and with the amount of fiber pullout that occurred. The NiTi wires were embedded at a 22 mm length. Because there was no clear indication of debonding, as was seen in the epoxy samples, the NiTi was stopped at various crosshead extensions 1 mm, 5 mm, 12 mm, and complete pullout. The samples were cut with a cutoff saw at the constrained end to verify the single fiber pullout behavior. The 5 and 12 mm embedded lengths showed evidence of pullout whereas the 1 mm embedded length did not. Th e plateau load experienced by the SMAs single fiber pullout samples correspond to the load at which the SMA martensite transformation takes place. As such, the martensite transformation is likely occurring simultaneously with pullout.

PAGE 142

142 The single fiber p ullout behavior of both the steel and NiTi samples can be explained by the thermal residual stresses that arise during the matrix solidification process. T hermal residual stresses are the result of the differences in coefficients of expansion of the matrix is greater than that of the fiber, this will result in the matrix contracting more than the fiber which would lead to a compressi ve state within the fiber. From DSC, the solidification temperature of the Zn Al alloy was determined to be 388 1.3C. The coefficient of thermal expansion, of the composite constituent materials are also listed in Table 7 1. Equation 7 1 shows the equation used to determine the thermal residual stress P, surrounding the NiTi and steel reinforcements ( Green, 1998 ) (7 1) E, T, and subscripts f, m, o, and A represent fiber, matrix, temperature at which residual stresses begin to arise, and ambient temperature respectively. A compressive thermal residual stress was calculated to be approximately 265 MPa for both the steel and NiTi reinforcements due to differences in the elastic modulus and coefficient of thermal expansion T o and T A were taken to be 388C and 25C, respectively. The large compressive residual stresses can explain the single fiber pullout behavior in the NiTi and steel single fiber pullout sample. The compressive residual stresses are similar to a clamping force on the wires effe ctively making debonding more difficult to occur.

PAGE 143

143 J Integral Fracture Toughness Figure 7 10 shows the J integral fracture toughness results of the monolithic, and NiTi and steel reinforced Zn Al reinforced samples. The J el was calculated to be on the o rder of 10 3 kJ/m 2 Since the contribution to the overall fracture toughness was minimal, the J el term was neglected and only J pl was is shown in Figure 7 10. The results show that the monolithic samples had the lowest fracture toughness of all the sample s, as compared to the NiTi and steel reinforced Zn Al composites. Based upon the fact that the steel reinforcements had the higher elastic modulus and yield strength as compared to the NiTi reinforcement, it was expected that the steel reinforced Zn Al co mposites would result in the greater fracture toughness values. All of the samples displayed R curve behavior with the monolithic Zn Al sample appearing to approach a critical J integral fracture toughness value. The resistance to stable crack growth, d was also considered for the monolithic and reinforced composites. Comparing the steel to the NiTi fracture toughness results, the steel reinforced Zn Al composites at all points have a greater indicating that the steel composites had a greater resistance to stable crack growth when compared to the NiTi reinforced Zn Al samples. This i ncrease is l i kely due to the inherent mechanical properties of the steel reinforcement. Both of the reinforced composites display a greater when compared t o the monolithic Zn Al fracture toughness. Fracture Surfaces In examining the fracture surfaces, it was clear the wires were able to impede crack growth. Since the wire placement was off center, the part of the sample that was devoid of the wires had larg er crack extensions as compared to the area that contained

PAGE 144

144 the wire reinforcements. This crack impendence was seen in both the NiTi and steel reinforced samples. Figures 7 11 and 7 12 show the wires were able to impede crack growth in both steel and NiT i reinforced Zn Al samples, respectively via crack bowing Figure 7 13 shows that without the wires, crack growth was fairly constant throughout the thickness of the sample. The figures also show the 3 different regions of crack growth on the fracture s urfaces, fatigue crack growth, stable crack growth, and quick fracture. The fatigue crack growth is indicated by the blue paint marker. The middle dark gray region shows stable crack growth. Lastly, quick fracture is the light gray region at the top of the samples. The images were also examined using SEM. Representative images of the fracture surfaces are shown in Figures 7 14 through 7 18 for the NiTi embedded fracture toughness samples. Figure 7 14 shows a distinct delineation between the fatigue cra cked region and the stable crack growth region, as indicated by the letters A and B, respectively. The arrows indicate the direction of crack growth. Also shown in Figure 7 14 is indications of microcracking. The microcracking could explain why tougheni ng is seen in the monolithic Zn Al alloy since it undergoes minimal plastic deformation. Figures 7 15 and 7 16 correspond to SEM images taken in regions A and B at a 250x magnification. There is a difference in surface morphology of the fracture surface between the fatigue and stable crack growth region, with the fatigue crack growth region showing a striation like fracture morphology. Figure 7 17 shows the microstructure of the quickly fractures region, which appears to be similar to that of the stable crack growth region. Figure 7 18 show s the microstructure surrounding the hole where the wire was. The microstructure surrounding the hole appears consistent with the microstructure away from the hole in

PAGE 145

145 the stable crack growth region as shown in Figure 7 19. Figure 7 20 shows the fatigue crack growth region within in the monolithic Zn Al alloy. The microstructure is consistent with the fatigue crack growth region in the NiTi and steel reinforced samples. The steel reinforced Zn Al composites and the m onolithic composites also had similar fracture surface morphologies. Summary J integral fracture toughness testing was used to determine the fracture toughness of NiTi SMA containing Zn Al matrix composites. In addition to the NiTi reinforcements, a non transforming carbon steel 1080 reinforcement was also used for comparative purposes. The effect of the composite fabrication process on the reinforcing elements was first considered. The NiTi elastic modulus and martensite transformation stress remain u nchanged by the Zn Al casting process. While the steel elastic modulus remained the same, the yield stress decreased by approximately 500 MPa. The fracture toughness results show that the steel reinforced Zn Al composites had a greater fracture toughnes s as compared to the NiTi SMA reinforced composites. This fracture toughness behavior was expected because the steel had a greater elastic modulus and yield strength as compared to the NiTi reinforcement. The was also compared between the tested samples and it was determined that the steel had a greater resistance to stable crack growth as compared to the steel and monolithic samples. This behavior is again likely attributed to the greater mechanical pr operties of the steel when compared to the NiTi or monolithic samples. The metal matrix had the added complexity of thermal residual stresses arising during the solidification of the matrix. The thermal residual stress dictated the single

PAGE 146

146 fiber pullout behavior and aided in the clamping force between the matrix and fiber reinforcement While it was determined that there was likely no chemical bonding, between the matrix and fiber, the compressive residual stress increased the interfacial capabilities of the composite. The fracture toughness results are in agreement with results seen using an epoxy matrix and further suggest that the SMA stress induced martensitic phase transformation does not play a direct role in increasing the fracture toughness of a SMA containing composite for the geometry and reinforcement configuration investigated in this study I nstead the mechanical properties of the reinforcements may be the parameters that determine the toughening behavior of wire containing composites.

PAGE 147

147 Figure 7 1. The zinc aluminum phase diagram was created using Thermocalc S oftware ( Mey and Effenberg, 1986 ; Software, 3 February 2013 ) The Zn 7wt%Al is indicated by the black dotted line.

PAGE 148

148 Figure 7 2. The figure shows the stress strain curve for the as cast Zn 7wt%Al (nominal) alloy, NiTi, and steel. Table 7 1. The table lists relevant mechanical properties of the NiTi, steel, and Zn Al used in the m Material Elastic Modulus Yield Stress Coef. of Thermal Expansion GPa MPa 10 6 /C -Steel 230 2555 14.2 0.29 NiTi 84 447 11 0.37 Zn Al 85 165 27.4 0.27

PAGE 149

149 Figure 7 3. The optical microscopy image shows the 93wt%Zn 7wt%Al as cast microstructure a) near the sample surface at 5x magnification and b) at 500x magnification. Figure 7 3. Continued. A) B )

PAGE 150

150 Figure 7 4. The optical microscopy image shows the NiTi 9 3wt%Zn 7wt%Al as cast composite microstructure A) 10x and B) 50x magnification. B ) A)

PAGE 151

151 Figure 7 5. The schematic shows the dimensions and wire placement of the 3 point bend fracture toughness samples.

PAGE 152

152 Figure 7 6. The DSC results show the change i n transformation temperature as a result of the Zn Al casting process. Figure 7 7. The figure shows the single fiber pullout curves for the steel reinforced Zn Al samples. The steel was embedded at depths of 8, 16, and 32 mm. After Cast Before Cast

PAGE 153

153 Figure 7 8. The fi gure shows the single fiber pullout curves for the NiTi reinforced Zn Al samples. Figure 7 9. The optical microscopy image shows an example of the fatigue pre crack at 10x magnification.

PAGE 154

154 Figure 7 10. The graph shows the fracture toughness results for the monolithic and NiTi and steel reinforced Zn Al composites. Figure 7 11. The fracture surface of a steel reinforced Zn Al matrix composite shows 3 distinct regions on the fracture surface. The blue coated, dark gray, and lighter gray regions indicate fatigue, stable, and quick fracture.

PAGE 155

155 Figure 7 12. The fracture surface of a NiTi reinforced Zn Al matrix composite shows 3 distinct regions on the fracture surface. The ruler is in units of mm. Figure 7 13. The fracture surf ace of a monolithic Zn Al composite shows 3 distinct crack growth regions on the fracture surface. The units are in mm. Quick fracture Stable crack growth Fatigue crack growth Stable crack growth Fatigue crack growth Quick fracture

PAGE 156

156 Figure 7 14. The representative SEM image of the NiTi reinforced Zn Al composites shows the interface between the fatigue and st able crack growth region. The white arrow indicates the direction of crack growth. The schematic shows the relative position of where the image was taken. A B

PAGE 157

157 Figure 7 15. The SEM image shows the microstructure in the fatigue cracked (region A) of the N iTi reinforced Zn Al matrix composites. The schematic shows the relative position of where the image was taken.

PAGE 158

158 Figure 7 16. The SEM image shows the microstructure of the stable crack growth region (region B) of the NiTi reinforced Zn Al matrix compo sites. The schematic shows the relative position of where the image was taken.

PAGE 159

159 Figure 7 17. The SEM image shows the microstructure of the NiTi reinforced Zn Al reinforced composites in the quick fracture region. The schematic shows the relative posi tion of where the image was taken.

PAGE 160

160 Figure 7 18. The SEM image shows the microstructure in the region surrounding a wire in the NiTi reinforced Zn Al composites. The schematic shows the relative position of where the image was taken.

PAGE 161

161 Figure 7 19. The SEM image shows the stable crack growth region of the NiTi reinforced Zn Al alloy. The schematic shows the relative position of where the image was taken.

PAGE 162

162 Figure 7 20. The SEM image shows the fatigue cracked region of the monolithic Zn Al allo y at 250x magnification. The schematic shows the relative position of where the image was taken.

