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Relating Interfacial Fracture Toughness to Core Thickness in Honeycomb-Core Sandwich Composites

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RELATING INTERFACIAL FRACTURE TOUGHNESS TO CORE THICKNESS IN HONEYCOMB-CORE SANDWICH COMPOSITES By DAVID GRAU A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2003

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Copyright 2003 By David Grau

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ACKNOWLEDGMENTS I would like to thank my advisor, sponsor, and friend (Dr. B. V. Sankar). Without his support and guidance, the work presented in this thesis would not have been possible. I would also like to thank all of my colleagues at the Center for Advanced Composites, for their help and support throughout my research and experience at the University of Florida. iii

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TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iii LIST OF TABLES.............................................................................................................vi LIST OF FIGURES.........................................................................................................viii ABSTRACT.......................................................................................................................x i CHAPTER 1 INTRODUCTION.....................................................................................................1 Background Information............................................................................................1 Literature Survey.......................................................................................................2 Scope of the Thesis....................................................................................................4 2 BACKGROUND........................................................................................................ 6 Theory........................................................................................................................ 6 Failure......................................................................................................................1 2 3 LITERATURE REVIEW.........................................................................................1 4 4 EXPERIMENTAL SETUP.......................................................................................1 7 Experimental Technique..........................................................................................1 7 Specimen Preparation.............................................................................................. 18 5 FRACTURE TESTS................................................................................................. 25 Predictions................................................................................................................ 25 Testing and Discussion............................................................................................2 7 6 FINITE ELEMENT ANALYSIS.............................................................................3 6 Concept....................................................................................................................3 6 Model Design...........................................................................................................3 6 iv

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Analysis....................................................................................................................4 0 Conclusions..............................................................................................................4 5 7 CONCLUSION.........................................................................................................4 8 APPENDIX A MATERIAL SPECIFICATIONS AND INFORMATION......................................5 1 B TORAY COMPOSITES CURE CYCLE FOR LAMINATES...............................5 2 C LOADING GRAPHS...............................................................................................5 3 D OUTLIER INVESTIGATION.................................................................................6 4 E CRITICAL FRACTURE TOUGHNESS VS. CORE THICKNESS PLOTS.......... 66 F CRACK TIP (MODE MIXITY) CALCULATIONS...............................................7 0 REFERENCE LIST..........................................................................................................7 5 BIOGRAPHICAL SKETCH............................................................................................76 v

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LIST OF TABLES Table page 5-1 Double cantilever beam test results for all core thicknesses................................. 30 5-2 Average fracture toughness (Gc) values for all points designated by core thickness (hc). ....................................................................................................................... 31 5-3 Average GcI values for all core thicknesses.......................................................... 33 5-4 Average values for Gc (lb/in) based on cycle/crack length and core thickness; slope relation for Gc's and core thicknesses.......................................................... 34 5-5 Percentage change of average Gc values from smallest core thickness................ 34 6-1 Material properties used in finite element (FE) analysis. ..................................... 37 6-2 Critical loads and corr esponding deflections for experimental specimens used in finite element analysis........................................................................................... 40 6-3 Crack length and related deflection for finite element models ............................. 40 6-4 Gc calculation using specimen deflection and applied load.................................. 42 6-5 Experimental and finite element Gc values and finite element mode mixity........ 43 6-6 Mode mixity for geometry of four different specimens........................................ 46 D-1 Statistical analysis on Gc values with outlier analysis for 1 inch core..................64 D-2 Statistical analysis on Gc values with outlier analysis for 0.5 inch core............... 65 D-3 Statistical analysis on Gc values with outlier analysis for 0.375 inch core........... 65 D-4 Statistical analysis on Gc values with outlier analysis for 0.25 inch core.............65 E-1 Average values for Gc based on cycle/crack length and core thickness; slope relation for Gc's and core thicknesses................................................................... 66 F-1 Sample of verification of crack tip stresses for 0.25 inch core............................. 70 vi

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F-2 Sample of calculation of stress intensity factors (KI and KII) for 0.25 inch core..72 F-3 Sample of mode mixity calculation from KI and KII for 0.25 inch core................74 vii

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LIST OF FIGURES Figure page 1-1 Typical sandwich construction. .............................................................................. 3 1-2 Typical celled core types. ....................................................................................... 3 2-1. Loading modes......................................................................................................10 4-1 Double cantilever beam (DCB) loading. .............................................................. 18 4-2 Example of a load vs. displacement graph in a DCB test..................................... 19 4-3 Facesheet delamination of a three layer unidirectional sandwich with bottom layer parallel to the crack............................................................................................... 20 4-4 Vacuum bag lay-up diagram................................................................................. 21 4-5 Vacuum bag lay-up before (right) and after (left) the vacuum bag is sealed. ...... 22 4-6 Autoclave before a sandwich cure cycle is run..................................................... 23 4-7 Typical specimen under loading conditions. ........................................................ 24 5-1 MTI testing machine with setup. .......................................................................... 28 5-2 Core propagation pictures..................................................................................... 29 5-3 Gc vs. hc plot for all Gc values and core thicknesses............................................. 31 5-4 Gc vs. estimated crack length for all data points................................................... 32 5-5 Plot of GcI vs. hc with averages and linear trend line............................................ 33 6-1 A DCB specimen model indicating boundary conditions (0.5 inch core)............ 38 6-2 Crack tip mesh refinement in all models. ............................................................. 39 6-3 Gc values for experimental and FE results............................................................ 42 viii

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6-4 Mode mixity from FE results................................................................................ 43 6-5 Mode mixity from FE results neglecting 0.25 inch core. ..................................... 44 6-6 Mode mixity from FE model. ............................................................................... 45 6-7 Mode mixity from FE model for same crack length and same load..................... 46 6-8 Mode mixity vs. Gc for FE and experimental Gc result........................................ 46 6-9 Mode mixity vs. Gc for all experimental Gc......................................................... 47 B-1 Toray Composites cure cycle for composite laminates. ....................................... 52 C-1 Load-displacement diagram for DCB01_1........................................................... 54 C-2 Load-displacement diagram for DCB02_1........................................................... 54 C-3 Load-displacement diagram for DCB03_1........................................................... 55 C-4 Load-displacement diagram for DCB04_1........................................................... 55 C-5 Load-displacement diagram for DCB05_1........................................................... 56 C-6 Load-displacement diagram for DCB01_0.5........................................................ 56 C-7 Load-displacement diagram for DCB02_0.5........................................................ 57 C-8 Load-displacement diagram for DCB03_0.5........................................................ 57 C-9 Load-displacement diagram for DCB04_0.5........................................................ 58 C-10 Load-displacement diagram for DCB05_0.5........................................................ 58 C-11 Load-displacement diagram for DCB01_0.375.................................................... 59 C-12 Load-displacement diagram for DCB02_0.375.................................................... 59 C-13 Load-displacement diagram for DCB03_0.375.................................................... 60 C-14 Load-displacement diagram for DCB04_0.375.................................................... 60 C-15 Load-displacement diagram for DCB05_0.375.................................................... 61 C-16 Load-displacement diagram for DCB01_0.25...................................................... 61 ix

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C-17 Load-displacement diagram for DCB02_0.25...................................................... 62 C-18 Load-displacement diagram for DCB03_0.25...................................................... 62 C-19 Load-displacement diagram for DCB04_0.25...................................................... 63 C-20 Load-displacement diagram for DCB05_0.25...................................................... 63 E-1 GcI vs. hc plot with linear fit to averages............................................................... 67 E-2 Gc2 vs. hc plot with linear fit to averages.............................................................. 67 E-3 Gc3 vs. hc plot with linear fit to averages.............................................................. 68 E-4 Gc4 vs. hc plot with linear fit to averages.............................................................. 68 E-5 Gc2, Gc3, Gc4 vs. hc plot with linear fit to averages............................................... 69 E-6 All Gc vs. hc plot with linear fit to averages......................................................... 69 F-1 Log S22 vs. Log r for 0.25 inch core...................................................................... 71 F-2 Log S12 vs. Log r for 0.25 inch core...................................................................... 71 F-3 KI vs. r for 0.25 inch core...................................................................................... 73 F-4 KII vs. r for 0.25 inch core..................................................................................... 73 x

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Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science RELATING INTERFACIAL FRACTURE TOUGHNESS TO CORE THICKNESS IN HONEYCOMB-CORE SANDWICH COMPOSITES By David Grau December 2003 Chair: Bhavani V. Sankar Major Department: Mechanical and Aerospace Engineering The research presented in this thesis is an effort to better understand the failure phenomenon in sandwich composites (specifically, a honeycomb core with laminated carbon/epoxy composite facesheets). A double cantilever beam experiment was designed and conducted for four different core thicknesses to determine a relationship between core thickness and interfacial fracture toughness. Relationships between fracture toughness and crack length were also explored. Finally, finite element modeling was performed to determine the effect of mode mixity on the interfacial fracture toughness of the sandwich composite. It is inferred that the increase in fracture toughness with the increase in core thickness is attributed to the change in mode mixity. xi

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CHAPTER 1 INTRODUCTION Background Information The aerospace, automobile, and marine transportation industries are constantly trying to refine construction and repair techniques for more efficient, less expensive, lightweight and safer structures. In doing so, new materials and procedures are regularly being invented that are not completely understood. Research must be conducted to determine how effective and safe a new design, technique, or idea is for future use. The present study concerns with one such concept for efficient structural design. For many years, sandwich composites have been used in various structures, although their fracture and failure behavior are not fully understood. Because of their low weight and high stiffness characteristics, sandwich composites are becoming more common in many structural applications. Research has been conducted to better understand their behavior and limitations. This study aimed to further understand the failure phenomena of sandwich composites constructed from carbon fiber/epoxy composite face sheets and Nomex honeycomb cores. To achieve this, the effect of core thickness on the interfacial fracture toughness of a honeycomb core sandwich composite was studied. The method used to characterize fracture toughness, techniques used and results are discussed in detail. 1

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2 Literature Survey Sandwich panels have been used in building construction for well over a hundred years. In 1849, Fairbairn [1] was first to document the idea of a sandwich composite. The concept of a sandwich is to have the facesheet (also known as the skin) absorb or withstand most of the bending load (or in plane loading); while the core absorbs most of the shear load. Individually, the components of the sandwich structure can be thought of as relatively weak; but together, the properties of a sandwich are typically superior to those of a solid of the same weight. The design of a sandwich composite allows for high stiffness and moment of inertia, while keeping structural weight to a minimum. An example of a basic sandwich using a honeycomb core is given in Figure 1-1. Because of the ability of the skin to carry a large load and the ability of the core to stabilize the construction of the sandwich, various material combinations have been tried together in an effort to optimize the physical properties of the sandwich. Paired materials for sandwich construction range from balsa wood and fiberglass to graphite and Nomex honeycomb. In the 1940s, advancements in adhesive rheology (flow during cure) allowed for a new type of sandwich to be fabricated [2]. Because new adhesives can remain on the cell edges of either a porous core or a celled core (such as honeycomb), sandwiches with superior strength-to-weight ratios could be constructed. Thus the celled hollow-core sandwich was born. Over the years, many types of celled-core/facesheet combinations were tested for optimum properties. Aluminum alloys, fiberglass/phenolic weaves, and Nomex/phenolic weaves were all tested as core materials; while graphite, fiberglass, aluminum, and plastic were used as typical facesheets. The typical celled-core

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3 configurations offered by Hexcel Composites [3] (Atlanta, GA, a major supplier of Honeycomb Material) are shown in Figure 1-2 and they include the Hexagonal, OX-CoreTM, Flex-Core, Tube-Core, reinforced hexagon, and Double-FlexTM designs. Figure 1-1. Typical sandwich construction. Figure 1-2. Typical celled core types. http://www.hexcelcomposites.com/Markets/ Products/Honeycomb/Hexweb_attrib/hw_p04.htm Hexcel Corporation, Accessed November 2003.

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4 The facesheet/core combination using a Nomex honeycomb core and a carbon fiber (graphite) facesheet is highly effective. This sandwich is common and is widely used in the aerospace industry to reduce the weight of aircraft and satellite components. Wings, floor decks, internal cabin components, and the main hull of aircrafts are common places where the Nomex core/carbon fiber facesheet sandwich composite is being used in airplane construction. This combination of facesheet and core material is likely the most common pair in the industry at this time; and is the topic of the present study. Other industries are also looking into practical uses for lightweight high-strength sandwich composites. Probably the most common secondary and tertiary markets for sandwich construction are railroad train companies and the marine industry. The railroads are making trains lighter by using composites for floor and ceiling panels; while the same idea being held by the U.S. Navy, will use composites for decking and bulkheads. Other common uses for composite materials include use in sailboats, race boats, racecars, and sporting goods. For instance, sporting goods manufacturers are looking into using composite in skis, kayaks, canoes, pool tables, and even platform tennis paddles. Scope of the Thesis In sandwich composites, small delaminations between the core and facesheet are sometimes inherent in a fabricated specimen. Delaminations can also be produced in composites after fabrication because of impact damage and thermal stresses within the composite. With the delamination comes a reduction in the strength of the sandwich composite. A delaminations effect on a composite must be understood if one is to repair or improve the strength of the composite before use. My aim was to create a better

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5 understanding of interfacial properties and failure due to a debond between the facesheet and core in sandwich composites. The organization of this thesis is as follows. First, a brief background of the theory associated with composite sandwiches and their failure are given. Then previous research is reviewed to promote a better understanding of failure in sandwich composites. Then the technique developed for testing interfacial fracture toughness in a sandwich composite is explained in detail. Then the tests conducted to characterize the interface properties of several core thicknesses of a composite sandwich are described. Finally, the finite element verification and analysis conducted on several experimental samples are discussed.

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CHAPTER 2 BACKGROUND Theory Because the use of sandwich composites is well established in many structural applications, they will likely remain a feasible option for reducing weight and retaining stiffness and strength. Therefore we must understand the failure phenomena; and how to prevent failure in composites structures during fabrication, service and after repair. To determine if a material will fail under a given loading condition typically the stress state in the material is analyzed. Stress is defined as load over applied area. The general equation for stress is PA (2-1) where P is the applied load, A is the cross sectional area (typically perpendicular to the load for normal stress and parallel for shear stress), and is the calculated stress [4]. A typical failure property that would be looked at in mechanics is the strength of a material, which is based on the material itself and can be either the ultimate stress or the yield stress. However, when a crack or interface is concerned we are not talking about the yielding of a material in a conventional way, but instead the separation of the molecules that make up the interface via localized stresses. Experimentation will show that the onset of crack propagation will not occur at the theoretical estimates suggested by atomic level calculations. It will typically occur below the theoretical value. This is caused by [5] a magnification of stresses in the area of the crack and is called stress concentration. The 6

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7 foundation of most modern fracture mechanics is based on this concept. In order to predict failure correctly the stress intensity factor K I (SIF) has to be calculated and compared to the material property called critical stress intensity factor, K Ic Using this parameter (K I ) we can completely understand the stress field in a linear elastic material in the vicinity of a crack tip. For instance, the relationship between stress and the stress intensity factor for an infinite flat plate with a crack length of 2a subject to a remote tensile stress is aKI (2-2) where K I is the stress intensity factor, is the tensile stress, and a is one half of the total crack length [5]. With the onset of failure during experimentation the critical stress intensity factor can be calculated (i.e., K I =K Ic ) at failure. So basically, K Ic is a measure of fracture toughness, which is a material property, which is independent of the crack size or specimen size, in general. Griffith proposed another way to characterize failure [5]. He proposed that crack extension occurs when the available energy for crack growth is sufficient to overcome the resistance or bond strength of the material [5] (i.e., for an incremental increase in crack area dA) 0 dAdWsdAddAdE (2-3) where E is the total energy, is the potential energy supplied by the internal strain energy and external forces, and Ws is the work required to create new surfaces. With Griffiths theories in hand G.R. Irwin developed the present day version of Griffiths energy methods [5]. Irwin proposed the concept energy release rate G,

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8 dAdG (2-4) which is defined as the rate of change in potential energy with crack area for a linear elastic material. Again, at failure G = G c the critical energy release rate or more commonly known as the fracture toughness. Now as a comparison of K Ic and G c one imagines the flat plate with a crack length of 2a subject to a remote tensile stress. The energy release rate is given as EaG2 (2-5) where E is the modulus of elasticity, is the tensile stress, a is one half the crack length, and G is the energy release rate [5]. We can see that both Equations 2-2 and 2-5 are related and with a little manipulation we can get the plane stress equation EKGI2 (2-6) So with this relationship we gain a relationship for G c and K Ic as well and an understanding of the relationships between energy conservation, fracture toughness, and stress intensity factor is realized. Using the above equations it is possible to accurately predict, when and how a crack will propagate in a given material. To fully grasp the concepts behind this research it is necessary to understand how a material stores energy when deformed. Strain () is defined as the deformation per unit length of a given material [4]. If length is given as L and deformation is given as then the strain in a linear setting can be found from Equation 2-7. L (2-7)

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9 The well known relation between stress and strain is Hookes law and is given in Equation 2-8 for one dimension. Where is the stress, E is the elastic modulus, and is the strain of a given material. For the three dimensional case Hookes law becomes Equation 2-9, where C 11 through C 66 are called elastic coefficients [6]. Equation 2-9 is the most general three dimensional case of Hookes law and is used for anisotropic materials. More specific equations for Hookes law have been developed for isotropic and orthotropic materials and can be found in reference material. E (2-8) yzxzxyzzyyxxyzyzxzxyzzyyxxxzyzxzxyzzyyxxxyyzxzxyzzyyxxzzyzxzxyzzyyxxyyyzxzxyzzyyxxxxCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC666564636261565554535251464544434241363534333231262524232221161514332211 (2-9) When a material is strained some work is done on the material to create the deformation. If the material does not yield, the energy from the work is stored within the material and is called the Strain Energy (U). This concept is better understood by picturing a rubber band (or a spring). When a tensile load P is applied to a rubber band the band stretches/deforms a length x 1 storing energy. When the band is returned to the original length the energy is released. The strain energy stored while the band was in tension can be calculated from Equation 2-10. Where is the stress, is the strain, and V is the volume of the band. 12U V (2-10)

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10 Now for clarification and completeness it is necessary to understand the differences in loading modes and how they are identified. There are three loading modes; Mode I, Mode II and Mode III. Figure 2-2 shows examples of how each mode would be loaded. Mode I is dominated by an opening load, Mode II is dominated by an in plane shearing load, and Mode III is dominated by an out of plane shear [5]. Figure 2-1. Loading modes. Typically, stress intensity factors will be denoted with a subscript, I, II, or III, indicating the loading condition. For example, the mode I and mode II singular stress fields in an isotropic material in the vicinity of the crack are rKIYYXX2 (2-11) 2IIXYYXKr where XX and YY are the normal stresses, XY is the shear stress in the xy plane, r is the distance from the crack tip, and K I and K II are the stress intensity factors for their respective loading conditions [5]. Mixed mode conditions are possible when two or more loading conditions are present. Generally, in any bulk material a crack will propagate in the direction that minimizes the mode II component of loading [5]. However, in constrained or interfacial

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11 loading, the crack can propagate such that the mode I and mode II components are both significant. It should be noted that the double cantilever beam (DCB, explained later) test is usually performed in Mode I fracture studies. For mixed mode loading the energy release rate becomes a function of all of the present loading conditions and can be calculated using '2'2'22IIIIIIKEKEKG (2-12) again assuming a planar crack remains planer and constant shape [5]. In the above equation for the cases of plane strain and plane stress we use the same equation, but assume E E for plane stress '21EE for plane strain Mixed-mode conditions are quantified by a mode mixity phase angle (Equation 2-13), which is 0 for pure mode I and 90 for pure mode II. Understanding the mode mixity of a loading condition is important because of its effects on crack propagation. IIIKK1tan (2-13) A crack in pure mode II loading commonly requires several times as much energy as a crack propagated under pure mode I loading [5]. Therefore, it becomes necessary to identify the mode mixity of an experimental setup in order to thoroughly understand results.

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12 Failure A large amount of research has been conducted to gain a better idea as to how and why failure, specifically interfacial failure, occurs in sandwich composites. A sandwich structure is considered to have failed when it can no longer sustain a usable load (i.e., it can no longer bare the required load in either bending or axial loading). This typically occurs when a face sheet is separated from the core and is simply known as interfacial failure. Interfacial failure on a small scale between the core and the facesheet is common in sandwich structures and can be the result of many factors. Johannsen cites the main causes of interfacial failure during manufacturing are: voids in cored laminates, resin drainage, excess roller pressure, lack of bonding resin, excess vacuum bag pressure, under cured skins, and resin rich skins [7]. Damage introduced after fabrication can also result in an interfacial failure. Examples of damage to a sandwich panel include: Impacts to the sandwich structure such as dropped tools on the top of an airplane wing; forklifts, trucks, or even other airplanes running into an airplane; maintenance crews walking on non-step locations of the airplane; environmental conditions can such as thermal stress cracking and moisture cracking can also lead to interfacial failure [2]. With such a vast array of possibilities to cause an interfacial failure it is important to understand the effect such a flaw can have on a composite. To further understand the effects an extreme interfacial failure can have on sandwich composites we consider a deck of playing cards. When the cards are loose and not bonded together and the deck is bent the cards can slide alongside one another and the average person can bend the deck. However, if the entire deck of cards are bonded to one another and the deck is bent the cards cannot slide and therefore the deck becomes

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13 extremely stiff, like a solid block, and if at all, will only flex a little. The average human could not possibly bend the deck when the cards have been bonded. This example is the concept behind a sandwich composite. When the face to core interface is failed the core, with low bending modulus, loses its ability to use the face sheets to resist bending and therefore the composite loses most of its strength. A better understanding of how the failure will act after it is already present will allow engineers to determine whether an interfacial failure is mild or catastrophic. As another example, consider an interfacial delamination on the wing of an airplane resulting from a tool being dropped by a maintenance worker. The damage will have to be evaluated to determine whether a repair is necessary before the airplane can take flight. The repairing engineer knowing the fracture toughness of the material can use the typical loading on the wing to determine the correct path to take for either repair of the wing or clearing the airplane for safe flight. This thesis will allow for a better understanding of failure surrounding the crack tip. Specifically, the mode mixity and critical fracture toughness of a sandwich composite currently in use will be determined. This will no doubt aid in determining how to designate, fabricate, and repair composite sandwiches for use.