PAGE 163

163 CHAPTER 8 CONCLUSIONS Throughout the dissertation document, the effect of the martensitic phase transformation and martensite variant reorientation mecha nisms in SMA embedded composites was examined. Specifically, the effect of the martensitic phase transformation and variant reorientation on the interfacial behavior of composites containing SMAs reinforcing elements in addition to the extent of toughenin g that can be attributed to the martensitic phase transformation was focused on. Results from this work suggests that the debonding behavior of SMA embedded composites was dependent upon the phase, either martensite or austenite, that the SMA is in during testing for the examined embedded lengths. SMA fibers that were deformed in the austenite phase had greater debonding loads as compared to SMAs that were deformed in the martensite phase. Through intrinsic and extrinsic J integral fracture toughness s tudies of SMA reinforced composites, it was determined that simply using SMAs as reinforcing elements within a matrix may not actively increase the fracture toughness of these composites even if the SMA is able to undergo the martensitic phase transformati on during composite deformation. SMA reinforcements were tested in conjunction with non transforming metal fibers. Composites containing non transforming fibers that had agreater elastic modulus or yield stress than the SMA reinforcements outperformed t heir SMA counterparts by experiencing greater fracture toughness values. Additionally, the following general argument was suggested, when using a common matrix, if the reinforcements possess a similar elastic modulus but different yield stress, the compos ite with the greater yield stress will experience a higher fracture toughness.

PAGE 164

164 Alternatively, if the reinforcement posses a similar yield stress but different elastic modulus, the composite with the greater elastic modulus will experience a greater fractu re toughness. The previously mentioned argument is valid for reinforcements with similar interfacial properties. The driving factor of toughening in fiber reinforced composites is the mechanical properties, elastic modulus and yield stress. The conclusi ons drawn were corroborated through the use of analytical studies. In order to maximize the SMA contribution to fracture toughness, SMAs may be pre strained prior to being embedded within a composite. Pre straining results in a compressive stress on the m atrix because the SMAs want to retract to recover its original shape. In this sense the compressive mechanism within the pre strained SMA and the stress induced phase transformation in stabilized zirconia are similar. Contribution to Field A systematic st udy was performed that investigated the effect of the shape memory alloy martensitic phase transformation on the debonding characteristics of composites and the extent to which the martensitic phase transformation effects the fraction toughness of SMA cont aining composites. While there have been several studies that have investigated the effect of martensite variant reorientation, and investigators have alluded to the fact that the martensitic phase transformation of constrained SMAs accelerates debonding, there has not been a study performed that has specifically addressed the martensitic phase transformation on the interfacial characteristics on composites. The results from this work improve the understanding of the martensitic phase transformation on de bonding in SMA composites.

PAGE 165

165 Future Work Since it has been suggested through this work and studies by other investigators, that SMAs may actively toughen a matrix as a consequence of pre straining, a natural progression in this dissertation work would incl ude a systematic study investigating the direct effect of pre straining on the fracture toughness behavior of SMA reinforced composites. The purpose should aim to determine the relationship between prestraining, crack growth, debonding, and fracture tough ness. Because debonding plays an integral role in the fracture toughness behavior of a composite, an in depth study would be needed to examine the SMA pre straining effect on interfacial debonding. A more extensive interfacial study that considers a wi der range of embedded fiber lengths should be performed to ensure that the debonding behavior seen in this dissertation work is applicable across all embedded lengths since only 2 embedded lengths were investigated in this work. Additionally, it is import ant to determine changes in debonding behavior (complete debonding versus gradual debonding) across different embedded length scales. Evaluation of composite interfacial behavior is important since the interfacial strength can dictate the mechanical respo nse of a composite. However, it is unclear how accurate existing models are when considering the SMA transformation and reorientation behavior. Therefore, further research must be performed to determine an accurate method for determining interfacial shea r stress of SMA composites. While the general fracture toughness behavior of the Zn Al metal matrix embedded with transforming and non transforming reinforcing elements was determined, a larger sample set should be tested to determine the statistical varia tion

PAGE 166

166 within the tested sample s Moreover, since SMAs can be used within an assortment of matrices, understanding the role that chemical bonding plays on the constrained martensitic phase transformation is critical. Although the influence of chemical bond ing on martensitic phase transformations was not needed in this dissertation work in order for SMAs to be widely implemented in matrices that potentially require high fabrication temperatures where diffusion may take place the effect on the SMA thermo me chanical properties must be investigated to ensure that changes associated with the chemical bonding is not preventing the SMA from exhibiting their characteristic pseudoelastic and shape memory effect properties. To determine the extent and understand the growth of the martensitic phase within a SMA composite, finite element modeling (FEM) should also be performed. FEM would allow for a more thorough understanding of the martensitic transformation during composite deformation and would yield more detailed information such as the martensite volume fraction at a particular element within the modeled composite that the analytical modeling performed in this dissertation could not provide. FEM results could then be confirmed experimentally via mechanical and n eutron diffraction testing. Lastly, neutron diffraction is a non destructive characterization technique that can provide structural information about a matrix and corresponding SMA reinforcements during deformation. Existing neutron beamlines with mechani cal testing machine setups can be used to apply and measure deformation during the neutron studies. The neutron penetration is deep enough to obtain information about an SMA reinforcement embedded inside a matrix as opposed to x ray diffraction studies Therefore, i n situ neutron diffraction experiments should be performed to empirically

PAGE 167

167 confirm the validity of the analytical modeling of the reinforcement bending stress during deformation and specifically to determine and confirm the extent of martensit e transformation within SMA reinforcing elements. The results from the neutron studies can then be correlated to the fracture toughness to confirm and monitor the martensitic transformation evolution Aside from neutron diffraction studies, electrical re sistivity experiments can potentially be used to determine the extent of transformation within a SMA reinforcement in a deformed composite. Further detail is given about electrical resistivity testing of SMA reinforced composites is given in Appendix D.

PAGE 168

168 APPENDIX A DESIGN OF MIXTURES A design of mixtures experiment is a n experiment in which the response is assumed to depend only on the relative proportions of the components present in the mixture The behavior of the response is said to be a function of t he joint blending property of the components in the mixture A design of mixtures experiment was performed to understand the ductility behavior of the 3 component epoxy mixture used in the intrinsic toughening chapter. The epoxy mixture contained Epon 82 8, Diethethylenetriamene, benzyl alcohol as the resin, hardener, and plasticizer, respectively. The purpose was to determine a mathematic ductility relation of the 3 component mixture. Preliminary experiments were performed to determine the boundary cond itions of the mixtures. The extreme compositions of the mixture are listed in Table A 1 and shown in Figure A 1. A mixture design was created in Minitab to determine the experimental run order and mixture compositions The design parameters 3 component 2 replicate Extreme Vertices mixture design with a degree of design of 3 to permit fitting of the cubic model. Minitab selected multiple compositions at the Resin and Plasticizer vertices as well as off center compositions since the initial compositiona l boundary triangle was not an equilateral triangle as show in Figure A 2 With 3 components the simplex shape is an equilateral triangle. Samples were prepared and run according to the Minitab randomization An example of the samples is shown in Figu re A 3. The experimental constants were curing location, time and temperature. Samples were tested using an Instron 5582 Mechanical Testing Machine. The uncontrollable variables were g rip force on sample

PAGE 169

169 and sample condition in regards to imperfections. The test was performed using a 5 mm/min extension rate. The experimental results were analyzed using equation A 1: ( A 1 ) where l f and l o are the final and initial gage lengths, respectively. The resin hardener interaction was d etermined to be the most significant interaction in the 3 component mixture. The 3 factor interaction is the least significant of all the factors and was subsequently removed. The addition of plasticizer results in a more rubbery like sample, but not neces sary greater ductility. Mixture experiments are different from a factorial design in regards to experimental balance Replicates can be performed on some data points and do not need to be completed on each mixture. Minitab averages the ductility values a t each mixture together for multiple data points. When only 1 point is present, it uses the value at that mixture. Response values were removed to allow for a better fitting regression model. Before removing responses, the fractured samples were examine d to determine the validity the data (where sample fractured). Using the series of reduced models approach, it was found that standard error (S e ) was minimized when the 3 factor interaction was removed for both the full data and modified data set. The mai n interaction terms are not significant in a mixture of designs experiment. The residual error degrees of freedom decreased by 6 when comparing the full data set to the modified data set. This is directly related to the removal of the 6 response values. Ideally, the residuals in the residual diagnostic plots should be normally distributed and homoscedastic with respect to the components, run order, and fitted

PAGE 170

170 values. This was not the case as seen in the latter runs. Runs 1, 3, 14, 15, 16, and 20 were rem oved as shown in Table A 2, to create a more random distribution in the Residual vs. Observation order plot. Equation A 2 shows the design of mixtures equation generated to calculate the ductility using the Epon 828, Diethethylenetriamene, benzyl alcoho l as the resin, hardener, and plasticizer, respectively. (A 2) Equation A 2 is plotted in Figures A 4 and A 5 where negative ductility implies that the material was very brittle.

PAGE 171

171 Table A 1. The table shows the maximum and minimum compositions of the epoxy mixture. Point Resin Hardener Plasticizer (%) (%) (%) A 95.2 4.8 0 B 71.4 28.6 0 C 74.1 3.7 22.2 Figure A 1 The plot shows the maximum and minimum compositions used. The compositions were determined by performing an initial set of experiments. The actual compositions of points A, B, and C are listed in Table A 1.

PAGE 172

172 Figure A 2 The plot shows the epoxy composition used to perform the design of experiments as determined by Minitab. Figure A 3 The plot shows an example of the variation in the epoxy properties based on composition.

PAGE 173

173 Table A 2 The table shows the run orders in addition to the mixture component weight ratios. The highlighted rows refer to the runs that were removed when performing the cal culations. Standard Order Run Order Blocks Resin Hardener Plasticizer Ductility wt ratio wt ratio wt ratio % 16 1 1 0.7408 0.037 0.2222 44.44 5 2 1 0.7408 0.037 0.2222 25.6 17 3 1 0.7143 0.1746 0.1111 57.43 9 4 1 0.9524 0.0423 0.0053 461.1 11 5 1 0.81484 0.09416 0.091 5.7 19 6 1 0.83335 0.16665 0 2.61 1 7 1 0.7143 0.2857 0 810.9 10 8 1 0.72755 0.05025 0.2222 8.4 13 9 1 0.7143 0.0635 0.2222 34.6 6 10 1 0.7143 0.1746 0.1111 78.5 4 11 1 0.9524 0.037 0.0106 436.9 8 12 1 0.83335 0.16665 0 2.5 1 5 13 1 0.9524 0.037 0.0106 518 18 14 1 0.8466 0.037 0.1164 42.9 2 15 1 0.7143 0.0635 0.2222 34.3 7 16 1 0.8466 0.037 0.1164 48.6 22 17 1 0.81484 0.09416 0.091 3.1 3 18 1 0.9524 0.0476 0 11.4 21 19 1 0.72755 0.05025 0.2222 13.4 20 20 1 0.9524 0.0423 0.0053 167.5 14 21 1 0.9524 0.0476 0 70.8 12 22 1 0.7143 0.2857 0 304.9

PAGE 174

174 Figure A 4 The graph shows the ductility response as a function of composition. Figure A 5 The graph show a 3 D ductility response as a function of composition.

PAGE 175

175 APPENDIX B EXPERIMENTAL DATA T he experimental data pre sented in Chapters 4, 5, and 6 is given in table form at the end of this chapter. The tables are explained in further detail in the following sections. Single Fiber Pullout Data The graphical data sh own in Chapter 4: Interfacial Strength: Effect of Martensite Transformation and Reorientation on Debonding, is shown in Table B 1 and B 2. T able B 1 shows the embedded fiber lengths, L e and corresponding debond loads, F d of the samples that were embed ded at approximately 3 mm. Table B 2 shows the embedded fiber lengths of the samples that were embedded at approximately 4 mm. The data is given for the A476, M341, M321, A347, M259, and A416 reinforced epoxy samples. Additionally, DSC and tensile tests were performed on the A476, M341, M321, A347, M259, and A416 SMAs. Average values with corresponding standard deviations were reported for the transformation temperatures, elastic moduli, and martensite transformation or variant reorientation stresses. F our different samples were run to determine the average values. Representative DSC and stress strain curves are also shown in Figures B 1 and B 2, respectively. Intrinsic Toughening Data The graphical data shown in Chapter 5: Intrinsic Toughening in Shape Memory Alloy Embedded Composites is given in Tables B 3 through B 7. B, W, a o Disp max Load max U t U i U, and J are the sample thickness, width, average initial crack length, sample maximum crosshead displacement experienced sample maximum sustained l oad total energy absorbed, indentation energy, energy absorbed by the sample, and

PAGE 176

176 the J integral. The numbers 1 5 under the stable crack growth extension heading in the tables refers to the position were the crack growth measurement was taken. The data is given for the monolithic and steel, NiTi, NiTi ht, and Al reinforced epoxy samples. Extrinsic Toughening Data The graphical data shown in Chapter 6: Extrinsic Toughening of Shape Memory Alloy Composite s is given in Tables B 8 through B 11. B, W, a o Di sp max Load max U t U i U, and J are the sample thickness, width, average initial crack length, sample maximum crosshead displacement experienced sample maximum sustained load total energy absorbed, indentation energy, energy absorbed by the sample, and the J integral. The numbers 1 5 under the stable crack growth extension heading in the tables refers to the position were the crack growth measurement was taken. The data is given for the monolithic and NiTi (austenite), NiTi (martensite), and aluminum r einforced epoxy samples.

PAGE 177

177 Figure B 1. The graphs show representative DSC curves for the SMAs used in Chapter 4. A) A476, A347, A416 and B) M341, M321, M259 conditions A) B)

PAGE 178

178 Figure B 2. The graphs show representative stress strain curves for the SMAs used in Chapter 4 A) A476, A347, A416 and B) M341, M321, M259 conditions. A) B)

PAGE 179

179 Table B 1. The table shows the actual embedded fiber length and corresponding debond loads of the sample were embedded at approximately 3 mm. A476 M341 M321 A3 47 M259 A416 Sample L e (mm) F d (N) L e (mm) F d (N) L e (mm) F d (N) L e (mm) F d (N) L e (mm) F d (N) L e (mm) F d (N) 1 2.99 164.55 2.95 86.9 3.01 126.3 2.73 153.4 2.72 98.5 2.92 134 2 3.06 160.26 3 108 3.11 156 2.94 129.6 2.88 123 2.95 124.1 3 3.2 141.36 3.03 124.4 3.15 118.2 2.97 146.7 3 122.5 2.96 137.6 4 3.22 165.14 3.1 112.2 3.18 148.5 3.05 153.9 3.01 121.5 3.09 145.6 5 3.35 150.24 3.12 129.9 3.3 133.8 3.26 153.3 3.05 123.4 --Table B 2. The table shows the actual embedded fiber length and correspo nding debond loads of the sample were embedded at approximately 4 mm. The asterisk indicate the samples that transformed (*) or reoriented (**) A476 M341 M321 A347 M259 A416 Sample L e (mm) F d (N) L e (mm) F d (N) L e (mm) F d (N) L e (mm) F d (N) L e (mm) F d (N) L e (mm) F d (N) 1 4.02 213.9 3.59 121.1 3.89 154.9 3.82 209.5 3.92 133 3.94 221 2 4.07 266.46 3.71 159.8 4.02 184.5 3.88 215.2* 3.96 155.7' 3.96 207.7 3 4.19 233.1 3.76 148.5 4.27 191.9' 3.95 196.3* 4.05 158.9' 3.96 236.7 4 4.29 271.2 3.84 161.9 4 .27 189.2 4.21 203* 4.06 156.1' 4.25 210.9 5 4.37 277.5 3.87 196.6 4.44 192.5' 4.22 206* 4.22 181.4' --

PAGE 180

180 Table B 3 The table shows relevant values used to calculate the J integral of the monolithic epoxy samples. The plots were shown in the Intrin sic Toughening Chapter. Stable Crack Growth Extension (mm) Disp max Load max Ut Ui U J Sample B (mm) W (mm) a o (mm) 1 2 3 4 5 average (mm) (N) (N*mm) (N*mm) (N*mm) (kJ/m 2 ) m1_6 8.07 15.15 7.83 0.07 0.12 0.13 0.11 0.06 0.11 1.69 105 102.9 4.8 98.1 3.3 m5_2 8.28 16.71 7.52 0.00 0.00 0.00 0.00 0.00 0.00 1.07 273 155.4 26.7 128.8 3.4 M.S2 8.21 16.92 7.58 0.04 0.13 0.19 0.14 0.08 0.13 1.09 270 162.1 26.3 135.8 3.5 m3_2 8.21 16.75 7.43 0.04 0.14 0.15 0.12 0.10 0.12 1.13 283 170.0 28.5 141.5 3.7 m1_1 8.00 15.91 7.70 0.10 0.18 0.19 0.16 0.07 0.16 1.95 117 140.3 6.0 134.3 4.1 M.1 7.97 16.79 7.46 0.14 0.23 0.24 0.20 0.13 0.20 1.26 271 191.2 26.4 164.8 4.4 M.S4 7.70 16.56 7.54 0.14 0.37 0.44 0.41 0.12 0.34 1.38 266 219.5 25.4 194.1 5.6 M.S3 7.87 1 6.46 7.43 0.08 0.28 0.53 0.37 0.11 0.32 1.47 275 236.5 26.9 209.7 5.9 m1_3 8.07 16.13 7.82 0.15 0.19 0.30 0.28 0.13 0.23 2.33 138 207.9 8.0 199.9 6.0 M.S6 7.83 16.74 7.53 0.18 0.44 0.46 0.38 0.13 0.36 1.47 296 269.0 30.9 238.1 6.6 m1_7 7.98 15.73 7.86 0 .28 0.45 0.52 0.44 0.25 0.42 2.78 133 253.9 7.5 246.5 7.8 m1_2 8.21 16.76 7.35 0.37 0.78 1.01 0.90 0.28 0.75 1.95 350 455.3 41.7 413.6 10.7 m2_2 8.25 16.59 7.66 0.45 1.20 1.26 1.18 0.43 1.02 2.34 320 517.4 35.6 481.8 13.1 m4_2 8.29 16.70 7.68 0.74 1.52 1.93 1.69 0.75 1.47 2.98 327 735.3 36.8 698.5 18.7

PAGE 181

181 Table B 4. The table shows relevant values used to calculate the J integral of the aluminum embedded epoxy samples. The plots were shown in the Intrinsic Toughening Chapter. Stable Crack Growth Extension (mm) Disp max Load max Ut Ui U J Sample B (mm) W (mm) a o (mm) 1 2 3 4 5 average (mm) (N) (N*mm) (N*mm) (N*mm) (kJ/m 2 ) A.S4 7.71 16.51 7.38 0.04 0.15 0.15 0.12 0.07 0.12 1.13 279.14 32.7 17.8 14.9 0.4 al1_7 8.05 16.83 7.33 0.00 0.00 0. 00 0.08 0.00 0.02 0.91 238.751 115.6 19.5 96.1 2.5 A.S3 8.15 16.03 7.50 0.09 0.15 0.17 0.11 0.06 0.13 0.98 201.203 109.7 9.3 100.4 2.9 A.S5 7.57 16.70 7.54 0.12 0.34 0.44 0.38 0.12 0.32 1.31 289.799 229.7 19.1 210.7 6.1 A.S1 7.59 16.46 7.71 0.18 0.32 0. 39 0.32 0.20 0.30 1.43 260.317 219.6 15.5 204.1 6.1 al1_1 8.34 16.53 7.50 0.13 0.35 0.41 0.37 0.14 0.32 1.54 308.411 271.1 29.9 241.2 6.4 A.S2 7.89 16.36 7.58 0.25 0.44 0.50 0.42 0.21 0.40 1.46 293.736 265.4 19.7 245.7 7.1 al1_2 8.24 17.03 7.65 0.20 0.5 4 0.58 0.55 0.27 0.48 1.71 329.804 348.9 33.4 315.5 8.2 al1_3 8.11 16.44 7.44 0.39 0.80 0.78 0.78 0.44 0.70 2.16 311.408 438.9 30.3 408.5 11.2 al1_4 8.34 16.24 7.60 0.50 1.13 1.24 1.08 0.53 0.99 2.37 317.708 547.7 31.3 516.4 14.3 al1_5 8.22 16.16 7.37 0 .76 1.40 1.84 1.50 0.80 1.38 2.96 325.64 723.4 32.8 690.5 19.1 al1_6 8.09 16.79 7.65 1.10 1.79 2.26 2.09 1.18 1.82 4.15 273.69 886.0 24.5 861.6 23.3

PAGE 182

182 Table B 5. The table shows relevant values used to calculate the J integral of the steel embedded epox y samples. The plots were shown in the Intrinsic Toughening Chapter. Stable Crack Growth Extension (mm) Disp max Load max Ut Ui U J Sample B (mm) W (mm) a o (mm) 1 2 3 4 5 average (mm) (N) (N*mm) (N*mm) (N*mm) (kJ/m 2 ) Steel 3 8.18 16.32 7.63 0 .00 0.00 0.10 0.04 0.00 0.03 0.96 330 45.8 30.2 15.5 0.4 Steel 7 7.96 16.06 7.53 0.02 0.04 0.06 0.05 0.04 0.05 0.73 279 113.1 22.5 90.6 2.7 Steel 4 8.2 16.39 7.63 0.10 0.10 0.11 0.09 0.10 0.10 1.04 348 198.6 32.9 165.6 4.6 Steel 2 8.06 15.98 7.47 0.09 0 .13 0.21 0.14 0.07 0.14 1.08 371 223.9 37.0 186.9 5.4 Steel 1 8.1 15.51 7.47 0.20 0.24 0.27 0.28 0.14 0.24 1.40 362 284.2 35.4 248.9 7.6