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CHAPTER 3 LITERATURE REVIEW Ural, Zehnder, and Ingraffea [8] performed tests using a double cantilever beam to evaluate the adhesive bond in honeycomb sandwich panels. The materials used were 24 and 32 ply carbon fiber composite face sheets with either a polyimide carbon fiber matrix composite or a titanium core. Various configurations of face sheet thickness and core materials were tested and proved to indicate that fracture toughness varied among all of the configurations. Further testing was conducted to determine whether the lay-up process (i.e., originating the crack on either the bag or tool sides), affects the fracture toughness of a sandwich composite. Since during the curing process resin tends to flow with gravity, the tool side of a composite generally contains more adhesive than the bagging side. Therefore, it is likely that depending on which side of the sandwich a delamination occurs the fracture toughness will vary. The conclusions were found to support this idea in that the fracture toughness differed according to which side of the panel was tested, whether the bag side was tested or the tool side. The results for which side had higher fracture toughness differed depending on face sheet thickness. So, Ural, et al. [8] found that face sheet thickness, core material, and the side of an interface failure all affect the fracture toughness of a honeycomb sandwich composite. Other experimental research was conducted by Carlsson and Viana [9] on varying densities and thicknesses of PVC foam core sandwiches using glass/vinylester, glass/polyester, and 6061-T6 aluminum face sheets. Experiments using tilted sandwich 14

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15 debond specimens (similar to DCB) was conducted to determine the effect of the core thickness and density on fracture toughness. To determine the effect of core thickness on fracture toughness the core thickness of two different core densities was varied from 2 mm to 15 mm. Each core was tested with standard thickness aluminum face sheets. The fracture toughness was found to increase as core thickness decreased and approach a constant value for larger core thicknesses. It should be noted that after reviewing the data for these experiments it is clear that further testing should have been conducted with thicker cores to determine whether the fracture toughness indeed approaches a constant. The effect of foam density on fracture toughness was tested using cores of five different densities. As the density of the foam increased it was found to increase the fracture toughness, which was noted to be independent of face sheet thickness. The results show that for PVC foam cores with varying face sheet materials, both density and core thickness play individual roles when determining fracture toughness. Much research has been conducted on honeycomb sandwich composites with carbon fiber face sheets in past years. One such researcher was Avery [10], who conducted DCB tests similar to that which will be used in this literature. Using a factorial test plan, Avery found general trends for fracture toughness as a function of facesheet thickness, core density, core thickness, and crack direction relative to the honeycomb core. An average of five specimens for a given combination was tested. DCB specimens ranged in core thickness, facesheet thickness, core density, and core direction (Figure 1-2). Experimentation determined several general trends for fracture toughness. Fracture toughness was found to increase with thicker facesheets and decreased with higher core densities. Fracture was also found dependent on crack direction relative to the core. With

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16 thicker cores, depending on the crack direction, fracture toughness was found to increase in the W-direction and decrease in the L-direction. It is on the basis of Averys findings that it was felt that further research should be done to quantify and show that core thickness does indeed affect fracture toughness for honeycomb composites. Understanding the different findings of Carlsson/Vianas and Averys research relating face-sheet thickness to fracture toughness, the idea that core material plays a large role in the properties of a sandwich is proven. Therefore, the findings that Carlsson and Viana showed for the fracture toughness of foam cores can only be used with those cores, and not assumed to be constant for all other core material of the same thickness. After reading the above information it is clear that fracture toughness is a function of the materials used and their configuration. However, the question still stands for a given specimen configuration is it possible to quantify fracture toughness? And, if so, can we relate that value to other specimens? Specifically, if a value of fracture toughness is proven for a specific core thickness in a standard composite configuration can we relate this value to other core thicknesses of the same material configuration? The following chapters will show that not only can critical fracture toughness be quantified for a particular specimen configuration, but there are trends that relate core thickness to fracture toughness. Furthermore, mode mixity is found to be quantifiable for certain core thicknesses and is shown related to changes in critical fracture toughness.

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CHAPTER 4 EXPERIMENTAL SETUP Experimental Technique In order to calculate the fracture toughness of an interface, an accurate experimental technique should be used. Various experimental configurations were reviewed which included the following tests: double cantilever beam, drum peel, and four point bending. After some consideration the double cantilever beam (DCB) test was chosen for determining the interfacial fracture toughness of the sandwich composite due to the ease of the test and its relatively high accuracy. ASTM standard D5528 describes in detail how to calculate the fracture toughness of a unidirectional fiber material using the DCB method. Experimental procedures presented in this thesis utilized a double cantilever beam comprised of layered carbon fiber composite facesheets bonded to a Nomex honeycomb core. Therefore the ASTM standard could not be used exactly as it was published for the unidirectional fiber composite. However, it was felt that the techniques described in the ASTM standard could be used as a guide for designing an experimental setup. In principle the DCB test is quite simple. A specimen is prepared with an initial crack of length a within the interface, where the fracture toughness is of interest. The specimen is then placed in a loading fixture created specifically for the DCB test. Loading of the specimen occurs such that the surfaces lying on the interface are separated as shown in Figure 4-1. 17

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18 Figure 4-1. Double cantilever beam (DCB) loading. The load and the corresponding displacement are recorded and the crack is allowed to propagate a given length a. Finally, the specimen is allowed to return to an unloaded state. Using a load/displacement graph (Figure 4-2) and the crack propagation length, the energy required for propagating the crack a given length and therefore the fracture toughness of the interface can be calculated. The fracture toughness, G c also known as the critical strain energy release rate is given by CUG B a (4-1) where U is the energy or work (area under the load vs. displacement curve) required to propagate the crack, B is the specimens width, and a is the crack extension length [10]. Specimen Preparation All specimens where fabricated using a Toray Composites unidirectional carbon fiber prepreg as a face sheet material (material designation A50TF266 S6 Class E, Fiber designation T800HB-12K-40B, matrix 3631) and a Euro-Composites aramid fiber ECA type honeycomb (1/8 inch cell size; 4 pcf density; 3 mil wall thickness; 1 in, 0.5 in, 0.375 in, and 0.25 in core thicknesses) for the core. An 8 inch 9-3/4 inch sandwich panel was

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19 constructed for all core thicknesses and was cut using a wet diamond saw to make individual 1 inch 7.5 inch specimens. Loading blocks were then super-glued to the specimens to finish the assembly. The process is described below in detail. Force displacement0246810121400.10.20.30.4Displacement (in)Force (lb) Figure 4-2. Example of a load vs. displacement graph in a DCB test. First, a lay-up for the composite sandwich was selected. Typically, an adhesive layer is place between the facesheet and the core (Figure 1-1) during a co-cure cycle to promote better adhesion. However, due to the properties of the prepreg material (typically prepreg contains 40% resin/adhesive) it was decided that a direct lay of the prepreg onto the top of the honeycomb core would provide sufficient bonding strength. Verification of this design was conducted by contacting a Hexel Composites representative who agreed that the direct bonding method would likely work. Next, a sequence for laying the unidirectional fiber within the facesheet was selected. Several experiments were conducted to find the minimum number of plies a specimen could have, yet be stiff enough to allow for separation from the core. Specimens with symmetric 3, 5, and 7 ply facesheets were all tested. An example of the

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20 low stiffness of a three-layer specimen can be seen in Figure 4-3. The optimum number of plies was found to be 7, layered in a (0,90,0,90,0,90,0) configuration. It is necessary to note that when layering unidirectional fiber the lay-up should be symmetric. If the layering for a facesheet is not symmetric residual stresses will be present after curing that will likely result in warping of the sandwich panel. Also, when testing for interfacial strength on a unidirectional fiber system the layer of unidirectional fiber in contact with the core should be perpendicular to the crack direction. A fiber laid on the core, parallel to the crack, will likely result in a delamination between the layers of the facesheet, as shown in Figure 4-3, and therefore will not predict the interfacial fracture toughness accurately. Figure 4-3. Facesheet delamination of a three layer unidirectional sandwich with bottom layer parallel to the crack. Vacuum bagging was chosen as the system for applying vacuum/pressure to the composite during the cure cycle. The lay-up sequence is as follows: A 3/8 in sheet of aluminum is used as a base tool; a Non-porous Teflon film (PTFE) is placed on top of the tool to release the sandwich after the cure cycle; a 7 ply (0,90,0,90,0,90,0) facesheet is

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21 laid as the bottom side of the sandwich; then a Nomex honeycomb core with a designated thickness of either 1 in, 0.5 in, 0.375 in or 0.25 in is placed atop the bottom facesheet; a strip of PTFE is used to create the artificial crack between the core and the top facesheet; then another 7 ply (0,90,0,90,0,90,0) facesheet is used on top of the core/PTFE strip; a PTFE sheet is placed over top of the sandwich; finally a breather material is laid atop the other components to allow for adequate air evacuation during the vacuum process. Around the top border of the aluminum a bag sealant is laid and a bag is pressed over the sealant. A vacuum plug is installed in the bag material near the edge of the tool to ensure it does not affect the sandwich. Figure 4-4 shows the schematic of the lay-up design without the vacuum plug. Figure 4-5, shows an actual lay-up before and after the vacuum bag is sealed. All of the material and its suppliers are documented in Appendix A. It is necessary to note that the release film used is not porous and therefore will not allow any excess epoxy to flow from the prepreg to the breather. This lay-up design requires all of the epoxy to remain in the sandwich to ensure adequate bond strength. Figure 4-4. Vacuum bag lay-up diagram. Finally, a procedure for curing the sandwich was explored. Several methods for fabricating the necessary sandwiches were attempted before a working method was established. Using an autoclave Toray Composites recommends the cure cycle described

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22 in Appendix B for composite laminates. The process involves vacuuming the bag down to 22 inches of Hg, gradually applying pressure to 20 psig, venting the bag and continuing to pressurize the autoclave until the pressure reaches 85 psig, then curing the sandwiches at 355F for a designated period of time. Figure 4-5. Vacuum bag lay-up before (right) and after (left) the vacuum bag is sealed. However, when this method was used to create the sandwich panels described above the pressure crushed the cores in the in-plane directions (L or W direction, Figure 1-1). After further discussion with Toray representatives the pressure was reduced to 45 psig and the fabrication was tried once more. Again, the core could not sustain the excess pressure. A means of reinforcing the core via a wooden dam with the same thickness as the sandwich was utilized, but was found to hinder more than help. The top facesheet did not bond sufficiently to the core and the edges were completely delaminated. Realizing that when creating a sandwich composite the core cannot sustain any force or pressure in the L or W direction the Toray cure cycle was used but with no pressure and a nominal vacuum of 23 psig Using only a vacuum, a sandwich composite with sufficient adhesion between the facesheets and core was created. It should be noted that further experimentation was conducted to evaluate whether any pressure (1-5 psig) could be

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23 applied to the sandwich. The results determined that for a 1 inch core no pressure could be used, but with the thinner cores (0.25 inch and 0.375 inch) the core crushing was minimal. However, for all of the experimentation documented in this literature the cure cycle in Appendix B was used with no autoclave pressure. Figure 4-6, shows the autoclave with a lay-up inserted before the cure cycle has begun. Figure 4-6. Autoclave before a sandwich cure cycle is run. After the autoclave cycle was complete the cured sandwich panel is removed from the autoclave and allowed to cool to room temperature. Using an MK diamond MK270 wet tile cutter the 8 in by 9 3/4 in sandwich panel is cut into strips of 7.5 inches in length and 1 inch in width nominally. All specimens are cut resulting in an initial 1 inch crack in the length direction. Specimens are then allowed two days drying time before they are sanded and super-glued to loading blocks. The loading blocks are cut from a rectangular steel rod and result in the dimensions 1.1 in (L) 0.8 in (W) 0.6 in (T). A 3/8 in hole is drilled through the center of each loading block to allow for insertion of a loading pin. Great care is taken when mounting the loading blocks to ensure symmetry of the specimen. Finally, the width (B) of each specimen is averaged over the length using three measurements. A photo of an actual specimen under loading conditions is given in Figure

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24 4-7. For each specimen the average distance from the center of load application, or the center of the loading pin, to the crack tip is found to be 0.95 inch. Figure 4-7. Typical specimen under loading conditions.

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CHAPTER 5 FRACTURE TESTS Predictions As explained previously when a material is strained, energy is stored in the form of strain energy. It is this concept, which gives rise to an idea that varying core thickness should affect the fracture toughness of sandwich composites. Cores with the same cross sectional area, same applied load, yet different core thicknesses will have the same stress and therefore the same strain via Hookes Law. However, from Equation 2-7 for the calculation of strain we see the difference in core thickness will result in different deformation lengths of the core. Using Equation 2-9 we then realize the strain energy stored in the cores will be larger for larger cores. To explain how the strain energy difference will affect the fracture toughness imagine the sandwich composite as two facesheets connected by springs in place of the honeycomb core. During a DCB test the springs will be loaded and stretched, therefore storing energy just as the honeycomb core would. Now, as an interface crack would propagate a length a when the critical load is reached, we picture a spring losing contact with the face sheet. When this happens the energy that was stored in the spring is lost or thought of as energy used to propagate the crack. With this concept we see that by varying core thickness (spring length) or by the same means strain energy, the value of fracture toughness should also vary. 25

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26 There are also other factors possibly affecting the fracture toughness while changing the core thickness. When the core is co-cured with the prepreg facesheets, the resin in the prepreg is used as an adhesive. This can cause several differences among specimens in itself: excess resin can bond to the inside of the core changing the cross sectional area, the stress (strain), and therefore the strain energy; Excess resin can reinforce the interface via small fillets between the core and the facesheet and force the crack to propagate within the core; Resin can spread thinly over the interface and reduce bond strength. However, the above are all properties introduced due to the difference in core thickness and therefore are under investigation as a direct result of changing core thickness. Understanding the role stress concentration plays when considering fracture toughness will also aid in analyzing the data acquired during experimentation. When fabricating the test specimens the initial crack tip will likely look and react different then all sequential cracks. The details of this theory will not be explained here, however, the reader should understand that when making an artificial crack the radius of the crack tip can only be proportionally equal to the thickness of the material used to prohibit bonding within the crack. A natural crack can have a crack tip radius on the order of atomic dimensions. Therefore, how the crack tip was formed will affect the stress concentration and in turn the fracture toughness. We expect to see non-agreement in the results from the first crack propagation (initiation) when compared to that of sequential crack propagations (natural). In the same sense the second, third and fourth crack propagations should be comparable in G c changes over all core thicknesses.

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27 With the above reasons it is obvious that by varying the core thickness of a sandwich composite the fracture toughness of the interface should vary as well. However, with the long list of factors affecting the fracture toughness of the sandwich it is impossible to accurately estimate the effect of core thickness and therefore testing is necessary. Testing and Discussion All testing was conducted on a 12,000 lb refurbished MTI Phoenix machine with a 5,000 lb interface load cell. Calibration/Verification of both the displacement of the MTI machine and the load detection of the load cell was conducted prior to testing. The MTI test machine and Interface load cell (bottom/blue) are shown in Figure 5-1, with a typical DCB test setup. As stated before, four specimen core thicknesses (h c ) were tested, 1/4 in; 3/8 in; 1/2 in; and 1 inch. The crosshead deflection rate was kept at a constant rate of 0.04 in/min to retain quasi-static conditions for all tests. Five specimens of each core thickness were tested for initiation (crack tip is made by nonporous Teflon film or NPTF) and natural (crack tip is made naturally by a crack propagation) fracture toughness. Each specimen was cyclically loaded and unloaded a series of four times (ideally) without disturbing the specimen setup. A typical cycle was loaded to propagate the crack a distance between inch and 1 inch. However, in some instances the crack grew in an unstable manner past the one-inch mark as seen in the third loading cycle of load displacement diagram DCB01_1 (Appendix C). When the crack propagation reached the designated length, the MTI machine was unloaded at 0.04 inches/minute, and the crack was marked on both sides of the specimen by hand using a bright light source to better identify the crack tip.

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28 After the final loading cycle was completed for a specimen, the specimen was removed from the MTI machine and each crack propagation (a 1 a 2 a 3 a 4 ) was averaged between the lengths measured on each side of the specimen. Figure 5-1. MTI testing machine with setup. Force-displacement diagrams were plotted for each cycle and can be found in Appendix C based on core thickness and order tested. The G c value was computed using the specimens width, the crack propagation length, and the strain energy/work loss for each cycle a specimen was loaded. The results of all testing are summarized in Table 5-1, based on core thickness and order tested.

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29 Table 5-1, indicates crack characteristics such as steadiness and core tearing. Example of core steadiness cannot be given since they would be identical to typical interface propagation. However, for better understanding Figure 5-2 shows partial and full crack propagation in the core. Figure 5-2. Core propagation pictures, partial (left), full (right). A statistical analysis was conducted on the experimental data to calculate the mean, standard deviation, and maximum deviation of G c for each individual cycle and set of cycles for all samples. Chauvenet's Criterion was used to locate outliers excluding any primarily unsteady values [11]. A table of calculations is given in Appendix D, which shows only a single value to be an outlier. The value for the second loading cycle of specimen DCB03_1 falls outside of the usable range, based on Chauvenet's Criterion [11]. Therefore, any information provided after this point will not include this point nor will data include any unsteady crack propagation (seeing as we are only interested in steady propagation). Initially, all data points for the 20 specimens were plotted together to first get a general sense of how core thickness (h c ) affects the fracture toughness (G c ). Figure 5-3, shows an inverse proportionality trend of G c to h c which is further understood when

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30 inspecting the average G c s in Table 5-2, found from the averages of all points for specimens of a given core thickness. Table 5-1. Double cantilever beam test results for all core thicknesses. Specimen G c1 a 1 G c2 a 2 G c3 a 3 G c4 a 4 DCB01_1 3.64 0.49 2.44 0.46 2.76 ^^1.25 DCB02_1 3.91 0.52 2.80 0.49 2.56 1.09 3.04 0.95 DCB03_1 3.02 0.73 3.94 0.66 3.76 ^*0.90 4.41 0.77 DCB04_1 3.22 0.67 2.39 0.81 3.59 0.87 3.32 0.85 DCB05_1 3.60 0.61 2.47 ^0.82 1.74 ^^1.36 1.18 ^^1.72 DCB01_0.5 3.84 0.68 3.10 0.58 4.23 0.85 4.98 *0.86 DCB02_0.5 3.50 0.69 5.20 0.64 5.97 0.50 5.82 0.52 DCB03_0.5 2.62 0.75 5.25 0.57 4.78 0.58 5.17 *1.06 DCB04_0.5 3.18 0.53 2.86 0.51 3.64 ^0.83 5.51 0.62 DCB05_0.5 2.99 0.69 3.89 0.71 6.03 0.60 5.98 *0.89 DCB01_0.375 3.23 0.68 2.28 0.64 3.72 0.85 3.87 0.73 DCB02_0.375 3.80 0.77 3.78 0.72 4.28 0.73 4.53 *0.64 DCB03_0.375 3.99 0.81 5.05 0.81 4.70 0.80 5.41 0.72 DCB04_0.375 4.00 0.67 4.40 0.56 4.83 0.63 4.88 ^0.85 DCB05_0.375 4.40 0.72 4.68 0.61 4.38 0.61 DCB01_0.25 3.32 0.61 5.14 *0.66 3.05 ^^2.24 DCB02_0.25 3.64 0.57 3.78 0.66 4.74 0.76 5.48 ^0.72 DCB03_0.25 3.54 0.70 3.87 0.59 4.11 0.71 1.78 ^^2.31 DCB04_0.25 4.98 **0.63 7.49 **0.59 7.00 *0.65 5.87 0.54 DCB05_0.25 4.59 *0.64 5.55 **0.62 6.19 **0.73 6.58 **0.65 ^ Partially Unsteady propagation ^^ Primarily Unsteady Propagation Partial core propagation (est. 25-50%) ** Propagated primarily within the core (est. 50-100%) G c (lb/in) and the associated crack propagation length, a (in) are indicated by their respective loading cycle and specimen identification. Before inspecting the relationship of initiation G c (G cI ) or natural G c to h c we must consider the effect of crack tip location or crack length on G c Figure 5-4, gives a plot of

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31 all data points found during experimentation and their associated crack tip locations. The crack tip location was estimated using the initial crack length and adding sequential crack extensions for the associated specimen. That is, looking at the first entry in Table 5-1, DCB01_1, the initial crack length for all specimens was measured at 0.95 in (not shown), therefore, the first point for that specimen would be (0.95, 3.64). Then the sequential points, using the information in Table 5-1, would be, (1.44, 2.44) and (1.9, 2.76). It is necessary to understand the crack length (a), as shown in Figure 4-1, is the length from All Gc vs hcy = -2.2019x + 5.4051R2 = 0.89210.001.002.003.004.005.006.007.008.000.200.400.600.801.00hc (in)Gc (lb/in) 1" 0.5" 0.375" 0.25" Averages Linear (Averages) Figure 5-3. G c vs. h c plot for all G c values and core thicknesses. Table 5-2. Average fracture toughness (G c ) values for all points designated by core thickness (h c ). Core Thickness(h c ) Average G c (lb/in) 1 in 3.21 0.5 in 4.46 0.375 in 4.22 0.25 in 5.05

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32 Gc vs a (estimated)y = 0.9868x + 3.3015y = 0.3923x + 3.452y = 1.2449x + 2.0406y = 0.1636x + 2.91570.001.002.003.004.005.006.007.008.000.91.41.92.42.93.4a (in)Gc (lb/in) 1" 0.5" 0.375 0.25" Linear (0.25") Linear (0.375) Linear (0.5") Linear (1") Figure 5-4. G c vs. estimated crack length for all data points. the load application point to the crack tip. From Figure 5-4, a basic trend is found for the relationship of G c and crack length; as crack length increases G c also increases. Recognizing that G c is in fact affected by both core thickness and crack length a closer examination of each G c with respect to crack length becomes necessary to isolate the effects of core thickness. Due to the monitoring of crack length during experiments, G c values of the same crack number (i.e., G c1 G c2 ...) are typically associated with the same relative crack length. This can be seen in the data found in Table 5-1 showing different values of G c and their associated crack length propagations. Therefore, a comparison of G c values for crack initiation, and sequential cracks can be done for different core thicknesses so long as crack length is comparable. Due to the crack tip being made artificially by a NPTF insert, each specimens first loading cycle was used as its initiation fracture toughness (G cI ). The plot of G cI vs. h c

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33 is given in Figure 5-5. From the linear trend line shown in the figure and obtained by examining the averages for G cI vs. h c found in Table 5-3, G cI is found to decrease as h c increases is with a slope of -0.6359. GcI vs hcy = -0.6359x + 3.9881R2 = 0.33130.001.002.003.004.005.006.000.20.40.60.811.2hc (in)GcI (lb/in) 1" 0.5" 0.375" 0.25" Averages Linear (Averages) Figure 5-5. Plot of G cI vs. h c with averages and linear trend line. Table 5-3. Average G cI values for all core thicknesses. Specimen Thickness(h c ) Average G cI (lb/in) 1 in 3.48 0.5 in 3.23 0.375 in 3.88 0.25 in 4.01 The same analysis was conducted for G c2 G c3 and G c4 and can be found in Appendix E. Table 5-4, summarizes the findings from the analysis including average G cI G c2 G c3 and G c4 and the slopes from their average values linearly relating them from 0.25 inches to 1 inch, just as shown in Figure 5-5.