PAGE 183

183 Table B 6. The table shows relevant values used to calculate the J integral of the NiTi embedded epoxy samples. T he plots were shown in the Intrinsic Toughening Chapter. Stable Crack Growth Extension (mm) Disp max Load max Ut Ui U J Sample B (mm) W (mm) a o (mm) 1 2 3 4 5 average (mm) (N) (N*mm) (N*mm) (N*mm) (kJ/m 2 ) N1_10 8.49 16.38 7.44 0.00 0.00 0.03 0 .06 0.00 0.02 0.81 314 128.2 23.8 104.3 2.7 AR.S 3 8.42 16.24 7.71 0.10 0.23 0.26 0.26 0.13 0.22 1.14 358 226.7 37.9 188.8 5.3 AR.S 6 8.08 16.01 7.38 0.13 0.31 0.32 0.32 0.12 0.27 1.29 347 251.5 36.0 215.6 6.2 N1_1 8.14 16.47 7.55 0.12 0.27 0.29 0.25 0. 11 0.23 1.31 379 275.5 33.4 242.1 6.7 N1_11 8.42 16.41 7.57 0.14 0.40 0.34 0.26 0.21 0.29 1.34 425 313.2 40.8 272.4 7.3 AR.S 4 8.05 16.37 7.58 0.13 0.30 0.40 0.37 0.35 0.33 1.46 364 299.5 39.2 260.3 7.4 AR.S 7 7.72 16.35 7.95 0.09 0.32 0.31 0.28 0.09 0. 25 1.27 339 274.9 34.5 240.4 7.4 AR.S 2 8.17 16.03 7.34 0.22 0.31 0.35 0.34 0.23 0.31 1.37 379 305.4 42.1 263.3 7.4 AR.S 5 8.09 16.33 7.10 0.32 0.48 0.53 0.49 0.28 0.45 1.55 402 378.7 46.8 331.9 8.9 N1_2 8.22 16.57 7.44 0.17 0.49 0.52 0.50 0.19 0.42 1.5 9 422 385.0 40.1 344.9 9.2 N1_3 8.26 16.60 7.42 0.22 0.79 1.04 0.64 0.29 0.68 1.77 469 516.9 48.4 468.5 12.4 AR.S 1 8.10 15.80 7.28 0.26 0.49 0.42 0.43 0.24 0.40 1.92 411 489.3 48.3 440.9 12.8 N1_4 8.18 16.30 7.29 0.42 1.08 1.05 0.80 0.30 0.82 2.10 460 634.9 46.9 588.0 15.9 N1_6 8.31 16.21 7.42 0.48 1.34 1.84 1.00 0.64 1.18 2.44 466 800.2 47.9 752.3 20.6 N1_9 8.39 16.43 7.36 0.75 1.87 1.91 2.09 0.57 1.63 3.04 494 1078.4 53.2 1025.2 26.9

PAGE 184

184 Table B 7. The table shows relevant values used to calculate th e J integral of the NiTi ht embedded epoxy samples. The plots were shown in the Intrinsic Toughening Chapter. Stable Crack Growth Extension (mm) Disp max Load max Ut Ui U J Sample B (mm) W (mm) a o (mm) 1 2 3 4 5 average (mm) (N) (N*mm) (N*mm) (N*mm) (kJ/m 2 ) nh2 8.22 16.52 7.41 0.02 0.03 0.03 0.00 0.00 0.02 0.57 215 62.1 11.6 50.6 1.3 nh12 8.32 16.40 7.66 0.00 0.03 0.05 0.00 0.00 0.02 0.56 219 61.3 12.0 49.2 1.4 nh11 8.42 16.58 7.31 0.00 0.03 0.07 0.00 0.00 0.03 0.74 278 100.7 18.2 82.4 2.1 nh5 8.15 16.47 7.45 0.06 0.06 0.09 0.09 0.00 0.07 0.82 295 122.4 20.4 102.0 2.8 nh7 8.25 16.75 7.54 0.25 0.26 0.21 0.13 0.00 0.18 1.24 371 246.3 31.4 214.9 5.7 nh9 8.17 16.54 7.28 0.14 0.31 0.31 0.30 0.14 0.27 1.20 426 280.0 40.7 239.2 6.3 nh1 8.21 16.7 3 7.69 0.15 0.34 0.32 0.35 0.18 0.29 1.40 430 343.8 41.3 302.5 8.1 nh3 8.47 16.77 7.76 0.30 0.56 0.56 0.58 0.27 0.49 1.85 447 504.6 44.5 460.1 12.1 nh4 7.87 16.39 7.07 0.32 0.71 0.65 0.56 0.27 0.55 1.79 469 533.8 48.5 485.3 13.2 nh6 8.26 16.76 7.48 0.59 1.03 0.99 0.99 0.36 0.87 2.34 464 797.6 47.6 749.9 19.6 nh10 8.40 16.33 7.78 0.81 1.66 1.12 1.69 0.55 1.29 3.33 452 1148.6 45.3 1103.3 30.7

PAGE 185

185 Table B 8 The table shows relevant values used to calculate the J integral of the monolithic samples. The pl ots were shown in the Extrinsic Toughening Chapter. Stable Crack Growth Extension (mm) Ut Ui U J Sample B (mm) W (mm) a o (mm) 1 2 3 4 5 average Disp max (mm) Load max (N) (N*mm) (N*mm) (N*mm) (kJ/m 2 ) jeff far mono 1 7.84 16.15 7.43 0.16 0. 34 0.28 0.28 0.15 0.27 1.51 341 285.7 28.1 257.6 7.5 jeff far mono 6 8.5 15.85 7.31 0.16 0.44 0.50 0.50 0.24 0.41 1.63 384 366.7 35.1 331.5 9.1 jeff far mono 2 7.75 15.78 7.27 0.30 0.36 0.30 0.21 0.00 0.25 1.75 334 360.8 27.0 333.9 10.1 jeff far mono 5 8.68 15.68 7.27 0.35 0.78 0.82 0.75 0.28 0.67 1.88 373 455.6 33.3 422.2 11.6 jeff far mono 3 8.03 15.7 7.18 0.32 0.67 0.73 0.63 0.39 0.60 1.99 355 456.5 30.3 426.2 12.5 jeff far mono 4 7.63 15.86 7.41 0.45 0.95 0.91 0.87 0.38 0.79 2.13 321 468.3 24.9 443 .4 13.7 jeff far mono 7 7.62 16.31 7.03 0.58 1.53 1.73 1.40 0.60 1.31 2.44 374 665.4 31.2 634.2 17.9 jeff far mono 8 8.33 16.5 6.52 0.81 1.95 2.34 2.11 0.79 1.80 2.78 417 845.9 38.2 807.7 19.4 jeff far mono 9 8.3 16.31 6.95 0.88 2.29 2.24 2.20 0.88 1.90 3.10 353 817.4 28.2 789.2 20.3 jeff far mono 13 8.29 15.83 7.69 1.19 2.18 2.69 2.23 1.42 2.10 3.38 341 866.5 25.8 840.7 24.9 jeff far mono 11 8.47 16.64 6.99 1.07 2.32 2.73 2.52 1.24 2.18 3.38 432 1069.3 40.8 1028.5 25.2 jeff far mono 14 8.36 15.99 7.6 7 1.46 2.15 2.77 2.61 1.33 2.23 3.76 350 975.1 27.0 948.1 27.2 jeff far mono 16 8.42 15.73 6.92 1.58 2.78 3.37 2.92 1.46 2.65 4.16 371 1147.1 30.2 1116.9 30.1 jeff far mono 12 8.51 15.96 7.10 1.52 3.66 4.10 3.30 2.12 3.22 4.51 370 1190.3 30.7 1159.6 30.8 jeff far mono 17 8.24 16.29 6.84 2.39 3.77 4.00 3.19 2.46 3.35 4.86 431 1486.0 40.3 1445.7 37.1 jeff far mono 10 8.42 16.72 7.26 2.38 4.46 4.89 4.12 2.69 4.00 5.40 424 1589.1 39.5 1549.7 38.9 jeff far mono 18 8.4 16.78 7.11 3.31 4.61 5.43 4.46 3.03 4.4 2 6.30 431 1762.3 40.3 1722.0 42.4

PAGE 186

186 Table B 9 The table shows relevant values used to calculate the J integral of the aluminum reinforced epoxy samples. Stable Crack Growth Extension (mm) Ut Ui U J Sample B (mm) W (mm) a o (mm) 1 2 3 4 5 average Disp max (mm) Load max (N) (N*mm) (N*mm) (N*mm) (kJ/m 2 ) jeff far aluminum 1 8.04 17.7 7.40 0.29 0.43 0.53 0.39 0.27 0.41 1.59 450 396.3 44.8 351.5 8.5 jeff far aluminum 2 8.52 17.64 7.73 0.38 0.88 1.04 0.80 0.45 0.78 2.00 496 634.1 53.5 580.6 13 .7 jeff far aluminum 20 8.45 17 7.44 0.62 1.28 1.49 1.25 0.62 1.16 2.31 457 765.3 46.7 718.6 17.8 jeff far aluminum 3 8.95 16.71 7.35 0.68 1.61 1.83 1.70 0.68 1.46 2.59 509 969.7 56.3 913.5 21.8 jeff far aluminum 4 8.51 17.16 7.61 0.92 2.02 2.33 2.14 0. 65 1.82 3.03 473 1034.9 49.0 985.8 24.3 jeff far aluminum 17 8.54 17.13 7.46 0.89 2.41 2.66 2.59 1.06 2.16 3.30 449 1150.8 45.4 1105.4 26.8 jeff far aluminum 5 8.41 17.73 7.26 1.38 2.98 3.35 2.72 1.28 2.60 3.51 550 1448.2 65.0 1383.2 31.4 jeff far alumi num 6 8.41 17.64 7.47 1.69 3.54 3.85 3.00 1.61 3.01 4.02 525 1572.1 59.6 1512.5 35.4 jeff far aluminum 7 8.31 17 7.12 2.70 3.65 4.08 3.80 2.80 3.57 4.74 483 1709.8 51.1 1658.7 40.4 jeff far aluminum 10 8.34 17.28 7.34 2.56 3.97 4.45 3.87 1.96 3.64 5.04 4 77 1784.4 52.3 1732.1 41.8 jeff far aluminum 11 8.62 16.51 7.42 2.28 3.80 4.54 3.85 3.00 3.71 5.61 419 1733.0 41.6 1691.4 43.2 jeff far aluminum 14 8.67 16.78 7.66 3.16 4.95 5.74 5.38 3.19 4.81 6.33 441 1866.9 43.7 1823.3 46.1 jeff far aluminum 13 8.48 17.12 7.42 3.21 4.43 5.03 4.40 2.65 4.20 6.05 469 1984.0 50.7 1933.4 47.0 jeff far aluminum 19 8.25 16.72 7.44 3.96 6.12 6.45 6.06 4.40 5.70 7.52 417 1963.0 39.5 1923.5 50.2 jeff far aluminum 15 8.44 17.19 7.64 4.27 6.13 6.27 5.84 3.96 5.59 7.15 458 2081 .3 47.1 2034.2 50.4 jeff far aluminum 12 8.06 17.07 7.29 3.75 4.83 5.93 5.16 3.60 4.90 6.69 460 2120.4 49.0 2071.3 52.5

PAGE 187

187 Table B 10 The table shows relevant values used to calculate the J integral of the NiTi austenite reinforced epoxy samples. Stable Crack Growth Extension (mm) Ut Ui U J Sample B (mm) W (mm) a o (mm) 1 2 3 4 5 average Disp max (mm) Load max (N) (N*mm) (N*mm) (N*mm) (kJ/m 2 ) jeff far nitib 1 8.74 15.89 7.46 0.17 0.29 0.35 0.33 0.19 0.29 1.55 465 397.4 45.4 352.1 9.6 je ff far nitib 2 8.73 15.65 7.10 0.28 0.51 0.53 0.52 0.32 0.46 1.68 506 514.8 53.3 461.5 12.4 jeff far nitib 3 8.57 15.85 7.17 0.29 0.39 0.68 0.52 0.26 0.47 1.86 520 586.9 55.9 531.0 14.3 jeff far nitib 4 8.36 15.87 7.29 0.26 0.46 0.50 0.47 0.32 0.43 2.00 561 674.8 64.4 610.4 17.0 jeff far nitib 5 8.79 17.07 7.50 0.51 0.76 0.82 0.89 0.24 0.71 2.24 674 937.2 87.5 849.7 20.2 jeff far nitib 6 9.15 16.66 7.34 0.52 0.68 0.92 0.72 0.54 0.71 2.44 695 1073.7 92.5 981.2 23.0 jeff far nitib 7 8.58 17.2 7.32 0.72 2 .19 1.65 1.01 0.61 1.38 2.80 677 1367.9 88.0 1279.8 30.2 jeff far nitib 10 8.41 17 7.91 0.99 0.99 1.60 1.85 1.93 1.48 3.20 612 1461.3 73.1 1388.2 36.3 jeff far nitib 13 8.5 16.92 7.26 0.96 1.86 1.83 1.90 0.72 1.61 3.45 630 1648.2 82.7 1565.5 38.1 jeff f ar nitib 12 8.29 16.07 7.53 1.12 1.86 2.51 2.23 1.22 1.94 4.10 498 1624.6 54.3 1570.2 44.3 jeff far nitib 11 8.56 17.26 7.67 1.08 2.28 2.57 2.01 1.37 2.02 4.41 640 2187.6 85.2 2102.4 51.2 jeff far nitib 16 8.3 17.11 7.73 1.82 2.80 2.84 2.54 1.65 2.48 4.9 0 595 2338.8 74.7 2264.1 58.1 jeff far nitib 9 8.56 15.84 7.41 2.18 2.78 3.01 3.34 1.80 2.62 5.73 569 2621.8 64.0 2557.8 70.9 jeff far nitib 21 8.41 16.87 7.54 1.70 3.13 3.49 3.06 2.22 2.91 6.54 655 3474.3 80.7 3393.6 86.5 jeff far nitib 19 8.61 16.87 7 .72 2.35 3.49 3.63 3.16 2.42 3.17 7.00 616 3609.5 72.2 3537.3 89.8 jeff far nitib 23 8.01 17.27 7.48 3.15 3.45 3.93 3.65 3.28 3.56 7.40 624 3844.8 73.5 3771.2 96.1 jeff far nitib 15 8.48 16.69 7.74 2.72 3.69 4.06 3.83 2.86 3.59 8.54 591 4116.8 73.8 4043. 0 106.5

PAGE 188

188 Table B 11 The table shows relevant values used to calculate the J integral of the NiTi martensite reinforced epoxy samples. Stable Crack Growth Extension (mm) Ut Ui U J Sample B (mm) W (mm) a o (mm) 1 2 3 4 5 average Disp max (mm) Load max (N) (N*mm) (N*mm) (N*mm) (kJ/m 2 ) jeff far nitib ht 1 8.23 16.84 7.56 3.62 4.41 4.49 3.97 3.33 4.09 9.41 545 4100.7 59.9 4040.8 105.8 jeff far nitib ht 3 8.18 16.76 7.51 0.40 0.73 1.01 0.94 0.33 0.76 2.50 543 857.6 59.5 798.1 21.1 jeff far n itib ht 4 8.22 16.86 7.28 0.39 0.65 0.76 0.56 0.38 0.59 1.93 495 572.8 49.7 523.1 13.3 jeff far nitib ht 5 8.55 16.66 7.34 0.33 0.63 0.77 0.63 0.32 0.59 2.12 557 697.5 62.4 635.1 15.9 jeff far nitib ht 6 8.33 17.36 7.59 2.65 3.40 3.50 2.88 1.88 3.01 5.25 571 2370.8 73.2 2297.6 56.5 jeff far nitib ht 7 8.32 16.92 7.38 2.85 4.00 4.33 3.92 3.13 3.81 8.11 526 3440.5 63.1 3377.4 85.1 jeff far nitib ht 9 8.55 17.36 7.29 1.98 2.04 2.53 2.16 1.92 2.17 4.00 575 1781.4 73.9 1707.5 39.7 jeff far nitib ht 12 8.33 17.19 7.28 4.63 5.10 5.43 4.86 4.17 4.95 9.84 621 4893.4 83.2 4810.2 116.5 jeff far nitib ht 13 8.59 17.03 7.32 3.70 4.47 4.29 4.27 3.55 4.16 8.50 595 4053.9 77.0 3976.9 95.3 jeff far nitib ht 17 8.53 17.53 7.45 2.31 3.97 4.30 4.03 2.52 3.68 6.01 615 294 1.3 81.6 2859.7 66.5 jeff far nitib ht 20 8.75 17.03 7.28 0.68 1.38 1.64 1.54 0.66 1.31 3.00 604 1274.3 87.4 1186.9 27.8 jeff far nitib ht 22 8.72 17.41 7.24 1.15 1.99 2.63 1.98 1.07 1.93 3.50 658 1712.2 101.4 1610.8 36.3

PAGE 189

189 APPENDIX C DERIVATION OF BENDI NG STRESS EQUATIONS This section shows how the bending stress equation used in Chapter s 5 and 6 were derived. The typical composite bending theory is only valid for elastic loading. As such the equations must be modified in order to account for plastic deformation With continued loading a ductile material will begin to plastically deform initially at the extremes of the composite. C ontinued deformation results in plastic region grow th towards the neutral axis. I n deriving the bending stresses, the fo llowing assumptions were made: t he constituent materials behave like an elastic plastic material p erfect bonding and t ension compression symmetry Neutral Axis In order to calculate the bending stress the neutral axis must first be determined, since s train is proportional to the distance from the neutral axis NA The location of the neutral axis was derived based on the sample geometry shown in Figure C 1 The neutral axis is defined as the plane within a beam that undergoes no deformation (stress o r strain) Therefore, the forces along the b eam neutral axis must equal 0. Since ( C 1 ) where respectively, then ( C 2 ) where the subscript i corresponds to the composite section number as shown in Figure C 2 Equation C 3 shows the relationship b

PAGE 190

190 y is the distance from the neutral axis to the centroid, D. Equation C 4 is shown graphically in Figure C 3 ( C 3 ) ( C 4 ) y will be negative if the centro id is located below the neutral axis. Substituting Equation C 1 and C 3 into Equation C 2 yields ( C 5 ) The areas A, of the material section were ca lculated for a circle and rectangular cross sectional area using equation C 6 a nd C 7, respectively. ( C 6 ) ( C 7 ) d, B, and H are the diameter, thickness, and height, respectively. Equations C 8 a f show the simplification of C 5 when substituting the composite geometry and equation s B 6 and B 7. ( C 8a ) ( C 8b ) ( C 8c ) ( C 8d )

PAGE 191

191 ( C 8e ) ( C 8f ) Equation C 8f was the governing equation used to de termine the neutral axis location. Reinforcement Bending Stress Figure C 4 shows the loading condition of the composite along with applied forces. To satisfy the conditions of static equilibrium, ( C 9 ) where M is the moment Therefore, ( C 10 ) Substituting equations C 2 and C 3 into equation C 9 and simplifying yields ( C 1 1 ) Simplifying Equation C 1 1 gives ( C 1 2 ) where the second moment of inert ia, I, is ( C 1 3 ) The parallel axis theorem must be used when the moment of inertia is being determined about an axis that does not coincide with the composite section centroid. Therefore, ( C 1 4 ) whe re the second moment of intertia of circular and rectangular members is

PAGE 192

192 ( C 1 5 ) ( C 1 6 ) B, W, and a are the sample thickness, width, and initial crack length, respectively. Substituting Equation C 1 3 into C 1 2 and solving for M gives ( C 1 7 ) Therefore, ( C 1 8 ) since ( C 1 9 ) then ( C 20 ) where ( C 2 1 ) Therefore the governing equation to determine the bending stress with in the reinforcements is ( C 2 2 )

PAGE 193

193 Figure C 1. The schematic shows the 3 point bend sample geometry used to derive the bending stress equations. Figure C 2. The schematic shows the cross sectional view of the 3 point bend s amples. The 3 7 point towards the reinforcements and 2 points towards the unbroken ligament length matrix area.

PAGE 194

194 Figure C 3. The schematic shows the relationship between the neutral axis (NA), centroid (D), and height from the neutral axis to the cen troid (y). Figure C 4. The schematic shows the 3 point bend sample and loading parameters. L, W, and P are the roller span, sample width, and applied load, respectively.

PAGE 195

195 APPENDIX D SHAPE MEMORY ALLOY ELECTRICAL RESISITIVITY CHARACTERIZATION T o deter mine the SMA martensitic phase transformation behavior a four probe measurement technique was used to measure the resistance changes of a deforming SMA wire. In addition to the four probe setup, an amplifier was used to increase the recorded voltage signa l. An AD524AD low noise signal amplifier, provided by Analog Devices was used. The electrical resistivity setup was provided by Dr. Fabio Mennella ( Antonucci et al., 2007 ) (D 1) where R, A, L, V, and I are the resistance, area, length, and current, respecti vely, measured within the material Figures D 1 and D 2 show data collected using the device.