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34 Table 5-4. Average values for G c (lb/in.) based on cycle/crack length and core thickness; slope relation for G c 's and core thicknesses. h c Avg G cI Avg G c2 Avg G c3 Avg G c4 1 in 3.48 2.53 3.3 3.59 0.5 in 3.23 4.06 4.93 5.46 0.375 in 3.88 4.04 4.38 4.67 0.25 in 4.01 5.16 5.51 5.98 Linear Slope -0.64 -3.17 -2.59 -2.78 Table 5-5. Percentage change of average G c values from smallest core thickness. h c % G cI % G c2 % G c3 % G c4 1 in -13.2% -51.0% -40.1% -40.0% 0.5 in -19.5% -21.3% -10.5% -8.7% 0.375 in -3.2% -21.7% -20.5% -21.9% 0.25 in 0.0% 0.0% 0.0% 0.0% A review of the information in Appendix E and Table 5-4 shows that the linear approximation is a poor fit, and in no way is it exact. However, in every case comparing the G c s for the 0.25 in, 0.375 in and 1 in cores, G c decreases with increasing core. Vice versa, if one compares 0.25 in, 0.5 in, and 1 in core thicknesses, in all cases, except G cI G c also decreases with increasing core thickness. Table 5-5, shows the percentage decrease in the G c values as core thickness increases. Again, we can see the good agreement in a decreasing natural G c vs. increasing h c when reviewing the data for h c having thickness 0.25 in, 0.375 in and 1.0 inch. In fact, the table shows an agreement of decreasing natural G c s to within 1.4% when comparing core thicknesses of 0.25 in and 0.375 in, and 11.0% when comparing core thicknesses of 0.25 in and 1.0 inch. The data in Table 5-4 shows similar values in linear slope for natural cracks, and a much lower slope value for the case of artificial cracking. This corresponds to theory since the crack front/tip has a different radius when it is natural opposed to when it is made artificially. The linear slopes of the average G c s for the natural crack agree to

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35 within a 23% difference when comparing G c2 to G c3 which is the largest discrepancy. However, this researcher feels strongly that testing a larger population of specimens will reduce this error and show improved agreement between the slopes of decreasing G c vs. h c Overall the range for the linear slope is estimated between -2.59 and -3.17, which unmistakably indicates a decrease in G c when increasing the core thickness from 0.25 inch to 1 inch. Therefore, it is safe to say even though there is not complete agreement within the data, core thickness for honeycomb sandwich laminates indeed affects the critical fracture toughness in an inversely proportional manner.

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CHAPTER 6 FINITE ELEMENT ANALYSIS Concept An explanation to why the critical fracture toughness of the DCB specimen increases as core thickness decreases is a question, which should be examined to complete this thesis. There are several possible explanations for the inverse relationship. One such rational theory is that mode mixity may play a role in affecting the G c values among the varying core thicknesses. Chapter 2 briefly explained mode mixity and its effects on G c Simply put, interfaces subject to higher percentage mode II stresses will have higher critical fracture toughness values. Model Design Using the ABAQUS finite element (FE) program several FE models were created, tested and verified using problems for which the solution is known. The validation process consisted of: creating a working model using only steel properties for tabs and aluminum properties for all other components; Calculating the stress components in front of the crack tip; Using the stresses to calculate the stress intensity factors K I and K II ; and finally calculating and verifying the G c for the aluminum specimen. The procedure is further explained below and is replicated for the actual material properties of the sandwich composite used in the tests. Once a working FE representation of the experimental DCB was found, four models, one of each core thickness, were created using ABAQUS. The choice for which 36

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37 individual experimental specimens would be modeled was made based on loading cycle and G c value. Only specimens in the third loading cycle were considered for modeling. The main reason for choosing the third cycle is the reduction in error when measuring the overall crack length. Specimens were then narrowed down by comparing their G c values to the average G c value, calculated by including all specimens with related core thickness and loading cycle (Table 6-2). Specifically, the four specimens modeled were DCB04_1, DCB01_0.5, DCB02_0.375, and DCB05_0.25. All models were created using structured 8 node, plane stress, shell elements. The FE models were designed using the experimental setup as a base. Replicas of the steel tabs, facesheets (0,90,0,90,0,90,0), and different core thicknesses were all modeled and assembled in ABAQUS to create the DCB specimens. The material properties used in the FE model can be found in Table 6-1. Steel is modeled as an isotropic material, while face sheet and core material are both modeled as orthotropic materials. The face sheet was separated into individual layers of 0 and 90 degrees with the properties given below. Table 6-1. Material Properties used in finite element (FE) analysis. E 1 E 2 12 13 23 G 12 G 13 G 23 Steel (isotropic) 30 0.3 T800/3631 23.6 1.1 0.34 0.34 0.25 0.64 0.64 0.44 ECA Honeycomb core 4lb/cu ft 0.001 0.028 0.31 0.0064 0.001 0.0099 Note: Moduli are in Msi. It is common knowledge that boundary conditions (B.C.s) are typically the root of error in an FE model; therefore the conditions at the loading pins were carefully assessed. Figures 4-7 and 5-1 show how the DCB specimens were loaded and therefore give the best information on how to establish the B.C.s for the model. The bottom pin is constrained from moving in the vertical or horizontal direction while it is still allowed to

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38 rotate. The top pin has a load applied and moves in the vertical direction but is fixed in the horizontal direction and is allowed to rotate. Looking at Figure 6-1, the two loading application areas that correspond to the pins are labeled A and B. Therefore, the B.C.s at A are A1 =0, and the B.C.s at B are B1 =0 and B2 =0. Both location A and B are free to rotate. Figure 6-1. A DCB specimen model indicating boundary conditions (0.5 inch core). From Figure 6-1 it is obvious that the mesh applied was quite fine. In fact around the crack tip the elements were only 4 -6 inch square and gradually increased in size to 6.25 -2 inch square as the distance from the crack tip increased. Figure 6-2, gives a better idea of meshing around the crack tip. Element shape and aspect ratio were kept within acceptable limits for the majority of the model. The aspect ratio was kept within 2 to 1 for any part of the model experiencing bending or high levels of stress. The largest aspect ratio noted was quite high at 16 to 1, but was only used in elements far in front of the crack tip. To verify the elements were accurate a full analysis of a model with all elements measuring less than a 2 to 1 ratio was conducted and compared to the model mentioned above. The stresses near the crack tip were found to match for both models and therefore verified all of the models.

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39 Figure 6-2. Crack tip mesh refinement in all models. Crack length and applied load needed to be determined from experimental data for use in all four models. It is known that when modeling the DCB over-stiffness of the model will prevent exact agreement in deflection between experimental and FE results. Therefore, it was decided that the experimental critical load would be used in the model and the crack length would be slightly increased to match the experimental deflection. The critical load, related deflection value, experimental G c and the average of G c value for the given core thickness of the modeled specimens are given in Table 6-2. Several FE simulations of each specimen model were performed to narrow down the crack length necessary to reproduce the experimental deflection. Table 6-3, gives the final values for the crack lengths used and their related FE deflections according to modeled specimen. The largest difference in FE vs. experimental deflection is 2.1% in the 0.5 inch thick core. It should be mentioned that the oscillating stress field in the vicinity of the crack tip is ignored in this study. It is found that the complex stress field is

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40 limited to a very small distance and the traditional r2/ 1 singularity dominates the stress field. Hence, traditional K I and K II are used to characterize the crack tip stress field. Table 6-2. Critical loads and corresponding deflections for experimental specimens used in finite element analysis. Specimen Experimental Crack Length (in) F c3 (lb) Experimental Deflection (in) Experimental G c (lb/in) Experimental Gc Average (lb/in) DCB04_1 2.98 7.75 0.80 3.59 3.30 DCB01_0.5 2.75 7.65 0.80 4.23 4.93 DCB02_0.375 2.82 7.90 0.95 4.38 4.38 DCB05_0.25 2.76 8.93 1.07 6.19 5.51 The increased crack length in the FE model requires some justification. It has been found that it is extremely difficult to assess the crack extension accurately. Very near the crack tip the crack opening is so small that it is not possible to use naked eye and even a microscope to measure the actual position of the crack tip. Researchers have used increased crack-length to account for increased compliance of the specimens observed in experiments. Table 6-3. Crack length and related deflection for finite element models. Specimen FE Crack Length (in) F c3 (lb) FE Deflection (in) DCB04_1 3.45 7.75 0.796 DCB01_0.5 3.24 7.65 0.783 DCB02_0.375 3.30 7.90 0.967 DCB05_0.25 3.18 8.93 1.076 Analysis After all models were accurately developed a stress analysis was conducted on each of them. Along the interface the stress YY and shear stress XY was calculated at each node in front of the crack for a distance of two laminate thickness (0.012 inch). The mode I (K I ) and mode II (K II ) stress intensity factors were calculated at each node using Equation 2-11. Then using K I and K II the mode mixity parameter was determined from

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41 Equation 2-13. The mode mixity at each node along the interface was averaged to determine a mean mode mixity. Nodes located from the crack tip to a length of one lamina thickness (0.006 inch) were included in the average. Any mode mixity values at individual nodes that had large discrepancies from the average were omitted from the final values (Appendix F gives calculations and figures). The critical fracture toughness was calculated using the change in strain energy between the models created and shown in Table 6-3 and models with a crack propagated a distance of 0.2 inch. The relation between deflection, force, energy, and critical fracture toughness for the two models is given in Equation 6-1. Equation 6-1 is simply the finite difference form of Equation 4-1 given again below. Computed G c values, deflections (v 1 ,v 2 ), crack lengths (a 1 ,a 2 ), and applied critical load (F c = F 1 ,F 2 ) are given in Table 6-4. CUG B a (4-2) aBvFvFaBUUGc)(21112212 (6-1) Table 6-5, gives the mode mixity values associated with the critical loads and geometries of the models tested. Also shown are the experimental, FE, and variation between all of the G c values. The agreement in G c for all models is generally good, under 20% for the 0.5 in specimen and under 11.5% for all others. Some error was expected due to the use of honeycomb in the actual experiment and a solid in the FE simulation. Error was also introduced, when adjusting crack tip length and estimating solid loading blocks. A review of all the G c values in Table 6-5 again proves that even in simulation the G c values decrease as core thickness increases for honeycomb sandwich composites. For each instance in both the experimental results and the FE results the G c values decrease

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42 by respectively the same proportion. Figure 6-3, plots the G c values for both the experimental specimen results and the FE results. Table 6-4. Gc calculation using specimen deflection and applied load. Specimen a 1 (in) a 2 (in) F c (lb) v 1 (in) v 2 (in) G c (lb/in) DCB04_1 3.45 3.65 7.75 0.80 0.96 3.18 DCB01_0.5 3.24 3.44 7.65 0.78 0.96 3.39 DCB02_0.375 3.30 3.50 7.91 0.97 1.18 4.25 DCB05_0.25 3.18 3.38 8.93 1.07 1.33 5.72 Gc vs hc 0.001.002.003.004.005.006.007.000.0000.5001.0001.500hc(in)Gc(lb/in) FEM Experimental Figure 6-3. G c values for experimental and FE results. The mode mixity values shown in Table 6-5 also seem to vary according to core thickness. Although the mode mixity for the 0.5 inch, 0.375 inch, and the 0.25 inch are relatively the same, varying from 9.74 10.98 degrees, the mode mixity of the 1-inch core is only half of that at 4.85 degrees. Knowing that the one-inch core is exposed to less mode II stress we intuitively expect there to be a lower G c which corresponds to the experimental G c relationship. The plot of mode mixity vs. core thickness (h c ) is shown in Figure 6-4, and shows a definite trend for the specimens with core thickness of 1 inch, 0.5 inch, and 0.375 inch.

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43 Figure 6-5 further illustrates the trend in mode mixity when between 1 in, 0.5 in, and 0.375 inch. Using a linear fit the R 2 value indicates that the line with slope of -10 degrees per inch is a good fit. It is possible that the FE model cannot accurately compute the mode mixity near the crack tip for the 0.25 inch core or perhaps crack length or critical load greatly affects the mode mixity. It is also possible that mode mixity returns to pure mode I as core thickness approaches zero as shown in Figure 6-6. Table 6-5. Experimental and finite element G c values and finite element mode mixity. Specimen Experimental G c (lb/in) G c (lb/in) G c % Difference Mode Mixity (degrees) DCB04_1 3.59 3.18 11.49 4.85 DCB01_0.5 4.23 3.39 19.97 10.10 DCB02_0.375 4.38 4.25 2.93 10.98 DCB05_0.25 6.19 5.65 8.72 9.74 Mode Mixity vs hc0246810120.2000.4000.6000.8001.000hc(in)Mode Mixiy(degrees) Figure 6-4. Mode mixity from FE results. A further inspection of mode mixity was conducted on the geometry of the four different core thicknesses by varying only core thickness in four different models. It was believed that since crack length affects mode mixity a true relationship for mode mixity may not have been determined. The crack length was set to 3.45 in and the load was

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44 applied at 7.75 lb for all four specimens. Again the procedure was repeated to determine mode mixity at the crack tip of each model. A similar relationship to that given in Table 6-5 for mode mixity and fracture toughness was found and is shown in Table 6-6. The plot of the points in Table 6-6 is shown in Figure 6-7 and resembles the same trends discussed for the results used in Figure 6-4. Mode Mixity vs hcy = -10.006x + 14.897R2 = 0.99680246810120.2000.4000.6000.8001.000hc(in)Mode Mixiy(degrees) Figure 6-5. Mode mixity from FE results neglecting 0.25 inch core. Finally, a relationship for mode mixity vs. G c was explored. Figure 6-8, shows the plot of the experimental solutions modeled in ABAQUS using both the FE solutions and the experimental solutions of G c (Table 6-5). Figure 6-9, shows the FE mode mixity for all the experimentally calculated G c values from the third crack propagation (Table 5-1). Both figures show that for the thinner cores as mode mixity increases G c increases. However, a decrease in mode mixity from the 0.375 in core to the 0.25 in core does not create a decrease in G c Therefore, we conclude that mode mixity may play a role in the decrease in G c especially in the thicker cores. The linear plot of all G c values verse mode mixity given in Figure 6-9 supports this concept.

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45 Conclusions Comparing the mode mixity of the specimens does not conclusively show that the variation in G c is a direct result of mode mixity changes. However due to the trends shown in Figures 6-4, 6-5, 6-6 and 6-9 it is highly likely that mode mixity does play a role in the value of G c for an individual specimen configuration. Overall it seems that several factors may actually play a role in the variation in G c Further investigation should be conducted to isolate exactly what causes G c to decrease as core thickness increases. Some concepts that should be investigated to better understand why G c varies are: (1) Localized differences in stored strain energy near the crack tip (i.e., it is possible there is more energy stored and therefore lost near the crack tip of a thinner core than a thicker core); (2) Core reinforcement via higher percentages of prepreg in thinner cores can affect stiffness, modulus, strain energy, cross section, and fillet radius along the core-facesheet interface inherently changing the critical fracture toughness. Mode Mixity vs. hc02468101200.20.40.60.811.2hc(in)Mode Mixity(degrees) Figure 6-6. Mode mixity from FE model. Note that the point (h c =0,=0 is included in the plot assuming that when the core is absent it will be a pure Mode I DCB specimen.

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46 Table 6-6. Mode mixity for geometry of four different specimens. hc(in) a(in) G c (lb/in) Mode Mixity (degrees) 1 3.45 3.88 4.85 0.5 3.45 4.51 10.18 0.375 3.45 5.23 11.05 0.25 3.45 5.99 9.83 Note: Crack length and applied load are kept constant. Mode Mixity vs hc 02468101200.20.40.60.811.2hc(in)Mode Mixity(degrees) Figure 6-7. Mode mixity from FE model for same crack length and same load. Mode Mixity vs. Gc01234567051015Mode Mixity (degrees)Gc (lb/in) Exp. FE Figure 6-8. Mode mixity vs. G c for FE and experimental G c results.

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47 Mode Mixity vs. Gc0.001.002.003.004.005.006.007.008.004681012Mode Mixity(degrees)Gc(lb/in) 1 inch 0.5 inch 0.375 inch 0.25 inch Averages Figure 6-9. Mode mixity vs. G c for all experimental G c

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CHAPTER 7 CONCLUSIONS An investigation into the relation of critical fracture toughness (G c ) versus core thickness (h c ) was conducted on a sandwich composite made of 7-ply carbon fiber composite as face sheet and with Nomex honeycomb core. Composite construction techniques and experimental procedures were designed specifically to test specimens using double cantilever beam. Four core thicknesses (0.25 inch, 0.375 inch, 0.5 inch and 1.0 inch) were tested using five 1 inch 7.5 inch nominal specimens for each composite sandwich configuration. Using an MTI compression-tension testing machine four loading cycles were run on each specimen to calculate the energy lost during crack propagation. Critical fracture toughness was calculated for each specimens loading cycle and plotted for various cases. Finally, a finite element analysis was conducted using ABAQUS commercial software to determine the effect of mode mixity on the individual configurations of four specimens. G c values were computed for the FE model and compared to experiments. Experimentation indicates that for a natural crack within the core-facesheet interface along the cores L-direction the fracture toughness decreases as core thickness increases. Linear fits of the G c vs. h c plots estimated the change in G c per unit core thickness to be between -3.17 and -2.59 for natural cracks. Comparing G c values for various crack lengths of the same core thickness indicated that crack length affects the 48

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49 value of G c As crack length increases F c (critical load) was found to decrease due to the increase in moment arm from loading pin to crack tip. A similar trend in G c vs. h c was found for the FE models. The G c values determined for the FE modeled specimens were within 20% for the 0.5 in core and 11.5% for all other core thicknesses. The techniques used in modeling the specimens introduced some errors into the results, however the results were considered acceptable. The FE models deviation in G c from one core thickness to the next was found comparable to that of the experimental results. Both the experimental and FE modeling results indicate that G c decreases as h c increase. The investigation into mode mixity was aimed to better understand why G c decreases as h c increases. Models of actual experimental specimens indicated that for the 0.375 inch, 0.5 inch, and 1.0 inch core thicknesses mode mixity decreased with decreasing core thickness. A slope of roughly -10 degrees per inch was found using a linear fit with an R 2 value of 0.9968. However, the value of the 0.25 inch core thickness did not fit near the trend found in the other core thicknesses. Assuming that crack length or critical load may have affected the comparison of mode mixity results, four models using the same characteristics and only varying core thickness between 0.25 inch and 1 inch were modeled using ABAQUS FE software. A similar trend to the experimental models was found for the relation between the 0.375 inch, 0.5 inch, and 1.0 inch core thicknesses. Again, the same results were found for the 0.25 inch model. These results indicate that although it seems mode mixity does play a role in the decreasing of G c as h c increases, there are other factors affecting the specimens as well.

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50 The investigation and results presented in this research have improved our understanding of a composite sandwich construction commonly used in many structural applications. With the understanding of various factors that affect the interfacial fracture toughness, such sandwich construction can be effectively used. However, further investigation should be conducted to isolate exactly why G c decreases as h c increases. A few suggestions to why this effect occurs were discussed at the end of Chapter 6.

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APPENDIX A MATERIAL SPECIFICATIONS AND INFORMATION Honeycomb Core Designation: ECA, 1/8 inch cell, 4.0 pcf (lb/ft 3 ) Manufacturer: Euro-Composites Distributor: Technology Marketing Inc. Unidirectional Carbon Fiber Pre-preg Designation: T800HB-12K-40B/3631, Roll Number B1-210-100-8-1 Manufacturer: Toray Composites (America) Inc. Distributor: Toray Composites (America) Inc. Vacuum Bag Material Designation: Econolon Nylon Film Manufacturer: Airtech International Distributor: Coastline International Breather Material Designation: Airweave N-10 10oz/yd 2 Manufacturer: Airtech International Distributor: Coastline International Non-Porous Teflon Designation: NA100-3/38 Non-Porous Teflon Coated fiberglass cloth Manufacturer: Distributor: National Aerospace Supply 51

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APPENDIX B TORAY COMPOSITES CURE CYCLE FOR LAMINATES 050100150200250300350400Time Pressure, psig Temperature, Fahrenheit Figure B-1. Toray Composites cure cycle for composite laminates. 1. Apply at least 560 mm (22 inches) Hg vacuum to the bag. 2. Pressurize the autoclave to 6.0 Kgf/cm 2 (85 psig). Vent the vacuum bag to the atmosphere when the pressure reaches 1.4 +0.7/-0.0 kgf/cm 2 (20 +10/-0 psig). Keep the bag vented until the end of the cure. The pressure under the vacuum bag shall be 0 [+0.35/-0.0] kgf/cm 2 (0 [+5/-0] psig) throughout the remainder of the cure cycle. 3. Start the temperature ramp after the autoclave has been fully pressurized. 4. The heat up ramp shall be 1.1 to 2.2 C/minute (2 to 4 F/minute). The nominal heat-up rate shall be 1.7 C/minute (3 F/minute) 5. Hold for 120 + 60/-0 minutes at 179.5 +/5.5C (355 +/10 F) and 6.0 +1.0/-0.0 kgf/cm 2 (85 +15/-0 psig). The temperature is based on an atmosphere thermocouple. The hold part of the cycle begins when the last thermocouple reaches the minimum cure temperature. 6. Cool down under pressure until the part temperature reaches 60 C (140 F) or below The natural pressure drop (1.3 kgf/cm 2 (19 psig) maximum) in the autoclave due to the cool down is allowed. The cool down rate shall be 2.7 C/minute ( 5 F/minute) maximum. 7. When the part temperature reaches below 60C (140 F), release the pressure and remove the part. 52

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APPENDIX C LOADING GRAPHS Loading graphs, load vs. displacement for all specimens. Each specimen is designated with a test number and core thickness. DCB03_1 indicates a 1 in core specimen, tested third within the series of the five specimens. DCB01_0.375 indicates a 0.375 in core specimen tested first in the series for that core thickness. A total of 20 specimens were tested in all. 53

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54 Force vs DisplacementDCB01_10246810121400.20.40.60.811.2Displacement, inForce, lb 1 2 3 Figure C-1. Load-displacement diagram for DCB01_1. Force vs DisplacementDCB02_1024681012141600.511.52Displacement, inForce, lb 1 2 3 4 Figure C-2. Load-displacement diagram for DCB02_1.