PAGE 196

196 Figure D 1 The graph shows the voltage versus extension curves with the NiTi load curve overlaid on the data. Figure D 2 The graph shows the voltag e versus extension curves with the NiTi load curve overlaid on the data at different extension rates.

PAGE 197

197 LIST OF REFERENCES Adharapurapu, R.R., Vecchio, K.S., 2007. Superelasticity in a New Bioimplant Material: Ni Rich 55niti Alloy. Exper imental Mechanics 47, 365 371. Albertsen, H., Ivens, J., Peters, P., Wevers, M., Verpoest, I., 1995. Interlaminar Fracture Toughness of Cfrp Influenced by Fiber Surface Treatment .1. Experimental Results. Composites Science and Technology 54, 133 145. Anto lovi, S.D., Singh B., 1971. Toughness Iincrement Associated with Austenite to Martensite Phase Transformation in Trip Steels. Metallurgical Transactions 2, 2135 2141. Antonucci, V., Faiella, G., Giordano, M., Mennella, F., Nicolais, L., 2007. Electrical Re sistivity Study and Characterization During Niti Phase Transformations. Thermochimica Acta 462, 64 69. Aranzabal, J., Guiterrez I, Rodriguez Ibabe Jm, Urcola Jj, 1997. Influence of the Amount and Morphology of Retained Austenite on the Mechanical Properite s of an Austempered Ductile Iron. Metallurgical and Materials Transactions A 28A, 1143 1156. Aranzabal, J., Gutierrez, I., Rodriguezibabe, J.M., Urcola, J.J., 1992. Influence of Heat Treatments on Microstructure and Toughness of Austempered Ductile Iron. M aterials Science and Technology 8, 263 273. Ashby, M.F., Blunt, F.J., Bannister, M., 1989. Flow Characteristics of Highly Constrained Metal Wires. Acta Metallurgica 37, 1847 1857. Astm, 1989. Annual Book of Astm Standards, Standard Test Method for Jic, A M easure of Fracture Toughness, Philadelphia. Bagwell, R.M., Wetherhold, R.C., 2005. End Shaped Copper Fibers in an Epoxy Matrix Predicted Versus Actual Fracture Toughening. Theoretical and Applied Fracture Mechanics 43, 181 188. Bao, G., Suo, Z., 1992. Re marks on Crack Bridging Concepts. Appl Mech Rev 45. Bartolome, J.F., Diaz, M., Moya, J.S., 2002. Influence of the Metal Particle Size on the Crack Growth Resistance in Mullite Molybdenum Composites. Journal of the American Ceramic Society 85, 2778 2784. Ba z, A., Chen, T., Ro, J., 2000. Shape Control of Nitinol Reinforced Composite Beams. Compos. Pt. B Eng. 31, 631 642. Ben Mekki, O., Auricchio, F., 2011. Performance Evaluation of Shape Memory Alloy Superelastic Behavior to Control a Stay Cable in Cable Stay ed Bridges. International Journal of Non Linear Mechanics 46, 470 477.

PAGE 198

198 Birman, V., 2008. Shape Memory Elastic Foundation and Supports for Passive Vibration Control of Composite Plates. International Journal of Solids and Structures 45, 320 335. Brahmakumar M., Pavithran, C., Pillai, R.M., 2005. Coconut Fibre Reinforced Polyethylene Composites: Effect of Natural Waxy Surface Layer of the Fibre on Fibre/Matrix Interfacial Bonding and Strength of Composites. Composites Science and Technology 65, 563 569. Bril l, T.M., Mittelbach, S., Assmus, W., Mullner, M., Luthi, B., 1991. Elastic Properties of Niti. Journal of Physics Condensed Matter 3, 9621 9627. Budiansky, B., Amazigo, J.C., Evans, A.G., 1988. Small Scale Crack Bridging and the Fracture Toughness of Parti culate Reinforced Ceramics. Journal of the Mechanics and Physics of Solids 36, 167 187. Cardwell, B.J., Yee, A.F., 1998. Toughening of Epoxies through Thermoplastic Crack Bridging. J. Mater. Sci. 33, 5473 5484. Chan, K.S., 1992. Influence of Microstructure on Intrinsic and Extrinsic Toughening in an Alpha Two Titanium Aluminide Alloy. Metallurgical Transactions A 23, 183 199. Chawla, K.K., Liu, H., Janczak Rusch, J., Sambasivan, S., 2000. Microstructure and Properties of Monazite (Lapo4) Coated Saphikon Fib er/Alumina Matrix Composites. Journal of the European Ceramic Society 20, 551 559. Chawla, N., Chawla, K. K., 2006. Metal Matrix Composites. Springer US. Cotterell, B., Reddel, J.K., 1977. Essential Work of Plane Stress Ductile Fracture. International Jour nal of Fracture 13, 267 277. D6068 96, 2002. Standard Test Method for Determining J R Curves of Plastic Materials. ASTM International, West Conshohocken, PA. Desroches, R., Delemont, M., 2002. Seismic Retrofit of Simply Supported Bridges Using Shape Memory Alloys. Engineering Structures 24, 325 332. Deve, H.E., Schmauder S, 1992. Role of Interface Properties on the Toughness of Brittle Matrix Composites Reinforced with Ductile Fibers. J Mater Res 7, 3132 3138. Difrancia, C., Ward Tc, Claus Ro, 1996. The Sin gle Fibre Pull out Test. 1. Review and Interpretation. Composites: Part A 27A, 597 612. Duerig, T., Pelton, A., Stockel, D., 1999. An Overview of Nitinol Medical Applications. Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process. 273, 149 160. Evan s, A., 1988. High Toughness Ceramics. Mat Sci Eng a Struct 105, 65 75.

PAGE 199

199 Evans, A.G., 1990. Perspective on the Development of High Toughness Ceramics. Journal of the American Ceramic Society 73, 187 206. Evans, A.G., Zok, F.W., Davis, J., 1991. The Role of I nterfaces in Fiber Reinforced Brittle Matrix Composites. Composites Science and Technology 42, 3 24. Feldhoff, A., Pippel, E., Woltersdorf, J., 1997. Interface Reactions and Fracture Behaviour of Fibre Reinforced Mg/Al Alloys. J. Microsc.. 185, 122 131. Fr iend, C.M., Armstrong, P.J., 1997. Real Time Control of Resonance in "Smart" Shape Memory Alloy Hybrid Laminates. Journal De Physique Iv 7, 649 653. Fu, S. Y., Feng, X. Q., Lauke, B., Mai, Y. W., 2008. Effects of Particle Size, Particle/Matrix Interface Ad hesion and Particle Loading on Mechanical Properties of Particulate Polymer Composites. Compos. Pt. B Eng. 39, 933 961. Furuya, Y., Sasaki, A., Taya, M., 1993. Enhanced Mechanical Properties of Tini Shape Memory Fiber/Al Matrix Composite. Mater. Trans. JIM 34, 224 227. Gall, K., Sehitoglu, H., Chumlyakov, Y.I., Kireeva, I.V., Maier, H.J., 1999. The Influence of Aging on Critical Transformation Stress Levels and Martensite Start Temperatures in Niti: Part I Aged Microstructure and Micro Mechanical Modeling Journal of Engineering Materials and Technology Transactions of the Asme 121, 19 27. Gao G, S.Y., 2003. Experimental Study on the Anisotropic Behavior of Textured Niti Pseudoelastic Shape Memory Alloys. Materials Science and Engineering A362, 107 111. Gi l, F.J., Guilemany, J.M., 1997. Friction and Stored Elastic Energy in Cu Zn Al Single Crystals with Pseudoelastic Behaviour. Thermochimica Acta 290, 167 171. Goto, K., Kagawa, Y., 1996. Fracture Behaviour and Toughness of a Plane Woven Sic Fibre Reinforced Sic Matrix Composite. Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process. 211, 72 81. Graesser, E.J., Cozzarelli, F.A., 1991. Shape Memory Alloys as New Materials for Aseismic Isolation. Journal of Engineering Mechanics Asce 117, 2590 2608. Gree n, D.J., 1998. An Introduction to the Mechanical Properties of Ceramics. Cambridge University Press, Cambridge. Griffith, A.A., 1921. The Phenomena of Rupture and Flow in Solids. Phil. Trans. R. Soc. Lond. A 221, 163 198. Grujicic, M., Dang, P., 1997. Mart ensitic Transformation in a Cispersed Ti Al V Fe Beta Phase and Its Effect on Fracture Toughness of Gamma Titanim Aluminide. Materials Science and Engineering A Structural Materials Properties Microstructure and Processing 224, 187 199.

PAGE 200

200 Gupta, T.K., Becht old Jh, Kuznicki, Rc, Cadoff, Lh, 1977. Stabilization of Tetragonal Phase in Polycrystalline Zirconia. J Mater Sci 12, 2421 2426. Hamilton, R.F., Sehitoglu, H., Chumlyakov, Y., Maier, H.J., 2004. Stress Dependence of the Hysteresis in Single Crystal Niti A lloys. Acta Materialia 52, 3383 3402. Hatcher, N., Kontsevoi, O.Y., Freeman, A.J., 2009. Role of Elastic and Shear Stabilities in the Martensitic Transformation Path of Niti. Physical Review B 80. Hutchinson, J.W., 1989. Mechanisms of Toughening in Ceramic s, in: Germain, P., Piau, M., Caillerie, D. (Eds.), IUTAM. Elsevier Science Publishers B. V., Zurich, Switzerland, pp. 139 144. Inczdy, J., Lengyel, T., Ure, A.M., 1998. Compendium of Analytical Nomenclature : Definitive Rules 3rd ed. Blackwell Science, O xford. International, A., 2004. Astm Standard E 8m 04, Standard Test Methods for Tension Testing of Metallic Materials [Metric]. ASTM International, West Conshohocken, PA. Iwabuchi, T., Suzuki, S., Ebina, K., Honma, T., 1975. Memory Clip for Intracranial A neurysm Surgery. Journal of Neurosurgery 42, 733 735. Jacques, P., Furnemont Q, Pardoen T, Delannay F, 2001. On the Role of the Martensitic Transformations on the Damage and Crack Resistance in Trip Assisted Multiphase Steels. Acta Mater 49, 139 152. Jang, B.K., Kishi, T., 2005. Adhesive Strength between Tini Fibers Embedded in Cfrp Composites. Materials Letters 59, 1338 1341. Ju, D.Y., Shimamoto, A., 1999. Damping Property of Epoxy Matrix Composite Beams with Embedded Shape Memory Alloy Fibers. Journal of Intelligent Material Systems and Structures 10, 514 520. Kato, H., Miura, S., 1995. Thermodynamical Analysis of the Stress Induced Martensitic Transformation in Cu 15.0 at Percent Sn Alloy Single Crystals. Acta Metallurgica Et Materialia 43, 351 360. Kaute D.a.W., Shercliff, H.R., Ashby, M.F., 1993. Delamination, Fiber Bridging and Toughness of Ceramic Matrix Composites. Acta Metallurgica Et Materialia 41, 1959 1970. Kelly, P.M., Rose, L.R.F., 2002. The Martensitic Transformation in Ceramics Its Role in Transformation Toughening. Progress in Materials Science 47, 463 557. Khalil Allafi, J., Dlouhy, A., Eggeler, G., 2002. Ni4ti3 Precipitation During Aging of Niti Shape Memory Alloys and Its Influence on Martensitic Phase Transformations. Acta Materialia 50 4255 4274.

PAGE 201

201 Kim, B., Lee, M.G., Lee, Y.P., Kim, Y.I., Lee, G.H., 2006. An Earthworm Like Micro Robot Using Shape Memory Alloy Actuator. Sensors and Actuators a Physical 125, 429 437. Kim, C., Park, B.S., Goo, N.S., 2002. Shape Changes by Coupled Bending a nd Twisting of Shape Memory Alloy Embedded Composite Beams. Smart Mater. Struct. 11, 519 526. Kim, J., Mai Y, 1991. High Strength, High Fracture Toughness Fibre Composites with Interface Control a Review. Composites Science and Technology 41. Kimura, H., A kiniwa, Y., Tanaka, K., Tanaka, H., Okumura, Y., 2006. Smart Structure for Suppression of Mode I and Ii Crack Propagation in Cfrp Laminates by Shape Memory Alloy Tini Actuator. International Journal of Fatigue 28, 1147 1153. Kirkby, E.L., Rule, J.D., Micha ud, V.L., Sottos, N.R., White, S.R., Manson, J.a.E., 2008. Embedded Shape Memory Alloy Wires for Improved Performance of Self Healing Polymers. Adv. Funct. Mater. 18, 2253 2260. Klingbeil, N.W., Beuth, J.L., 2000. On the Design of Debond Resistant Bimateri als Part I: Free Edge Singularity Approach. Engineering Fracture Mechanics 66, 93 110. Kruzic, J., Nalla, R.K., Kinney, J.H., Ritchie, R.O., 2003. Crack Blunting, Crack Bridging and Resistance Curve Fracture Mechanics in Dentin: Effect of Hydration. Biom aterials 24, 5209 5221. Kurita, T., Matsumoto, H., Abe, H., 2004. Transformation Behavior in Roiled Niti. Journal of Alloys and Compounds 381, 158 161. Lagoudas, D.C., 2008. Shape Memory Alloys: Modeling and Engineering Applications. Springer Science+Busi ness Media, LLC, New York. Lange, F., 1982a. Transformation Toughening .1. Size Effects Associated with the Thermodynamics of Constrained Transformations. J Mater Sci 17, 225 234. Lange, F.F., 1970. Interaction of a Crack Front with a Second Phase Dispersi on. Philosophical Magazine 22, 983 &. Lange, F.F., 1982b. Transformation Toughening .3. Experimental Observations in the Zro2 Y2o3 System. J. Mater. Sci. 17, 240 246. Launey, M.E., Ritchie, R.O., 2009. On the Fracture Toughness of Advanced Materials. Advan ced Materials 21, 2103 2110. Legresy, J.M., Prandi, B., Raynaud, G.M., 1991. Effects of Cold Rolling and Post Deformation Annealing on the Martensitic Transformation of a Tini Shape Memory Alloy. Journal De Physique Iv 1, 241 246.

PAGE 202

202 Liang, C., Rogers, C.A., Fuller, C.R., 1991. Acoustic Transmission and Radiation Analysis of Adaptive Shape Memory Alloy Reinforced Laminated Plates. Journal of Sound and Vibration 145, 23 41. Lind, R.J., Doumanidis, C.C., 2003. Active Deformable Sheets: Prototype Implementation, Modeling, and Control. Opt. Eng. 42, 304 316. Liu, Y., Van Humbeeck J, Stalmans R, Delaey L, 1997. Some Aspects of the Properties of Niti Shape Memory Alloy. J. Alloy. Compd. 247, 115 121. Mai, Y.W., Cotterell, B., 1986. On the Essential Work of Ductile Fr acture in Polymers. International Journal of Fracture 32, 105 125. Manuel, M.V., 2007. Design of a Self Healing Biomimetic Self Healing Alloy Composite, Materials Science and Engineering. Northwestern University, Evanston. Manuel, M.V., Olson, G.B., 2007. Biomimetic Self Healing Metals. Proceedings of the First INternational Conference on Self Healing Materials 100. Mccormick, J., Desroches, R., Fugazza, D., Auricchio, F., 2006. Seismic Vibration Control Using Superelastic Shape Memory Alloys. Journal of En gineering Materials and Technology Transactions of the Asme 128, 294 301. Mei, Z., Morris, J.W., 1990. Influence of Deformation Induced Martensite on Fatigue Crack Propagation in 304 Type Steels. Metallurgical Transactions a Physical Metallurgy and Materia ls Science 21, 3137 3152. Melton, K., 1990. Ni Ti Based Shape Memory Alloys, in: Duerig, T.W., Melton, K. N., Stockel, D., Wayman, C. M. (Ed.), Engineering Aspects of Shape Memory Alloys. Butterworth Heinemann London, pp. 21 35. Mendiratta, M.G., Lewandows ki, J.J., Dimiduk, D.M., 1991. Strength and Ductile Phase Toughening in the 2 Phase Nb/Nb5si3 Alloys. Metallurgical Transactions a Physical Metallurgy and Materials Science 22, 1573 1583. Mey, S.A., Effenberg, G., 1986. A Thermodynamic Evaluation of the Al uminum Zinc System. Zeitschrift Fur Metallkunde 77, 449 453. Michel, D., Mazerolles L, Perez Myj, 1983. Fracture of Metastable Tetragonal Zirconia Crystals. J Mater Sci 18, 2618 2628. Miller, D.A., Lagoudas, D.C., 2001. Influence of Cold Work and Heat Trea tment on the Shape Memory Effect and Plastic Strain Development of Niti. Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process. 308, 161 175. Miyazaki, S., Otsuka, K., 1989. Development of Shape Memory Alloys. Isij International 29, 353 377.

PAGE 203

203 Mohamed H.A., Washburn, J., 1976. Mechanism of Shape Memory Effect in Ni Ti Alloy. Metallurgical Transactions a Physical Metallurgy and Materials Science 7, 1041 1043. Murasawa, G., Tohgo, K., Ishii, H., 2004a. Deformation Behavior of Niti/Polymer Shape Memory A lloy Composites Experimental Verifications. J. Compos Mater. 38, 399 416. Murasawa, G., Tohgo, K., Ishii, H., 2004b. Deformation Behavior of Niti/Polymer Shape Memory Alloy Composites Experimental Verifications. Journal of Composite Materials 38, 399 4 16. Nagendra, N., Jayaram, V., 2000. Fracture and R Curves in High Volume Fraction Al2o3/Al Composites. Journal of Materials Research 15, 1131 1144. Nakayama, H., Tsuchiya, K., Umemoto, M., 2001. Crystal Refinement and Amorphisation by Cold Rolling in Tini Shape Memory Alloys. Scripta Materialia 44, 1781 1785. Nalla, R.K., Kinney, J.H., Ritchie, R.O., 2003. Mechanistic Fracture Criteria for the Failure of Human Cortical Bone. Nature Materials 2, 164 168. Naslain, R.R., 1998. The Design of the Fibre Matrix I nterfacial Zone in Ceramic Matrix Composites. Composites Part a Applied Science and Manufacturing 29, 1145 1155. Nishida, M., Wayman, C.M., Honma, T., 1986. Precipitation Processes in near Equiatomic Tini Shape Memory Alloys. Metallurgical Transactions a P hysical Metallurgy and Materials Science 17, 1505 1515. Ona, M., Wakabayashi, N., Yamazaki, T., Takaichi, A., Igarashi, Y., 2013. The Influence of Elastic Modulus Mismatch between Tooth and Post and Core Restorations on Root Fracture. International Endodon tic Journal 46, 47 52. Otsuka, K., Kakeshita, T., 2002. Science and Technology of Shape Memory Alloys. New Developments. Mrs Bulletin 27, 91 100. Otsuka, K., Ren, X., 2005. Physical Metallurgy of Ti Ni Based Shape Memory Alloys. Progress in Materials Scien ce 50, 511 678. Otsuka, K., Ren, X.B., 1999. Recent Developments in the Research of Shape Memory Alloys. Intermetallics 7, 511 528. Otsuka, K., Wayman, C.M., 1998. Shape Memory Materials. Cambridge University Press, London. Paine, J.S.N., Rogers, C.A., 199 4. The Response of Sma Hybrid Composite Materials to Low Velocity Impact. Journal of Intelligent Material Systems and Structures 5, 530 535.

PAGE 204

204 Parlinska, M., Balta, J.A., Michaud, V., Bidaux, J.E., Manson, J.A., Gotthardt, R., 2001. Vibrational Response of A daptive Composites. Journal De Physique Iv 11, 129 134. Payandeh, Y., Meraghni, F., Patoor, E., Eberhardt, A., 2010. Debonding Initiation in a Niti Shape Memory Wire Epoxy Matrix Composite. Influence of Martensitic Transformation. Materials & Design 31, 10 77 1084. Payandeh, Y., Meraghni, F., Patoor, E., Eberhardt, A., 2012. Study of the Martensitic Transformation in Niti Epoxy Smart Composite and Its Effect on the Overall Behavior. Materials & Design 39, 104 110. Pelton, A.R., Dicello, J., Miyazaki, S., 200 0. Optimisation of Processing and Properties of Medical Grade Nitinol Wire. Minim. Invasive Ther. Allied Technol. 9, 107 118. Peterlik, H., Roschger, P., Klaushofer, K., Fratzl, P., 2006. From Brittle to Ductile Fracture of Bone. Nature Materials 5, 52 55. Pezzotti, G., Sbaizero, O., Sergo, V., Muraki, N., Maruyama, K., Nishida, T., 1998. In Situ Measurements of Frictional Bridging Stresses in Alumina Using Fluorescence Spectroscopy. Journal of the American Ceramic Society 81, 187 192. Pommet, M., Juntaro, J., Heng, J.Y.Y., Mantalaris, A., Lee, A.F., Wilson, K., Kalinka, G., Shaffer, M.S.P., Bismarck, A., 2008. Surface Modification of Natural Fibers Using Bacteria: Depositing Bacterial Cellulose onto Natural Fibers to Create Hierarchical Fiber Reinforced Nan ocomposites. Biomacromolecules 9, 1643 1651. Pompe, W., Bahr, H.A., Gille, G., Kreher, W., 1978. Increased Fracture Toughness of Brittle Materials by Microcracking in an Energy Dissipative Zone at Crack Tip. J. Mater. Sci. 13, 2720 2723. Pothan, L.A., Thom as, S., Neelakantan, N.R., 1997. Short Banana Fiber Reinforced Polyester Composites: Mechanical, Failure and Aging Characteristics. Journal of Reinforced Plastics and Composites 16, 744 765. Qiu, S., Clausen, B., Padula, S.A., Ii, Noebe, R.D., Vaidyanathan R., 2011. On Elastic Moduli and Elastic Anisotropy in Polycrystalline Martensitic Niti. Acta Materialia 59, 5055 5066. Raddatz, O., Schneider, G.A., Claussen, N., 1998. Modelling of R Curve Behaviour in Ceramic/Metal Composites. Acta Materialia 46, 6381 6395. Raddatz, O., Schneider, G.A., Mackens, W., Voss, H., Claussen, N., 2000. Bridging Stresses and R Curves in Ceramic/Metal Composites. Journal of the European Ceramic Society 20, 2261 2273. Redon, C., Li, V.C., Wu, C., Hoshiro, H., Saito, T., Ogawa, A. 2001. Measuring and Modifying Interface Properties of Pva Fibers in Ecc Matrix. Journal of Materials in Civil Engineering 13, 399 406.