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55 Force vs DisplacementDCB03_1024681012141600.511.522.5Displacement, inForce, lb 1 2 3 4 Figure C-3. Load-displacement diagram for DCB03_1. Force vs DisplacementDCB04_1024681012141600.511.52Displacement, inForce, lb 1 2 3 4 Figure C-4. Load-displacement diagram for DCB04_1.

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56 Force vs DisplacementDCB05_10246810121400.511.52Displacement, inForce, lb 1 2 3 4 Figure C-5. Load-displacement diagram for DCB05_1. Force vs DisplacementDCB01_050246810121400.511.522.5Displacement, inForce, lb 1 2 3 4 Figure C-6. Load-displacement diagram for DCB01_0.5.

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57 Force vs DisplacementDCB02_050246810121400.511.52Displacement, inForce, lb 1 2 3 4 Figure C-7. Load-displacement diagram for DCB02_0.5. Force vs DisplacementDCB03_050246810121400.511.522.5Displacement, inForce, lb 1 2 3 4 Figure C-8. Load-displacement diagram for DCB03_0.5.

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58 Force vs DisplacementDCB04_050246810121400.511.522.5Displacement, inForce, lb 1 2 3 4 Figure C-9. Load-displacement diagram for DCB04_0.5. Force vs DisplacementDCB05_050246810121400.511.522.5Displacement, inForce, lb 1 2 3 4 Figure C-10. Load-displacement diagram for DCB05_0.5.

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59 Force vs DisplacementDCB01_0.37502468101200.511.522.5Displacement, inForce, lb 1 2 3 4 Figure C-11. Load-displacement diagram for DCB01_0.375. Force vs DisplacementDCB02_0.3750246810121400.511.522.5Displacement, inForce, lb 1 2 3 4 Figure C-12. Load-displacement diagram for DCB02_0.375.

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60 Force vs DisplacementDCB03_0.3750246810121400.511.522.53Displacement, inForce, lb 1 2 3 4 Figure C-13. Load-displacement diagram for DCB03_0.375. Force vs DisplacementDCB04_0.3750246810121400.511.522.5Displacement, inForce, lb 1 2 3 4 Figure C-14. Load-displacement diagram for DCB04_0.375.

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61 Force vs DisplacementDCB05_0.3750246810121400.511.5Displacement, inForce, lb 1 2 3 Figure C-15. Load-displacement diagram for DCB05_0.375. Force vs DisplacementDCB01_0.2502468101200.20.40.60.811.21.41.6Displacement, inForce, lb 1 2 3 4 Figure C-16. Load-displacement diagram for DCB01_0.25.

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62 Force vs DisplacementDCB02_0.250246810121400.511.52Displacement, inForce, lb 1 2 3 4 Figure C-17. Load-displacement diagram for DCB02_0.25. Force vs DisplacementDCB03_0.250246810121400.511.52Displacement, inForce, lb 1 2 3 4 Figure C-18. Load-displacement diagram for DCB03_0.25.

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63 Force vs DisplacementDCB04_0.250246810121400.511.52Displacement, inForce, lb 1 2 3 4 Figure C-19. Load-displacement diagram for DCB04_0.25. Force vs DisplacementDCB05_0.25024681012141600.511.522.53Displacement, inForce, lb 1 2 3 4 Figure C-20. Load-displacement diagram for DCB05_0.25.

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APPENDIX D OUTLIER INVESTIGATION A statistical analysis was conducted on the experimental data to calculate the mean, standard deviation, and maximum deviation for each set of G c values. Chauvenet's Criterion was used to locate outliers excluding any primarily unsteady values. Chauvenet's Criterion states that the ratio of the maximum deviation of a single sample to the mean of a group of samples must be less than a designated value for the number of samples [11]. In other words, xiSXX Where X i is the value of a sample, X(bar) is the mean of all samples, and S x is the standard deviation of all of the samples. For five samples the above ratio must be less than 1.65, and for four samples the above ratio must be less than 1.54, for a sample to be considered valid [11]. Table D-1. Statistical Analysis on G c values with outlier analysis for 1 inch core. Specimen G c 1 G c1 G c2 G c2 G c3 G c3 G c4 G c4 DCB01_1 3.64 0.16 2.44 0.37 DCB02_1 3.91 0.43 2.80 0.01 2.56 0.74 3.04 0.55 DCB03_1 3.02 0.46 3.94 1.13 3.76 0.46 4.41 0.82 DCB04_1 3.22 0.26 2.39 0.42 3.59 0.29 3.32 0.27 DCB05_1 3.60 0.12 2.47 0.34 Mean G c 3.48 2.81 3.30 3.59 S x 0.35 0.65 0.65 0.72 max 0.46 1.13 0.74 0.82 Chauvenet's Criterion 1.29 1.73 1.14 1.13 Note: All G c values are in lb/inches, standard deviation is indicated by the symbol 64

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65 Table D-2. Statistical Analysis on G c values with outlier analysis for 0.5 inch core. Specimen G c 1 G c1 G c2 G c2 G c3 G c3 G c4 G c4 DCB01_0.5 3.84 0.61 3.10 0.96 4.23 0.70 4.98 0.51 DCB02_0.5 3.50 0.27 5.20 1.14 5.97 1.04 5.82 0.33 DCB03_0.5 2.62 0.60 5.25 1.19 4.78 0.15 5.17 0.32 DCB04_0.5 3.18 0.05 2.86 1.20 3.64 1.29 5.51 0.02 DCB05_0.5 2.99 0.24 3.89 0.17 6.03 1.10 5.98 0.49 Mean G c 3.23 4.06 4.93 5.49 S x 0.47 1.13 1.06 0.42 max 0.61 1.20 1.29 0.51 Chauvenet's Criterion 1.31 1.06 1.22 1.21 Note: All G c values are in lb/inches, standard deviation is indicated by the symbol Table D-3. Statistical Analysis on G c values with outlier analysis for 0.375 inch core. Specimen G c 1 G c1 G c2 G c2 G c3 G c3 G c4 G c4 DCB01_0.375 3.23 0.65 2.28 1.76 3.72 0.66 3.87 0.81 DCB02_0.375 3.80 0.08 3.78 0.26 4.28 0.10 4.53 0.14 DCB03_0.375 3.99 0.10 5.05 1.01 4.70 0.32 5.41 0.74 DCB04_0.375 4.00 0.11 4.40 0.36 4.83 0.45 4.88 0.21 DCB05_0.375 4.40 0.52 4.68 0.65 4.38 0.01 Mean G c 3.88 4.04 4.38 4.67 S x 0.43 1.09 0.43 0.65 max 0.65 1.76 0.66 0.81 Chauvenet's Criterion 1.53 1.62 1.52 1.25 Note: All G c values are in lb/inches, standard deviation is indicated by the symbol Table D-4. Statistical Analysis on G c values with outlier analysis for 0.25 inch core. Specimen G c 1 G c1 G c2 G c2 G c3 G c3 G c4 G c4 DCB01_0.25 3.32 0.69 5.14 0.02 DCB02_0.25 3.64 0.37 3.78 1.38 4.74 0.77 5.48 0.50 DCB03_0.25 3.54 0.47 3.87 1.29 4.11 1.40 DCB04_0.25 4.98 0.97 7.49 2.32 7.00 1.49 5.87 0.11 DCB05_0.25 4.59 0.58 5.55 0.38 6.19 0.68 6.58 0.61 Mean G c 4.01 5.16 5.51 5.98 S x 0.73 1.32 0.56 max 0.97 2.32 1.49 0.61 Chauvenet's Criterion 1.33 1.54 1.13 1.08 1.51 Note: All G c values are in lb/inches, standard deviation is indicated by the symbol

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APPENDIX E CRITICAL FRACTURE TOUGHNESS VS. CORE THICKNESS PLOTS Table E-1. Average values for G c based on cycle/crack length and core thickness; slope relation for G c 's and core thicknesses. h c Avg G cI Avg G c2 Avg G c3 Avg G c4 1 in 3.48 2.53 3.30 3.59 0.5 in 3.23 4.06 4.93 5.46 0.375 in 3.88 4.04 4.38 4.67 0.25 in 4.01 5.16 5.51 5.98 Slope -0.64 -3.17 -2.59 -2.78 Note: All G c values are in lb/inches, slope indicates the slope of a linear line fitted to the averages of the associated G c value originating at h c = 0.25 in and ending at h c = 1 inch. 66

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67 GcI vs hcy = -0.6359x + 3.9881R2 = 0.33130.001.002.003.004.005.006.000.20.40.60.811.2hc (in)GcI (lb/in) 1" 0.5" 0.375" 0.25" Averages Linear (Averages) Figure E-1. G cI vs. h c plot with linear fit to averages. Gc2 vs hcy = -3.1669x + 5.6294R2 = 0.92250.001.002.003.004.005.006.007.008.000.20.40.60.811.2hc (in)Gc2 (lb/in) 1" 0.5" 0.375" 0.25" Averages Linear (Averages) Figure E-2. G c2 vs. h c plot with linear fit to averages.

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68 Gc3 vs hcy = -2.5877x + 5.9061R2 = 0.82240.001.002.003.004.005.006.007.008.000.20.40.60.811.2hc (in)Gc3 (lb/in) 1" 0.5" 0.375" 0.25" Averages Linear (Averages) Figure E-3. G c3 vs. h c plot with linear fit to averages. Gc4 vs hcy = -2.7755x + 6.4072R2 = 0.76290.001.002.003.004.005.006.007.000.20.40.60.811.2hc (in)Gc4 (lb/in) 1" 0.5" 0.375" 0.25" Averages Linear (Averages) Figure E-4. G c4 vs. h c plot with linear fit to averages.

PAGE 80

69 Gc2, Gc3, Gc4 vs hc y = -2.8629x + 5.9535R2 = 0.85750.001.002.003.004.005.006.007.008.000.2000.4000.6000.8001.000hc (in)Gc (lb/in) 1" 0.5" 0.375" 0.25" Avg Gc Linear (Avg Gc) Figure E-5. G c2 G c3 G c4 vs. h c plot with linear fit to averages. All Gc vs hcy = -2.2019x + 5.4051R2 = 0.89210.001.002.003.004.005.006.007.008.000.200.400.600.801.00hc (in)Gc (lb/in) 1" 0.5" 0.375" 0.25" Averages Linear (Averages) c Figure E-6. All G c vs. h c plot with linear fit to averages.

PAGE 81

APPENDIX F CRACK TIP (MODE MIXITY) CALCULATIONS Below are tables and figures that include examples of how the stresses near the crack tip were used to calculate the stress intensity factors and mode mixity. Table F-1. Sample of verification of crack tip stresses for 0.25 inch core. NODE X S 22 S 12 r log r log |S 22 | log |S 12 | 9 3.18000 236728.0 136485.0 1.00E-07 -7.00 5.37 5.14 25268 3.18000 87127.9 3918.4 1.00E-07 -7.00 4.94 3.59 135 3.18000 103542.0 21965.8 1.00E-07 -7.00 5.02 4.34 25261 3.18001 99784.1 16980.0 1.01E-05 -5.00 5.00 4.23 134 3.18001 46592.1 13150.0 1.01E-05 -5.00 4.67 4.12 25254 3.18001 58962.7 11903.9 1.01E-05 -5.00 4.77 4.08 8 3.18001 56513.8 10722.0 1.01E-05 -5.00 4.75 4.03 25243 3.18002 50640.4 9638.8 2.01E-05 -4.70 4.70 3.98 131 3.18002 45414.1 8735.7 2.01E-05 -4.70 4.66 3.94 25246 3.18002 44368.2 8423.2 2.01E-05 -4.70 4.65 3.93 130 3.18002 42459.0 8067.3 2.01E-05 -4.70 4.63 3.91 25248 3.18002 40531.3 7709.1 2.01E-05 -4.70 4.61 3.89 7 3.18003 38447.1 7323.8 3.01E-05 -4.52 4.58 3.86 25349 3.18003 36236.3 6789.5 3.01E-05 -4.52 4.56 3.83 163 3.18003 33795.3 6291.6 3.01E-05 -4.52 4.53 3.80 25351 3.18004 31999.2 5952.6 3.99E-05 -4.40 4.51 3.77 162 3.18004 30233.1 5592.1 3.99E-05 -4.40 4.48 3.75 25353 3.18005 28889.8 5344.7 4.99E-05 -4.30 4.46 3.73 18 3.18005 27578.1 5095.9 4.99E-05 -4.30 4.44 3.71 25490 3.18006 25721.6 4713.9 5.99E-05 -4.22 4.41 3.67 201 3.18007 23828.3 4337.8 6.99E-05 -4.16 4.38 3.64 25492 3.18007 22675.2 4098.3 6.99E-05 -4.16 4.36 3.61 200 3.18008 21415.1 3857.4 7.99E-05 -4.10 4.33 3.59 25494 3.18009 20496.5 3677.7 9.00E-05 -4.05 4.31 3.57 28 3.18010 19569.3 3493.6 1.00E-04 -4.00 4.29 3.54 70

PAGE 82

71 log S22 vs log ry = -0.5158x + 2.2316R2 = 0.99530.001.002.003.004.005.006.00-5.5-4.5-3.5-2.5-1.5-0.5log rlog S22 Figure F-1. Log S 22 vs. Log r for 0.25 inch core. log S12 vs log ry = -0.5506x + 1.3467R2 = 0.99840.001.002.003.004.005.00-5.5-4.5-3.5-2.5-1.5-0.5log rlog S12 Figure F-2. Log S 12 vs. Log r for 0.25 inch core.

PAGE 83

72 Table F-2. Sample of calculation of stress intensity factors (K I and K II ) for 0.25 inch core. NODE S 22 S 12 r K I K II K 2 9 236728.0 136485.0 1.00E-07 187.65 108.19 4.69E+04 25268 87127.9 3918.4 1.00E-07 69.06 3.11 4.78E+03 135 103542.0 21965.8 1.00E-07 82.07 17.41 7.04E+03 25261 99784.1 16980.0 1.01E-05 794.90 135.27 6.50E+05 134 46592.1 13150.0 1.01E-05 371.16 104.76 1.49E+05 25254 58962.7 11903.9 1.01E-05 469.71 94.83 2.30E+05 8 56513.8 10722.0 1.01E-05 450.20 85.41 2.10E+05 25243 50640.4 9638.8 2.01E-05 569.10 108.32 3.36E+05 131 45414.1 8735.7 2.01E-05 510.36 98.17 2.70E+05 25246 44368.2 8423.2 2.01E-05 498.61 94.66 2.58E+05 130 42459.0 8067.3 2.01E-05 477.15 90.66 2.36E+05 25248 40531.3 7709.1 2.01E-05 455.49 86.63 2.15E+05 7 38447.1 7323.8 3.01E-05 528.73 100.72 2.90E+05 25349 36236.3 6789.5 3.01E-05 498.33 93.37 2.57E+05 163 33795.3 6291.6 3.01E-05 464.76 86.52 2.23E+05 25351 31999.2 5952.6 3.99E-05 506.66 94.25 2.66E+05 162 30233.1 5592.1 3.99E-05 478.70 88.54 2.37E+05 25353 28889.8 5344.7 4.99E-05 511.55 94.64 2.71E+05 18 27578.1 5095.9 4.99E-05 488.32 90.23 2.47E+05 25490 25721.6 4713.9 5.99E-05 499.00 91.45 2.57E+05 201 23828.3 4337.8 6.99E-05 499.37 90.91 2.58E+05 25492 22675.2 4098.3 6.99E-05 475.20 85.89 2.33E+05 200 21415.1 3857.4 7.99E-05 479.83 86.43 2.38E+05 25494 20496.5 3677.7 9E-05 487.41 87.45 2.45E+05 28 19569.3 3493.6 1E-04 490.53 87.57 2.48E+05

PAGE 84

73 KI vs r020040060080010000.0000.0050.0100.0150.0200.025r(in)KI Figure F-3. K I vs. r for 0.25 inch core. KII vs r0501001500.0000.0050.0100.0150.0200.0250.030r (in)KII Figure F-4. K II vs. r for 0.25 inch core.

PAGE 85

74 Table F-3. Sample of mode mixity calculation from K I and K II for 0.25 inch core. Node K I K II Mode Mixity 9 187.65 108.19 29.97 25268 69.06 3.11 2.58 135 82.07 17.41 11.98 25261 794.90 135.27 9.66 134 371.16 104.76 15.76 25254 469.71 94.83 11.41 8 450.20 85.41 10.74 25243 569.10 108.32 10.78 131 510.36 98.17 10.89 25246 498.61 94.66 10.75 130 477.15 90.66 10.76 25248 455.49 86.63 10.77 7 528.73 100.72 10.79 25349 498.33 93.37 10.61 163 464.76 86.52 10.55 25351 506.66 94.25 10.54 162 478.70 88.54 10.48 25353 511.55 94.64 10.48 18 488.32 90.23 10.47 25490 499.00 91.45 10.39 201 499.37 90.91 10.32 25492 475.20 85.89 10.24 200 479.83 86.43 10.21 25494 487.41 87.45 10.17 28 490.53 87.57 10.12

PAGE 86

REFERENCE LIST [1] Fairbairn, W., An Account of the Construction of the Britannia and Conway Tubular Bridges, J. Weale, London, 1849. [2] Bitzer, T. Honeycomb Technology, Chapman and Hill, London, 1997. [3] http://www.hexcelcomposites.com/Markets/Products/Honeycomb/Hexweb_attrib/ hw_p04.htm Hexcel Corporation, November 2003. [4] Beer, F.P, and Johnston, E.J. Jr., Mechanics of Materials, McGraw-Hill, Inc., New York, 1992. [5] Anderson, T.L., Fracture Mechanics, (Second Edition) CRC Press LLC, Boca Raton, FL, 1995. [6] Boresi, P.A., Schmidt, R.J., and Sidebottom, O.M., Advanced Mechanics of Materials (5 th Edition), John Wiley and Sons, New York, 1993. [7] Johannsen, T. J., Correct Core Instillation, Bonding Techniques, and Two Core-Replacement/Repair Case Histories. Sandwich Construction 2, Proceedings of the Second International Conference on Sandwich Constructions Gainesville, Florida, U.S.A., March 9-12, 1992. [8] Ural, A., Zehnder A.T., and Ingraffea, A.R., Fracture mechanics approach to facesheet delamination in honeycomb: measurement of energy release rate of the adhesive bond. Engineering Fracture Mechanics, Volume 70, Issue 1, 2003, Pages 93-103. [9] Viana, G.M., Carlsson, L.A., Influences of Foam Density and Core Thickness on Debond Toughness of Sandwich Specimens with PVC Foam Core. Journal of Sandwich Structures and Materials. Vol. 5 April 2003. [10] Avery, J.L., III Compressive Failure of Delaminated Sandwich Composites. Masters thesis, University of Florida, Gainesville, 1998. [11] Coleman, H.W., Steele W.G. Jr., Experimental and Uncertainty Analysis for Engineers (2 nd Edition), John Wiley and Sons, New York, 1999. 75

PAGE 87

76 BIOGRAPHICAL SKETCH David Grau was born in Broward County, Florida on December 18 th 1978. For the first 18 years of his life he lived in the same area of Sunrise, Florida. He attended local public schools and was highly involved in middle and high school academics. In July of 1997, he graduated from Piper High School and soon began studying engineering at the University of Florida. Throughout his years at the University, David was involved in many extracurricular activities. He was involved in AIAA and Si gma Gamma Tau; and played many intramural sports. For a few mont hs of his junior year he worked as a volunteer lab assistant. David graduated with honors in December 2001 with a B.S. in aerospace engineering. David began graduate school the next Janua ry, on track to earn an M.S. in the same field. When he first began graduate school, he was unsure of his direction. However, after speaking with Dr. Sankar, he se cured an assistant research position at the Center for Advanced Composites at the Univer sity of Florida. David conducted research for roughly 2 years on composite sandwiches. He is now on track to graduate after the submission of this thesis. As of right now, wh at Davids future holds is uncertain, but he is excited at the possibili ties that await him.


Permanent Link: http://ufdc.ufl.edu/UFE0002701/00001

Material Information

Title: Relating Interfacial Fracture Toughness to Core Thickness in Honeycomb-Core Sandwich Composites
Physical Description: Mixed Material
Copyright Date: 2008

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Holding Location: University of Florida
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Permanent Link: http://ufdc.ufl.edu/UFE0002701/00001

Material Information

Title: Relating Interfacial Fracture Toughness to Core Thickness in Honeycomb-Core Sandwich Composites
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0002701:00001


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RELATING INTERFACIAL FRACTURE TOUGHNESS TO CORE THICKNESS IN
HONEYCOMB-CORE SANDWICH COMPOSITES
























By


DAVID GRAU


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE


UNIVERSITY OF FLORIDA


2003







































Copyright 2003

By

David Grau


















ACKNOWLEDGMENTS


I would like to thank my advisor, sponsor, and friend (Dr. B. V. Sankar). Without

his support and guidance, the work presented in this thesis would not have been possible.

I would also like to thank all of my colleagues at the Center for Advanced Composites,

for their help and support throughout my research and experience at the University of

Florida.



















TABLE OF CONTENTS





ACKNOWLEDGMENTS ................... ................... ................... ........._


LIST OF TABLES ................... ................... ............. .........


LIST OF FIGURES ............. ................. ................ .........


ABSTRACT................................ xi


CHAPTER


1 INTRODUCTION ........................................ 1


Background Information.............................. 1
Literature Survey ........................................ 2
Scope of the Thesis ........................................ 4

2 BACKGROUND ........................................ 6


Theory .................. ................ .................. ...........
Failure ........................................ 12


3 LITERATURE REVIEW ........................................ 14


4 EXPERIMENTAL SETUP................................... 17


Experimental Technique ................. ............... ................. ..........
Specimen Preparation ........................................ 18

5 FRACTURE TESTS .........___. .........___. .........___. .........


Predictions............................. 25

Testing and Discussion ............... .................. ................ .........

6 FINITE ELEMENT ANALYSIS ........................................ 36


Concept .................. ................. ............... ...........
Model Design.................................. 36












Analysis................................ 40
Conclusions ................... ................... ............. ...........


7 CONCLUSION.............................. 48


APPENDIX


A MATERIAL SPECIFICATIONS AND INFORMATION............................. 51


B TORAY COMPOSITES CURE CYCLE FOR LAMINATES ............................... 52


C LOADING GRAPHS .........___. .........___. .........___. .........


D OUTLIER INVESTIGATION........................... 64


E CRITICAL FRACTURE TOUGHNESS VS. CORE THICKNESS PLOTS.......... 66


F CRACK TIP (MODE MIXITY) CALCULATIONS ........................................ 70


REFERENCE LIST .........___. .........___. .........___. ..........


BIOGRAPHICAL SKETCH ........................................ 76

















LIST OF TABLES


Table

5-1 Double cantilever beam test results for all core thicknesses............................. 30


5-2 Average fracture toughness (G,) values for all points designated by core thickness
(h,). ........................................ 31

5-3 Average GI values for all core thicknesses. ........................................ 33

5-4 Average values for G, (Ib/in) based on cycle/crack length and core thickness;
slope relation for G,'s and core thicknesses. ........................................ 34

5-5 Percentage change of average G, values from smallest core thickness. ............... 34

6-1 Material properties used in finite element (FE) analysis. ..................................... 37

6-2 Critical loads and corresponding deflections for experimental specimens used in
finite element analysis................................ 40

6-3 Crack length and related deflection for finite element models. ............................ 40

6-4 G, calculation using specimen deflection and applied load. ................... .............. 42

6-5 Experimental and finite element G, values and finite element mode mixity........ 43

6-6 Mode mixity for geometry of four different specimens.. .................. ................. ... 46

D-l Statistical analysis on G, values with outlier analysis for 1 inch core.................. 64

D-2 Statistical analysis on G, values with outlier analysis for 0.5 inch core............... 65

D-3 Statistical analysis on G, values with outlier analysis for 0.375 inch core........... 65

D-4 Statistical analysis on G, values with outlier analysis for 0.25 inch core............. 65

E-l Average values for G, based on cycle/crack length and core thickness; slope
relation for G,'s and core thicknesses. ........................................ 66

F-l Sample of verification of crack tip stresses for 0. 25 inch core. ................... ......... 70











F-2 Sample of calculation of stress intensity factors (KI and KII) for 0.25 inch core.. 72

F-3 Sample of mode mixity calculation from KI and KII for 0.25 inch core. ............... 74
















LIST OF FIGURES


Figure

1-1 Typical sandwich construction. ........................................ 3

1-2 Typical celled core types. ........................................ 3

2-1. Loading modes. ................... ................... ................... .........

4-1 Double cantilever beam (DCB) loading. ........................................ 18

4-2 Example of a load vs. displacement graph in a DCB test. ................. ................ 19

4-3 Facesheet delamination of a three layer unidirectional sandwich with bottom layer
parallel to the crack. .................. ................ .................. ........

4-4 Vacuum bag lay-up diagram. .............. ................ ............. .......

4-5 Vacuum bag lay-up before (right) and after (left) the vacuum bag is sealed. ...... 22

4-6 Autoclave before a sandwich cure cycle is run..................................... 23

4-7 Typical specimen under loading conditions. ........................................ 24

5-1 MTI testing machine with setup. ........................................ 28

5-2 Core propagation pictures. ........................................ 29

5-3 G, vs. h, plot for all G, values and core thicknesses. ................... ................... ...... 31

5-4 G, vs. estimated crack length for all data points. ................... ................... ............ 32

5-5 Plot of GI vs. h, with averages and linear trend line. ............ ............ ..... 33

6-1 A DCB specimen model indicating boundary conditions (0.5 inch core)............ 38

6-2 Crack tip mesh refinement in all models. ........................................ 39

6-3 G, values for experimental and FE results................................. 42











Mode mixity from FE results. ................... ............ ................... .......


Mode mixity from FE results neglecting 0.25 inch core. ..................................... 44


Mode mixity from FE model. ........................................ 45


Mode mixity from FE model for same crack length and same load. ............... 46


Mode mixity vs. Gfor FE and experimental G, result. ................... .................. .. 46


Mode mixity vs. G, for all experimental G,. ........................................ 47


Toray Composites cure cycle for composite laminates. ....................................... 52


Load-displacement


Load-displacement


Load-displacement


Load-displacement


Load-displacement


Load-displacement


Load-displacement


Load-displacement


Load-displacement


Load-displacement


Load-displacement


Load-displacement


Load-displacement


Load-displacement


Load-displacement


Load-displacement


diagram


diagram


diagram


diagram


diagram


diagram


diagram


diagram


diagram


diagram


diagram


diagram


diagram


diagram


diagram


diagram


DCBO1


DCB02


DCB03


DCB04


DCBOS


DCBO1


DCB02


DCB03


DCB04


DCBOS


DCBO 1


DCB02


DCB03


DCB04


DCBOS


DCBO1


1 .........____ .........____ .........____ .. 54


1 .........____ .........____ .........____ .. 54


1 .........____ .........____ .........____ .. 55


1 .........____ .........____ .........____ .. 55


1 .........____ .........____ .........____ .. 56


0.5 .........____ .........____ .........___ 56


0.5 .........____ .........____ .........___ 57


0.5 .........____ .........____ .........___ 57


0.5 .........____ .........____ .........___ 58


0.5 .........____ .........____ .........___ 58


0.375 .........____ .........____ .........__ 59


0.375 .........____ .........____ .........__ 59


0.375 .........____ .........____ .........__ 60


0.375 .........____ .........____ .........__ 60


0.375 .........____ .........____ .........__ 61


0.25. ........................................ 61











Load-displacement diagram

Load-displacement diagram

Load-displacement diagram

Load-displacement diagram

GI vs. h, plot with linear fit

Gz vs. h, plot with linear fit

G,~ vs. h, plot with linear fit

Gc4 vs. h, plot with linear fit


for DCB02 0.25. ........................................

for DCB03 0.25. ........................................

for DCB04 0.25. ........................................

for DCB05 0.25. ........................................


to averages................................

to averages. ........................................

to averages. ........................................

to averages. ........................................


Gz, G,~, Gc4 VS. he plot with linear fit to averages. ........................................

All G, vs. h, plot with linear fit to averages. ........................................

Log Szz vs. Log r for 0.25 inch core ................... ............ ..................

Log Sit vs. Log r for 0.25 inch core ................... ............ .................

KI vs. r for 0.25 inch core....................................

KII vs. r for 0.25 inch core....................................


















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

RELATING INTERFACIAL FRACTURE TOUGHNESS TO CORE THICKNESS IN
HONEYCOMB-CORE SANDWICH COMPOSITES


By

David Grau

December 2003

Chair: Bhavani V. Sankar
Major Department: Mechanical and Aerospace Engineering

The research presented in this thesis is an effort to better understand the failure

phenomenon in sandwich composites (specifically, a honeycomb core with laminated

carbon/epoxy composite facesheets). A double cantilever beam experiment was designed

and conducted for four different core thicknesses to determine a relationship between

core thickness and interfacial fracture toughness. Relationships between fracture

toughness and crack length were also explored. Finally, finite element modeling was

performed to determine the effect of mode mixity on the interfacial fracture toughness of

the sandwich composite. It is inferred that the increase in fracture toughness with the

increase in core thickness is attributed to the change in mode mixity.

















CHAPTER 1
INTRODUCTION


Backrround Information

The aerospace, automobile, and marine transportation industries are constantly

trying to refine construction and repair techniques for more efficient, less expensive,

lightweight and safer structures. In doing so, new materials and procedures are regularly

being invented that are not completely understood. Research must be conducted to

determine how effective and safe a new design, technique, or idea is for future use. The

present study concerns with one such concept for efficient structural design.

For many years, sandwich composites have been used in various structures,

although their fracture and failure behavior are not fully understood. Because of their low

weight and high stiffness characteristics, sandwich composites are becoming more

common in many structural applications. Research has been conducted to better

understand their behavior and limitations.


This study aimed to further understand the failure phenomena of sandwich

composites constructed from carbon fiber/epoxy composite face sheets and Nomex~

honeycomb cores. To achieve this, the effect of core thickness on the interfacial fracture

toughness of a honeycomb core sandwich composite was studied. The method used to

characterize fracture toughness, techniques used and results are discussed in detail.










Literature Survey

Sandwich panels have been used in building construction for well over a hundred

years. In 1849, Fairbaim [1] was first to document the idea of a sandwich composite. The

concept of a sandwich is to have the facesheet (also known as the skin) absorb or

withstand most of the bending load (or in plane loading); while the core absorbs most of

the sheat load. Individually, the components of the sandwich structure can be thought of

as relatively weak; but together, the properties of a sandwich are typically superior to

those of a solid of the same weight. The design of a sandwich composite allows for high

stiffness and moment of inertia, while keeping structural weight to a minimum. An

example of a basic sandwich using a honeycomb core is given in Figure 1-1. Because of

the ability of the skin to carry a large load and the ability of the core to stabilize the

construction of the sandwich, various material combinations have been tried together in

an effort to optimize the physical properties of the sandwich. Paired materials for

sandwich construction range from balsa wood and fiberglass to graphite and Nomex~

honeycomb.

In the 1940s, advancements in adhesive theology (flow during cure) allowed for a

new type of sandwich to be fabricated [2]. Because new adhesives can remain on the cell

edges of either a porous core or a celled core (such as honeycomb), sandwiches with

superior strength-to-weight ratios could be constructed. Thus the celled hollow-core

sandwich was born. Over the years, many types of celled-core/facesheet combinations

were tested for optimum properties. Aluminum alloys, fiberglass/phenolic weaves, and

Nomex~/phenolic weaves were all tested as core materials; while graphite, fiberglass,

aluminum, and plastic were used as typical facesheets. The typical celled-core










configurations offered by Hexcel Composites [3] (Atlanta, GA, a malor suppher of

Honeycomb Material) are shown in Figure 1-2 andthey include the Hexagonal, OX-

CoreTM, Flex-Core@, Tube-Core@, reinforced hexagon, and Double-FlexTM designs


~Facesheet


Facesheet


Figue 1-2 Typical called core types http //ww hexcelcompsus com/Markets
Prcduct~~os/mHoney~acomdbxwe~atnh/w~pth, Hexcel Corporation,










The facesheet/core combination using a Nomex~ honeycomb core and a carbon

fiber (graphite) facesheet is highly effective. This sandwich is common and is widely

used in the aerospace industry to reduce the weight of aircraft and satellite components.

Wings, floor decks, internal cabin components, and the main hull of aircrafts are common

places where the Nomex~ core/carbon fiber facesheet sandwich composite is being used

in airplane construction. This combination of facesheet and core material is likely the

most common pair in the industry at this time; and is the topic of the present study.

Other industries are also looking into practical uses for lightweight high-strength

sandwich composites. Probably the most common secondary and tertiary markets for

sandwich construction are railroad train companies and the marine industry. The railroads

are making trains lighter by using composites for floor and ceiling panels; while the same

idea being held by the U.S. Navy, will use composites for decking and bulkheads. Other

common uses for composite materials include use in sailboats, race boats, racecars, and

sporting goods. For instance, sporting goods manufacturers are looking into using

composite in skis, kayaks, canoes, pool tables, and even platform tennis paddles

Scope ofthe Thesis

In sandwich composites, small delaminations between the core and facesheet are

sometimes inherent in a fabricated specimen. Delaminations can also be produced in

composites after fabrication because of impact damage and thermal stresses within the

composite. With the delamination comes a reduction in the strength of the sandwich

composite. A delamination's effect on a composite must be understood if one is to repair

or improve the strength of the composite before use. My aim was to create a better










understanding of interfacial properties and failure due to a debond between the facesheet

and core in sandwich composites.

The organization of this thesis is as follows. First, a brief background of the

theory associated with composite sandwiches and their failure are given. Then previous

research is reviewed to promote a better understanding of failure in sandwich composites.

Then the technique developed for testing interfacial fracture toughness in a sandwich

composite is explained in detail. Then the tests conducted to characterize the interface

properties of several core thicknesses of a composite sandwich are described. Finally, the

tinite element verification and analysis conducted on several experimental samples are

discussed.

















CHAPTER 2
BACKGROUND


Theory

Because the use of sandwich composites is well established in many structural

applications, they will likely remain a feasible option for reducing weight and retaining

stiffness and strength. Therefore we must understand the failure phenomena; and how to

prevent failure in composites structures during fabrication, service and after repair.

To determine if a material will fail under a given loading condition typically the

stress state in the material is analyzed. Stress is defined as load over applied area. The

general equation for stress is


o=l (2-1)


where P is the applied load, A is the cross sectional area (typically perpendicular to the

load for normal stress and parallel for shear stress), and ~ is the calculated stress [4]

A typical failure property that would be looked at in mechanics is the strength of a

material, which is based on the material itself and can be either the ultimate stress or the

yield stress. However, when a crack or interface is concerned we are not talking about the

yielding of a material in a conventional way, but instead the separation of the molecules

that make up the interface via localized stresses. Experimentation will show that the onset

of crack propagation will not occur at the theoretical estimates suggested by atomic level

calculations. It will typically occur below the theoretical value. This is caused by [5] a

magnification of stresses in the area of the crack and is called stress concentration. The










foundation of most modem fracture mechanics is based on this concept. In order to

predict failure correctly the stress intensity factor KI (SIF) has to be calculated and

compared to the material property called critical stress intensity factor, KI,. Using this

parameter (KI) we can completely understand the stress field in a linear elastic material in

the vicinity of a crack tip. For instance, the relationship between stress and the stress

intensity factor for an infinite flat plate with a crack length of 2a subject to a remote

tensile stress is


K, = oJ~ (2-2)

where KI is the stress intensity factor, ~ is the tensile stress, and a is one half of the total

crack length [5]. With the onset of failure during experimentation the critical stress

intensity factor can be calculated (i.e., KI=KI,) at failure. So basically, KI, is a measure of

~acture toughness, which is a material property, which is independent of the crack size or

specimen size, in general.

Griffith proposed another way to characterize failure [5]. He proposed that crack

extension occurs when the available energy for crack growth is sufficient to overcome the

resistance or bond strength of the material [5] (i.e., for an incremental increase in crack

area dA)

dE dn a'Ws
=--+~=O (2-3)
dAdAdA

where E is the total energy, 17 is the potential energy supplied by the internal strain

energy and external forces, and Ws is the work required to create new surfaces.

With Griffiths theories in hand G.R. Irwin developed the present day version of

Griffith's energy methods [5]. Irwin proposed the concept energy release rate G,










dn
G=-- (2-4)
dA

which is defined as the rate of change in potential energy with crack area for a linear

elastic material. Again, at failure G = G, the critical energy release rate or more

commonly known as the fracture toughness.

Now as a comparison ofKI, and G, one imagines the flat plate with a crack length

of 2a subject to a remote tensile stress. The energy release rate is given as

IroZa
G= (2-5)


where E is the modulus of elasticity, ~ is the tensile stress, a is one half the crack length,

and G is the energy release rate [5]. We can see that both Equations 2-2 and 2-5 are

related and with a little manipulation we can get the plane stress equation

KZ
G=- (2-6)


So with this relationship we gain a relationship for G, and KI, as well and an

understanding of the relationships between energy conservation, fracture toughness, and

stress intensity factor is realized. Using the above equations it is possible to accurately

predict, when and how a crack will propagate in a given material.

To fully grasp the concepts behind this research it is necessary to understand how

a material stores energy when deformed. Strain (E) is defined as the deformation per unit

length of a given material [4]. If length is given as L and deformation is given as 6 then

the strain in a linear setting can be found from Equation 2-7.










The well known relation between stress and strain is Hooke's law and is given in

Equation 2-8 for one dimension. Where ~ is the stress, E is the elastic modulus, and E is

the strain of a given material. For the three dimensional case Hooke's law becomes

Equation 2-9, where Cllthrough C66 are called elastic coefficients [6]. Equation 2-9 is the

most general three dimensional case of Hooke's law and is used for anisotropic materials.

More specific equations for Hooke's law have been developed for isotropic and

orthotropic materials and can be found in reference material.

o=EE (2-8)

o, = C~1E, + CZZEyy + C33E, + C14 Y*y + C1S Ya + C16Yyl
o, = CZE, + CzzEyy + CZ3E, + CZ4Y~ + CZS Ya + CZ6 Yyl
o_ = C3,E_ + C3ZEyy + C33E_ + C34 Y*y + C35 Ya + C36YyI
(2-9)
o~ = C,, E_ + C4ZEyy + C43EII + C44 Y~ + C45 Ya + C46 Yyl
o, = CSE, + CSZEyy + CS3E, + CS4 Y*y + CSS Ya + CS6Yyl
o,, = CsE, + CSZEyy + CS3E, + Cs4 Y*y + CsS Ya + Cs6 Yyl

When a material is strained some work is done on the material to create the

deformation. If the material does not yield, the energy from the work is stored within the

material and is called the Strain Energy (U). This concept is better understood by

picturing a rubber band (or a spring). When a tensile load P is applied to a rubber band

the band stretches/deforms a length xl storing energy. When the band is returned to the

original length the energy is released. The strain energy stored while the band was in

tension can be calculated from Equation 2-10. Where ~ is the stress, E is the strain, and I

is the volume of the band.


U=_o~V (2-10)









Now for clarifcatlon and completeness it is necessary to understand the

differences in loading modes and how they are identified There are three loading modes,

Mode I, Mode Hl and Mode HI Figure 2-2 shows examples of how each mode would be

loaded Mode I ts dominated by an opening load, Mode Hl is dominated by an m plane

shearing load, and Mode IH is dominated by an out of plane shear [5]




F







Figure 2-1 Loading modes

Typically, stress mtensity factors will be denoted with a subscript, I, Hl, or III,

mdicatmg the loading conditon For example, the mode I and mode II singular stress

fields m an isootropi matenal m the vicmity of the crack are


4. cr,, KI (2-11)




where exx and cry are the normal stresses, oxy is the shear stress in the xy plane, r is the

distance from the crack tip, and Ri and Kn are the stress intensity factors for their

respective lan oiloadng codiios

Mixed mode conditons are possible when two or more loading conditions are

present Generally, in any bulk material a crack will propagate in the direction that

mlnlmlzes the mode Hl component of loading [51 However, in constraned or mnteracia










loading, the crack can propagate such that the mode I and mode II components are both

significant. It should be noted that the double cantilever beam (DCB, explained later) test

is usually performed in Mode I fracture studies. For mixed mode loading the energy

release rate becomes a function of all of the present loading conditions and can be

calculated using

K: K:~ KZ
G=-+-+ (2-12)
E E 2~u

again assuming a planar crack remains planer and constant shape [5]. In the above

equation for the cases of plane strain and plane stress we use the same equation, but

assume

E =E forplanestress


E = for plane strain
l-vZ

Mixed-mode conditions are quantified by a mode mixity phase angle cy (Equation

2-13), which is 0" for pure mode I and 90" for pure mode II. Understanding the mode

mixity of a loading condition is important because of its effects on crack propagation.



.=~( KK, (2-13)

A crack in pure mode II loading commonly requires several times as much energy

as a crack propagated under pure mode I loading [5]. Therefore, it becomes necessary to

identify the mode mixity of an experimental setup in order to thoroughly understand

results.










Failure

A large amount of research has been conducted to gain a better idea as to how and

why failure, specifically interfacial failure, occurs in sandwich composites. A sandwich

structure is considered to have failed when it can no longer sustain a usable load (i.e., it

can no longer bare the required load in either bending or axial loading). This typically

occurs when a face sheet is separated from the core and is simply known as interfacial

failure. Interfacial failure on a small scale between the core and the facesheet is common

in sandwich structures and can be the result of many factors. Johannsen cites the main

causes of interfacial failure during manufacturing are: voids in cored laminates, resin

drainage, excess roller pressure, lack of bonding resin, excess vacuum bag pressure,

under cured skins, and resin rich skins [7]. Damage introduced after fabrication can also

result in an interfacial failure. Examples of damage to a sandwich panel include: Impacts

to the sandwich structure such as dropped tools on the top of an airplane wing; forklifts,

trucks, or even other airplanes running into an airplane; maintenance crews walking on

non-step locations of the airplane; environmental conditions can such as thermal stress

cracking and moisture cracking can also lead to interfacial failure [2]. With such a vast

array of possibilities to cause an interfacial failure it is important to understand the effect

such a flaw can have on a composite.

To further understand the effects an extreme interfacial failure can have on


sandwich composites we consider a deck of playing cards. When the cards are loose and

not bonded together and the deck is bent the cards can slide alongside one another and the

average person can bend the deck. However, if the entire deck of cards are bonded to one

another and the deck is bent the cards cannot slide and therefore the deck becomes










extremely stiff, like a solid block, and if at all, will only flex a little. The average human

could not possibly bend the deck when the cards have been bonded. This example is the

concept behind a sandwich composite. When the face to core interface is failed the core,

with low bending modulus, loses its ability to use the face sheets to resist bending and

therefore the composite loses most of its strength.

A better understanding of how the failure will act after it is already present will

allow engineers to determine whether an interfacial failure is mild or catastrophic. As

another example, consider an interfacial delamination on the wing of an airplane resulting

~om a tool being dropped by a maintenance worker. The damage will have to be

evaluated to determine whether a repair is necessary before the airplane can take flight.

The repairing engineer knowing the fracture toughness of the material can use the typical

loading on the wing to determine the correct path to take for either repair of the wing or

clearing the airplane for safe flight.

This thesis will allow for a better understanding of failure surrounding the crack

tip. Specifically, the mode mixity and critical fracture toughness of a sandwich composite

currently in use will be determined. This will no doubt aid in determining how to

designate, fabricate, and repair composite sandwiches for use.

















CHAPTER 3
LITERATURE REVIEW


Ural, Zehnder, and Ingraffea [8] performed tests using a double cantilever beam

to evaluate the adhesive bond in honeycomb sandwich panels. The materials used were

24 and 32 ply carbon fiber composite face sheets with either a polyimide carbon fiber

matrix composite or a titanium core. Various configurations of face sheet thickness and

core materials were tested and proved to indicate that fracture toughness varied among all

of the configurations. Further testing was conducted to determine whether the lay-up

process (i.e., originating the crack on either the bag or tool sides), affects the fracture

toughness of a sandwich composite. Since during the curing process resin tends to flow

with gravity, the tool side of a composite generally contains more adhesive than the

bagging side. Therefore, it is likely that depending on which side of the sandwich a

delamination occurs the fracture toughness will vary. The conclusions were found to

support this idea in that the fracture toughness differed according to which side of the

panel was tested, whether the bag side was tested or the tool side. The results for which

side had higher fracture toughness differed depending on face sheet thickness. So, Ural,

et al. [8] found that face sheet thickness, core material, and the side of an interface failure

all affect the fracture toughness of a honeycomb sandwich composite.

Other experimental research was conducted by Carlsson and Viana [9] on varying

densities and thicknesses of PVC foam core sandwiches using glass/vinylester,

glass/polyester, and 6061-T6 aluminum face sheets. Experiments using tilted sandwich










debond specimens (similar to DCB) was conducted to determine the effect of the core

thickness and density on fracture toughness. To determine the effect of core thickness on

~acture toughness the core thickness of two different core densities was varied from

2 mm to 15 mm. Each core was tested with standard thickness aluminum face sheets. The

fracture toughness was found to increase as core thickness decreased and approach a

constant value for larger core thicknesses. It should be noted that after reviewing the data

for these experiments it is clear that further testing should have been conducted with

thicker cores to determine whether the fracture toughness indeed approaches a constant.

The effect of foam density on fracture toughness was tested using cores of five different

densities. As the density of the foam increased it was found to increase the fracture

toughness, which was noted to be independent of face sheet thickness. The results show

that for PVC foam cores with varying face sheet materials, both density and core

thickness play individual roles when determining fracture toughness.

Much research has been conducted on honeycomb sandwich composites with

carbon fiber face sheets in past years. One such researcher was Avery [10], who

conducted DCB tests similar to that which will be used in this literature. Using a factorial

test plan, Avery found general trends for fracture toughness as a function of facesheet

thickness, core density, core thickness, and crack direction relative to the honeycomb

core. An average of five specimens for a given combination was tested. DCB specimens

ranged in core thickness, facesheet thickness, core density, and core direction (Figure

1-2). Experimentation determined several general trends for fracture toughness. Fracture

toughness was found to increase with thicker facesheets and decreased with higher core

densities. Fracture was also found dependent on crack direction relative to the core. With










thicker cores, depending on the crack direction, fracture toughness was found to increase

in the W-direction and decrease in the L-direction.

It is on the basis of Avery's findings that it was felt that further research should be

done to quantify and show that core thickness does indeed affect fracture toughness for

honeycomb composites. Understanding the different findings of Carlsson/Viana's and

Avery's research relating face-sheet thickness to fracture toughness, the idea that core

material plays a large role in the properties of a sandwich is proven. Therefore, the

findings that Carlsson and Viana showed for the fracture toughness of foam cores can

only be used with those cores, and not assumed to be constant for all other core material

ofthe same thickness.

After reading the above information it is clear that fracture toughness is a function

of the materials used and their configuration. However, the question still stands for a

given specimen configuration is it possible to quantify fracture toughness? And, if so, can

we relate that value to other specimens? Specifically, if a value of fracture toughness is

proven for a specific core thickness in a standard composite configuration can we relate

this value to other core thicknesses of the same material configuration?

The following chapters will show that not only can critical fracture toughness be

quantified for a particular specimen configuration, but there are trends that relate core

thickness to fracture toughness. Furthermore, mode mixity is found to be quantifiable for

certain core thicknesses and is shown related to changes in critical fracture toughness.

















CHAPTER 4
EXPERIMENTAL SETUP

Experimental Technique

In order to calculate the fracture toughness of an interface, an accurate

experimental technique should be used. Various experimental configurations were

reviewed which included the following tests: double cantilever beam, drum peel, and four

point bending. After some consideration the double cantilever beam (DCB) test was

chosen for determining the interfacial fracture toughness of the sandwich composite due

to the ease of the test and its relatively high accuracy. ASTM standard D5528 describes

in detail how to calculate the fracture toughness of a unidirectional fiber material using

the DCB method. Experimental procedures presented in this thesis utilized a double

cantilever beam comprised of layered carbon fiber composite facesheets bonded to a

Nomex honeycomb core. Therefore the ASTM standard could not be used exactly as it

was published for the unidirectional fiber composite. However, it was felt that the

techniques described in the ASTM standard could be used as a guide for designing an

experimental setup.

In principle the DCB test is quite simple. A specimen is prepared with an initial

crack of length a within the interface, where the fracture toughness is of interest. The

specimen is then placed in a loading fixture created specifically for the DCB test.

Loading of the specimen occurs such that the surfaces lying on the interface are separated

as shown in Figure 4-1.
























Figure4-1 Double cantdleverbeam (DCB)10adin

The load and the corresponding displacement are recorded and the crack is

allowed to propagate a given length ba Fmally, the specimen is allowed to return to an

unloaded state Usmg aload/displacement graph(Figure 4-2) andthe crackpropagation

length, the eneg querye qurdorpropaghgh rckaleegthanthe ngethe rak gvneth dhreo te

fracture toughness of the mnterace can be calculated The fracture toughness, Ge, also

known as the entical strain energy release rate is given by

AU
Gc=- (4-1)
Bna

where AUls the energy or work (area under the load displacement curve) required to

propagate the crack, B is the specimen's width, and ba is the crack extension length [10]

Specmen Prp r eprtio

All specimens where fabncated using a Torays Composites umdirectlonal carbon

fiber prepreg as a face sheet material (matenal deslgnation A50TF266 S6 Class E, Fiber

deslgnation T800HB-12K -40B, matnx 3631) and a~r-opsts Euro-ompoites armiibr C

type honeycomb (1/8 inch cell size, 4 pcf density, 3 mil wall thickness, 1 in, O 5 In, O 375

m, and 0 25 in core thicknesses) for the core An 8 inch x 9-3/4 inch sandwich panel was










constructed for all core thicknesses and was cut using a wet diamond saw to make

individual 1 inch x 7.5 inch specimens. Loading blocks were then super-glued to the

specimens to finish the assembly. The process is described below in detail.



Force displacement







6





0 01 02 03 04
Displacement tin)


Figure 4-2. Example of a load vs. displacement graph in a DCB test.

First, a lay-up for the composite sandwich was selected. Typically, an adhesive

layer is place between the facesheet and the core (Figure 1-1) during a co-cure cycle to

promote better adhesion. However, due to the properties of the prepreg material (typically

prepreg contains 40% resin/adhesive) it was decided that a direct lay of the prepreg onto

the top of the honeycomb core would provide sufficient bonding strength. Verification of

this design was conducted by contacting a Hexel Composites representative who agreed

that the direct bonding method would likely work.

Next, a sequence for laying the unidirectional fiber within the facesheet was

selected. Several experiments were conducted to find the minimum number of plies a

specimen could have, yet be stiff enough to allow for separation from the core.

Specimens with symmetric 3, 5, and 7 ply facesheets were alltested. An example of the









low stiffness of a three-layer specimen can be seen m Figure 4-3 The optimum number

of phes was found to be 7, layered m a (0,90,0,90,0,90,0) configuration It is necessary to

note that when layenng urmdrectional fiber the lay-up should be symmetnc If the

layenng for a facesheet is not symmetric residual stresses will1 be present after curmg that

will1 hkely result m warpmg of the sandwich panel Also, when testmg for mterfaclal

strength on a urmdrectional fiber system the layer ofumdimrectional fiber m contact wilth

the core should be perpendicular to the crack direction A fiber laid on the core, parallel

to the crack, will1 hkely result m a delarmmation between the layers of the facesheet, as

shown m Figure 4-3, and therefore will1 not predict the mterfaclal fr-acture toughness

accurately




















Figure 4-3 Facesheet delarmmation of a three layer urmdrectional sandwich with bottom
layer parallel to the crack

Vacuum baggmg was chosen as the system for applymg vacuum/pressure to the

composite dunng the cure cycle The lay-up sequence is as follows A 3/8 m sheet of

alurmmum is used as a base tool, a Non-porous Teflon film (PTFE) Is placed on top of the

tool to release the sandwich after the cure cycle, a 7 ply (0,90,0,90,0,90,0) facesheet is










laid as the bottom slde of the sandwch, then a Nomex honeycomb core with a designated

thickness of either 1 m, O 5 m, O 3751n or 0 25 m is placed atop the bottom facesheet,

stnp of PIFE is used to create the artificial crack beteen the core and the top facesheet,

then another 7 ply (0,90,0,90,0,90,0) facesheet is used on top of the core/PIFE stnp, a

PI'FE sheet i s placed over top o f the sandwch, finally a breather material is laid atop the

other components to allow for adequate air evacuation dunng the vacuum process

Around h o od ithetoprnw abordserofnthe a adaatuminumabagsoealniadadbgipeseovrh

sealant A vacuum plug is installed i the bag matenal near the edge of the tool to ensure

It does not affect the sandwch Figure 4-4 shows the schematic of the lay-up design

witO~ toevautt uhgevacuumps n ctallug u F eiure45 sn le howsan culayubfreadferhvcu

bag is sealed All of the matenal and its supphers are documented i Appendix A It is

necessary to note that the release film usedis not porous and therefore will not allow any

excess epoxy to flow from the prepreg to the breater This lay-up design requires all of

the epoxy to remain m the sanchich to ensure adequate bond strength


Vacuum Bag
Facesheeti
PTFE Core Brethe Bheaan

ToolI







Figure 4-4 Vacuum bag lay-up dtagra

Fmally, a procedure for curing the sandwichwas explored Several methods for

fabrlcatmg the necessa y san dwches were attempted before working method was

established Using an autoclave Toray Composites recommends the cure cycle desenrbed









m Appendix B for composite lanunates The process mvolves vacuunung the bag down

to 22 mches of Hg, gradually applymg pressure to 20 psig, ventmng the bag and

contnunmng to pressunze the autoclave until the pressure reaches 85 psig, then curmg the

sandwiches at 3550F for a designated penod of time















Figure 4-5 Vacialm bag lay-up before (right) and after (left) the vacuum bag is sealed

However, when tlus method was used to create the sandwich panels desenbed

above the pressure crushed the cores m the m-plane directions (L or W direction, Figure

1-1) After further discussion wilth Toray representatives the pressure was reduced to 45

psig and the fabncallon was tned once more Agamn, the core could not sustamn the excess

pressure A means of remforemg the core via a wooden dam wilth the same tluckness as

the sandwich was utihzed, but was found to under more than help The top facesheet mdd

not bond sufficiently to the core and the edges were completely delammated Reahztng

that when creating a sandwich composite the core camiot sustamn any force or pressure m

the L or W direction the Toray cure cycle was used but with no pressure and a nonunal

vacialm of 23 psig Usmg only a vacialm, a sandwich composite wilth sufficient adhesion

between the facesheets and core was created It should be noted that further

experimentation was conducted to evaluate whether any pressure (1-5 pslg) could be









apphied to the sandwich The results determmed that for a 1 mch core no pressure could

be used, but with the thimler cores (0 25 mch and 0 375 mch) the core crushmg was

rmimmal However, for all of the exper-imentation documented m tlus hterature the cure

cycle m Appendix B was used wilth no autoclave pressure Figure 4-6, shows the

autoclave wilth a lay-up mserted before the cure cycle has begun














Figure 4-6 Autoclave before a sandwich cure cycle is run

After the autoclave cycle was complete the cured sandwich panel ls removed from

the autoclave and allowed to cool to room temperature Usmg an MK diamond MK270

wet tile cutter the 8 m by 9 3/4 m sandwich panel ls cut mto strips of 7 5 mches m length

and 1 mch m width nommally All specimens are cut resulting m an imutial 1 1/5 mch crack

m the length direction Specimens are then allowed two days drymg time before they are

sanded and super-glued to loadmng blocks The loading blocks are cut from a rectangular

steel rod and result m the dimensions 1 1 m (L) x 0 8 m (W) x 0 6 mn (T) A 3/8 m hole is

drilled through the center of each loadmng block to allow for mnsertion of a loadmng pm

Great care is taken when mounting the loadmng blocks to ensure symmetry of the

specimen Fmally, the width (B) of each specimen is averaged over the length usmg three

measurements A photo of an actual specimen under loadmng condillons Is given m Figure









4-7 For each specimen the average distance fr-om the center of load apphcation, or the

center of the loadmg pm, to the crack tip is found to be 0 95 mch


Figure 4-7 Typical specimen under loadmg conditions

















CHAPTER 5
FRACTURE TESTS

Predictions


As explained previously when a material is strained, energy is stored in the form

of strain energy. It is this concept, which gives rise to an idea that varying core thickness

should affect the fracture toughness of sandwich composites. Cores with the same cross

sectional area, same applied load, yet different core thicknesses will have the same stress

and therefore the same strain via Hooke's Law. However, from Equation 2-7 for the

calculation of strain we see the difference in core thickness will result in different


deformation lengths of the core. Using Equation 2-9 we then realize the strain energy

stored in the cores will be larger for larger cores.

To explain how the strain energy difference will affect the fracture toughness

imagine the sandwich composite as two facesheets connected by springs in place of the

honeycomb core. During a DCB test the springs will be loaded and stretched, therefore

storing energy just as the honeycomb core would. Now, as an interface crack would

propagate a length a when the critical load is reached, we picture a spring losing contact

with the face sheet. When this happens the energy that was stored in the spring is lost or

thought of as energy used to propagate the crack. With this concept we see that by

varying core thickness (spring length) or by the same means strain energy, the value of

fracture toughness should also vary.










There are also other factors possibly affecting the fracture toughness while

changing the core thickness. When the core is co-cured with the prepreg facesheets, the

resin in the prepreg is used as an adhesive. This can cause several differences among

specimens in itself: excess resin can bond to the inside of the core changing the cross

sectional area, the stress (strain), and therefore the strain energy; Excess resin can

reinforce the interface via small fillets between the core and the facesheet and force the

crack to propagate within the core; Resin can spread thinly over the interface and reduce

bond strength. However, the above are all properties introduced due to the difference in

core thickness and therefore are under investigation as a direct result of changing core

thickness.

Understanding the role stress concentration plays when considering fracture

toughness will also aid in analyzing the data acquired during experimentation. When

fabricating the test specimens the initial crack tip will likely look and react different then

all sequential cracks. The details of this theory will not be explained here, however, the

reader should understand that when making an artificial crack the radius of the crack tip

can only be proportionally equal to the thickness of the material used to prohibit bonding

within the crack. A natural crack can have a crack tip radius on the order of atomic

dimensions. Therefore, how the crack tip was formed will affect the stress concentration

and in turn the fracture toughness. We expect to see non-agreement in the results from the

first crack propagation (initiation) when compared to that of sequential crack

propagations (natural). In the same sense the second, third and fourth crack propagations

should be comparable in G, changes over all core thicknesses.










With the above reasons it is obvious that by varying the core thickness of a

sandwich composite the fracture toughness of the interface should vary as well. However,

with the long list of factors affecting the fracture toughness of the sandwich it is

impossible to accurately estimate the effect of core thickness and therefore testing is

necessary.

Testinr and Discussion

All testing was conducted on a 12,000 ib refurbished MTI Phoenix machine with

a 5,000 ib interface load cell. Calibration/Verification of both the displacement of the

MTI machine and the load detection of the load cell was conducted prior to testing. The

MTI test machine and Interface load cell (bottom/blue) are shown in Figure 5-1, with a

typical DCB test setup.

As stated before, four specimen core thicknesses (h,) were tested, 1/4 in; 3/8 in;

1/2 in; and 1 inch. The crosshead deflection rate was kept at a constant rate of 0.04 in/min

to retain quasi-static conditions for all tests. Five specimens of each core thickness were

tested for initiation (crack tip is made by nonporous Teflon film or NPTF) and natural

(crack tip is made naturally by a crack propagation) fracture toughness. Each specimen

was cyclically loaded and unloaded a series of four times (ideally) without disturbing the

specimen setup. A typical cycle was loaded to propagate the crack a distance between

% inch and 1 inch. However, in some instances the crack grew in an unstable manner past

the one-inch mark as seen in the third loading cycle of load displacement diagram

DCBO11 (Appendix C). When the crack propagation reached the designated length, the

MTI machine was unloaded at 0.04 inches/minute, and the crack was marked on both

sides of the specimen by hand using a bright light source to better identify the crack tip.









After the final loadmg cycle was completed for a specimen, the specimen was removed

fr-om the MTI machmne and each crack propagation (al, a2, a3, a4) WaS aVeraged between

the lengths measured on each side of the specimen


Figure 5-1 MTI testing mache wilth setup

Force-displacement diagrams were plotted for each cycle and can be found m

Appendix C based on core thickness and order tested The Go value was computed usmng

the specimen's width, the crack propagation length, and the stramn energy/work loss for

each cycle a specimen was loaded The results of all testing are summarized m Table 5-1,

based on core thickness and order tested









Table 5-1, mdicates crack charactenstics such as steadmess and core teanng

Example of core steadmess cannot be given smee they would be identical to typical

mterface propagation However, for better understandmg Figure 5-2 shows partial and

full crack propagation m the core














Figure 5-2 Core propagation pictures, partial (left), full (right)

A statistical analysis was conducted on the experimental data to calculate the

mean, standard deviation, and maximum deviation of Go for each mdividual cycle and set

of cycles for all samples Chauvenef s Cntenon was used to locate outhlers excluding any

pnmanly unsteady values [11] A table of calculations is given m Appendix D, which

shows only a smgle value to be an outhler The value for the second loadmg cycle of

specimen DCBO3_1 falls outside of the usable range, based on Chauvenet's Cntenon

[11] Therefore, any mformation provided after this pomnt will1 not melude this pomt nor

will data melude any unsteady crack propagation (seemg as we are only mterested m

steady propagation)

Imut~ally, all data points for the 20 specimens were plotted together to first get a

general sense of how core thickness (he) affects the fr-acture toughness (Ge) Figure 5-3,

shows an mverse proportionally trend of Go to he, which is further understood when













inspecting the average G,'s in Table 5-2, found from the averages of all points for


specimens of a given core thickness.


Table 5-1. Double cantilever beam test results for all core thicknesses.


Specimen G,1 al Gz at G,~ a~ Gcq aq


DCBO 1

DCB02

DCB03

DCB04

DCBOS



DCBO 1

DCB02

DCB03

DCB04

DCBOS



DCBO1

DCB02

DCB03

DCB04

DCBOS



DCBO1

DCB02

DCB03

DCB04

DCBOS


0.49

0.52

0.73

0.67

0.61



0.68

0.69

0.75

0.53

0.69



0.68

0.77

0.81

0.67

0.72



0.61

0.57

0.70

**0.63

*0.64


0.46

0.49

0.66

0.81

^0.82



0.58

0.64

0.57

0.51

0.71



0.64

0.72

0.81

0.56

0.61



*0.66

0.66

0.59

**0.59


""1.25

1.09

/\*0.90

0.87

""1.36



0.85

0.50

0.58

^0.83

0.60



0.85

0.73

0.80

0.63

0.61



""2.24

0.76

0.71

*0.65


0.95

0.77

0.85

""1.72



*0.86

0.52

*1.06

0.62

*0.89



0.73

*0.64

0.72

^0.85






^0.72

""2.31

0.54


**0.62 6.19 ""0.73 6.58 **0.65


Partially Unsteady propagation

^^ Primarily Unsteady Propagation

Partial core propagation test. 25-50%)

** Propagated primarily within the core test. 50-100%)
G, (Ib/in) and the associated crack propagation length, a tin) are indicated by their
respective loading cycle and specimen identlflcatlon


Before inspecting the relationship of initiation G, (GI) or natural G, to h, we must


consider the effect of crack tip location or crack length on G,. Figure 5-4, gives a plot of











all data points found during experimentation and their associated crack tip locations. The


crack tip location was estimated using the initial crack length and adding sequential crack


extensions for the associated specimen. That is, looking at the first entry in Table 5-1,


DCBO11, the initial crack length for all specimens was measured at 0.95 in (not shown),


therefore, the first point for that specimen would be (0.95, 3.64). Then the sequential


points, using the information in Table 5-1, would be, (1.44, 2.44) and (1.9, 2.76). It is


necessary to understand the crack length (a), as shown in Figure 4-1, is the length from



All Ge vs he


s 00

700

600
1"
~ 5 00 0 5"
0 375"
400 i t 0 25"

(3 300 1 A~erages
y -2 2019x + 5 4051
R2 0 8921 -- Linear (Alerages
200

100

0 00
0 20 0 40 0 60 0 80 100

he tin)



Figure 5-3. G, vs. h, plot for all G, values and core thicknesses.


Table 5-2. Average fracture toughness (G,) values for all points designated by core
thickness (h,).
Core Thlckness(h,) Average G,(lblln)
1 in 321
051n 446
0 375 in 4 22
0 25 in 5 05













Ge vs a (estimated)

8 00

700

600 ~
y=09868x+33015 *1"
5 00 0 5"
C ~2449x+2~~ 0 375
Y = O 3923x i 3 ~52
00 0 25"
V
O --Llnear (0 25")
~3 300 y=01636x+2 9157 + Linear (0 375)
2 00 --Llnear (0 5")
--Llnear(l")
100

0 00
09 14 19 24 29 34

a tin)


Figure 5-4. G, vs. estimated crack length for all data points.

the load application point to the crack tip. From Figure 5-4, a basic trend is found for the

relationship of G, and crack length; as crack length increases G, also increases.

Recognizing that G, is in fact affected by both core thickness and crack

length a closer examination of each G, with respect to crack length becomes necessary to

isolate the effects of core thickness. Due to the monitoring of crack length during

experiments, G, values of the same crack number (i.e., G,1, Gz, ...) are typically

associated with the same relative crack length. This can be seen in the data found in

Table 5-1 showing different values of G, and their associated crack length propagations.

Therefore, a comparison of G, values for crack initiation, and sequential cracks can be

done for different core thicknesses so long as crack length is comparable.

Due to the crack tip being made artificially by a NPTF insert, each specimen's

first loading cycle was used as its initiation fracture toughness (GI). The plot of GI vs. h,











is given in Figure 5-5. From the linear trend line shown in the figure and obtained by

examining the averages for GI vs. h, found in Table 5-3, GI is found to decrease as h,


increases is with a slope of-0.6359.



Gel vs he


600


500

1"
,4 00
(2~2~_ O 511
-- 0 375"
~300
y -0 6359x + 3 9881 0 25"
O R2 ~ 0 3313 A~erages
(3 200
Linear (A~erages)

100


0 00
02 04 06 08 1 12

he tin)


Figure 5-5. Plot of GI vs. h, with averages and linear trend line.

Table 5-3. Average GI values for all core thicknesses.

Specimen Thlckness(h,) Avera~e Gl(lblln)
1 in 348
051n 323
0 375 in 3 88
0 25 in 4 01


The same analysis was conducted for Gz, G,~ and Gcq and can be found in

Appendix E. Table 5-4, summarizes the findings from the analysis including average GI,


Gz, G,~ and Gcq and the slopes from their average values linearly relating them from

0.25 inches to 1 inch, just as shown in Figure 5-5.















h, Avg GI Avg Gc2 AVS Gc3 AVS Gc4


Table 5-4. Average values for G, (Ib/in.) based on cycle/crack
slope relation for G,'s and core thicknesses.


length and core thickness;


1 in 348 253
051n 323 406
0 375 in 3 88 4 04
0 25 in 4 01 516

Linear Slope -0 64 -3 17


Table 5-5. Percentage change of average G, values

h, %n GI %n Gc2
1 in -132% -51 0%
051n -195% -21 3%
0 375 in -3 2% -21 7%
0 25 in 0 0% 0 0%


A review of the information in Appendix E


33 359
493 546
438 467
551 598
2 59 -2 78


~om smallest core thickness.

%n Gc3 ~on Gc4
-401% -40 0%
10 5% -8 7%
20 5% 21 9%
00% 00%


and Table 5-4 shows that the linear


approximation is a poor fit, and in no way is it exact. However, in every case comparing


the G,'s for the 0.25 in, 0.375 in and 1 in cores, G, decreases with increasing core. Vice


versa, if one compares 0.25 in, 0.5 in, and 1 in core thicknesses, in all cases, except GI,


G, also decreases with increasing core thickness.


Table 5-5, shows the percentage decrease in the G, values as core thickness


increases. Again, we can see the good agreement in a decreasing natural G, vs. increasing


h, when reviewing the data for h, having thickness 0.25 in, 0.375 in and 1.0 inch. In fact,


the table shows an agreement of decreasing natural G,'s to within 1.4% when comparing


core thicknesses of 0.25 in and 0.375 in, and 1 1.0% when comparing core thicknesses of

0.25 in and 1.0 inch.


The data in Table 5-4 shows similar values in linear slope for natural cracks, and a


much lower slope value for the case of artificial cracking. This corresponds to theory


since the crack front/tip has a different radius when it is natural opposed to when it is


made artificially. The linear slopes of the average G,'s for the natural crack agree to










within a 23% difference when comparing Gz to G,~, which is the largest discrepancy.

However, this researcher feels strongly that testing a larger population of specimens will

reduce this error and show improved agreement between the slopes of decreasing G, vs.

h,. Overall the range for the linear slope is estimated between -2.59 and -3.17, which

unmistakably indicates a decrease in G, when increasing the core thickness from 0.25

inch to 1 inch. Therefore, it is safe to say even though there is not complete agreement

within the data, core thickness for honeycomb sandwich laminates indeed affects the

critical fracture toughness in an inversely proportional manner.

















CHAPTER 6
FINITE ELEMENT ANALYSIS


Concept

An explanation to why the critical fracture toughness of the DCB specimen

increases as core thickness decreases is a question, which should be examined to

complete this thesis. There are several possible explanations for the inverse relationship.

One such rational theory is that mode mixity may play a role in affecting the G, values

among the varying core thicknesses. Chapter 2 briefly explained mode mixity and its

effects on G,. Simply put, interfaces subject to higher percentage mode II stresses will

have higher critical fracture toughness values.

Model Desirn

Using the ABAQUS finite element (FE) program several FE models were created,

tested and verified using problems for which the solution is known. The validation

process consisted of: creating a working model using only steel properties for tabs and

aluminum properties for all other components; Calculating the stress components in front

of the crack tip; Using the stresses to calculate the stress intensity factors KI and KII; and

finally calculating and verifying the G, for the aluminum specimen. The procedure is

further explained below and is replicated for the actual material properties of the

sandwich composite used in the tests.

Once a working FE representation of the experimental DCB was found, four

models, one of each core thickness, were created using ABAQUS. The choice for which










individual experimental specimens would be modeled was made based on loading cycle

and G, value. Only specimens in the third loading cycle were considered for modeling.

The main reason for choosing the third cycle is the reduction in error when measuring the

overall crack length. Specimens were then narrowed down by comparing their G, values

to the average G, value, calculated by including all specimens with related core thickness

and loading cycle (Table 6-2). Specifically, the four specimens modeled were DCB041,

DCBO1 0.5,DCB02 0.375,andDCB05 0.25.

All models were created using structured 8 node, plane stress, shell elements. The

FE models were designed using the experimental setup as a base. Replicas of the steel

tabs, facesheets (0,90,0,90,0,90,0), and different core thicknesses were all modeled and

assembled in ABAQUS to create the DCB specimens. The material properties used in the

FE model can be found in Table 6-1. Steel is modeled as an isotropic material, while face

sheet and core material are both modeled as orthotropic materials. The face sheet was

separated into individual layers of 0 and 90 degrees with the properties given below.

Table 6-1. Material Properties used in finite element (FE) analysis.
E1 Ez vlz vl~ vz~ Glz G1~ Gz~
Steel (isotropic) 30 0.3
T800/3631 23.6 1.1 0.34 0.34 0.25 0.64 0.64 0.44
ECA Honeycomb
core 4lb/cu ft 0.001 0.028 0.31 0.0064 0.001 0.0091


Note: Moduli are in Msi.


It is common knowledge that boundary conditions (B.C.'s) are typically the root

of error in an FE model; therefore the conditions at the loading pins were carefully

assessed. Figures 4-7 and 5-1 show how the DCB specimens were loaded and therefore

give the best information on how to establish the B.C.'s for the model. The bottom pin is

constrained from moving in the vertical or horizontal direction while it is still allowed to









rotate The top pm has a load apphed and moves m the vertical direction but is fixed m

the honzontal direction and is allowed to rotate Loolong at Figure 6-1, the two loading

apphcation areas that correspond to the pms are labeled A and B Therefore, the B C's at

A are 8Al=0, and the B C's at B are 6sm=0 and 8B2-0 Both location A and B are free to

rotate


/A













Figure 6-1 A DCB specunen model mdicating boundary conditions (0 5 mch core)

From Figure 6-1 it is obvious that the mesh apphed was quite fmne In fact around

the crack tip the elements were only 4x10 mch square and gradually mereased m size to

6 25x10-2 mch square as the distance from the crack tip mereased Figure 6-2, gives a

better idea of meslung around the crack tip Element shape and aspect ratio were kept

withn acceptable hrmts for the malonty of the model The aspect ratio was kept withm 2

to 1 for any part of the model expenencmg bendmg or Ingh levels of stress The largest

aspect ratio noted was quite lugh at 16 to 1, but was only used in elements far m front of

the crack tip To venfy the elements were accurate a full analysis of a model with all

elements measunng less than a 2 to 1 ratio was conducted and compared to the model

mentioned above The stresses near the crack tip were found to match for both models

and therefore venfied all of the models




























Figure 6-2 Crack tip mesh refmement m all models

Crack length and apphed load needed to be determmed from experimental data

for use m all four models It is lm own that when modelmg the DCB over-stiffess of the

model will prevent exact agreement m denectio between experimental and FE results

Therefore, it was decided that the expenmental critcal load would be used m the model

and the crack length would be shghtly mereased to match the expenmental denection

The entical load, related denectio value, expenmental ac, and the average of Go value

for the given core thiclmess of the modeled specimens are given in Table 6-2

Several FE simulations of each specimen model were performed to narrow down

the crack length necessary to reproduce the expenmental denection Table 6-3, gives the

final values for the crack lengths used and ther related FE denections according to

modeled spe cime The largest difference m FE vs expenmental denectio is 2 1% m

the 0 5 inch thick core It should be mentinedthat the oscillatng stress field m the

vicinty of the crack tip is ignored in this study It is found that the complex stress field is











limited to a very small distance and the traditional 1/J2m singularity dominates the


stress field. Hence, traditional KI and KII are used to characterize the crack tip stress field.

Table 6-2. Critical loads and corresponding deflections for experimental specimens used
in finite element analysis.
Experimental Experimental
Crack Length F,, Deflection Experimental Experimental Gc
Specimen tin) (Ib) tin) G, (Ib/in) Average (Ib/in)

DCB04 1 2.98 7.75 0.80 3.59 3.30
DCBO1 0.5 2.75 7.65 0.80 4.23 4.93
DCB02 0.375 2.82 7.90 0.95 4.38 4.38
DCBOS 0.25 2.76 8.93 1.07 6.19 5.51


The increased crack length in the FE model requires some justification. It has

been found that it is extremely difficult to assess the crack extension accurately. Very

near the crack tip the crack opening is so small that it is not possible to use naked eye and

even a microscope to measure the actual position of the crack tip. Researchers have used

increased crack-length to account for increased compliance of the specimens observed in

experiments.

Table 6-3. Crack length and related deflection for finite element models.

Specimen FE Crack Length tin) F,~ (Ib) FE Deflection tin)

DCB04 1 3.45 7.75 0.796
DCBO 1 0.5 3.24 7.65 0.783
DCB02 0.375 3.30 7.90 0.967
DCBOS 0.25 3.18 8.93 1.076


Analysis

After all models were accurately developed a stress analysis was conducted on

each of them. Along the interface the stress ~vv and shear stress ~xu was calculated at

each node in front of the crack for a distance of two laminate thickness (0.012 inch). The

mode I (KI) and mode II (KII) stress intensity factors were calculated at each node using

Equation 2-11. Then using KI and KII the mode mixity parameter was determined from










Equation 2-13. The mode mixity at each node along the interface was averaged to

determine a mean mode mixity. Nodes located from the crack tip to a length of one

lamina thickness (0.006 inch) were included in the average. Any mode mixity values at

individual nodes that had large discrepancies from the average were omitted from the

final values (Appendix F gives calculations and figures).

The critical fracture toughness was calculated using the change in strain energy

between the models created and shown in Table 6-3 and models with a crack propagated

a distance of 0.2 inch. The relation between deflection, force, energy, and critical fracture

toughness for the two models is given in Equation 6-1. Equation 6-1 is simply the finite

difference form of Equation 4-1 given again below. Computed G, values, deflections

(vlvz), cracklengths (alaz), and applied critical load (F,=F1~F2) are given in Table 6-4.

au
c, (4-2)
Baa


u, u, 1(Fv, -Fv,)
Gc=~= (6-1)
Baa 2 Baa


Table 6-5, gives the mode mixity values associated with the critical loads and

geometries of the models tested. Also shown are the experimental, FE, and variation

between all of the G, values. The agreement in G, for all models is generally good, under

20% for the 0. 5 in specimen and under 11.5% for all others. Some error was expected due

to the use of honeycomb in the actual experiment and a solid in the FE simulation. Error

was also introduced, when adjusting crack tip length and estimating solid loading blocks.

A review of all the G, values in Table 6-5 again proves that even in simulation the

G, values decrease as core thickness increases for honeycomb sandwich composites. For

each instance in both the experimental results and the FE results the G, values decrease











by respectively the same proportion. Figure 6-3, plots the G, values for both the

experimental specimen results and the FE results.

Table 6-4. Gc calculation using specimen deflection and applied load.

Specimen al(in) az(in) F,(lb) vl(in) vz(in) G, (Ib/in)

DCB04 1 3.45 3.65 7.75 0. 80 0.96 3.18
DCBO 1 0.5 3.24 3.44 7.65 0.78 0.96 3.39
DCB02 0.375 3.30 3.50 7.91 0.97 1.18 4.25
DCBOS 0.25 3.18 3.38 8.93 1.07 1.33 5.72



Ge vs he


700
600
~- 500
~ FE M
~4 00 =~L,,,
3 00 ~ Ex pen mental
~3 200
100
0 00
0 000 0 500 1 000 1 500

hc(in)


Figure 6-3. G, values for experimental and FE results.

The mode mixity values shown in Table 6-5 also seem to vary according to core

thickness. Although the mode mixity for the 0.5 inch, 0.375 inch, and the 0.25 inch are

relatively the same, varying from 9.74 10.98 degrees, the mode mixity of the i-inch

core is only half of that at 4. 85 degrees. Knowing that the one-inch core is exposed to less

mode II stress we intuitively expect there to be a lower G,, which corresponds to the

experimental G, relationship. The plot of mode mixity vs. core thickness (h,) is shown in

Figure 6-4, and shows a definite trend for the specimens with core thickness of 1 inch,

0.5 inch, and 0.375 inch.











Figure 6-5 further illustrates the trend in mode mixity when between 1 in, 0.5 in,

and 0.375 inch. Using a linear fit the RZ value indicates that the line with slope of -10

degrees per inch is a good fit. It is possible that the FE model cannot accurately compute

the mode mixity near the crack tip for the 0.25 inch core or perhaps crack length or

critical load greatly affects the mode mixity. It is also possible that mode mixity returns

to pure mode I as core thickness approaches zero as shown in Figure 6-6.

Table 6-5. Experimental and finite element G, values and finite element mode mixity.

Experimental G, G, G, % Mode Mixity
Specimen (Ib/in) (Ib/in) Difference (degrees)

DCB04 1 3.59 3.18 11.49 4.85
DCBO 1 0.5 4.23 3.39 19.97 10.10
DCB02 0.375 4.38 4.25 2.93 10.98
DCBOS 0.25 6.19 5.65 8.72 9.74


Figure 6-4. Mode mixity from FE results.

A further inspection of mode mixity was conducted on the geometry of the four

different core thicknesses by varying only core thickness in four different models. It was

believed that since crack length affects mode mixity a true relationship for mode mixity

may not have been determined. The crack length was set to 3.45 in and the load was


Mode Mixity vs he


12
10
8

.2 6

4
2
0
0 200 0 400 0 600 0 800 1 000

hc(in)










applied at 7.75 ib for all four specimens. Again the procedure was repeated to determine

mode mixity at the crack tip of each model. A similar relationship to that given in Table

6-5 for mode mixity and fracture toughness was found and is shown in Table 6-6. The

plot of the points in Table 6-6 is shown in Figure 6-7 and resembles the same trends

discussed for the results used in Figure 6-4.


Mode Mixity vs he



,10
8
= -10 006x+14 897
:~ 6 R2=09958
I 4
2


0 200 0 400 0 600 0 800 1 000

hc(in)


Figure 6-5. Mode mixity from FE results neglecting 0.25 inch core.

Finally, a relationship for mode mixity vs. G, was explored. Figure 6-8, shows the

plot of the experimental solutions modeled in ABAQUS using both the FE solutions and

the experimental solutions of G, (Table 6-5). Figure 6-9, shows the FE mode mixity for

all the experimentally calculated G, values from the third crack propagation (Table 5-1).

Both figures show that for the thinner cores as mode mixity increases G, increases.

However, a decrease in mode mixity from the 0.375 in core to the 0.25 in core does not

create a decrease in G,. Therefore, we conclude that mode mixity may play a role in the

decrease in G,, especially in the thicker cores. The linear plot of all G, values verse mode

mixity given in Figure 6-9 supports this concept.










Conclusions

Comparing the mode mixity of the specimens does not conclusively show that the

variation in G, is a direct result of mode mixity changes. However due to the trends

shown in Figures 6-4, 6-5, 6-6 and 6-9 it is highly likely that mode mixity does play a

role in the value of G, for an individual specimen configuration. Overall it seems that

several factors may actually play a role in the variation in G,. Further investigation

should be conducted to isolate exactly what causes G, to decrease as core thickness

increases. Some concepts that should be investigated to better understand why G, varies

are: (1) Localized differences in stored strain energy near the crack tip (i.e., it is possible

there is more energy stored and therefore lost near the crack tip of a thinner core than a

thicker core); (2) Core reinforcement via higher percentages of prepreg in thinner cores

can affect stiffness, modulus, strain energy, cross section, and fillet radius along the core-

facesheet interface inherently changing the critical fracture toughness.



Nlode Nlixity vs. he

12

~10
8

F6

14

2

0 02 04 06 08 1 12

hc(in)


Figure 6-6. Mode mixity from FE model. Note that the point (h,=O,\V=O is included in the
plot assuming that when the core is absent it will be a pure Mode I DCB
specimen.








Table 6-6. Mode mixity for geometry of four different specimens.
hc(in) a(in) G,(lb/in) Mode Mixity (degrees)
1 3.45 3.88 4. 85
0.5 3.45 4.51 10.18
0.375 3.45 5.23 11.05
0.25 3.45 5.99 9. 83
Note: Crack length and applied load are kept constant.


Mode Mixity vs he

~i 12
10

E6
4
2
---.~
0 02 04 06 08 1 12
hc(in)


Mode Mixity vs. Ge




~ Exp.
c.
3 ~ FE
(32


0 5 10 15
Mode Mixity (deg rees)


Figure 6-7. Mode mixity from FE model


for same crack length and same load.


Figure 6-8. Mode mixity vs.


G, for FE and experimental G, results.





















*


~1 inch
05lnch
O 375 inch
O 25 inch

x ALerages


Figure 6-9. Mode mixity vs. G, for all experimental G,.


Mode Mixity vs. Go


Nlode Nlixity(degrees)

















CHAPTER 7
CONCLUSIONS


An investigation into the relation of critical fracture toughness (G,) versus core

thickness (h,) was conducted on a sandwich composite made of 7-ply carbon fiber

composite as face sheet and with Nomex honeycomb core. Composite construction

techniques and experimental procedures were designed specifically to test specimens

using double cantilever beam. Four core thicknesses (0.25 inch, 0.375 inch, 0.5 inch and

1.0 inch) were tested using five 1 inch x 7.5 inch nominal specimens for each composite

sandwich configuration. Using an MTI compression-tension testing machine four loading

cycles were run on each specimen to calculate the energy lost during crack propagation.

Critical fracture toughness was calculated for each specimen's loading cycle and plotted

for various cases. Finally, a finite element analysis was conducted using ABAQUS

commercial software to determine the effect of mode mixity on the individual

configurations of four specimens. G, values were computed for the FE model and

compared to experiments.

Experimentation indicates that for a natural crack within the core-facesheet

interface along the core's L-direction the fracture toughness decreases as core thickness

increases. Linear fits of the G, vs. h, plots estimated the change in G, per unit core

thickness to be between -3.17 and -2.59 for natural cracks. Comparing G, values for

various crack lengths of the same core thickness indicated that crack length affects the










value of G,. As crack length increases F, (critical load) was found to decrease due to the

increase in moment arm from loading pin to crack tip.

A similar trend in G, vs. h, was found for the FE models. The G, values

determined for the FE modeled specimens were within 20% for the 0.5 in core and 11.5%

for all other core thicknesses. The techniques used in modeling the specimens introduced

some errors into the results, however the results were considered acceptable. The FE

model's deviation in G, from one core thickness to the next was found comparable to that

of the experimental results. Both the experimental and FE modeling results indicate that

G, decreases as h, increase.

The investigation into mode mixity was aimed to better understand why G,

decreases as h, increases. Models of actual experimental specimens indicated that for the

0.375 inch, 0.5 inch, and 1.0 inch core thicknesses mode mixity decreased with

decreasing core thickness. A slope of roughly -10 degrees per inch was found using a

linear fit with an RZ value of 0.9968. However, the value of the 0.25 inch core thickness

did not fit near the trend found in the other core thicknesses.

Assuming that crack length or critical load may have affected the comparison of

mode mixity results, four models using the same characteristics and only varying core

thickness between 0.25 inch and 1 inch were modeled using ABAQUS FE software. A

similar trend to the experimental models was found for the relation between the

0.375 inch, 0.5 inch, and 1.0 inch core thicknesses. Again, the same results were found

for the 0.25 inch model. These results indicate that although it seems mode mixity does

play a role in the decreasing of G, as h, increases, there are other factors affecting the

specimens as well.










The investigation and results presented in this research have improved our

understanding of a composite sandwich construction commonly used in many structural

applications. With the understanding of various factors that affect the interfacial fracture

toughness, such sandwich construction can be effectively used. However, further

investigation should be conducted to isolate exactly why G, decreases as h, increases. A

few suggestions to why this effect occurs were discussed at the end of Chapter 6.


















APPENDIX A
MATERIAL SPECIFICATIONS AND INFORMATION


,re


Honeycomb Cc
Designation:
Manufacturer:
Distributor:


Unidirectional
Designation
Manufacturer:
Distributor:


EGA, 1/8 inch cell, 4.0 pcf (lb/ft')
Euro-Composites
Technology Marketing Inc.


Carbon Fiber Pre-preg
TX00HB-12K-40B/3631 Roll Number B1-210-100-8-1
Toray Composites (America) Inc.
Toray Composites (America) Inc.


Vacuum Bag Material
Designation: Econolon Nylon Film
Manufacturer: Airtech International
Distributor: Coastline International


Breather Material
Designation: Ainueave~ N-10 l0oz/yd2
Manufacturer: Airtech International
Distributor: Coastline International


Non-Porous Teelon
Designation: NA100-3/38 Non-Porous Teflon Coated fiberglass cloth
Manufacturer:
Distributor: National Aerospace Supply

















APPENDIX B
TORAY COMPOSITES CURE CYCLE FOR LAMINATES


400

350

300

250

200 Pressure. pslg
~~~~~r~~~~. ~ ~~~~~~~~~~
150

100





Time


Figure B-l. Toray Composites cure cycle for composite laminates.

1. Apply at least 560 mm (22 inches) Hg vacuum to the bag.
2. Pressurize the autoclave to 6.0 Kgf/cmz (85 psig). Vent the vacuum bag to the
atmosphere when the pressure reaches 1.4 +0.7/-0.0 kgf/cm2 (20 +10/-0 psig).
Keep the bag vented until the end of the cure. The pressure under the vacuum
bag shall be 0 [+0.35/-0.0] kgf/cm2 (0 [+5/-0] psig) throughout the remainder
ofthe cure cycle.
3. Start the temperature ramp after the autoclave has been fully pressurized.
4. The heat up ramp shall be 1.1 to 2.2 "C/minute (2 to 4 OF/minute). The
nominal heat-up rate shall be 1.7 "C/minute (3 "F/minute)
5. Hold for 120 + 60/-0 minutes at 179.5 +/- 5.5"C (355 ~- 10 "F) and 6.0 +1.0/-
0.0 kgf/cm2 (85 +15/-0 psig). The temperature is based on an atmosphere
thermocouple. The hold part of the cycle begins when the last thermocouple
reaches the minimum cure temperature.
6. Cool down under pressure until the part temperature reaches 60 "C (140 "F) or
below The natural pressure drop (1.3 kgf/cm2 (19 psig) maximum) in the
autoclave due to the cool down is allowed. The cool down rate shall be 2.7
"C/minute(S "F/minute) maximum.
7. When the part temperature reaches below 60"C (140 "F), release the pressure
and remove the part.


















APPENDIX C
LOADING GRAPHS


Loading graphs, load vs. displacement for all specimens. Each
designated with a test number and core thickness. DCB031 indicates
specimen, tested third within the series of the five specimens. DCBO 1
0.375 in core specimen tested first in the series for that core thickness.
specimens were tested in all.


specimen is
a 1 in core
0.375 indicates a
A total of 20











Force vs Displacement
DCBO1 1


14

12

10
n
8 t. ttl

o
64 3




0 02 04 06 08 1 12

Displacement, in


Figure C-l. Load-displacement


diagram for DCBO11.


Force vs Displacement
DCB02 1


16
14
12
n 10 ~1
O -c2
8
O
LL 6
I:
4



o 05 1 15 2

Dis placemen t, in


Figure C-2. Load-displacement diagram for DCB021.





0 05 1 15
Displacement, in


Force vs Displacement
DCB03 1


Displacement, in


1.5


Figure C-3. Load-displacement diagram for DCB031.


Force vs Displacement
DCB04 1


3
O4


Figure C-4. Load-displacement diagram for DCB041.


0 0.5 1







56





Force vs Displacement
DCBOS 1


14

12

10
~CI IV~ I

'I I I 1 1~2
~,II I I 1 3
LL 4
4




0; -
0 05 1 15 2

Displacement, in


Figure C-5. Load-displacement diagram for DCBOS1.




Force vs Displacement

DCBO1 05


14

12

10
n ~1

Q)- 8 -c2
~6 3
LLO 4 4



2 i

0'
0 05 1 15 2 25

Displacement, in


Figure C-6. Load-displacement


diagram for DCBO1O.S.











Force vs Displacement
DCB02 05

14
12
10
n II I I I
-c2
~6 3
4



0'
0 05 1 15 2

Displacement, in


Figure C-7. Load-displacement diagram for DCB020. 5.


Force vs Displacement
DCB03 05

14
12
10
n tl

r
LL I




0 05 1 15 2 25

Dis placemen t, in


Figure C-8. Load-displacement diagram for DCB03).5.









Force vs Displacement
DCB04 05

14
12
10
n ~1
8 -c2
r
LL
~L r

0 05 1 15 2 25
Displacement, in


Figure C-9. Load-displacement diagram for DCB040.5.


Force vs Displacement
DCBOS 05

14
12
10
n tl
Q) ~2

ii
6
LL

~
0'
0 05 1 15 2 25


Displacement, in


Figure C-10.


Load-displacement diagram for DCBOSO. 5.












Force vs Displacement
DCBO1 0.375


12

10


n "li '1 I
-c2
6
LL nll I 1 4




0:
0 05 1 15 2 25

Dis placement, in


Figure C-ll.


Load-displacement diagram for DCB010.375.


Force vs Displacement
DCB02 0.375


14

12

10
n 86 I:
-c2


4




0 05 1 15 2 25

Displacement, in


Figure C-12.


Load-displacement diagram for DCB020.375.











Force vs Displacement
DCB03 0.375

14

12
10
n I CI~- I ~1
I 1 ~2
3
LL I 1 4




0 05 1 15 2 25 3

Dis placement, in


Figure C-13.


Load-displacement diagram for DCB030.375.


Force vs Displacement
DCB04 0.375


-e 2
3
I:4


0 05 1 15

Displacement, in


Figure C-14.


Load-displacement diagram for DCB040.375.













Force vs Displacement

DCBOS 0.375


14

12

10
n
8 i

3






0 05 1 15

Dis placement, in


Figure C-15.


Load-displacement diagram for DCB050.375.


Figure C-16.


Load-displacement diagram for DCB010.25.


Force vs Displacement

DCBO1 0.25


12

10


n8 ~1

-c2


LL 4





0 02 04 06 08 1 12 14 16

Displacement, in





14
12
10







o:
o 05 1

Displacement, in


tl

3
I:4


Figure C-17. Load-displacement diagram for DCB020.25.


Force vs Displacement
DCB03 0.25


0 05 1

Displacement, in


Figure C-18.


Load-displacement diagram for DCB03).25.


Force vs Displacement
DCB02 0.25


-c2






























Figure C-19. Load-displacement


diagram for DCB040.25.


Figure C-20.


Load-displacement diagram for DCB050.25.


Force vs Displacement
DCB04 0.25

14
12
10
n tl
-c2
~6 3
4

~

0 05 1 15 2
Displacement, in


Force vs Displacement
DCBOS 0.25

16
14
12
rr itl

8
6
4




0 05 1 15 2 25 3
Displacement, in



















APPENDIX D
OUTLIER INVESTIGATION


A statistical analysis was conducted on the experimental data to calculate the
mean, standard deviation, and maximum deviation for each set of G, values. Chauvenet's
Criterion was used to locate outliers excluding any primarily unsteady values.
Chauvenet's Criterion states that the ratio of the maximum deviation of a single
sample to the mean of a group of samples must be less than a designated value for the
number of samples [11]. In other words,
X-X



Where X, is the value of a sample, X(barl is the mean of all samples, and S, is the
standard deviation of all of the samples. For five samples the above ratio must be less
than 1.65, and for four samples the above ratio must be less than 1.54, for a sample to be
considered valid [11].


Table D-l. Statistical Analysis on G, values with outlier analysis for 1 inch core.
Specimen G,1 Gz Gz~ G,~ G.q G.q~

DCBO1 1 3 64 016 2 44 0 37
DCB02 1 3 91 0 43 2 80 0 01 2 56 0 74 3 04 0 55
DCB03 1 3 02 0 46 3 94 1 13 3 76 0 46 4 41 0 82
DCB04 1 3 22 0 26 2 39 0 42 3 59 0 29 3 32 0 27
DCB05 1 3 60 012 2 47 0 34
Mean G, 3 48 2 81 3 30 3 59
s, 0 35 0 65 0 65 0 72
0 46 1 13 0 74 0 82
Chauvenet's Cntenon 1.29 1.73 1.14 1.13
Note: All G, values are in ib/inches, standard deviation is indicated by the symbol o.












Table D-2. Statistical Analysis on G, values with outlier analysis for 0.5 inch core.

Specimen G,1 Gz Gz~ G,~ G.q G.q~


DCBO1 0 5 3 84 0 61 3 10 0 96 4 23 0 70 4 98 051
DCB02 0 5 3 50 0 27 5 20 1 14 5 97 104 5 82 0 33
DCB03 0 5 2 62 0 60 5 25 1 19 4 78 0 15 5 17 0 32
DCB04 0 5 318 0 05 2 86 120 3 64 129 5 51 0 02
DCB05 0 5 2 99 0 24 3 89 0 17 6 03 1 10 5 98 0 49

Mean G, 3 23 4 06 4 93 5 49
s, 0 47 1 13 106 0 42
0 61 120 129 051
Chauvenet's Cntenon 1.31 1.06 1.22 1.21

Note: All G, values are in ib/inches, standard deviation is indicated by the symbol o.


Table D-3. Statistical Analysis on G, values with outlier analysis for 0.375 inch core.
Specimen G,1 Gz Gz~ G,~ G.q G.q~


DCBO1 0 375 3 23 0 65 2 28 176 3 72 0 66 3 87 081
DCB02 0 375 3 80 0 08 3 78 0 26 4 28 0 10 4 53 014
DCB03 0 375 3 99 0 10 5 05 101 4 70 0 32 5 41 0 74
DCB04 0 375 4 00 011 4 40 0 36 4 83 0 45 4 88 0 21
DCB05 0 375 4 40 0 52 4 68 0 65 4 38 0 01

Mean G, 3 88 4 04 4 38 4 67
s, 0 43 109 0 43 0 65
0 65 176 0 66 081
Chauvenet's Cntenon 1.53 1.62 1.52 1.25

Note: All G, values are in ib/inches, standard deviation is indicated by the symbol o.


Table D-4. Statistical Analysis on G, values with outlier analysis for 0.25 inch core.

Specimen G,1 Gz Gz~ G,~ G.q G.q~


DCBO1 0 25 3 32 0 69 5 14 0 02
DCB02 0 25 3 64 0 37 3 78 138 4 74 0 77 5 48 0 50
DCB03 0 25 3 54 0 47 3 87 129 411 140
DCB04 0 25 4 98 0 97 7 49 2 32 7 00 149 5 87 011
DCB05 0 25 4 59 0 58 5 55 0 38 6 19 0 68 6 58 0 61
Mean G, 4 01 5 16 5 51 5 98
s, 0 73 151 132 0 56
0 97 2 32 149 0 61
Chauvenet's Cntenon 1.33 1.54 1.13 1.08

Note: All G, values are in ib/inches, standard deviation is indicated by the symbol o.





1 in 3.48 2.53 3.30 3.59
0.5 in 3.23 4.06 4.93 5.46
0.375 in 3.88 4.04 4.38 4.67
0.25 in 4.01 5.16 5.51 5.98

Slope -0.64 -3.17 -2. 59 -2.78
Note: All G, values are in ib/inches, slope indicates the slope of a linear line fitted to the
averages of the associated G, value originating at h, = 0.25 in and ending at h, = 1 inch.


h, Avg GI Avg Gz Avg G,~ Avg Gcq


APPENDIX E
CRITICAL FRACTURE TOUGHNESS VS. CORE THICKNESS PLOTS


Table E-l. Average values for G, based on cycle/crack length and core thickness; slope
relation for G,'s and core thicknesses.













Gel vs he


600


500

1"
C i 5"

~ 3 00 o 375
y -0 6359x + 3 9881 0 25"
O R2 ~ 0 3313 A~erages
(3 200
Linear (A~erages)

100


0 00
02 04 06 08 1 12

he tin)


Gc2 vs he


s 00

700

600
r 1"
c 00 0 5"
~CI I I 0 375"
0 25"
hi
0300 I *Alerages
(3
Linear (A~erages)
200
y31669x+5 6294
R2 ~ 0 9225
100

0 00
02 04 06 08 1 12

he tin)


Figure E-l. GI


vs. h, plot with linear fit to averages.


Figure E-2. Gz


vs. h, plot with linear fit to averages.














Gc3 vs he


s 00

700

600
r 1"
C 5 00 ~ 0 5"
~CI 0 375"
~. 400 L
f I 0 25"
O 300 A~erages
(3 Y'- +
2 00 1 R2 ~ 0 8224 1 Linear (A~erages)

100

0 00
02 04 06 08 1 12

he tin)


Gc4 vs he


700


600-~

500 u 1"
c I r I 0 5"
400
~CI 0 375"
y 27755x+6 4072
R2 ~ 0 7629 ? I 0 25"
63 00
O *Alerages
(3
2 00 I Linear (A~erages)

100

0 00
02 04 06 08 1 12

he tin)


Figure E-3. G,~ vs. h, plot with linear fit to averages.


Figure E-4. Gcq VS. he plot with linear fit to averages.

















































All Ge vs he


s 00

700

600
i I ~1"
~ 5 00 -~- I I 0 5"
~CI
400 i I 0 375"
I f 0 2s~
o
(3 300 A~erages
y -2 2019x + 5 4051
R2 0 8921 LlneaT (Alerages)
200

100

0 00
0 20 0 40 0 60 0 80 100

he tin)


Gc2, Gc3, Gc4 vs he


s 00

700

600
1"

;- 5 00 ,,, I 0 5"
o I 0 375"
400
3 1 I 0 25"
O
(3 3 00 O Avg Ge
R2 0 8575 1 -Llnear (Avg Gel
200

100

0 00
0 200 0 400 0 600 0 800 1000

he tin)


Figure E-5. Gz, G,~, Gcq


vs. h, plot with linear fit to averages.


Figure E-6.


All G, vs. h, plot with linear fit to averages























APPENDIX F

CRACK TIP (MODE MIXITY) CALCULATIONS




Below are tables and figures that include examples of how the stresses near the crack tip

were used to calculate the stress intensity factors and mode mixity.


Table F-l. Sample of verification of crack tip stresses for 0.25 inch core.

log log
NODE X S22 S12 I log r


318000
318000
318000
318001
318001
318001
318001
318002
318002
318002
318002
318002
318003
318003
318003
318004
318004
318005
318005
318006
318007
318007
318008
318009
318010


236728 0
87127 9
103542 0
997841
465921
58962 7
565138
50640 4
454141
44368 2
42459 0
40531 3
384471
36236 3
33795 3
31999 2
302331
28889 8
275781
25721 6
23828 3
22675 2
214151
20496 5
19569 3


136485 0
3918 4
21965 8
16980 0
13150 0
11903 9
10722 0
9638 8
8735 7
8423 2
8067 3
77091
7323 8
6789 5
6291 6
5952 6
55921
5344 7
5095 9
4713 9
4337 8
4098 3
3857 4
3677 7
3493 6


100E-07
100E-07
100E-07
101E-05
101E-05
101E-05
101E-05
201E-05
201E-05
201E-05
201E-05
201E-05
301E-05
301E-05
301E-05
399E-05
399E-05
499E-05
499E-05
599E-05
699E-05
699E-05
799E-05
900E-05
100E-04













log S22 vs log r


6.00
5.00
hi
hi 4.00
u) ,,,
y=-0.5158x+2.2316
O 2.00
R2=0.9953
1.00
0.00
5.5 -4.5 -3.5 -2.5 -1.5 -0.5


log r


Figure F-l. Log Szz vs. Log


r for 0.25 inch core.


log S~2 vs log r


5.00
4.00
hi
3.00
U)
o) 2.00 lY=~0.5506x+1.3467
O R2=0.9984

0.00
5.5 -4.5 -3.5 -2.5 -1.5 -0.5


log r


Figure F-2. Log Sit vs. Log r for 0.25 inch core.
















Table F-2. Sample of calculation of stress intensity factors (KI and KII) for 0.25 inch core.

NODE S22 S12 I K~ K~I K2


236728 0
87127 9
103542 0
997841
465921
58962 7
56513 8
50640 4
454141
44368 2
42459 0
40531 3
384471
36236 3
33795 3
31999 2
302331
28889 8
275781
25721 6
23828 3
22675 2
21 4151
20496 5
19569 3


136485 0
3918 4
21965 8
16980 0
13150 0
11903 9
10722 0
9638 8
8735 7
8423 2
8067 3
77091
7323 8
6789 5
6291 6
5952 6
55921
5344 7
5095 9
4713 9
4337 8
4098 3
3857 4
3677 7
3493 6


00E-07
00E-07
00E-07
01E-05
01E-05
01E-05
01E-05
01E-05
01E-05
01E-05
01E-05
01E-05
01E-05
01E-05
01E-05
99E-05
99E-05
99E-05
99E-05
99E-05
99E-05
99E-05
99E-05
9E-05
1 E-04


10819
311
17 41
135 27
104 76
94 83
85 41
108 32
9817
94 66
90 66
86 63
100 72
93 37
86 52
94 25
88 54
94 64
90 23
91 45
90 91
85 89
86 43
87 45
87 57


469E+04
478E+03
704E+03
650E+05
149E+05
230E+05
210E+05
336E+05
270E+05
258E+05
236E+05
215E+05
290E+05
257E+05
223E+05
266E+05
237E+05
271E+05
247E+05
257E+05
258E+05
233E+05
238E+05
245E+05
248E+05













KI vs r


1000

800

600
KI
400

200


0.000 0.005 0.010 0.015 0.020 0.025


r(in)


KII vs r


150


100
KII
50



0.000 0.005 0.010 0.015 0.020 0.025 0.030


r tin)


Figure F-3. KI vs. r for 0.25 inch core.


Figure F-4. KII vs. rfor 0.25 inch core.














Table F-3. Sample of mode mixity calculation from KI and KII for 0.25 inch core.

Node KI KII Mode Mixity


9
25268
135
25261
134
25254
8
25243
131
25246
130
25248
7
25349
163
25351
162
25353
18
25490
201
25492
200
25494
28


187.65
69.06
82.07
794.90
371.16
469.71
450.20
569.10
510.36
498.61
477. 15
455.49
528.73
498.33
464.76
506.66
478.70
511.55
488.32
499.00
499.37
475.20
479.83
487.41
490.53


108.19
3.11
17.41
135.27
104.76
94.83
85.41
108.32
98.17
94.66
90.66
86.63
100.72
93.37
86.52
94.25
88.54
94.64
90.23
91.45
90.91
85.89
86.43
87.45
87.57
















REFERENCE LIST


[1] Fairbairn, W., An Account of the Construction of the Bntannla and Conway
Tubular Bndges, J. Weale, London, 1849.

[2] Bitter, T., Honeycomb Technology, Chapman and Hill, London, 1997.

[3] http:~www. hexcelcomposltes. com~/(arkets/Products/Honeycom b/Hexwebattn b/
hwg04.htm, Hexcel Corporation, November 2003.

[4] Beer, F.P, and Johnston, E.J. Jr., h~echanlcs ofh~atenals, McGraw-Hill, Inc.,
New York, 1992.

[5] Anderson, T.L., Fracture h~echanlcs, (Second Edition) CRC Press LLC, Boca
Raton, FL, 1995.

[6] Boresi, P.A., Schmidt, R.J., and Sidebottom, O.M., Advancedh~echanlcs of
h~atenals (5" Edition), John Wiley and Sons, New York, 1993.

[7] Johannsen, T. J., "Correct Core Instillation, Bonding Techniques, and Two
Core-Replacement/Repair Case Histories." Sandwich Construction 2, Proceedings
of the Second International Conference on Sandwich Constructions Gainesville,
Florida, U.S.A., March 9-12, 1992.

[8] Ural, A., Zehnder A.T., and Ingraffea, A.R., "Fracture mechanics approach to
facesheet delamination in honeycomb. measurement of energy release rate of the
adhesive bond." Englneenng Fracture h~echanlcs, Volume 70, Issue 1, 2003,
Pages 93-103.

[9] Viana, G.M., Carlsson, L.A., "Influences of Foam Density and Core Thickness on
Debond Toughness of Sandwich Specimens with PVC Foam Core." Journal of
Sandwich Structures andh~atenals. Vol. 5 April 2003.

[10] Avery, J.L., III Compressive Failure ofDelamlnated Sandwich Composites.
Master's thesis, University of Florida, Gainesville, 1998.

[11] Coleman, H.W., Steele W.G. Jr., Expenmental and UncertalntyAnalyslsfor
Engineers (2"d Edition), John Wiley and Sons, New York 1999
















BIOGRAPHICAL SKETCH

David Grau was born in Broward County, Florida on December 18'", 1978. For

the first 18 years of his life he lived in the same area of Sunrise, Florida. He attended

local public schools and was highly involved in middle and high school academics. In

July of 1997, he graduated from Piper High School and soon began studying engineering

at the University of Florida. Throughout his years at the University, David was involved

in many extracurricular activities. He was involved in AIAA and Sigma Gamma Tau; and

played many intramural sports. For a few months of his junior year he worked as a

volunteer lab assistant. David graduated with honors in December 2001 with a B.S. in

aerospace engineering.

David began graduate school the next January, on track to earn an M.S. in the

same field. When he first began graduate school, he was unsure of his direction.

However, after speaking with Dr. Sankar, he secured an assistant research position at the

Center for Advanced Composites at the University of Florida. David conducted research

for roughly 2 years on composite sandwiches. He is now on track to graduate after the

submission of this thesis. As of right now, what David's future holds is uncertain, but he

is excited at the possibilities that await him.