PAGE 205

205 Rice, J.R., 1968. A Path Independent Integral and Approximate Analysis of Strain Concentration by Notches and Cracks. J ournal of Applied Mechanics 35, 379 +. Ritchie, R.O., 1988. Mechanisms of Fatigue Crack Propagation in Metals, Ceramics and Composites Role of Crack Tip Shielding. Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process. 103, 15 28. Ritchie, R.O., 1 999. Mechanisms of Fatigue Crack Propagation in Ductile and Brittle Solids. International Journal of Fracture 100, 55 83. Rogers, C.A., 1988. Novel Design Concepts Utilizing Shape Memory Alloy Reinforced Composites. Proceedings of the American Society for Composites Third Technical Conference Integrated Composites Technology, 719 731. Rogers, C.A., 1990. Active Vibration and Structural Acoustic Control of Shape Memory Alloy Hybrid Composites Experimental Results. Journal of the Acoustical Society of Ameri ca 88, 2803 2811. Ruf, H., Evans, A.G., 1983. Toughening by Monoclinic Zirconia. Journal of the American Ceramic Society 66, 328 332. Saadat, S., Noori, M., Davoodi, H., Hou, Z., Suzuki, Y., Masuda, A., 2001. Using Nitisma Tendons for Vibration Control of Coastal Structures. Smart Materials & Structures 10, 695 704. Saadat, S., Salichs, J., Noori, M., Hou, Z., Davoodi, H., Bar On, I., Suzuki, Y., Masuda, A., 2002. An Overview of Vibration and Seismic Applications of Niti Shape Memory Alloy. Smart Materials & Structures 11, 218 229. Sbaizero, O., Pezzotti, G., 2000. Influence of the Metal Particle Size on Toughness of Al2o3/Mo Composite. Acta Materialia 48, 985 992. Sbaizero, O., Pezzotti, G., Nishida, T., 1998. Fracture Energy and R Curve Behavior of Al2o3/M o Composites. Acta Materialia 46, 681 687. Sciences, C.L., 2008. Properties of Pyrex, Pyrexplus and Low Actinic Pyrex Code 7740 Glasses, in: Sciences, C.L. (Ed.). Sehitoglu, H., Hamilton, R., Canadinc, D., Zhang, X.Y., Gall, K., Karaman, I., Chumlyakov, Y., Maier, H.J., 2003. Detwinning in Niti Alloys. Metall and Mat Trans A 34, 5 13. Shannag, M.J., Brincker, R., Hansen, W., 1997. Pullout Behavior of Steel Fibers from Cement Based Composites. Cement and Concrete Research 27, 925 936. Shaw, J.A., Kyriakide s, S., 1995. Thermomechanical Aspects of Niti. Journal of the Mechanics and Physics of Solids 43, 1243 1281.

PAGE 206

206 Simon, T., Kroeger, A., Somsen, C., Dlouhy, A., Eggeler, G., 2010. On the Multiplication of Dislocations During Martensitic Transformations in Niti Shape Memory Alloys. Acta Materialia 58, 1850 1860. Software, T. C.S., 3 February 2013. Ssol2. http://www.thermocalc.com Song, G.B., Kelly, B., Agrawal, B.N., 2000. Active Position Control of a Shape Memory All oy Wire Actuated Composite Beam. Smart Mater. Struct. 9, 711 716. Spinner, S., Rozner, A.G., 1966. Elastic Properties of Niti as a Function of Temperature. J. Acoustical Soc. America 40, 1009. Stebner, A., Gao, X., Brown, D.W., Brinson, L.C., 2011. Neutron Diffraction Studies and Multivariant Simulations of Shape Memory Alloys: Empirical Texture Development Mechanical Response Relations of Martensitic Nickel Titanium. Acta Materialia 59, 2841 2849. Sun, C.T., 2007. Mechanics of Aircraft Structures, Second E dition ed. John Wiley & Sons, New York. Sun, X.D., Yeomans, J.A., 1996. Ductile Phase Toughened Brittle Materials. Journal of Materials Science & Technology 12, 124 134. Swanson, P.L., Fairbanks, C.J., Lawn, B.R., Mai, Y.W., Hockey, B.J., 1987. Crack Inter face Grain Bridging as a Fracture Resistance Mechanism in Ceramics .1. Experimental Study on Alumina. Journal of the American Ceramic Society 70, 279 289. T. Todoroki, Tamura, H., 1987. Effect of Heat Treatment after Cold Working on the Phase Transformatio n in Tini Alloy. Transactions of the Japan Institute of Metals 28, 83 94. Takaku, A., Arridge, R.G.C., 1973. Effect of Interfacial Radial and Shear Stress on Fiber Pull out in Composite Materials. Journal of Physics D Applied Physics 6, 2038 2047. Treppman n, D., Hornbogen, E., 1997. On the Influence of Thermomechanical Treatments on Shape Memory Alloys. Journal De Physique Iv 7, 211 220. Van Humbeeck, J., Liu, Y., 2000. Shape Memory Alloys as Damping Materials, in: Saburi, T. (Ed.), Shape Memory Materials, pp. 331 338. Villanueva, A.A., Joshi, K.B., Blottman, J.B., Priya, S., 2010. A Bio Inspired Shape Memory Alloy Composite (Bismac) Actuator. Smart Mater. Struct. 19. Viswanathan, L., Ikuma Y, Virkar Av, 1983. Transformation Toughening of Beta" Alumina by In corporation of Zirconia. J Mater Sci 18, 109 113.

PAGE 207

207 Waitz, T., Antretter, T., Fischer, F.D., Simha, N.K., Karnthaler, H.P., 2007. Size Effects on the Martensitic Phase Transformation of Niti Nanograins. Journal of the Mechanics and Physics of Solids 55, 419 444. Watanabe, Y., Miyazaki, E., Okada, H., 2002. Enhanced Mechanical Properties of Fe Mn Si Cr Shape Memory Fiber/Plaster Smart Composite. Materials Transactions 43, 974 983. Wetherhold, R., Bos J., 2000. Ductile Reinforcements for Enhancing Fracture Resi stance in Composite Materials. Theoretical and Applied Fracture Mechanics 33, 83 91. White, S.R., Sottos, N.R., Geubelle, P.H., Moore, J.S., Kessler, M.R., Sriram, S.R., Brown, E.N., Viswanathan, S., 2001. Autonomic Healing of Polymer Composites. Nature 40 9, 794 797. Wu, J.S., Mai, Y.W., Cotterell, B., 1993. Fracture Toughness and Fracture Mechanisms of Pbt Pc Im Blend .1. Fracture Properties. J. Mater. Sci. 28, 3373 3384. Xu, G., Bower, A.F., Ortiz, M., 1998. The Influence of Crack Trapping on the Toughnes s of Fiber Reinforced Composites. Journal of the Mechanics and Physics of Solids 46, 1815 1833. Yang, Z., Tirry, W., Schryvers, D., 2005. Analytical Tem Investigations on Concentration Gradients Surrounding Ni4ti3 Precipitates in Ni Ti Shape Memory Materia l. Scripta Materialia 52, 1129 1134. Yue, C.Y., Padmanabhan, K., 1999. Interfacial Studies on Surface Modified Kevlar Fibre Epoxy Matrix Composites. Compos. Pt. B Eng. 30, 205 217. Zhang, J.S., Cai, W., Ren, X.B., Otsuka, K., Asai, M., 1999. The Nature of Reversible Change in M S Temperatures of Ti Ni Alloys with Alternating Aging. Mater. Trans. JIM 40, 1367 1375. Zhang, R. X., Ni, Q. Q., Masuda, A., Yamamura, T., Iwamoto, M., 2006. Vibration Characteristics of Laminated Composite Plates with Embedded Shape Memory Alloys. Composite Structures 74, 389 398. Zhang, W., Kim, J.M., Koratkar, N., 2003. Energy Absorbent Composites Featuring Embedded Shape Memory Alloys. Smart Materials & Structures 12, 642 646. Zhang, X., Gubbels, G.H.M., Terpstra, R.A., Metselaar, R., 1997. Toughening of Calcium Hydroxyapatite with Silver Particles. J. Mater. Sci. 32, 235 243. Zhou, L.M., Kim, J.K., Mai, Y.W., 1992. On the Single Fiber Pull out Problem Effect of Loading Method. Composites Science and Technology 45, 153 160.

PAGE 208

208 Zhu, X. K., Joyce, J.A., 2012. Review of Fracture Toughness (G, K, J, Ctod, Ctoa) Testing and Standardization. Engineering Fracture Mechanics 85, 1 46. Zhu, Y.T., Beyerlein, I.J., 2002. Bone Shaped Short Fiber Composites an Overview. Mater. Sci. Eng. A Struct Mater. Prop. Microstruct. Process. 326, 208 227.

PAGE 209

209 BIOGRAPHICAL SKETCH Fatmata Barrie was born in Washington, D.C. Her parents are Nancy Kargbo and Sarjoh Barrie both of whom were born in Sierra Leone. She was raised in Alexandria, Virginia where she attended elementary, middle, and high school. Upon completion of high school, Fatmata attended Carnegie Mellon University in Pittsburgh, PA. There she majored in m echanical e ngineering and during her second semester decided to pursue an additional major of International Relations focusing on Africa and Russia. After graduating from Carnegie Mellon, Fatmata then attended Texas A&M University, where she earned a Master of Science from the Mechanical Engineering Department. She completed her thesis entitle d Effects of Constrained Aging on the Shape Memory Response of Nickel Rich NiTi Shape Memory Alloys under the guidance of Dr. Ibrahim Karaman.


xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E158BCSTU_YKNL7B INGEST_TIME 2014-05-13T21:26:30Z PACKAGE UFE0045416_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES