Citation
Quantitative Fractography: A Comparative Study to Evaluate Polymer Fracture Toughness

Material Information

Title:
Quantitative Fractography: A Comparative Study to Evaluate Polymer Fracture Toughness
Creator:
DIFRANCESCO, STEPHANIE ( Author, Primary )
Copyright Date:
2008

Subjects

Subjects / Keywords:
Crack propagation ( jstor )
Fractography ( jstor )
Fracture mechanics ( jstor )
Fracture strength ( jstor )
Geometry ( jstor )
Polymers ( jstor )
Razor blades ( jstor )
Specimens ( jstor )
Stress fractures ( jstor )
Toughness ( jstor )

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright Stephanie Difrancesco. Permission granted to University of Florida to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
3/1/2007
Resource Identifier:
658230417 ( OCLC )

Downloads

This item has the following downloads:

difrancesco_s ( .pdf )

difrancesco_s_Page_62.txt

difrancesco_s_Page_22.txt

difrancesco_s_Page_12.txt

difrancesco_s_Page_08.txt

difrancesco_s_Page_41.txt

difrancesco_s_Page_56.txt

difrancesco_s_Page_61.txt

difrancesco_s_Page_06.txt

difrancesco_s_Page_39.txt

difrancesco_s_Page_07.txt

difrancesco_s_Page_24.txt

difrancesco_s_Page_42.txt

difrancesco_s_Page_21.txt

difrancesco_s_Page_18.txt

difrancesco_s_Page_14.txt

difrancesco_s_Page_09.txt

difrancesco_s_Page_57.txt

difrancesco_s_Page_31.txt

difrancesco_s_Page_23.txt

difrancesco_s_Page_15.txt

difrancesco_s_Page_16.txt

difrancesco_s_Page_10.txt

difrancesco_s_Page_25.txt

difrancesco_s_Page_28.txt

difrancesco_s_Page_04.txt

difrancesco_s_Page_50.txt

difrancesco_s_Page_63.txt

difrancesco_s_Page_03.txt

difrancesco_s_Page_46.txt

difrancesco_s_Page_30.txt

difrancesco_s_Page_29.txt

difrancesco_s_Page_34.txt

difrancesco_s_Page_53.txt

difrancesco_s_Page_05.txt

difrancesco_s_Page_26.txt

difrancesco_s_pdf.txt

difrancesco_s_Page_58.txt

difrancesco_s_Page_01.txt

difrancesco_s_Page_60.txt

difrancesco_s_Page_54.txt

difrancesco_s_Page_64.txt

difrancesco_s_Page_02.txt

difrancesco_s_Page_49.txt

difrancesco_s_Page_32.txt

difrancesco_s_Page_37.txt

difrancesco_s_Page_36.txt

difrancesco_s_Page_40.txt

difrancesco_s_Page_59.txt

difrancesco_s_Page_52.txt

difrancesco_s_Page_13.txt

difrancesco_s_Page_55.txt

difrancesco_s_Page_11.txt

difrancesco_s_Page_43.txt

difrancesco_s_Page_17.txt

difrancesco_s_Page_20.txt

difrancesco_s_Page_38.txt

difrancesco_s_Page_27.txt

difrancesco_s_Page_45.txt

difrancesco_s_Page_48.txt

difrancesco_s_Page_47.txt

difrancesco_s_Page_51.txt

difrancesco_s_Page_35.txt

difrancesco_s_Page_19.txt

difrancesco_s_Page_44.txt

difrancesco_s_Page_33.txt


Full Text





QUANTITATIVE FRACTOGRAPHY: A COMPARATIVE STUDY FOR POLYMER
TOUGHNESS EVALUATION




















By

STEPHANIE DIFRANCESCO


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2006
































Copyright 2006

by

Stephanie DiFrancesco









ACKNOWLEDGMENTS

This work was supported by Motorola's Advanced Product Technology Center in Fort

Lauderdale, Florida. I would also like to thank my graduate committee members Dr. Elliot

Douglas, Dr. John J. Mecholsky Jr., and Dr. Charles Beatty for their support and expertise.












TABLE OF CONTENTS


page

ACKNOWLEDGMENTS .............. ...............3.....


LIST OF TABLES ................ ...............6............ ....


LIST OF FIGURES .............. ...............7.....


AB S TRAC T ......_ ................. ............_........9


CHAPTER


1 INTRODUCTION ................. ...............11.......... ......


2 BACKGROUND ................. ...............13.......... .....


SENB and Chevron Advantages / Disadvantages ................. ...............17...............
Quantitative Fractography Advantages/Di advantages ......___ ..... .._._. ......._.._......18
Perspective ...._ _. ................. ........_.._.........19
Fracture Mechanics............... ...............1
Fractography ................. ...............21......... ......


3 EXPERIMENTAL ................. ...............24......__ ......


M material s .............. ...............24....
M ol ds ................ ...............24...

Sample Preparation................ ..............2
Quantitative Fractography ................. ...............25......... .....
SENB Pre-crack ................. ...............25.................
SENB Sample Geometries .............. ...............25....
Chevron Notch in Flexure .............. ...............26....
M ethods ............... .. .... ... .... .. .. .. .... .........2

Quantitative Fractography Uniaxial Tensile Test............... ...............26..
Single Edge Notch Bend (SENB)............... ...............26.
Chevron Notch in Flexure .............. ...............26....
Fracture Toughness Calculation ............... ... ...............27..
Quantitative Fractography Fracture Toughness .............. ...............27....
SENB Fracture Toughness Calculation............... ..............2
Chevron Fracture Toughness Calculation .............. ...............28....


4 EXPERIMENTAL DATA AND DISCUS SION ................ ...............31...............


Quantitative Fractography .............. ...............3 1....
Stand ardized SENB Method ............... ...............3 1
SENB Method Development ................. .......... ..... .. ...............31.....
Quantitative Fractography performed on SENB Samples............... ...............32












Method Development: Innovative Pre-crack and Acetone Fixture ................. ...............33
Quantitative Fractography Results for the Optimized SENB Test Method ....................34
SENB Section Conclusions .............. ...............34....
Chevron Notch in Flexure .............. ...............37....


5 CONCLUSIONS .............. ...............54....


LIST OF REFERENCES ................. ...............62................


BIOGRAPHICAL SKETCH .............. ...............64....










LIST OF TABLES


Table page

2-1 Notch geometry specified per fracture technique ................ .............. ......... .....23

4-1 Fracture toughness for DER @150C evaluated with the Instron uniaxial tensile test.......40

4-2 Three point bend SENB fracture toughness values tested at different crosshead rates.....43

4-3 Standard SENB Kwc with acetone and evaluated per standardized SENB method........... .44

4-4 Alternative SENB Kmc with acetone and evaluated per standardized SENB method........45

4-5 Fracture toughness, KIc, values when quantitative fractography was applied to the
fracture features for the failed alternative SENB samples prepared with acetone ............46

4-6 Mean Kwc for various techniques .............. ...............46....

4-7 Test results for the chevron sample fractured in 4-point bend ................. ............... ....49

4-8 Chevron flexure fracture toughness ................. ...............50........_. ...

4-9 Test data for chevron samples tested with acetone and no pre-load ............... ............._....52

4-10 Standard chevron fracture toughness for samples tested with acetone and no pre-load....53










LIST OF FIGURES


Figure page

2-1 Idealized fracture surface showing flaw, mirror, mist, and hackle regions. ......................23

2-2 Typical brittle epoxy fracture surface. .............. ...............23....

3-1 Single Edge Notch Bend (SENB). ................ ...............29........... ..

3-2 Standard notched SENB sample ................ ...............29........... ...

3-3 Alternative SENB sample ................. ...............29................

3-4 Chevron notch flexure............... ...............29.

3-5 Top and side views of the chevron notch sample ................. ...............30.............

4-1 Fracture toughness evaluated with quantitative fractography .............. .....................4

4-2 Optical images of Instron fracture surfaces and flaw boundaries (arrows) .................. .....41

4-3 Load vs. displacement behavior for SENB sample tested at different displacement
rates. .............. ...............42....

4-4 Fracture features for a 0.05 mm/inch crosshead rate ................ ............................43

4-5 Twist/hackle (arrows) fracture features observed at a 0.5 mm/inch crosshead rate..........43

4-6 Secondary crack formation (arrow) evident at a 5.0 mm/min crosshead rate ...................44

4-7 Innovative pre-crack fixture designed to hold a straight edge razor blade and attach
directly to the Instron Dynamight load cell. ............. ...............44.....

4-8 Quantitative fractography images of localized flaws on the failed SENB samples
(arrows mark boundaries of flaw origin) .............. ...............45....

4-9 Fracture toughness for the SENB techniques .............. ...............46....

4-10 Ideal (A) vs. corrected (B) fracture toughness, KIc, for alternative SENB samples
treated with acetone .............. ...............47....

4-11 Ideal (A) vs. corrected (B) fracture toughness, KIc, for the standard SENB samples
treated with acetone .............. ...............47....

4-12 Alternative SENB samples treated with acetone (A) vs. without (B)............... ................48

4-13 Standard SENB samples treated with acetone (A) vs. without (B) .............. .................48










4-14 Standard (A) vs. alternative (B) SENB samples treated with acetone............... ................49

4-15 Top view of an empty flexure fixture and side view with a loaded sample ......................49

4-16 Load vs. displacement behavior typically observed for a tested chevron sample. The
line of best fit (red line) is applied to each curve for analysis. ............. .....................5

4-17 Chevron fracture features due to a 500N load cell and 0.05 mm/min displacement
rate............... ...............51..

4-18 Higher magnification of catastrophic failure at chevron notch tip (red arrow) .................52

4-19 Load vs. displacement curves for chevron samples tested with acetone ................... ........53

5-1 Fracture toughness vs. technique ................ ...............57........... ...

5-2 Fracture toughness for the tensile quantitative fractography (A) vs. chevron flexure
technique (B)............... ...............58..

5-3 Fracture toughness for the tensile Instron quantitative fractography (A) vs.
alternative SENB acetone (B) ................. ...............58.......... .....

5-4 Statistical comparison of fracture toughness evaluated with standardized techniques
for an ANOVA analysis at a 95% confidence level .............. ...............59....

5-5 Statistical comparison of fracture toughness evaluated with standardized and
quantitative fractography techniques for an ANOVA analysis at a 95% confidence
level ................ ............. ............ ..60..









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

QUANTITATIVE FRACTOGRAPHY: A COMPARATIVE STUDY TO EVALUATE
POLYMER FRACTURE TOUGHNESS

By

Stephanie DiFrancesco

December 2006

Chair: Elliot P. Douglas
Major Department: Materials Science and Engineering

Current technology demands high strength polymeric materials. Thermosetting materials,

such as epoxy resins, are potential candidates due to their high strength, good adhesion, thermal,

chemical, and environmental stability, and ability to change stoichiometries and cure

temperatures to tailor end properties of the product. When fully cured, however, epoxies exhibit

brittleness characterized by poor resistance to crack propagation and low fracture toughness.

Since epoxies are primarily designed to perform in the glassy state (well below their glass

transition temperature), the possibility of failure due to crack propagation makes polymer

fracture toughness a basic material parameter that needs to be evaluated.

Previous studies suggest quantitative fractography could provide a reliable technique for

determining fracture toughness, KIc, of brittle polymers. The first obj ective is to determine if

fractography can reliably estimate polymer fracture toughness. The investigated material was

DER 383, a commercial bisphenol-A based epoxy manufactured by Dow that was formulated

with sulfanilamide (SAA) for a 1:1 amine to epoxy ratio and cured at 150C. To confirm validity

of the fractographic technique, fracture toughness was evaluated from the fracture surface

patterns and the quantitative fractography results were compared to those evaluated by the more

standardized SENB and chevron techniques. Both standardized techniques assume that failure is









due to crack propagation from the macro notch of the specimen. In reality, however, it is

possible that failure results from crack growth at some local region along the notch in the

sample. The second obj ective is to apply quantitative fractography to analyze the fracture surface

of the failed SENB and chevron samples to identify the failure origin, determine the actual crack

length from which failure occurred, and compare fracture toughness results.

At a 95% confidence level, the student t-test verified quantitative fractography fracture

toughness was not statistically different from the standardized SENB or chevron flexure

methods. Fracture toughness evaluated at different W/B sample ratios also did not change SENB

KIc measurements. Although the chevron samples demonstrated unstable crack extension due to

catastrophic failure from the chevron notch tip, the mean critical chevron fracture toughness was

not statistically different from the other standardized techniques. Acetone also did not affect the

KIc measurements regardless of technique.

An ANOVA analysis performed at a 95% confidence level determined no statistical

difference between fracture toughness measured with standardized techniques. A statistical

difference, however, was detected when fracture toughness using quantitative fractography was

applied to the failed SENB fracture features. Quantitative fractography on the failed SENB

fracture features showed that the crack assumed to occur along the entire length of the SENB

macro notch by the SENB standardized technique seldom occurs in reality. In contrast, failure in

the tested samples typically resulted from semi-elliptical flaws which suggest the flaw size

assumed by the standardized techniques is not appropriate. Modeling methods such as finite

element analysis should be used in the future to combine independent notch, pre-crack, and semi-

elliptical elements to model the observed behavior more effectively.









CHAPTER 1
INTTRODUCTION

Current technology demands high strength polymeric materials. The diversity of

applications ranges from the automotive and aerospace industries to ship building and

microelectronics. For such applications, it is important to understand the mechanical response of

the material under loading.l Thermosetting materials, such as epoxy resins, are potential

candidates due to their high strength, good adhesion, thermal, chemical, and environmental

stability, and the ability to change initial parameters (cure temperatures, stoichiometries) to tailor

end properties of the product. When fully cured, however, epoxies exhibit brittleness

characterized by poor resistance to crack propagation and low fracture toughness.2 Since these

materials are primarily designed to perform in the glassy state (well below their glass transition

temperature), the possibility of failure due to crack propagation makes polymer fracture

toughness a basic material parameter that needs evaluated. Accurate and reliable measurement of

the fracture toughness property, i.e. the polymer's resistance to fast fracture is therefore critical.

Since fracture toughness plays an integral role in understanding the mechanical response of

a material under loading,3 interest has been generated regarding the different methods and

geometries to determine fracture toughness. Fracture toughness is measured using standard

stress-intensity methods developed from linear elastic fracture mechanics. A wide variation in

the fracture toughness, KIc, values exist for the different test methods and geometries cited in

literature. These differences may be attributed to differences in the material's composition and

microstructure and partially to differences in the fracture behavior (i.e., fast cracking or slow

crack growth) for the test method employed.

Although fracture toughness has been well characterized for ceramics, glass, and metal, it

has not been as extensively studied for polymers. Fracture toughness values of epoxies vary over









a wide range from 0.4 1.8 MPa M V/2 depending on the type of epoxy resin, the curing agent,

stoichiometry of the mix, temperature, cure profie and rate of testing.4 As a result, it is difficult

to predict trends in the fracture toughness values based on a utilized fracture technique.

The maj ority of techniques require a macro notch in the sample. The general assumption is

that crack growth initiates from the sharp macro notch. In reality, however, it is possible that

failure results from crack growth at some local region along the notch in the sample. By

analyzing fracture features of samples failed by standardized techniques with quantitative

fractography, we can identify the exact failure origin and investigate if differences in crack

length account for the variations in measured fracture toughness values.

Previous studies by Oborn" utilized quantitative fractography to measure the fracture

toughness of a commercial bisphenol-A based epoxy (DER3 83) formulated with sulfanilamide

(SAA). The experimental results suggest fractography could provide a reliable technique for

determining KIc of brittle polymers. The first obj ective of this research is determine if

fractography can be reliably used to estimate the fracture toughness of polymers. To confirm

validity of the fractographic technique, one should compare these results to fracture toughness

values obtained from a more standardized method. The two standardized techniques selected for

comparison were single edge notch bend (SENB) and chevron notch in flexure. Fracture

toughness values will be evaluated for each corresponding method and compared to the

quantitative fractography tests. Both SENB and chevron techniques assume that failure is due to

crack propagation from the macro notch of the specimen. The second obj ective is to utilize

quantitative fractography to analyze the fracture surface of the failed SENB and chevron samples

to identify the failure origin and determine the actual crack length from which failure occurred.









CHAPTER 2
BACKGROUND

Within the last few years, research has expressed increased interest in the improvement of

mechanical properties for engineering structural materials. Fracture toughness measures the

resistance of a material to propagate cracks. Fracture behavior depends on the material strength,

stress level, flaw concentration, and failure mechanism.6

Material strength depends strongly on the size of defects, flaws, and cracks in the material.

A crack decreases material strength and strength decreases with increased crack size. Failure, in

many cases, is dominated from fracture initiated by these internal micro cracks and surface

flaws. The study of cracks and their structure led to the evolution of the engineering Hield known

as fracture mechanics; which stems from the basic concepts proposed by Griffith.7 From

Griffith's contributions, its been recognized that material strength is not a characteristic material

property, but a parameter strongly dependent on the distribution and size of defects, flaws, and

cracks within the material.

Different test methods and specimen geometries can be used to determine the fracture

toughness which are measured using stress intensity methods developed from linear elastic

fracture mechanics. The test methods are based on the principle of initiating a controlled crack

that propagates under an applied load through a specimen. The type of measurement required,

the research objectives, and the fracture behavior or microstructure of the material should govern

test method and specimen geometry selection. Factors that should be evaluated when selecting

the appropriate test method and geometry include specimen size, notch and crack geometries,

notch tip acuity, and toughness determination at peak load.

The two types of notch crack geometry prevalent in testing brittle materials are macro

cracks (or macro notches) and indentation induced micro cracks (or micro flaws). Macro cracks










(or macro notches), which create a crack in the form of a diamond sawed-notch, are utilized by

the maj ority of fracture techniques. Induced micro cracks result from surface cracks or flaws

induced by Vickers and Knoop indentation tests.

Notch tip acuity is important for macro notched specimens, which were the focus of this

study. Macro notched specimens are often prepared by creating a crack in the form of a

diamond-sawed notch. Notching the test specimen is done to simulate an ideal planar crack with

a zero root radius to coincide with Linear Elastic Fracture Mechanic9 (LEFM) assumptions.

In LEFM theory, the stress intensity factor, K, describes the stress-strain field in the

vicinity of the crack tip. The origin of failure is assumed to be a sharp crack flaw. A small scale

'process zone', relative to the geometrical dimensions of the elastic body, exists at the crack tip

and implies a 'linear' relation between the load (stress) and the displacement (strain). A crack

propagates when the stress intensity factor reaches a critical value called the "fracture

toughness," KIc.9

Because brittle materials have a limited extent of plastic deformation at the notch tip, the

maj ority of macro notch samples require a delicate pre-cracking procedure. The pre-crack can be

introduced in a variety of ways and its size is dependent on the material and the pre-cracking

procedure selected by the researcher. The most rigorously standardized tests, SENB and CT,

both require a machined macro notch sharpened by a razor blade pre-crack. Some propose the

sharpness of the razor blade cut crack tips is not sufficient compared to the sharpness of a natural

crack. Fatigue sharpened notches are thought to provide more accurate and reliable fracture

toughness data for polymers. If the cyclic stress intensity factor is small enough, fatigue crack

tips are thought to more closely resemble the sharpness of a natural crack. Although fatigue

grown crack tips are common for fracture testing metals, sharpening notches with fatigue crack









in polymers is difficult due to unstable fatigue crack growth and the low frequencies (< 4 Hz in

some polymers) used to avoid hysteresis heating that creates blunt notch and damaged tips.

Because brittle materials have limited extent of plastic deformation at the notch tip, some

materials incorporate a pop-in crack" techniques that typically combine wedge loading at the

root of a sawed notch with some type of crack arrestor attachment, such as a vice. For brittle

materials with notch bend geometry, alternative pre-cracking techniques such as compressive

cyclic fatiguell and bridge indentation methodsl2 have been reported.

Pre-cracking creates difficulties in evaluating the critical stress intensity at the onset of

crack extension, KIc, for brittle materials in particular that exhibit sharply increasing crack

growth resistance (R-curve behavior).13 Pre-crack extensions create an active wake region behind

the crack tip and the residual stresses, micro cracking affects, and crack bridging that occur in

this wake region are believed to be the cause of the rising R-curve behavior. The Kwc fracture

toughness obtained from a pre-cracked specimen is always higher than the true Kwc value of the

material. When possible, it is desirable to avoid pre-cracking procedures in brittle materials.

Several fracture techniquesl4 are available and have been summarized in Table 2-1 that

includes: single edge notched bend (SENB), compact tension (CT), double cantilever beam

(DCB), double torsion (DT), chevron notch (CNB), and fractography. In contrast to the maj ority

of fracture techniques that use macro notched specimens, quantitative fractography analyzes

tensile bars failed in uniaxial tension on an Instron machine. Fracture toughness is determined

from the observed fracture surface patterns. The chevron notch test is a desirable macro notch

technique since it eliminates the need to introduce a pre-crack in the sample, which is extremely

difficult to do with brittle materials.









Fracture toughness of epoxies have been investigated by several researchers using different

techniques that include single edge notched bend (SENB), compact tension (CT), double

cantilever beam (DCB), double torsion (DT), chevron notch (CNB), and quantitative

fractography.

Ritter et al.15 introduced controlled flaws into poly (methyl methacrylate) samples using a

Vickers indenter and liquid acetone to investigate the effect of acetone on pre-crack formation.

During the indent period, a drop of acetone was placed on the contact surface to produce an

aggressive environment that enhanced crack formation. For comparison to more conventional

techniques, standard single-edged notched three-point bend tests were also performed. SENB

samples with and without acetone were tested for comparison. A significant difference between

fracture toughness values measured for the acetone and non-acetone SENB samples was not

found. These results suggest the acetone did not affect the subsequent strength measurement.

In another study, Choi and Saleml6 also used indentation cracks produced in liquid acetone

to evaluate PMMA fracture toughness. They took the evaluation a step further by comparing the

indentation method to CT, DCB, and SENB fracture techniques. In their approach, however, the

liquid acetone was only introduced into the indentation samples. Liquid acetone was not

introduced into the SENB macro notch. The SENB pre-crack was created by inserting a razor

blade in and along the mouth of the sawed notch. Stable crack growth was observed for all the

techniques. Fracture values from conventional testing techniques were consistent with published

PMMA data. The indentation method fracture toughness values, however, were greater than the

conventional pre-cracked specimen. Due to these unexpected results, the authors felt using

indentation cracks produced in liquid acetone to evaluate PMMA fracture toughness should be

done with reservation.









Chial7 investigated the influence of crack tip on bisphenol-A based epoxy fracture

toughness. The epoxy material was machined into SENB specimens with a pre-crack aspect ratio

of 0.5. A Micro Tester was used to conduct the three point bend test at a crosshead displacement

rate of 0. 1 mm/min. In the study, both fatigue and razor blade cut cracks were used to sharpen

the SENB notch tip. The KIc from both pre-cracking methods were in close agreement. The KIc

specimens with the fatigue pre-crack gave slightly lower minimum KIc values than the razor

blade pre-crack specimens. KIc for the fatigue pre-crack and the razor blade pre-crack

specimens were 0.6 and 0.619 respectively.

Ting and Cottingtonls utilized several laboratory techniques to determine the polymer

fracture toughness of unmodified bisphenol A diglycidy ether (DGEBA) epoxies. Double

cantilever beam specimens determined the fracture toughness of the bulk resin. Fracture

toughness of bulk resin was also evaluated by both rectangular and round compact tension

specimens. The study revealed that the fracture toughness of the round CTS specimen, 0. 171

kj/m2, Seemed to agree well with the rectangular CTS specimens (0.187 kj/m2). Although the

rectangular CTS results were similar to the bulk fracture toughness obtained by double cantilever

specimens, the rectangular CTS values were generally higher. Izod impact tests were also

conducted to determine fracture toughness at high loading rates. For the base epoxy, the izod

impact test results (0.23 kj/m2) were in good agreement with the rectangular CTS fracture

toughness (0.23 kj/m2)

SENB and Chevron Advantages / Disadvantages

Single edge notch bend and chevron notch in flexure were the two standardized techniques

selected for comparison to quantitative fractography. SENB advantages include a small sample

size and the simplest geometry compared to other conventional geometries. In addition, a large

body of data, particularly for metals, is available for comparison.









SENB disadvantages include difficulties introducing a sharp pre-crack and that an unstable

mode of crack extension makes it difficult to obtain crack growth data.

Chevron notch advantages also include a small sample size. The chevron configuration is

known to enable stable crack growth for the initial stage of crack extension until catastrophic

fracture occurs. Critical fracture toughness, KIc, is determined from the maximum load at

fracture regardless of crack length. The chevron notch is a desirable macro notch technique since

it eliminates the need to introduce a pre-crack in the sample, which is extremely difficult to do in

brittle materials. The complex chevron geometry is a disadvantage, however, because it increases

machining costs compared to other methods. A two-step loading technique is sometimes

recommended since a single loading rate can fail to produce consistent results.

Quantitative Fractography Advantages/Disadvantages

The maj ority of fracture techniques use a macro notched specimen to determine fracture

toughness. Quantitative fractography, in contrast, determines the fracture toughness of a material

from fracture surface observations. Compared to conventional SENB and CT techniques,

quantitative fractography requires significantly less time for sample preparation and

dimensioning. Fractography appears to reflect real crack growth conditions and simplifies

calculations.

In summary, single edge notch bend (SENB) and chevron notch are less desirable because

of the relatively complex sample preparation and dimensioning compared to quantitative

fractography samples. Pre-cracked single edge notch bend specimens require a critical pre-crack

that is difficult to consistently introduce due to crack branching and crack microstructure

interactions but necessary to encourage stable crack growth. A stable crack provides the best

scenario to investigate the strength of materials because the crack can be more easily duplicated

and provides a platform to investigate different materials.









Fractography is the most desirable technique because of the simplified test method and

relatively straightforward calculations used to determine fracture toughness from the observed

fracture surface patterns. The absence of a macro notch on tensile bar samples is advantageous

because it eliminates the variability associated with notch placement, notch geometry, and notch

acuity.

Perspective

Previous studies by Oborn" utilized quantitative fractography to measure the fracture

toughness of a commercial bisphenol A based epoxy (DER3 83) formulated with sulfanilamide

(SAA). The experimental results suggest fractography could provide a reliable technique for

determining fracture toughness, KIc, of brittle polymers. To confirm validity of this fractography

technique, one should compare these results to fracture toughness values obtained from a more

standardized method. The two standardized techniques selected for comparison were single edge

notch bend and chevron notch in flexure. Fracture toughness values will be evaluated for each

corresponding method and compared to the quantitative fractography results. Both SENB and

chevron techniques assume that failure is due to crack propagation from the macro notch of the

specimen. The second objective is to utilize quantitative fractography to analyze the fracture

surface of the failed SENB & chevron samples to determine the actual crack length from which

failure occurred.

Fracture Mechanics

Based on linear fracture mechanics (LEFM), Irwinl9 developed a relationship between

stress intensity local to the crack tip, K, and the applied stress and geometry of the structure

during loading. The fracture toughness of a brittle material can be expressed by the critical stress

intensity factor, KIc. According to Irwin,19 in an elastic material, the stress field near a crack tip

is described by the stress intensity factor, K, and is material independent but depends on the









sample geometry and distance from the crack tip. Equation 2-1 evaluates the critical value at

which the stress on a sample exceeds that the material is capable of resisting and is called the

fracture toughness, KIc.20 21

Kic "G~ne) /#(2-1)

where

oc = surface correction factor (1.12)

of = stress at fracture

c = crack size

$ = elliptical integral of the second kind

As Oborns previously described, the elliptical integral accounts for the variation in the

stress field due to the shape of the crack tip. For a semi-circular crack the value is n/2. The

crack size is taken to be the radius of a circular or semi-circular crack. However, elliptical or

semi-elliptical crack can be modeled as a semi-circular crack by c = (ab)1/2, where 2a and 2b are

the lengths of the axes of the elliptical crack.22 The calculation of Kw assumes that the material

is linear elastic, that there are no effects due to the edges of the sample, and that the loading is

purely tensile. Equation 2-2 incorporates minor modifications made to standard LEFM theory to

account for a small zone of plasticity near the crack tip.21

K,2c = (a2 2rf c/(#X -(0.2120r /O2 )) (2-2)


where

ovs = yield stress

Taking into consideration the preceding conditions, Equation 2-1 simplifies to Equation 2-3.

Kwc = (1.26)*( of )* (c)1/2 (2-3)









The fracture toughness can be expressed as the critical energy release rate, GI,, which is the

energy required to extend the crack over a unit area under tensile loading. This term is derived

in the energy balance theory developed by Irwin21 based on the work of Inglis,23 Griffith,24 and

Orowan,25 in which the mechanical free energy stored in the material is in equilibrium with the

free energy used to create new crack surfaces. KIc and GI, can be calculated from each other if

Poisson' s ratio and the elastic modulus of the material are known. Flaw size, however, is the

simplest quantitative information available and can be used to evaluate fracture toughness by

Equations 2-1 and Equation 2-2. As described by Mecholsky,26 this technique was developed on

glasses and confirmed on epoxies by Plangsangmas et al.27

Fractography

Fracture features are dependent on the type of failure28, 29 and much of the information is

qualitative, such as the differences between brittle or ductile failure. Figure 2-1 shows the key

features characteristic of brittle29 fracture: the flaw origin, and the mirror, mist, and hackle

regions. The fracture surface typically originates from a volume or surface flaw. When the flaw

itself cannot be measured, patterns on the fracture surface indicate the region from which failure

occurred. The mirror is the smooth region immediately surrounding the fracture origin and

indicates slow crack growth. The mist region contains small radial ridges that surround the

mirror region and reflect an increase in crack velocity. As the crack velocity accelerates, a more

fibrous texture results. Hackle represents a rougher region containing larger radial ridges. Crack

branching begins in the hackle region. The mist and hackle regions are sometimes referred to as

the smooth and rough regions, 28 as seen in Figure 2-2.

Fracture mirrors are typically centered on the strength-limiting origins.30 If the specimen is

highly stressed or the material is fine-grained and dense, the distinct fracture features shown in

Figure 2-1 form. Fracture features for lower energy fractures, coarse-grained, or porous ceramic










materials, however, are usually not as distinct. If a fracture mirror is not evident, the hackle lines

are useful in locating the fracture origin. Hackle lines radiate from, and thus point the way back

to, the fracture origin.









Table: 2-1: Notch geometry specified per fracture technique
Fracture Technique Notch Geometry Pre-crack
Single edge notched bend (SENB) Macro notch Required
Compact tension (CT) Macro notch Required
Double cantilever beam (DCB) Macro notch Required
Chevron notch (CNB) Macro notch Not required
Indentation Not Applicable inherent
Quantitative fractography Not Applicable pre-exisiting


Figure 2-1: Idealized fracture surface showing flaw, mirror, mist, and hackle regions.29


Figure 2-2: Typical brittle epoxy fracture surface.31









CHAPTER 3
EXPERIMENTAL

Materials

DER 383, a commercial bisphenol-A based epoxy manufactured by Dow Chemical, was

prepared and cured with sulfanilamide (SAA), a tetra-functional amine hardener manufactured

by Aldrich, according to the procedure described by Oborn.s Thirty grams of liquid DER3 83 are

weighed into a 60 mL Qorpak bottle and heated at 1700C. Once the epoxy has completed

melted, the sulfanilamide hardener is added in a 1:1 ratio by weight of amine to epoxy. The

mixture is stirred occasionally with a wooden craft stick until the SAA completely dissolves

which typically takes 25-30 minutes. The solution remains heated for an additional 2-3 minutes

and is then removed and degassed for one minute. The solution is placed back into the oven,

heated an additional 2-3 minutes, then removed and degassed a second time. After the second

degassing, the epoxy/amine solution is poured into a mold preheated to 1500C to prevent fast

cooling of the resin and cured at 1500C for four hours. The temperature is then increased at

loC/min for one hour of post-cure at 1750C, followed by an additional loC/min for four hours of

post-cure at 2000C. The epoxy plaques are extracted from the molds and sample geometries were

machined per ASTM specifications for a given technique. Six samples were run for each

technique and the mean fracture toughness and standard deviation calculated.

Molds

Specimen molds for the epoxy plaques consisted of two 8.5 X 4" aluminum plates

separated by '/ inch teflon sheet. Six 1" binder clips hold the plates together. Prior to each use,

the mold surface is sanded with Emory cloth, then 200, 400, & 600-grit sandpaper, and finally

washed with water and then acetone. Plates are air-dried and sprayed with Crown Dry Film

Lubricant and Mold Release Agent (TFE).










Sample Preparation


Quantitative Fractography

A Tensilhut router was used to machine the DER 383 epoxy plaques into Type V tensile

bars per ASTM D63 8.

SENB Pre-crack

The SENB method requires a pre-crack be introduced into the macro notch of the SENB

samples. The crack length, a, is the total depth of the machined notch plus the pre-crack. This

crack length is typically defined so that 0.45 < a/W< 0.55. An a/w ratio of 0.5 was selected for

this study. The pre-crack is initiated by inserting a fresh razor blade and tapping per ASTM

D5045 guidelines.31 If a natural crack cannot be successfully initiated by tapping, the ASTM

recommends sliding a razor blade across the notch root by hand to generate a sufficiently sharp

pre-crack.

SENB Sample Geometries

Both standard and alternative geometries were tested for the method based on dimensions

shown in Figure 3-1. Sample geometries are based on the sample thickness, B. Standard

specimens have a W/B ratio equal to two. Alternative specimens have a W/B ratio equal to 4.

The MathCAD program created evaluated sample dimensions based on ASTM notch

specifications, Motorola's available tool sizes, and sample thickness. Standard SENB dimensions

are shown in Figure 3-2 and include a 3.18 mm thickness, 6.4 mm height, a 0.79 mm notch

width, 1.59 mm notch depth, and 27.98 mm length.

Alternative SENB specimens shown in Figure 3-3 have a sample height, W = 4B. Sample

dimensions include a 3.18 mm thickness, 12.72 mm height, a 1.59 mm notch width, a 3.19 mm

notch depth, and a 55.97 mm length.









Chevron Notch in Flexure

Chevron dimensions are shown in Figure 3-4 below. Because our samples were thicker

than the spec, the dimensions were slightly adjusted to maintain the ratios specified in ASTM

C1421.32 Sample thickness, B, is 3.18 mm. The height, W, is 6.4 mm and sample length, L, is 45

mm. The vertex of the chevron notch angle was calculated to be approximately 56 degrees.

The MathCAD program created evaluated chevron dimensions based on ASTM notch

specifications and Motorola's available tool sizes. The vertex angle machined into the chevron

flexure bar is 53 degrees; notch thickness is less than or equal to 0.25 mm. Chevron notch

samples are shown in Figure 3-5.

Methods

Quantitative Fractography Uniaxial Tensile Test

ASTM D638 tensile dog bone samples were fractured in uniaxial tension on an Instron at

0.5 in/min in order to ensure brittle fracture. The fracture surfaces of each tensile sample are then

analyzed using an optical microscope at 50, 100, or 200 magnification. The flaw depth (a) and

width (2b) of the semicircular flaws and the maj or and minor axis (2b, 2a) of the elliptical flaws

in the bulk of the sample were measured with a reticular eyepiece. The flaw size was calculated

by c = (ab)1/2 and the fracture toughness was determined from Equation 1.1.

Single Edge Notch Bend (SENB)

SENB samples were fractured at 10mm/min in 3-point bend on an Instron with a 500

Newton load cell and a support span equal to four times the sample width.

Chevron Notch in Flexure

Chevron samples were fractured in 4-point bend on an Instron with the recommended

40mm outer and 20mm inner loading span. During testing, the chevron tip is oriented toward the

longer support span so the chevron tip section points toward the tensile surface. A 500 Newton









load cell and a 0.05 mm/min displacement rate fractured the chevron samples in 4 point bend. A

0.05 mm/min (or 0.002 in/min) displacement rate was selected since this rate is most common

for epoxy testing and fell within the 0.03 mm/min to 0.3 mm/min recommended ASTM range for

chevron testing.

Fracture Toughness Calculation

Quantitative Fractography Fracture Toughness

A detailed description of the fracture toughness calculation for the quantitative

fractography technique is provided in the background section.

SENB Fracture Toughness Calculation

The single-edge notched bend test uses a center-notched beam loaded in three or four point

bending to measure plane strain fracture toughness, KIc, or toughness parameter indicative of a

material's resistance to fracture. SENB characterizes the toughness of plastics in terms of the

critical stress intensity factor, KIc, and the energy per unit area of crack surface, or critical strain

energy release rate at fracture initiation, GIc.31 Equation 3-1, derived on the basis of elastic stress

analysis for the specimen type described in the method, determine the value of KIc from the load.

The validity of the calculated KIc value is dependent on the establishment of a sharp crack

condition at the crack tip and exhibited linear elastic behavior.31


KCSNB= [Pq/(B*W )]* fx (3-1)

fxc= 6*"x1/2 [(1.99-_x *(1- x)* (2. 15 -3.93 x +2.7 x2))/(1+ 2* x)* (1- x)' ]

x = 0.5

where

Pq = Load, kN

B = width, cm










x = assumed ideal a/w ratio = 0.5

KICSEMB = SENB fracture toughness, MPA~ml/2

Chevron Fracture Toughness Calculation

Chevron critical fracture toughness, as outlined in ASTM 1421, is evaluated from the

maximum load at fracture and is defined in Equation 3-2:32

KIchevron = Y min* [P max* (So S, )*"10-6]/[B W1 ] (3 -2)

where

KIC chevron = chevron fracture toughness, MPA m V/2

Y min = minimum stress intensity factor coefficient

P max = peak load at fracture

So = outer support span, m

Si = inner loading span, m

B = width, m

W = height, m


The stress intensity factor coefficient, Y min, for the selected chevron geometry in four

point flexure is also outlined in ASTM 1421 and defined in Equation 3-3:32


1.4680+ 5.51641 5.2737 .48 .31
Ymin chevron :_ 33
fa\ fa0\ fa0 al avg
1+3.755- 4.183 +lYI 2.0932 .99
W/ W/ W W











t-


I 1j
2.2W 2.2W B-Wr2
a Three Point Bend Specimen (SENB)
Figure 3-1: Single Edge Notch Bend (SENB).31


Figure 3-2: Standard notched SENB sample


Figure 3-3: Alternative SENB sample


c.. nn~lame Configuration C
Figure 3-4: Chevron notch flexure Configuration C32


B















gure 3-5: Top and side views of the chevron notch sample









CHAPTER 4
EXPERIMENTAL DATA AND DISCUSSION

Quantitative Fractography

Fracture toughness evaluated with quantitative fractography is summarized in Table 4-1.

Quantitative fractography fracture toughness vs. sample for the uniaxial Instron tensile test is

summarized in Figure 4-1.The average critical fracture toughness, KIc, for the Instron

quantitative fractography samples was 1.49 MPa~ml/2. Previous studies Oborn conducted on a

1:1 epoxy to hardener ratio determined a mean critical fracture toughness of 0.93 MPa ml/2


Tensile samples failed from edge flaws due to surface bubbles, machining, or inclusion.

Most flaws appear to have resulted from defects along gauge length that probably resulted from

machining. Distinct boundaries are clearly evident between the fracture features as is the

expected increase in roughness away from the flaw origin.

Standardized SENB Method

SENB Method Development

The single edge notch bend (SENB) technique was the first standardized method selected

for comparison to the quantitative fractography method technique. The SENB method requires a

pre-crack be introduced into the sample. The ASTM recommended a tapping method to

introduce the pre-crack into the SENB macro notch. Our epoxy samples, however, were entirely

too brittle and completely fractured with this approach. The second technique recommended by

the ASTM slid a razor blade by hand across the macro notch. SENB samples were fractured in

3-point bend Instron. A 500 Newton load cell and an S=4W, support span were used. Crosshead

rates of 0.05 mm/min, 0.5 mm/min, 5 mm/min, and 10 mm/min were initially tested to determine

the condition that resulted in stable crack propagation. The load vs. displacement behavior

shown in Figure 4-3 indicates that all SENB samples exhibited brittle fracture independent of the









selected crosshead rate. The 10 mm/min crosshead rate was selected for subsequent testing since

it was the most common rate referenced in epoxy SENB literature.

Fracture toughness for SENB samples tested at different crosshead rates are summarized in

Table 4-2. Optical microscopy was used to inspect the fracture features of the failed SENB

samples tested at different crosshead rates. All samples had similar fracture features: uneven

crack propagation along the specimen macro notch as shown in Figure 4-4. The twist hackle

shown in Figure 4-5 probably resulted from a crack that propagated out of plane. A traveling

macro crack typically diverges; the original crack branches into successively more cracks that

rarely rej oin another crack. Twist hackle, in contrast, usually originates as finely spaced parallel

lines that merge in the direction of crack propagation creating the well know river patters shown

in Figure 4-5. The merger of twist hackle in the direction of crack propagations is opposite the

tendency of macro cracks to diverge. The second pre-crack technique recommended by the

ASTM slid a razor blade by hand along the SENB macro notch but yielded uneven crack

propagation. As a result, in Figure 4-6 an alternative pre-crack approach was attempted where a

triangular razor blade was attached to the vice of a milling machine and dragged across the notch

surface in attempt to control notch depth. This alternative approach, however, still resulted in

uneven crack propagation along SENB macro notch. Rather than smoothly sliding across the

epoxy surface, the blade stuck in the epoxy and formed a secondary crack.

Quantitative Fractography performed on SENB Samples

Because the pre-crack introduced into the SENB macro notch increases the local stress

intensity, the stress correction shown in Equation 4-1 is required for the quantitative fractography

fracture toughness calculation.

0 corrected = 0(max) *k (4-1)

where











o corrected = corrected stress
a (max) = break stress
k = stress concentration factor

The stress-concentration factor, k, incorporates the effect of crack geometry on the local

crack-tip stress level and takes into consideration both the flaw shape and SENB loading

configuration. The Deformation of Fracture Mechanics for Engineering Materials by Hertzberg33

cites a stress concentration factor range from 1.7 to 2.7 for our SENB configuration. The low and

high range for the stress concentration factor was used to evaluate the average fracture toughness

for each sample set for comparison to the standardized techniques.

When quantitative fractography was applied to the failed SENB fracture features to

evaluate fracture toughness, Equation 2-3 therefore simplifies to Equation 4-2.

KIc = (1.26)*(0 corrected) (C)1/2 (4-2)

Method Development: Innovative Pre-crack and Acetone Fixture

Since a consistent pre-crack could not be successfully introduced into our samples with

either recommended ASTM technique, a unique challenge was posed. An innovative pre-crack

Eixture was designed to introduce a consistent pre-crack depth along the entire length of the

SENB macro notch. The Eixture was designed to hold a straight edge razor blade and attach

directly to the Dynamite load cell. Since the amount of load applied to the pre-crack could now

be controlled with the Instron, a consistent pre-crack depth could be applied along the entire

length of the SENB macro notch. A fresh razor blade was used to pre-crack each specimen.

Several pre-crack loads were investigated, however, a 20 lbf pre-crack was chosen since it

yielded the best results without specimen damage. In addition to the introduction of a consistent

pre-crack, a drop of acetone was added to the alternative SENB macro notch and allowed to dry

24 hrs prior to testing.










The innovative pre-crack fixture combined with acetone appeared to yield more even crack

propagation along the macro notch, therefore, this sample preparation was utilized for all

subsequent testing. Compared to hand controlled razor blade cutting, the straight edge razor

pre-crack fixture offered better control in achieving the sharp pre-crack needed for stress

intensity measurement. SENB samples prepared with this optimized technique were fractured in

3 point bend on an Instron at 10 mm/min. SENB test data is summarized in the Table 4-3 and

Table 4-4.

Quantitative Fractography Results for the Optimized SENB Test Method

Typical fracture features observed when quantitative fractography was applied to the failed

single edge notch bend (SENB) surface patterns are shown in Figure 4-8. Quantitative

fractography on the failed single edge notch bend fracture features revealed that the crack

assumed to occur along the entire length of the SENB macro notch by the standardized SENB

technique seldom occurs in reality. In contrast, failure in the tested samples typically resulted

from semi-elliptical flaws which suggest the flaw size assumed by the standardized techniques in

not appropriate.

The measured critical fracture toughness, KIc, for the standard SENB epoxy specimens

treated with acetone was 1.1 MPA~m '/. Critical fracture toughness, KIc, for the alternative

SENB epoxy specimens treated with acetone was 1.4 MPA~m '/.

Table 4-5 summarizes the fracture toughness values evaluated by Equation 4-2 when

quantitative fractography was applied to the failed SENB features.



SENB Section Conclusions

Mean critical fracture toughness for both the standard and alternative SENB samples are

summarized in Table 4-6. The first column represents the fracture toughness, KIc, calculated by









the standardized SENB method using the assumed ideal a/w ratio of 0.5. The second column, KIc

SENB corrected, represents the corrected SENB KIc values determined when optical microscopy

was used to measure the actual crack length from which failure occurred on the fracture surface

rather than the ideal ratio assumed by the standardized method. The third column represents the

fracture toughness when quantitative fractography was applied to the failed SENB fracture

features.

Based on the ideal 0.5 a/w ratio assumed by the standardized technique, mean critical

fracture toughness for the alternative SENB samples tested with and without acetone were 2.6

and 3.0 MPA~m '/ respectively. Based on the ideal 0.5 a/w ratio assumed by the standardized

technique, mean critical fracture toughness for the standard SENB samples tested with and

without acetone were 2.1 and 2.0 MPA~m '/ respectively.

When optical microscopy was used to inspect the failed SENB fracture features and

measure the actual critical crack length, a, from which failure occurred the corrected SENB

fracture toughness were significantly different than those determined using the ideal 0.5 a/w ratio

assumed by the standardized SENB technique.

Critical fracture toughness, KIc, for the standard, alternative, and quantitative fractography

SENB samples are summarized in Figure 4-9. The corrected critical fracture toughness, KIc, for

the standard SENB epoxy samples treated with and without acetone were 1.1 and 1.1 MPA~m '/

respectively. The corrected critical fracture toughness, KIc, for the alternative SENB epoxy

specimens treated with acetone and without acetone were 1.4 and 1.6 MPA~m '/ respectively .

When quantitative fractography was applied to the alternative SENB samples treated with

and without acetone, the mean critical fracture toughness were 1.2 and 1.5 MPA~m '/

respectively.










When quantitative fractography was applied to the standard SENB samples treated with

and without acetone, the mean critical fracture toughness were 0.7 and 0.6 MPA~m V/2

respectively. The crack size assumed to occur along the entire length of the SENB macro notch

by the SENB standardized technique seldom occurs in reality. This proves it is critical to utilize

optical microscopy to inspect the SENB failed surface for an accurate fracture toughness

measurement.

The student t-test, t(10) =4.63, P < 0.05 (two-tail), executed at a 95% confidence level in

Figure 4-10 verified a statistical difference between the ideal vs. the corrected KIc SENB fracture

toughness value for the standardized SENB method.

The student t-test, t(8) = 7.4, P<0.05 (two-tail) executed at a 95% confidence in Figure 4-

11 also verified a statistical difference between the ideal (x=0.5) vs. corrected (x=scope

measurement) standard SENB acetone fracture toughness value for the standardized SENB

method.

The analysis shown in Figures 4-10 and 4-11 verified a statistical difference between the

ideal (x=0.5) vs. corrected (x= scope measurement) fracture toughness measured for the

standardized SENB technique. This proves it is critical to utilize optical microscopy to inspect

the failed SENB fracture features for an accurate fracture toughness measurement or else the

fracture toughness values reported by the standardized SENB methods will be higher than the

material's true fracture toughness.

The student t-test, t(9) = -1.21, P < 0.05 (two tail), executed at a 95% confidence level in

Figure 4-12 verified that acetone did not effect alternative SENB fracture toughness

measurements. The student t-test, t(8) = 0.34, P < 0.05 (two tail), executed at a 95% confidence










level in Figure 4-13 also verified that acetone did not effect standard SENB fracture toughness

measurements.

To investigate the effect of sample geometry on fracture toughness, the SENB alternative

(W= 4B) vs. standard (W=2B) acetone sets were compared where B represented sample

thickness. Because acetone affects were determined negligible, only the acetone sets were

compared. Mean critical fracture toughness, KIc, for the alternative SENB epoxy specimens

treated with acetone was 1.4 MPA~m '/. Mean critical fracture toughness, KIc, for the standard

SENB epoxy specimens treated with acetone was 1.1 MPA~m '/.

The student t-test, t(9) = 1.87, P < 0.05 (two tail), executed at a 95% confidence level in

Figure 4-14 verified that fracture toughness evaluated for the different W/B ratios of the standard

vs. alternative SENB geometries were not statistically different. For the same technique,

differences in sample geometry did not affect SENB fracture toughness.

Chevron Notch in Flexure

Chevron notch in flexure was the second standardized technique selected for comparison to

quantitative fractography results. Motorola's Prototype Shop machined the fixture per ASTM

guidelines. An adjustable support span and stopper blocks were added to center the sample and

ensure consistent loading. Chevron samples were fractured in 4-point bend on an Instron with

the recommended 40 mm outer and 20 mm inner loading span.

A 500 Newton load cell and a 0.05mm/min displacement rate fractured the chevron

samples in 4 point bend. A 0.05 mm/min (or 0.002 in/min) displacement rate was selected since

this rate was the most common for epoxy testing and fell within the 0.03 mm/min to 0.3 mm/min

recommended ASTM range for chevron testing. Pre-loading the sample prior to testing is

sometime recommended to help promote stable crack propagation. Three different preload









techniques were investigated and are summarized in Table 4-7. Chevron fracture toughness for

the pre-loaded samples are summarized in Table 4-8.

An example of typical load vs. displacement curves for the pre-loaded chevron samples is

provided below in Figure 4-16. The blue sample line had a 20N preload applied prior to sample

testing. The green sample line was pre-loaded per chevron ASTM methods. Samples with no

pre-load exhibited behavior similar to the blue line.

Load vs. displacement graphs for all tested chevron samples confirmed catastrophic

failure. As shown in Figure 4-16, these samples exhibited a sudden drop in load from the linear

portion that was not followed by a subsequent load increase; this curve behavior suggests

unstable fracture from the chevron notch tip. Per chevron ASTM guidelines, this load vs.

displacement behavior is indicative of invalid results for this particular technique. Pre-loading

was supposed to promote stable fracture, however, based on catastrophic failure shown in the

load vs. displacement graphs, pre-load did not effect fracture behavior.

The failed chevron fracture features shown in Figure 4-17 verified the pre-load did not

promote stable fracture in the tested samples. Images a and b had no preload applied to the

sample. Images c and d had a 20N preload applied prior to testing. Sample images e, f, g, and h

were pre-loaded per chevron ASTM methods. All fractography images on the failed chevron

samples shown in Figure 4-17 indicated catastrophic failure at chevron notch tip.

Quantitative fractography performed on the fracture features of the failed chevron samples

confirmed catastrophic failure from the chevron notch tip in all samples.

Since catastrophic failure occurred in all of the tested chevron samples, a drop of acetone

was added to the chevron notch to determine if a more aggressive environment might encourage

stable crack propagation from the notch. A drop of acetone was placed in the chevron notch and









allowed to dry for 24 hrs prior to testing. Test data for the chevron samples tested with acetone

and no pre-load are summarized in Table 4-9.

The load vs. displacement graphs indicated that the presence of acetone did not affect the

crack propagation. All tested samples still demonstrated catastrophic failure from the chevron

tip.

Chevron fracture toughness is summarized in Table 4-10. The mean critical fracture

toughness, KIc, for the chevron samples was 1.58 MPA m 1/2; however, the observed load vs.

displacement behavior were characteristic of catastrophic failure from the chevron notch tip and

considered invalid per chevron ASTM. Future work could investigate different sample geometry

ratios or chevron notch angles that might promote stable crack propagation but was not deemed

necessary for the scope of this study.











Table 4-1: Fracture togness for DER @150C evaluated with the Instron uniaxial tensile test
mple Break Stress flaw width, 2b depth, a crack size, c Klc = 1.26 *of c 1/2
(MPA) (meters) (meters) (meters) (MPA*ml/2
1 101.4 3.E-04 2.6E-04 2.E-04 1.8
2 101.3 3.E-04 2.8E-04 2.E-04 1.9
3 101.3 1.E-04 1.3E-04 9.E-05 1.2
4 97.6 3.E-04 1.7E-04 2.E-04 1.5
6 99.2 2.E-04 1.9E-04 1.E-04 1.4
7 100.8 3.E-04 1.8E-04 2.E-04 1.6
8 102.5 9.E-05 9.4E-05 7.E-05 1.1
MEAN 100.6 2.E-04 2.E-04 1.E-04 1.5
STN D 1.6 9.E-05 7E-05 5.E-05 0.3


|g Instron KC IC


1 2 3 4
Sam pie


5 6


Figure 4-1: Fracture toughness evaluated with quantitative fractography







































C) a)


Figure 4-2: Optical images of Instron fracture surfaces and flaw boundaries (arrows) a) edge flaw
from surface bubble b) edge flaw c) edge flaw from inclusion d) edge flaw


































Figure 4-3: Load vs. displacement behavior for SENB sample tested at different displacement
rates. 1) 5.0 mm/min blue line, 2) aborted, 3) 0.05 mm/min aqua line, 4) 0.5
mm/min red line and 5) 10 mm/min recommended ASTM rate-pink line











Table 4-2: Three point bend SENB fracture toughness values tested at different crosshead rates
Sample rate Width Thickness Peak UlIti mate Modulus Energy at Kic chevron
(mm/min) (cm) (cm) Load tensile (MPA) Break (MPA* ml/2)
(kN) strength (N*mm)
(MPA)


47.7
47.5
40.0
39.9


5.0
0.05
0.5
10.0


0.08
0.07
0.06
0.06


5902.1
7217.2
6060.2
6655.4


15.1
9.3
8.5
7.2


Figure 4-4: F`racture features for a U.US mm/Inch crosshead rate


Figure 4-5: Twist/hackle (arrows) fracture features observed at a 0.5 mm/inch crosshead rate



















































Figure 4-7: Innovative pre-crack fixture designed to hold a straight edge razor blade and attach
directly to the Instron Dynamight load cell. Now that the applied pre-crack load could
be controlled, a consistent pre-crack depth could be made along the entire length of
the SENB macro notch.


Table 4-3: Standard SENB KIc with acetone and evaluated per standardized SENB method
Sample Width Thickness Peak Load Klc ideal SENB Klc ideal SENB corrected
(mm) (mm) (kN) (MPA *m 1/2) (MPA *m 1/2
2 6.5 3.0 0.05 2.2 1.1
3 6.4 3.0 0.04 1.7 0.9
4 6.4 3.2 0.05 2.1 1.1
5 6.5 3.2 0.06 2.5 1.3
6 6.5 3.1 0.05 2.1 1.1
Mean 6.5 3.1 0.05 2.1 1.1
Std. Dev. 0.03 0.06 0.01 0.3 0.2


Figure 4-6: Secondary crack formation (arrow) evident at a 5.0 mm/min crosshead rate











Table 4-4: Alternative SENB KIc with acetone and evaluated per standardized SENB method
Sample Width Thickness Peak Klc ideal SENB Klc ideal SENB
(cm) (cm) Load (MPA *m 1/2) COrrected
(kN) (MPA *m 1/2)
1 1.3 0.3 0.1 2.1 1.3
2 1.3 0.3 0.1 2.1 1 1
4 1.3 0.3 0.1 2.4 1.3
5 1.3 0.3 0.1 2.1 1 1
6 1.3 0.3 0.1 3.0 1.6
7 1.3 0.3 0.1 3.5 1 8
Mean 1.3 0.3 0.1 2.6 1.4
Std. Dev. 0.0 0.0 0.0 0.6 0.3


20 microns 20 microns


Figure 4-8: Quantitative fractography images of localized flaws on the failed SENB samples
(arrows mark boundaries of flaw origin)






































































Figure 4-9: Fracture toughness for the SENB techniques


L___1__ _~~~ ~ ~ ~ ~ p_1_ pV ____ __ __ V I_ 1
Sample o (max) c= (ab) Klc = (1.26)*( o corrected )* (c)
(M PA) (m) (MPa ml/2)
1 42.6 1.E-04 1.3
2 45.3 8.E-05 1.2
4 47.4 6.E-05 1.0
5 46.1 4.E-05 0.8
6 64.1 9.E-05 1.7
7 71.7 6.E-05 1.5
Mean 52.9 7.E-05 1.2
Std. Dev. 12 3.E-05 0.3



Table 4-6: Mean KIc for various techniques
Kic SENB Kic SENB QF Kic SENB
ideal corrected (a corrected)
(MPA*ml/2) (MPA*ml/2) (MPA*ml/2)

Alternative SENB no acetone 3.0 1.6 1.5
Alternative SENB acetone 2.6 1.4 1.2
Standard SENB no acetone 2.0 1.1 0.6
Standard SENB acetone 2.1 1.1 0.7


Table 4-5:


Fracture toughness, KIc, values when quantitative fractography was applied to the
e rutcarf features for the failed alter e


____1____















3.5-



3.0-



2.5-



2.0-



1.5-



1.0-
A B



Figure 4-10: Ideal (A) vs. corrected (B) fracture toughness, KIc, for alternative SENB samples
treated with acetone



































Figure 4-11: Ideal (A) vs. corrected (B) fracture toughness, KIc, for the standard SENB samples
treated with acetone
















47





































1.0-







Fiue41:SanadSN aplstetdwthaeoe()vs ihu B










E4































































Table 4-7: Test results for the chevron sample fractured in 4-point bend
Sample Width Thickness Peak Tensile Modulus Yield strain Energy at Break
(mm) (mm) Load strength (MPA) Stress at Break stress
(N) (MPA) (MPA) break (N*mm) (MPA)

A 6.4 3.2 54.0 25.0 9437.9 25.0 0.3 8.6 25.0
B 6.4 3.2 53.3 24.7 9580.7 24.7 0.3 8.8 24.7
C 6.5 3.1 42.2 20.9 9391.4 20.9 0.2 6.1 20.9
A = No preload was applied to sample
B = A 20N preload was applied per the standard 4-pt bend test position shown before testing
C = Sample was first inverted and the 20N preload was applied per the chevron ASTM method


Ic;


ir D
X:


Figure 4-14: Standard (A) vs. alternative (B) SENB samples treated with acetone


Figure 4-15: Top view of an empty flexure fixture and side view with a loaded sample











Table 4-8: Chevron flexure fracture toughness
Sample Width Thickness Peak Load Y min Klc chevron
(mm) (mm) (N) (MPA *m 1/2

A 6.4 3.2 53.5 2.8 1.9
B 6.4 3.2 54.0 2.9 1.9
C 6.4 3.2 53.3 2.8 1.8
D 6.5 3.1 42.2 2.8 1.5


Figure 4-16: Load vs. displacement behavior typically observed for a tested chevron sample. The
line of best fit (red line) is applied to each curve for analysis.
























Cll


UJ


C0I


g) h)


Figure 4-17: Chevron fracture features due to a 500N load cell and 0.05 mm/min displacement
rate.





















































Table 4-9: Test data for chevron samples tested with acetone and no pre-load
Sample Width Thickness Peak Tensile Modulus Energy At Energy At Stress At
(mm) (mm) Load Strength (MPa) Yield Break Break
(N) (MPa) (N*mm) (N*mm) (Pa)
1 6.6 3.1 47.7 22.7 8452.8 0.3 8.1 22.5
2 6.6 3.1 54.5 26.0 9261.5 0.3 9.2 26.0
3 6.7 3.1 34.2 16.0 7492.1 0.3 4.4 16.0
4 6.6 3.1 56.0 26.7 8769.6 0.4 10.0 26.7
5 6.7 3.1 53.6 25.7 8917.5 **** 9.0 25.7
Mean 6.6 3.1 49.2 23.4 8578.7 0.3 8.1 23.4
St. Dev. 0.1 0.0 9.0 4.4 673.4 0.0 2.2 4.5


gure 4-18: Higher magnification of catastrophic failure at chevron notch tip (red arrow)



















































Table 4-10: Standard chevron fracture toughness for samples tested with acetone and no pre-load
Sample \Mdth Thickness Peak Stress At Peak Y min chevron Chevron Klc
(mm) (mm) Load Breake Load (MPA m 1/2)
(N) (MPa) (kN)


1 6.6 3.1 47.7 22.5 0.05 2.7 1.6
2 6.6 3.1 54.5 26.0 0.05 2.7 1.8
3 6.7 3.1 34.2 16.0 0.03 2.6 1.1
4 6.6 3.1 56.0 26.7 0.06 2.7 1.8
5 6.7 3.1 53.6 25.7 0.05 2.7 1.7
Mean 6.6 3.1 49.2 23.4 0.05 2.7 1.6
St. Dev. 0.1 0.0 9.0 4.5 0.01 0.0 0.3


Figure 4-19: Load vs. displacement curves for chevron samples tested with acetone









CHAPTER 5
CONCLUSIONS

Critical fracture toughness, KIc, for the various tested techniques are summarized in Table

5-1. The student t-test, t(11) = 0.36, P < 0.05 (two tail), executed at a 95% confidence level in

Figure 5-2 verified the uniaxial tensile test to evaluate quantitative fractography fracture

toughness (Instron) was not statistically different from the standardized chevron flexure method.

The student t-test, t(11) = 0.90, P < 0.05 (two tail), executed at a 95% confidence level in

Figure 5-3 verified that the uniaxial tensile test to evaluate quantitative fractography fracture

toughness was not statistically different from the standardized SENB method.

The ANOVA analysis, F( 5, 27) = 3.89, P >0.05, executed at a 95% confidence level in

Figure 5-4 determined no statistical difference between fracture toughness comparisons

measured with the standardized techniques.

The load vs. displacement behavior of the tested chevron samples revealed unstable crack

extension due to catastrophic failure from the chevron notch tip. Fracture toughness results were

therefore higher than those from chevron tests with stable crack extension, however, the mean

critical chevron fracture toughness was not statistically different from the other standardized

techniques.

The ANOVA analysis, F( 9, 52) = 9.5, P >0.05, executed at a 95% confidence level for all

tested fracture techniques is provided in Figure 5-5. For quantitative fractography applied to

failed SENB surfaces, the KIc average was reported based on the stress concentration factor that

ranged from 1.7 (low) to 2.7 (high).

In summary, at a 95% confidence level, the student t-test verified that the determination of

fracture toughness using quantitative fractography from fracture surfaces of uniaxial tensile

specimens was not statistically different from the standardized SENB or chevron flexure









methods. At a 95% confidence level, the student t-test verified that acetone did not affect the KIc

measurements regardless of technique.At a 95% confidence level, the student t-test also verified

that the alternative vs. standard SENB samples yielded similar KIc results. For the same SENB

technique, different W/B sample ratios did not change the KIc calculations. An ANOVA analysis

performed at a 95% confidence level determined that there is not statistical difference between

fracture toughness measured with standardized techniques.

When applying quantitative fractography to the failed SENB fracture features, a stress

concentration factor must be used to account for the effect of crack geometry on the local crack-

tip stress level due to the SENB pre-crack at the base of the SENB macro notch. A stress

correction factor that ranged from 1.7 to 2.7 was selected based on literature. ANOVA analysis

performed at a 95% confidence level determined a statistical difference in the fracture toughness

evaluated with the standardized techniques vs. those measured when quantitative fractography

was applied to the failed SENB fracture features. When quantitative fractography was applied to

the failed SENB features, the lower fracture toughness shown for standard SENB sets G and H in

Figure 5-5 resulted from a lower break stress. Because the measured flaw sizes between samples

were similar, this lower break stress was unexpected and due to some other effect not being

measured .

The load vs. displacement behavior of the tested chevron notch samples showed unstable

crack extension due to catastrophic failure from the chevron notch tip. Although the fracture

toughness results were greater than results that would have generated had stable crack extension

occurred, the mean critical chevron fracture toughness was not statistically different from the

other standardized techniques. Future work could investigate different ratios or chevron notch










angles to promote stable crack propagation but was not deemed necessary for the scope of this

study .

This study demonstrated the importance of quantitative fractography as a failure analysis

tool to accurately identify intrinsic material flaws and failure origin. Quantitative fractography

on the failed SENB fracture features revealed that the crack assumed to occur along the entire

length of the SENB macro notch by the SENB standardized technique seldom occurs in reality.

In contrast, failure in the tested samples typically resulted from semi-elliptical flaws, which

suggests the flaw size assumed by the standardized techniques is not appropriate. Modeling

methods such as finite element analysis, should be used to combine independently notch, pre-

crack, and semi-elliptical elements to model the observed behavior more effectively.










Table 5-1: Average Fracture Toughness, KIc, for the various techniques tested
Technique SENB Klc corrected Klc with QF applied to SENB
(standardized method) (a corrected)
(MPA *m 1/2) (MPA *m 1/2
Alternative SENB no acetone 1.6 1.5
Alternative SENB with acetone 1.4 1.2
Standard SENB no acetone 1.1 0.6
Standard SENB with acetone 1.1 0.7
Chevron 1.6
Quantitative Fractography method 1.5



m KlC Technique
SKlC SENB corrected
o QF KlCSEN B
4.0
3.5

E 2.5








Techiqu


Figure 5-1: Fracture toughness vs. technique




















1.4



1.2









A B




Figure 5-2: Fracture toughness for the tensile quantitative fractography (A) vs. chevron flexure
technique (B)







1. 8-




1.6




1.4-




1.2-




A B


Figure 5-3: Fracture toughness for the tensile Instron quantitative fractography (A) vs. alternative
SENB acetone (B)



































A B C D E F

Figure 5-4: Statistical comparison of fracture toughness evaluated with standardized techniques
for an ANOVA analysis at a 95% confidence level

Where A = Corrected alternative SENB KIC no acetone
B = Corrected alternative SENB KIC with acetone
C = Corrected standard SENB KIC no acetone
D = Corrected standard SENB with acetone
E = Instron KIC
F = Chevron KIC






















A B CE PH I
1.X









Figure 5-5: Statistical comparison of fracture toughness evaluated with standardized and
quantitative fractography techniques for an ANOVA analysis at a 95% confidence
level

where A = Corrected alternative SENB KIC no acetone
B = Corrected alternative SENB KIC with acetone
C = Corrected standard SENB KIC no acetone
D = Corrected standard SENB with acetone
E = Instron KIC
F = Chevron KIC
G = Quantitative Fractography KIC for failed standard SENB no acetone
H = Quantitative Fractography KIC for failed standard SENB with acetone
I = Quantitative Fractography KIC for failed alternative SENB acetone
J= Quantitative Fractography KIC for failed alternative SENB no acetone









CHAPTER 6
FUTURE WORK

The effect of sharp vs. blunt cracks on polymer fracture toughness could be evaluated by

repeating these fracture toughness tests using acetone on a brittle thermoplastic polymer such as

poly (methyl methacrylate).

Since all tested chevron samples revealed unstable crack extension due to catastrophic

failure from the chevron notch tip, future work could investigate different chevron geometries or

chevron notch angles that promote stable crack propagation but was not deemed necessary for

the scope of this study.

Quantitative fractography on the failed SENB fracture features revealed that the crack

assumed to occur along the entire length of the SENB macro notch by the standardized SENB

technique seldom occurs in reality. Therefore, in the future more effective modeling methods,

such as finite element analysis, should be developed and utilized to combine independent notch,

pre-crack, and semi-elliptical elements to more effectively model the observed crack propagation

behavior.










CHAPTER 7
LIST OF REFERENCES

1. A. A. Griffith: Philos. Trans R. Soc., 1920, 221,163-198.

2. L. Plangsangmas, J. Mecholsky, Jr., and A.B. Brennan: J. Appl. Polym. Sci., 1999, 72, 257-
268.

3. G. Medri, C. Cali, and R. Ricci: Plastics, Rubber and Composites Processing and
Applications, 1995, 23(4), 260-268.

4. R.Y Ting and R.L Cottington: Journal ofAppliedPolymer Science, 1980, 25(9), 1815-
1823.

5. E.J. Oborn: Fracture Toughness ofa Liquid Crystalline Epoxy, Department of Materials
Science and Engineering, University of Florida, Gainesville, Florida 32611, 2000, p. 18-53.

6. M. Sakai and M. Inagaki: J. Am. Ceram. Soc., 1989, 72, 388-394.

7. A. A. Griffith: Philos. Trans R. Soc., 1920, 221,163-198.

8. F.I. Baratta: "The Effect of Crack Instability/Stability of Fracture Toughness of Brittle
Material s," Fatigue and Fracture M~echanics: 28th Volume, ASTM STP (1321), J.H.
Underwood, B.D. Macdonald, and M.R. Mitchell, Eds., American Society for Testing and
Materials, Philadelphia, PA, 1997, p. 577- 601.

9. ASTM Designation: E1823-96E1, "Standard Terminology Relating to Fatigue and Fracture
Testing," Annual Book ofASTM\~S tan~ddd~~~dddards,~ American Society for Testing and Materials,
Philadelphia, PA, 1996, p. 1027-1044.

10. M. Sakai and M. Inagaki: J. Am. Ceram. Soc., 1989, 72, 388-394.

11. L. Ewart and S. Suresh: J. Mater. Sci. Lett., 1986, 5, 774-778.

12. T. Nose and T. Fuji: J. Am. Ceram. Soc., 1988, 71, 328-333.

13. A. Meyers and K. Chawla: M~echanical Behavior of2aterials, Prentice-Hall, Inc., Upper
Saddle River, NJ, 1999, p. 363-364.

14. S. Bandyopadhyay: Materials Science and Engineering, 1990, A125, 158-165.

15. J.E. Ritter, M.R. Lin, and T.J. Lardner: Journal of2aterials Science, 1988, 23, 2370-2378.

16. S.R. Choi and J.A. Salem: J. Mater. Res., 1993, 8, 3210-3217.

17. J. Chia: Institute of2aterials Research and Engineering, 2004, 4, 1-4.










18. R.Y Ting and R.L Cottington: Journal ofAppliedPolymer Science, 1980, 25(9), 1815-
1823.

19. G. W. Irwiin: Trans. ASM~E J. Appl. M~ech., 1957, 24, 361-364.

20. G. W. Irwiin: Trans. ASM~E J. Appl. M~ech., 1962, 29, 651-654.

21. P. N. Randall: ASTM~STP 410, 1967, 88-126.

22. J. J. Mecholsky, S. W. Freiman, and R.W. Rice: J. Am. Ceram. Soc., 1977, 60, 114-117.

23. C. E. Inglis: Transactions of the Institute ofNavalArchitects, 1 913, 55, 2 19-24 1.

24. A. A. Griffith: Phil. Trans. Roy. Soc., 1921, A221, 163-198.

25. E. Orowan: Repts. Prog. Phys., 1948, 12, 185.

26. J. Mechol sky Jr.: Quantitative Fracture Surface Analysis of Glass Materials; Simmons, C.
J. and El-Bayoumi, O. H., Ed.; American Ceramic Society, Westerville, Ohio, 1993.

27. L. Plangsangmas, J. Mecholsky Jr., and A.B. Brennan: J. Appl. Polym. Sci., 1999, 72, 257-
268.

28. A. C. Roulin-Moloney: Fractography and Failure M~echanisms of Polymers and
Composites, Elsevier Science Publishers Ltd., New York, 1989.

29. L. Engel, H. Klingele, G. W Ehrenstein, and H. Schaper: An Atlas of Polymer Damage,
Prentice-Hall, Inc., Englewood Cliffs, NJ, 1981.

30. ASTM Designation: C1322-96a, "Standard Practice for Fractography and Characterization
of Fracture Origins in Advanced Ceramics," Annual Book ofASTM~Standard~~dddsddddd~~~~ American
Society for Testing and Materials, Philadelphia, 1996, p 421-465.

31. ASTM Designation: D5045-99, "Standard Test Methods for Plane-Strain Fracture
Toughness and Strain Energy Release Rate of Plastic Materials," Annual Book ofASTM\~
Standard~~~dddsdddd~~~~ American Society for Testing and Materials, Philadelphia, 1999, p. 347-355.

32. ASTM Designation: C1421-99, Standard Test Methods for Determination of Fracture
Toughness of Advanced Ceramics at Ambient Temperature," Annual Book ofASTM\~
Standards, American Society for Testing and Materials, Philadelphia, 1999, p. 641-669.

33. R. Hertzberg: Deformation and Fracture M~echanics of Engineering Materals; 3rd ed.;
John Wiley & Sons, Inc., New York, 1989.









BIOGRAPHICAL SKETCH

Stephanie DiFrancesco graduated from Villanova University in 1997 with a bachelor' s

degree in chemical engineering and a minor in chemistry. Stephanie DiFrancesco is employed by

Motorola's Advanced Product Technology Center in Fort Lauderdale, FL. Technical skills

include thermal, mechanical and theological material characterization techniques. As the Plastic

Lab Administrator, Stephanie supports global product development sectors as their needs relate

to material and plastic development.




Full Text

PAGE 1

1 QUANTITATIVE FRACTOGRAPHY: A COMPARATIVE STUDY FOR POLYMER TOUGHNESS EVALUATION By STEPHANIE DIFRANCESCO A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2006

PAGE 2

2 Copyright 2006 by Stephanie DiFrancesco

PAGE 3

3 ACKNOWLEDGMENTS This work was supported by Motorolas A dvanced Product Technology Center in Fort Lauderdale, Florida. I would also like to thank my graduate committee members Dr. Elliot Douglas, Dr. John J. Mecholsky Jr., and Dr. Char les Beatty for their support and expertise.

PAGE 4

4 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................3 LIST OF TABLES................................................................................................................. ..........6 LIST OF FIGURES................................................................................................................ .........7 ABSTRACT....................................................................................................................... ..............9 CHAPTER 1 INTRODUCTION..................................................................................................................11 2 BACKGROUND....................................................................................................................13 SENB and Chevron Advantages / Disadvantages..................................................................17 Quantitative Fractography Advantages/Disadvantages..........................................................18 Perspective.................................................................................................................... ..........19 Fracture Mechanics............................................................................................................. ....19 Fractography................................................................................................................... ........21 3 EXPERIMENTAL..................................................................................................................24 Materials...................................................................................................................... ...........24 Molds.......................................................................................................................... ............24 Sample Preparation............................................................................................................. ....25 Quantitative Fractography...............................................................................................25 SENB Pre-crack...............................................................................................................25 SENB Sample Geometries..............................................................................................25 Chevron Notch in Flexure...............................................................................................26 Methods........................................................................................................................ ..........26 Quantitative Fractography Uniaxial Tensile Test............................................................26 Single Edge Notch Bend (SENB)....................................................................................26 Chevron Notch in Flexure...............................................................................................26 Fracture Toughness Calculation.............................................................................................27 Quantitative Fractography Fracture Toughness..............................................................27 SENB Fracture Toughness Calculation...........................................................................27 Chevron Fracture Toughness Calculation.......................................................................28 4 EXPERIMENTAL DATA AND DISCUSSION...................................................................31 Quantitative Fractography......................................................................................................31 Standardized SENB Method...................................................................................................31 SENB Method Development...........................................................................................31 Quantitative Fractography performed on SENB Samples...............................................32

PAGE 5

5 Method Development: Innovative Precrack and Acetone Fixture.................................33 Quantitative Fractography Results for the Optimized SENB Test Method....................34 SENB Section Conclusions.............................................................................................34 Chevron Notch in Flexure...............................................................................................37 5 CONCLUSIONS....................................................................................................................54 LIST OF REFERENCES............................................................................................................. ..62 BIOGRAPHICAL SKETCH.........................................................................................................64

PAGE 6

6 LIST OF TABLES Table page 2-1 Notch geometry specified per fracture technique..............................................................23 4-1 Fracture toughness for DER @150C evaluated with the In stron uniaxial tensile test.......40 4-2 Three point bend SENB fract ure toughness values tested at different crosshead rates.....43 4-3 Standard SENB KIC with acetone and evaluated pe r standardized SENB method............44 4-4 Alternative SENB KIC with acetone and evaluated pe r standardized SENB method........45 4-5 Fracture toughness, KIC, values when quantitative fractography was applied to the fracture features for the failed alternativ e SENB samples prepared with acetone............46 4-6 Mean KIC for various techniques.......................................................................................46 4-7 Test results for the chevron sample fractured in 4-point bend...........................................49 4-8 Chevron flexure fracture toughness...................................................................................50 4-9 Test data for chevron samples tested with acetone and no pre-load..................................52 4-10 Standard chevron fracture toughness for sa mples tested with acetone and no pre-load....53

PAGE 7

7 LIST OF FIGURES Figure page 2-1 Idealized fracture surface showing fl aw, mirror, mist, and hackle regions.......................23 2-2 Typical brittle epoxy fracture surface................................................................................23 3-1 Single Edge Notch Bend (SENB ). .....................................................................................29 3-2 Standard notched SENB sample........................................................................................29 3-3 Alternative SENB sample..................................................................................................29 3-4 Chevron notch flexure...................................................................................................... ..29 3-5 Top and side views of the chevron notch sample..............................................................30 4-1 Fracture toughness evaluated w ith quantitative fractography...........................................40 4-2 Optical images of Instron fractur e surfaces and flaw boundaries (arrows).......................41 4-3 Load vs. displacement behavior for SENB sample tested at different displacement rates.......................................................................................................................... ..........42 4-4 Fracture features for a 0.05 mm/inch crosshead rate.........................................................43 4-5 Twist/hackle (arrows) fr acture features observed at a 0.5 mm/inch crosshead rate..........43 4-6 Secondary crack formation (arrow) ev ident at a 5.0 mm/min crosshead rate...................44 4-7 Innovative pre-crack fixture designed to hold a straight edge razor blade and attach directly to the Instron Dynamight load cell.......................................................................44 4-8 Quantitative fractography images of localized flaws on the failed SENB samples (arrows mark boundaries of flaw origin)...........................................................................45 4-9 Fracture toughness for the SENB techniques....................................................................46 4-10 Ideal (A) vs. corrected (B) fracture toughness, KIC, for alternative SENB samples treated with acetone...........................................................................................................47 4-11 Ideal (A) vs. corrected (B) fracture toughness, KIC, for the standard SENB samples treated with acetone...........................................................................................................47 4-12 Alternative SENB samples treated with acetone (A) vs. without (B)................................48 4-13 Standard SENB samples treate d with acetone (A) vs. without (B)..................................48

PAGE 8

8 4-14 Standard (A) vs. alternative (B) SENB samples treated with acetone...............................49 4-15 Top view of an empty flexure fixtur e and side view with a loaded sample......................49 4-16 Load vs. displacement behavior typically observed for a tested chevron sample. The line of best fit (red line) is a pplied to each curve for analysis...........................................50 4-17 Chevron fracture features due to a 50 0N load cell and 0.05 mm/min displacement rate........................................................................................................................... ...........51 4-18 Higher magnification of catastrophic failure at chev ron notch tip (red arrow).................52 4-19 Load vs. displacement curves for chevron samples tested with acetone...........................53 5-1 Fracture toughness vs. technique.......................................................................................57 5-2 Fracture toughness for the te nsile quantitative fractogr aphy (A) vs. chevron flexure technique (B).................................................................................................................. ....58 5-3 Fracture toughness for the tensile In stron quantitative fractography (A) vs. alternative SENB acetone (B)............................................................................................58 5-4 Statistical comparison of fracture toughness evaluated with standardized techniques for an ANOVA analysis at a 95% confidence level..........................................................59 5-5 Statistical comparison of fracture to ughness evaluated with standardized and quantitative fractography techniques for an ANOVA analysis at a 95% confidence level.......................................................................................................................... ..........60

PAGE 9

9 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science QUANTITATIVE FRACTOGRAPHY: A COMPARATIVE STUDY TO EVALUATE POLYMER FRACTURE TOUGHNESS By Stephanie DiFrancesco December 2006 Chair: Elliot P. Douglas Major Department: Materials Science and Engineering Current technology demands high strength polymer ic materials. Thermosetting materials, such as epoxy resins, are potenti al candidates due to their high strength, good adhesion, thermal, chemical, and environmental stability, and ab ility to change stoichiometries and cure temperatures to tailor end propert ies of the product. When fully cured, however, epoxies exhibit brittleness characterized by poor resistance to crack propagation and low fracture toughness. Since epoxies are primarily designed to perform in the glassy state (well below their glass transition temperature), the po ssibility of failure due to cr ack propagation makes polymer fracture toughness a basic material para meter that needs to be evaluated. Previous studies suggest quant itative fractography could prov ide a reliable technique for determining fracture toughness, KIC, of brittle polymers. The first objective is to determine if fractography can reliably estimate polymer fract ure toughness. The investigated material was DER 383, a commercial bisphenol-A based epoxy manufactured by Dow that was formulated with sulfanilamide (SAA) for a 1:1 amine to e poxy ratio and cured at 150C. To confirm validity of the fractographic technique, fracture toughne ss was evaluated from the fracture surface patterns and the quantitative fract ography results were compared to those evaluated by the more standardized SENB and chevron te chniques. Both standardized techniques assume that failure is

PAGE 10

10 due to crack propagation from the macro notch of the specime n. In reality, however, it is possible that failure results from crack growth at some local region along the notch in the sample. The second objective is to apply quantitati ve fractography to analyz e the fracture surface of the failed SENB and chevron samples to identify the failure origin, determine the actual crack length from which failure occurred, and compare fracture toughness results. At a 95% confidence level, the student t-test verified quantitative fractography fracture toughness was not statistically different from the standardized SENB or chevron flexure methods. Fracture toughness evaluated at different W/B sample ratios also did not change SENB KIC measurements. Although the chevron samples de monstrated unstable crack extension due to catastrophic failure from the ch evron notch tip, the mean critical chevron fracture toughness was not statistically different from th e other standardized techniques. Acetone also did not affect the KIC measurements regardless of technique. An ANOVA analysis performed at a 95% c onfidence level determined no statistical difference between fracture toughness measured w ith standardized techniques. A statistical difference, however, was detected when fract ure toughness using quantitative fractography was applied to the failed SENB fracture features. Quantitative fractography on the failed SENB fracture features showed that the crack assumed to occur along the enti re length of the SENB macro notch by the SENB standardized technique sel dom occurs in reality. In contrast, failure in the tested samples typically resulted from semi -elliptical flaws which suggest the flaw size assumed by the standardized techniques is not appropriate. Modeling methods such as finite element analysis should be used in the future to combine independent notch, pre-crack, and semielliptical elements to model the ob served behavior more effectively.

PAGE 11

11 CHAPTER 1 INTRODUCTION Current technology demands high strength pol ymeric materials. The diversity of applications ranges from the automotive a nd aerospace industries to ship building and microelectronics. For such applications, it is im portant to understand the mechanical response of the material under loading.1 Thermosetting materials, such as epoxy resins, are potential candidates due to their high strength, good adhe sion, thermal, chemical, and environmental stability, and the ability to change initial parameters (cure temperatures, stoichiometries) to tailor end properties of the product. When fully cured, however, epoxies exhibit brittleness characterized by poor resist ance to crack propagati on and low fracture toughness.2 Since these materials are primarily designed to perform in th e glassy state (well below their glass transition temperature), the possibility of failure due to crack propagation makes polymer fracture toughness a basic material parameter that needs ev aluated. Accurate and reliable measurement of the fracture toughness property, i.e. the polymers resi stance to fast fracture is therefore critical. Since fracture toughness plays an in tegral role in understanding the mechanical response of a material under loading,3 interest has been generated re garding the different methods and geometries to determine fracture toughness. Fr acture toughness is measured using standard stress-intensity methods developed from linear elas tic fracture mechanics. A wide variation in the fracture toughness, KIC, values exist for the different test methods and geometries cited in literature. These differences may be attributed to differences in the materials composition and microstructure and partially to differences in th e fracture behavior (i.e., fast cracking or slow crack growth) for the test method employed. Although fracture toughness has been well characte rized for ceramics, glass, and metal, it has not been as extensively studied for polymers. Fracture toughness values of epoxies vary over

PAGE 12

12 a wide range from 0.4 1.8 MPa M depending on the type of epoxy resin, the curing agent, stoichiometry of the mix, temperature, cure profile and rate of testing.4 As a result, it is difficult to predict trends in the fract ure toughness values based on a utilized fractu re technique. The majority of techniques require a macro not ch in the sample. The general assumption is that crack growth initiates from the sharp macr o notch. In reality, however, it is possible that failure results from crack growth at some local region along the notch in the sample. By analyzing fracture features of samples failed by standardized techniques with quantitative fractography, we can identify the exact failure or igin and investigate if differences in crack length account for the variations in measured fracture toughness values. Previous studies by Oborn5 utilized quantitative fractogra phy to measure the fracture toughness of a commercial bisphenol-A based ep oxy (DER383) formulated with sulfanilamide (SAA). The experimental results suggest fract ography could provide a re liable technique for determining KIC of brittle polymers. The first objective of this research is determine if fractography can be reliably used to estimate th e fracture toughness of polymers. To confirm validity of the fractographic technique, one shou ld compare these results to fracture toughness values obtained from a more standardized met hod. The two standardized t echniques selected for comparison were single edge notch bend (SENB) and chevron notch in flexure. Fracture toughness values will be evaluated for each corresponding method and compared to the quantitative fractography tests. Bo th SENB and chevron techniques a ssume that failure is due to crack propagation from the macro notch of th e specimen. The second obj ective is to utilize quantitative fractography to analyze the fracture surface of the failed SENB and chevron samples to identify the failure origin and determine the ac tual crack length from wh ich failure occurred.

PAGE 13

13 CHAPTER 2 BACKGROUND Within the last few years, research has expres sed increased interest in the improvement of mechanical properties for engineering structur al materials. Fracture toughness measures the resistance of a material to pr opagate cracks. Fracture behavior depends on the material strength, stress level, flaw concentr ation, and failure mechanism.6 Material strength depends strongly on the size of defects, flaws, and cracks in the material. A crack decreases material strengt h and strength decrea ses with increased crack size. Failure, in many cases, is dominated from fracture initiated by these internal micro cracks and surface flaws. The study of cracks and th eir structure led to the evoluti on of the engineering field known as fracture mechanics; which stems from the basic concepts proposed by Griffith.7 From Griffith's contributions, its been recognized that material strength is not a characteristic material property, but a parameter strongly dependent on th e distribution and size of defects, flaws, and cracks within the material. Different test methods and specimen geometri es can be used to determine the fracture toughness which are measured using stress inte nsity methods developed from linear elastic fracture mechanics. The test methods are based on the principle of initia ting a controlled crack that propagates under an applied load through a specimen. The type of measurement required, the research objectives, and the fr acture behavior or microstructure of the material should govern test method and specimen geometry selection. Fact ors that should be eval uated when selecting the appropriate test method and geometry incl ude specimen size, notch and crack geometries, notch tip acuity, and toughness determination at peak load. The two types of notch crack geometry8 prevalent in testing brittle materials are macro cracks (or macro notches) and indentation induced micro cracks (or micro flaws). Macro cracks

PAGE 14

14 (or macro notches), which create a crack in th e form of a diamond sawed-notch, are utilized by the majority of fracture techni ques. Induced micro cracks resu lt from surface cracks or flaws induced by Vickers and K noop indentation tests. Notch tip acuity is important for macro notched specimens, which were the focus of this study. Macro notched specimens are often prepar ed by creating a crack in the form of a diamond-sawed notch. Notching the test specimen is done to simulate an ideal planar crack with a zero root radius to coincide w ith Linear Elastic Fracture Mechanic9 (LEFM) assumptions. In LEFM theory, the stress intensity factor, K, describes the stress -strain field in the vicinity of the crack tip. The origin of failure is assumed to be a sharp crack flaw. A small scale 'process zone, relative to the geometrical dimens ions of the elastic body, exists at the crack tip and implies a 'linear' relation betw een the load (stress) and the di splacement (strain). A crack propagates when the stress intensity factor re aches a critical valu e called the fracture toughness, KIC. 9 Because brittle materials have a limited extent of plastic deformation at the notch tip, the majority of macro notch samples require a delica te pre-cracking procedure. The pre-crack can be introduced in a variety of ways and its size is dependent on the material and the pre-cracking procedure selected by the researcher. The most rigorously standardized tests, SENB and CT, both require a machined macro notch sharpened by a razor blade pre-crack. Some propose the sharpness of the razor blade cut crack tips is not su fficient compared to the sharpness of a natural crack. Fatigue sharpened notches are thought to provide more accurate and reliable fracture toughness data for polymers. If the cyclic stress intensity factor is small enough, fatigue crack tips are thought to more closely resemble th e sharpness of a natural crack. Although fatigue grown crack tips are common for fracture testing me tals, sharpening notches with fatigue crack

PAGE 15

15 in polymers is difficult due to uns table fatigue crack growth and th e low frequencies (< 4 Hz in some polymers) used to avoid hysteresis heati ng that creates blunt notch and damaged tips. Because brittle materials have limited extent of plastic deformation at the notch tip, some materials incorporate a pop-in crack technique10 that typically combine wedge loading at the root of a sawed notch with some type of crack ar restor attachment, such as a vice. For brittle materials with notch bend geometry, alternativ e pre-cracking techniques such as compressive cyclic fatigue11 and bridge indentation methods12 have been reported. Pre-cracking creates difficulties in evaluating the critical stre ss intensity at the onset of crack extension, KIC, for brittle materials in particular that exhibit sharply increasing crack growth resistance (R-curve behavior).13 Pre-crack extensions create an active wake region behind the crack tip and the residual stresses, micro crack ing affects, and crack bridging that occur in this wake region are believed to be the cause of the rising R-curve behavior. The KIC fracture toughness obtained from a pre-cracked speci men is always higher than the true KIC value of the material. When possible, it is desirable to avoi d pre-cracking procedures in brittle materials. Several fracture techniques14 are available and have been summarized in Table 2-1 that includes: single edge notched bend (SENB), compact tension (CT), double cantilever beam (DCB), double torsion (DT), chevron notch (CNB), and fractography. In contrast to the majority of fracture techniques that use macro notched specimens, quantitative fractography analyzes tensile bars failed in uniaxial tension on an In stron machine. Fracture toughness is determined from the observed fracture surface patterns. The chevron notch test is a desirable macro notch technique since it eliminates the need to introduc e a pre-crack in the sample, which is extremely difficult to do with brittle materials.

PAGE 16

16 Fracture toughness of epoxies have been inves tigated by several researchers using different techniques that include single edge notc hed bend (SENB), compact tension (CT), double cantilever beam (DCB), double torsion (DT), chevron notch (CNB), and quantitative fractography. Ritter et al.15 introduced controlled flaws into poly (methyl methac rylate) samples using a Vickers indenter and liquid acetone to investig ate the effect of acetone on pre-crack formation. During the indent period, a drop of acetone wa s placed on the contact surface to produce an aggressive environment that enhanced crack formation. For comparison to more conventional techniques, standard single-edg ed notched three-point bend test s were also performed. SENB samples with and without acetone were tested for comparison. A significant difference between fracture toughness values measured for the ace tone and non-acetone SENB samples was not found. These results suggest the acetone did not a ffect the subsequent strength measurement. In another study, Choi and Salem16 also used indentation cracks produced in liquid acetone to evaluate PMMA fracture toughness. They took the evaluation a step further by comparing the indentation method to CT, DCB, and SENB fractur e techniques. In their approach, however, the liquid acetone was only introduced into the i ndentation samples. Liquid acetone was not introduced into the SENB macro notch. The SENB pre-crack was create d by inserting a razor blade in and along the mouth of the sawed notch. Stable crack growth was observed for all the techniques. Fracture values from conventional testing techniques were consistent with published PMMA data. The indentation method fracture to ughness values, however, were greater than the conventional pre-cracked specimen. Due to these unexpected results, th e authors felt using indentation cracks produced in liquid acetone to evaluate PMMA fracture toughness should be done with reservation.

PAGE 17

17 Chia17 investigated the influence of crack tip on bisphenol-A based epoxy fracture toughness. The epoxy material was machined into SE NB specimens with a pre-crack aspect ratio of 0.5. A Micro Tester was used to conduct the th ree point bend test at a crosshead displacement rate of 0.1 mm/min. In the study, both fatigue and razor blade cut cracks were used to sharpen the SENB notch tip. The KIC from both pre-cracking methods were in close agreement. The KIC specimens with the fatigue pre-crack gave slightly lower minimum KIC values than the razor blade pre-crack specimens. KIC for the fatigue pre-crack a nd the razor blade pre-crack specimens were 0.6 and 0.619 respectively. Ting and Cottington18 utilized several la boratory techniques to determine the polymer fracture toughness of unmodified bisphenol A diglycidy ether (DGEBA) epoxies. Double cantilever beam specimens determined the fr acture toughness of the bulk resin. Fracture toughness of bulk resin was also evaluated by bo th rectangular and round compact tension specimens. The study revealed that the fr acture toughness of the round CTS specimen, 0.171 kj/m2, seemed to agree well with the rectangular CTS specimens (0.187 kj/m2). Although the rectangular CTS results were similar to the bulk fracture toughness obtained by double cantilever specimens, the rectangular CTS values were gene rally higher. Izod impact tests were also conducted to determine fracture toughness at high loading rates. For the base epoxy, the izod impact test results (0.23 kj/m2) were in good agreement with the rectangular CTS fracture toughness (0.23 kj/m2). SENB and Chevron Advantages / Disadvantages Single edge notch bend and chevron notch in fl exure were the two standardized techniques selected for comparison to quantitative fractogr aphy. SENB advantages include a small sample size and the simplest geometry compared to other conventional geometries. In addition, a large body of data, particularly for meta ls, is available for comparison.

PAGE 18

18 SENB disadvantages include diffi culties introducing a sharp precrack and that an unstable mode of crack extension makes it diffic ult to obtain crack growth data. Chevron notch advantages also include a sma ll sample size. The chevron configuration is known to enable stable crack growth for the in itial stage of crack ex tension until catastrophic fracture occurs. Critical fracture toughness, KIC is determined from the maximum load at fracture regardless of crack length. The chevron not ch is a desirable macro notch technique since it eliminates the need to introdu ce a pre-crack in the sample, whic h is extremely difficult to do in brittle materials. The complex chevron geometry is a disadvantage, however, because it increases machining costs compared to other methods. A two-step loading technique is sometimes recommended since a single loading rate can fail to produce consistent results. Quantitative Fractography Advantages/Disadvantages The majority of fracture techniques use a m acro notched specimen to determine fracture toughness. Quantitative fractography, in contrast, de termines the fracture toughness of a material from fracture surface observations. Compared to conventional SENB and CT techniques, quantitative fractography requi res significantly less time for sample preparation and dimensioning. Fractography appears to reflect r eal crack growth conditions and simplifies calculations. In summary, single edge notch bend (SENB) and chevron notch are less desirable because of the relatively complex sample preparati on and dimensioning compared to quantitative fractography samples. Pre-cracked single edge no tch bend specimens require a critical pre-crack that is difficult to consistently introduce due to crack branching and crack microstructure interactions but necessary to encourage stable crack growth. A stable crack provides the best scenario to investigate the strength of material s because the crack can be more easily duplicated and provides a platform to inve stigate different materials.

PAGE 19

19 Fractography is the most desirable technique because of the simplified test method and relatively straightforward calculations used to determine fracture toughness from the observed fracture surface patterns. The absence of a macr o notch on tensile bar samples is advantageous because it eliminates the variabil ity associated with notch placement, notch geometry, and notch acuity. Perspective Previous studies by Oborn5 utilized quantitative fractogra phy to measure the fracture toughness of a commercial bisphenol A based ep oxy (DER383) formulated with sulfanilamide (SAA). The experimental results suggest fract ography could provide a re liable technique for determining fracture toughness, KIC, of brittle polymers. To conf irm validity of this fractography technique, one should compare these results to fr acture toughness values obtained from a more standardized method. The two sta ndardized techniques selected fo r comparison were single edge notch bend and chevron notch in flexure. Frac ture toughness values will be evaluated for each corresponding method and compared to the quan titative fractography results. Both SENB and chevron techniques assume that failure is due to crack propagation from the macro notch of the specimen. The second objective is to utilize qua ntitative fractography to analyze the fracture surface of the failed SENB & chevron samples to determine the actual crack length from which failure occurred. Fracture Mechanics Based on linear fracture mechanics (LEFM), Irwin19 developed a relationship between stress intensity local to the crack tip, K, and th e applied stress and geometry of the structure during loading. The fracture toughness of a brittle material can be expressed by the critical stress intensity factor, KIC. According to Irwin,19 in an elastic material, the stress field near a crack tip is described by the stress intens ity factor, K, and is material independent but depends on the

PAGE 20

20 sample geometry and distance from the crack tip. Equation 2-1 evaluates the critical value at which the stress on a sample exceeds that the materi al is capable of resisting and is called the fracture toughness, KIC.20, 21 / ) (2 / 1c Kf IC (2-1) where = surface correction factor (1.12) f = stress at fracture c = crack size = elliptical integral of the second kind As Oborn5 previously described, the elliptical in tegral accounts for th e variation in the stress field due to the shape of the crack tip. For a semi-circular crack the value is /2. The crack size is taken to be the radi us of a circular or semi-circular crack. However, elliptical or semi-elliptical crack can be modeled as a semi-circular crack by c = (ab)1/2, where 2a and 2b are the lengths of the axes of the elliptical crack.22 The calculation of KIC assumes that the material is linear elastic, that there are no effects due to the edge s of the sample, and that the loading is purely tensile. Equation 2-2 incorp orates minor modifications made to standard LEFM theory to account for a small zone of pl asticity near the crack tip.21 )) / 212 0 ( /( ) (2 2 2 2 2 2 ys f f ICc K (2-2) where ys = yield stress Taking into consideration the preceding conditions, Equation 21 simplifies to Equation 2-3. KIC = (1.26)*( f )* (c)1/2 (2-3)

PAGE 21

21 The fracture toughness can be expressed as the critical energy release rate, GIc, which is the energy required to extend the crack over a unit ar ea under tensile loading. This term is derived in the energy balance theory developed by Irwin21 based on the work of Inglis,23 Griffith,24 and Orowan,25 in which the mechanical free energy stored in the material is in equilibrium with the free energy used to create new crack surfaces. KIC and GIc can be calculated from each other if Poissons ratio and the elastic modulus of the material are known. Flaw size, however, is the simplest quantitative information available and can be used to evaluate fracture toughness by Equations 2-1 and Equation 22. As described by Mecholsky,26 this technique was developed on glasses and confirmed on epoxi es by Plangsangmas et al.27 Fractography Fracture features are depende nt on the type of failure28, 29 and much of the information is qualitative, such as the differences between brit tle or ductile failure. Figure 2-1 shows the key features characteristic of brittle29 fracture: the flaw origin, and the mirror, mist, and hackle regions. The fracture surface typically originates from a volume or surface flaw. When the flaw itself cannot be measured, patterns on the fractur e surface indicate the region from which failure occurred. The mirror is the smooth region immediately surrounding the fracture origin and indicates slow crack growth. The mist region contains small radial ridges that surround the mirror region and reflect an increase in crack velo city. As the crack velocity accelerates, a more fibrous texture results. Hackle re presents a rougher region containi ng larger radial ridges. Crack branching begins in the hackle region. The mist and hackle regi ons are sometimes referred to as the smooth and rough regions, 28 as seen in Figure 2-2. Fracture mirrors are typically cente red on the strength-limiting origins.30 If the specimen is highly stressed or the material is fine-grained and dense, the dis tinct fracture features shown in Figure 2-1 form. Fracture features for lower en ergy fractures, coarse-grained, or porous ceramic

PAGE 22

22 materials, however, are usually not as distinct. If a fracture mirror is not ev ident, the hackle lines are useful in locating the fracture origin. Hackle lines radiate from, and thus point the way back to, the fracture origin.

PAGE 23

23 Table: 2-1: Notch geometry sp ecified per fracture technique Fracture Technique Notch Geometry Pre-crack Single edge notched bend (S ENB) Macro notch Required Compact tension (CT) Macro notch Required Double cantilever beam (D CB) Macro notch Required Chevron notch (CNB) Macro notch Not required Indentation Not Applicable inherent Quantitative fractography Not Applicable pre-exisiting Figure 2-1: Idealized fracture surface show ing flaw, mirror, mist, and hackle regions.29 Figure 2-2: Typical brittle epoxy fracture surface.31

PAGE 24

24 CHAPTER 3 EXPERIMENTAL Materials DER 383, a commercial bisphenol-A based e poxy manufactured by Dow Chemical, was prepared and cured with sulfanilamide (SAA), a tetra-functional amine hardener manufactured by Aldrich, according to the pr ocedure described by Oborn.5 Thirty grams of liquid DER383 are weighed into a 60 mL Qorpak bottle and heated at 170 C. Once the epoxy has completed melted, the sulfanilamide hardener is added in a 1:1 ratio by weight of amine to epoxy. The mixture is stirred occasionally with a wooden craft stick until the SAA completely dissolves which typically takes 25-30 minutes. The solution remains heated for an additional 2-3 minutes and is then removed and degassed for one minute. The solution is placed back into the oven, heated an additional 2-3 minutes, then remove d and degassed a second time. After the second degassing, the epoxy/amine solution is pour ed into a mold preheated to 150 C to prevent fast cooling of the resin and cured at 150 C for four hours. The temperature is then increased at 1 C/min for one hour of post-cure at 175 C, followed by an additional 1 C/min for four hours of post-cure at 200 C. The epoxy plaques are extracted from the molds and sample geometries were machined per ASTM specifications for a give n technique. Six samples were run for each technique and the mean fracture toughne ss and standard deviation calculated. Molds Specimen molds for the epoxy plaques consis ted of two 8.5 X 4 aluminum plates separated by inch teflon sheet. Six 1 binder cl ips hold the plates together. Prior to each use, the mold surface is sanded with Emory cloth, then 200, 400, & 600-grit sandpaper, and finally washed with water and then acetone. Plates ar e air-dried and sprayed with Crown Dry Film Lubricant and Mold Release Agent (TFE).

PAGE 25

25 Sample Preparation Quantitative Fractography A Tensilhut router was used to machine th e DER 383 epoxy plaques into Type V tensile bars per ASTM D638. SENB Pre-crack The SENB method requires a pre-crack be intr oduced into the macro notch of the SENB samples. The crack length, a, is the total depth of the machined notch plus the pre-crack. This crack length is typically define d so that 0.45 < a/W< 0.55. An a/w ratio of 0.5 was selected for this study. The pre-crack is initiated by inser ting a fresh razor blade and tapping per ASTM D5045 guidelines.31 If a natural crack cannot be successfully initiated by tapping, the ASTM recommends sliding a razor blade across the notc h root by hand to generate a sufficiently sharp pre-crack. SENB Sample Geometries Both standard and alternative geometries we re tested for the method based on dimensions shown in Figure 3-1. Sample geometries are ba sed on the sample thickness, B. Standard specimens have a W/B ratio equal to two. Altern ative specimens have a W/B ratio equal to 4. The MathCAD program created evaluated sa mple dimensions based on ASTM notch specifications, Motorolas available tool sizes, an d sample thickness. Standard SENB dimensions are shown in Figure 3-2 and include a 3.18 mm thickness, 6. 4 mm height, a 0.79 mm notch width, 1.59 mm notch depth, and 27.98 mm length. Alternative SENB specimens shown in Figure 33 have a sample height, W = 4B. Sample dimensions include a 3.18 mm thickness, 12.72 mm height, a 1.59 mm notch width, a 3.19 mm notch depth, and a 55.97 mm length.

PAGE 26

26 Chevron Notch in Flexure Chevron dimensions are shown in Figure 3-4 below. Because our samples were thicker than the spec, the dimensions were slightly adju sted to maintain the ratios specified in ASTM C1421.32 Sample thickness, B, is 3.18 mm. The hei ght, W, is 6.4 mm and sample length, L, is 45 mm. The vertex of the chevron notch angle wa s calculated to be a pproximately 56 degrees. The MathCAD program created evaluated ch evron dimensions based on ASTM notch specifications and Motorolas available tool size s. The vertex angle machined into the chevron flexure bar is 53 degrees; notch thickness is less than or equal to 0.25 mm. Chevron notch samples are shown in Figure 3-5. Methods Quantitative Fractography Uniaxial Tensile Test ASTM D638 tensile dog bone samples were frac tured in uniaxial tens ion on an Instron at 0.5 in/min in order to ensure brittle fracture. Th e fracture surfaces of each tensile sample are then analyzed using an optical microscope at 50, 100, or 200 magnification. The flaw depth (a) and width (2b) of the semicircular flaws and the majo r and minor axis (2b, 2a) of the elliptical flaws in the bulk of the sample were measured with a reticular eyepiece. The flaw size was calculated by c = (ab)1/2 and the fracture toughness was determined from Equation 1.1. Single Edge Notch Bend (SENB) SENB samples were fractured at 10mm/min in 3-point bend on an Instron with a 500 Newton load cell and a support span equa l to four times the sample width. Chevron Notch in Flexure Chevron samples were fractur ed in 4-point bend on an Instron with the recommended 40mm outer and 20mm inner loading span. During te sting, the chevron tip is oriented toward the longer support span so the chevron tip section points toward the tens ile surface. A 500 Newton

PAGE 27

27 load cell and a 0.05 mm/min displacement rate fr actured the chevron samples in 4 point bend. A 0.05 mm/min (or 0.002 in/min) displacement rate wa s selected since this rate is most common for epoxy testing and fell within the 0.03 mm/m in to 0.3 mm/min recommended ASTM range for chevron testing. Fracture Toughness Calculation Quantitative Fractography Fracture Toughness A detailed description of the fractur e toughness calculation for the quantitative fractography technique is provi ded in the background section. SENB Fracture Toughness Calculation The single-edge notched bend test uses a center-notched beam lo aded in three or four point bending to measure plane stra in fracture toughness, KIC, or toughness parameter indicative of a materials resistance to fracture. SENB characterizes the toughne ss of plastics in terms of the critical stress intensity factor, KIC, and the energy per unit area of crack surface, or critical strain energy release rate at fracture initiation, GIC.31 Equation 3-1, derived on the basis of elastic stress analysis for the specimen type describe d in the method, determine the value of KIC from the load. The validity of the calculated KIC value is dependent on the es tablishment of a sharp crack condition at the crack tip and e xhibited linear elastic behavior.31 fx W B Pq KSENB IC* )] /( [2 1 (3-1) ] ) 1 ( ) 2 1 /( )) 7 2 93 3 15 2 ( ) 1 ( 99 1 [( 65 1 2 2 / 1x x x x x x x fx 5 0 x where Pq = Load, kN B = width, cm

PAGE 28

28 x = assumed ideal a/w ratio = 0.5 SENB ICK = SENB fracture toughness, MPA*m1/2 Chevron Fracture Toughness Calculation Chevron critical fracture toughness, as outlin ed in ASTM 1421, is evaluated from the maximum load at fracture and is defined in Equation 3-2:32 ] /[ ] 10 ) ( max* [ min* K5 1 6 0 chevron ICW B S S P Yi (3-2) where KIC chevron = chevron fracture toughness, MPA m Y min = minimum stress intensity factor coefficient P max = peak load at fracture So = outer support span, m Si = inner loading span, m B = width, m W = height, m The stress intensity factor coefficient, Y min, for the selected chevron geometry in four point flexure is also outlined in ASTM 1421 and defined in Equation 3-3:32 Ymin_chevron 1.46805.5164 a0 W 5.2737 a1_avg W 8.4498 a1_avg W 2 7.9341 a1_avg W 3 13.2755 a0 W 4.3183 a0 W 2 2.0932 a0 W 3 1.9892 a1_avg W (3-3)

PAGE 29

29 Figure 3-1: Single E dge Notch Bend (SENB).31 Figure 3-2: Standard notched SENB sample Figure 3-3: Alternative SENB sample Figure 3-4: Chevron notch flexure Configuration C32

PAGE 30

30 Figure 3-5: Top and side views of the chevron notch sample

PAGE 31

31 CHAPTER 4 EXPERIMENTAL DATA AND DISCUSSION Quantitative Fractography Fracture toughness evaluated with quantitative fractography is summarized in Table 4-1. Quantitative fractography fracture toughness vs. sample for the uniaxial Instron tensile test is summarized in Figure 4-1.The averag e critical fracture toughness, KIC, for the Instron quantitative fractography samples was 1.49 MPa*m1/2. Previous studies Oborn conducted on a 1:1 epoxy to hardener ratio determined a m ean critical fracture toughness of 0.93 MPa m1/2. Tensile samples failed from edge flaws due to surface bubbles, machining, or inclusion. Most flaws appear to have resulted from def ects along gauge length that probably resulted from machining. Distinct boundaries are clearly ev ident between the fractur e features as is the expected increase in roughness aw ay from the flaw origin. Standardized SENB Method SENB Method Development The single edge notch bend (SENB) technique was the first standard ized method selected for comparison to the quantitative fractogra phy method technique. The SENB method requires a pre-crack be introduced into the sample. The ASTM recommended a tapping method to introduce the pre-crack into the SENB macro notch. Our epoxy samples, however, were entirely too brittle and completely fractured with this approach. The second technique recommended by the ASTM slid a razor blade by hand across the m acro notch. SENB sample s were fractured in 3-point bend Instron. A 500 Newton load cell and an S=4W, support span were used. Crosshead rates of 0.05 mm/min, 0.5 mm/min, 5 mm/min, and 10 mm/min were initially tested to determine the condition that resulted in stable crack pr opagation. The load vs. displacement behavior shown in Figure 4-3 indicates that all SENB samp les exhibited brittle fract ure independent of the

PAGE 32

32 selected crosshead rate. The 10 mm/min crosshead ra te was selected for s ubsequent testing since it was the most common rate referenced in epoxy SENB literature. Fracture toughness for SENB samples tested at different crosshead rates are summarized in Table 4-2. Optical microscopy was used to insp ect the fracture features of the failed SENB samples tested at different crosshead rates. Al l samples had similar fracture features: uneven crack propagation along the specim en macro notch as shown in Figure 4-4. The twist hackle shown in Figure 4-5 probably resulted from a cr ack that propagated out of plane. A traveling macro crack typically diverges; the original crack branches into successively more cracks that rarely rejoin another crack. Twist hackle, in cont rast, usually originates as finely spaced parallel lines that merge in the directi on of crack propagation creating th e well know river patters shown in Figure 4-5. The merger of twist hackle in th e direction of crack propa gations is opposite the tendency of macro cracks to diverge. The s econd pre-crack technique recommended by the ASTM slid a razor blade by hand along the SE NB macro notch but yielded uneven crack propagation. As a result, in Figure 4-6 an alte rnative pre-crack approach was attempted where a triangular razor blade was attached to the vice of a milling machine and dragged across the notch surface in attempt to control notch depth. This alternative approach, however, still resulted in uneven crack propagation along SE NB macro notch. Rather than smoothly sliding across the epoxy surface, the blade stuck in the epoxy and formed a secondary crack. Quantitative Fractography performed on SENB Samples Because the pre-crack introduced into the SE NB macro notch increa ses the local stress intensity, the stress correction show n in Equation 4-1 is required for the quantitative fractography fracture toughness calculation. corrected = (max) k (4-1) where

PAGE 33

33 corrected = corrected stress (max) = break stress k = stress concentration factor The stress-concentration factor, k, incorporates the effect of crack geometry on the local crack-tip stress level and takes into consider ation both the flaw shape and SENB loading configuration. The Deformation of Fracture Mechanics for Engin eering Materials by Hertzberg33 cites a stress concentration factor range from 1. 7 to 2.7 for our SENB configuration. The low and high range for the stress concentration factor wa s used to evaluate the average fracture toughness for each sample set for comparison to the standardized techniques. When quantitative fractography was applied to the failed SENB fracture features to evaluate fracture toughness, Equation 23 therefore simplifies to Equation 4-2. KIC = (1.26)*( corrected)*(c)1/2 (4-2) Method Development: Innovative Pre-crack and Acetone Fixture Since a consistent pre-crack could not be successfully introduced into our samples with either recommended ASTM tec hnique, a unique challenge was posed. An innovative pre-crack fixture was designed to introduce a consistent pre-crack depth along the entire length of the SENB macro notch. The fixture wa s designed to hold a straight edge razor blade and attach directly to the Dynamite load cell. Since the amount of load a pplied to the pre-crack could now be controlled with the In stron, a consistent pre-crack dept h could be applied along the entire length of the SENB macro notch. A fresh razor blade was used to pre-crack each specimen. Several pre-crack loads were investigated, how ever, a 20 lbf pre-crack was chosen since it yielded the best results without specimen damage. In addition to the introduction of a consistent pre-crack, a drop of acetone was added to the alte rnative SENB macro notch and allowed to dry 24 hrs prior to testing.

PAGE 34

34 The innovative pre-crack fixture combined with acetone appeared to yield more even crack propagation along the macro notch, therefore, this sample preparation was utilized for all subsequent testing. Compared to hand controlle d razor blade cutting, the straight edge razor pre-crack fixture offered better control in ach ieving the sharp pre-crack needed for stress intensity measurement. SENB samples prepared w ith this optimized technique were fractured in 3 point bend on an Instron at 10 mm/min. SENB test data is summarized in the Table 4-3 and Table 4-4. Quantitative Fractography Results for the Optimized SENB Test Method Typical fracture features observed when quant itative fractography was applied to the failed single edge notch bend (SENB) surface patter ns are shown in Figure 4-8. Quantitative fractography on the failed single edge notch bend fracture features revealed that the crack assumed to occur along the entire length of th e SENB macro notch by th e standardized SENB technique seldom occurs in reality. In contrast, failure in the tested sa mples typically resulted from semi-elliptical flaws which suggest the flaw size assumed by the standardized techniques in not appropriate. The measured critical fracture toughness, KIC, for the standard SENB epoxy specimens treated with acetone was 1.1 MPA*m Critical fracture toughness, KIC, for the alternative SENB epoxy specimens treated with acetone was 1.4 MPA*m Table 4-5 summarizes the fracture toughness values evaluated by Equation 4-2 when quantitative fractography was applie d to the failed SENB features. SENB Section Conclusions Mean critical fracture toughness for both the st andard and alternative SENB samples are summarized in Table 4-6. The first colu mn represents the fracture toughness, KIC, calculated by

PAGE 35

35 the standardized SENB method using the assumed ideal a/w ratio of 0.5. The second column, KIC SENB corrected, represents the corrected SENB KIC values determined when optical microscopy was used to measure the actual crack length from which failure occurred on the fracture surface rather than the ideal ratio assu med by the standardized method. The third column represents the fracture toughness when quantit ative fractography was applied to the failed SENB fracture features. Based on the ideal 0.5 a/w ratio assumed by the standardized technique, mean critical fracture toughness for the alterna tive SENB samples tested with and without acetone were 2.6 and 3.0 MPA*m respectively. Based on the ideal 0.5 a/w ratio assumed by the standardized technique, mean critical fracture toughness for the standard SENB samples tested with and without acetone were 2.1 and 2.0 MPA*m respectively. When optical microscopy was used to insp ect the failed SENB fracture features and measure the actual critical crack length, a, from which failure occurred the corrected SENB fracture toughness were signi ficantly different than those determ ined using the ideal 0.5 a/w ratio assumed by the standardized SENB technique. Critical fracture toughness, KIC, for the standard, alternative, and quantitative fractography SENB samples are summarized in Figure 4-9. The corrected critical fracture toughness, KIC for the standard SENB epoxy samples treated with and without acetone were 1.1 and 1.1 MPA*m respectively. The corrected critical fracture toughness, KIC, for the alternative SENB epoxy specimens treated with acetone and without ac etone were 1.4 and 1.6 MPA*m respectively When quantitative fractography was applied to the alternative SENB samples treated with and without acetone, the mean critical fr acture toughness were 1.2 and 1.5 MPA*m respectively.

PAGE 36

36 When quantitative fractography was applied to the standard SENB samples treated with and without acetone, the mean critical fr acture toughness were 0.7 and 0.6 MPA*m respectively. The crack size assumed to occur al ong the entire length of the SENB macro notch by the SENB standardized technique seldom occurs in reality. This proves it is critical to utilize optical microscopy to inspect the SENB faile d surface for an accurate fracture toughness measurement. The student t-test, t(10) =4.63, P < 0.05 (two-tail), executed at a 95% confidence level in Figure 4-10 verified a statis tical difference between the ideal vs. the corrected KIC SENB fracture toughness value for the standardized SENB method. The student t-test, t(8) = 7.4, P<0.05 (two-tail) executed at a 95% confidence in Figure 411 also verified a statistical difference betw een the ideal (x=0.5) vs. corrected (x=scope measurement) standard SENB acetone fractur e toughness value for the standardized SENB method. The analysis shown in Figures 4-10 and 4-11 ve rified a statistical difference between the ideal (x=0.5) vs. corrected (x=scope measur ement) fracture toughne ss measured for the standardized SENB technique. This proves it is critical to util ize optical microscopy to inspect the failed SENB fracture features for an accura te fracture toughness measurement or else the fracture toughness values reported by the standard ized SENB methods will be higher than the materials true fracture toughness. The student t-test, t(9) = -1. 21, P < 0.05 (two tail), executed at a 95% confidence level in Figure 4-12 verified that acetone did not effect alternative SENB fracture toughness measurements. The student t-test, t(8) = 0.34, P < 0.05 (two tail), executed at a 95% confidence

PAGE 37

37 level in Figure 4-13 also veri fied that acetone did not effect standard SENB fracture toughness measurements. To investigate the effect of sample geomet ry on fracture toughness, the SENB alternative (W= 4B) vs. standard (W=2B) acetone sets we re compared where B represented sample thickness. Because acetone affect s were determined negligible only the acetone sets were compared. Mean critical fracture toughness, KIC, for the alternative SENB epoxy specimens treated with acetone was 1.4 MPA*m Mean critical fracture toughness, KIC, for the standard SENB epoxy specimens treated with acetone was 1.1 MPA*m The student t-test, t(9) = 1.87, P < 0.05 (two tail), executed at a 95% confidence level in Figure 4-14 verified that fracture toughness evaluated for the diffe rent W/B ratios of the standard vs. alternative SENB geometries were not st atistically different. For the same technique, differences in sample geometry di d not affect SENB fracture toughness. Chevron Notch in Flexure Chevron notch in flexure was the second standa rdized technique select ed for comparison to quantitative fractography results. Motorolas Prototype Shop machined the fixture per ASTM guidelines. An adjustable support span and stopper blocks were added to center the sample and ensure consistent loading. Chevron samples we re fractured in 4-point bend on an Instron with the recommended 40 mm outer and 20 mm inner loading span. A 500 Newton load cell and a 0.05mm/min di splacement rate fractured the chevron samples in 4 point bend. A 0.05 mm/min (or 0.002 in/min) displacement rate was selected since this rate was the most common for epoxy testing and fell within the 0.03 mm/min to 0.3 mm/min recommended ASTM range for chevron testing. Pre-loading the sample prior to testing is sometime recommended to help promote stable crack propagation. Th ree different preload

PAGE 38

38 techniques were investigated and are summarized in Table 47. Chevron fracture toughness for the pre-loaded samples are summarized in Table 4-8. An example of typical load vs. displacement cu rves for the pre-loaded chevron samples is provided below in Figure 4-16. The blue sample li ne had a 20N preload applied prior to sample testing. The green sample line was pre-loaded per chevron ASTM methods. Samples with no pre-load exhibited behavior similar to the blue line. Load vs. displacement graphs for all test ed chevron samples confirmed catastrophic failure. As shown in Figure 4-16, these samples exhibited a sudden drop in load from the linear portion that was not followed by a subsequent load increase; th is curve behavior suggests unstable fracture from the chevron notch tip. Per chevron ASTM guidelines, this load vs. displacement behavior is indicative of invalid results for this particular technique. Pre-loading was supposed to promote stable fracture, howev er, based on catastrophic failure shown in the load vs. displacement graphs, pre-load did not effect fracture behavior. The failed chevron fracture features shown in Figure 4-17 verified the pre-load did not promote stable fracture in the tested samples. Images a and b had no preload applied to the sample. Images c and d had a 20N preload applied pr ior to testing. Sample images e, f, g, and h were pre-loaded per chevron ASTM methods. All fractography images on the failed chevron samples shown in Figure 4-17 indicated cat astrophic failure at chevron notch tip. Quantitative fractography performed on the fracture features of the failed chevron samples confirmed catastrophic failure from th e chevron notch tip in all samples. Since catastrophic failure occurr ed in all of the tested chev ron samples, a drop of acetone was added to the chevron notch to determine if a more aggressive environment might encourage stable crack propagation from th e notch. A drop of acetone was pl aced in the chevron notch and

PAGE 39

39 allowed to dry for 24 hrs prior to testing. Test data for the chevron samples tested with acetone and no pre-load are summarized in Table 4-9. The load vs. displacement graphs indicated th at the presence of acetone did not affect the crack propagation. All tested samples still demo nstrated catastrophic failure from the chevron tip. Chevron fracture toughness is summarized in Table 4-10. The mean critical fracture toughness, KIC, for the chevron samples was 1.58 MPA m 1/2; however, the observed load vs. displacement behavior were charac teristic of catastrophic failure from the chevron notch tip and considered invalid per chevron ASTM. Future wo rk could investigate different sample geometry ratios or chevron notch angles that might promote stable crack propagation but was not deemed necessary for the scope of this study.

PAGE 40

40 Table 4-1: Fracture toughness for DER @150C evaluated with the Instron uniaxial tensile test Sample Break Stress (MPA) flaw width, 2b (meters) depth, a (meters) crack size, c (meters) KIC = 1.26 f c 1/2 (MPA*m1/2) 1 101.4 3.E-042.6E-042.E-041.8 2 101.3 3.E-042.8E-042.E-041.9 3 101.3 1.E-041.3E-049.E-051.2 4 97.6 3.E-041.7E-042.E-041.5 6 99.2 2.E-041.9E-041.E-041.4 7 100.8 3.E-041.8E-042.E-041.6 8 102.5 9.E-059.4E-057.E-051.1 MEAN 100.6 2.E-04 2.E-04 1.E-041.5 STND 1.6 9.E-05 7E-05 5.E-050.3 Figure 4-1: Fracture toughness evaluate d with quantitative fractography

PAGE 41

41 a) b) c) d) Figure 4-2: Optical images of In stron fracture surfaces and flaw bounda ries (arrows) a) edge flaw from surface bubble b) edge flaw c) edge flaw from inclusion d) edge flaw

PAGE 42

42 Figure 4-3: Load vs. displacement behavior for SENB sample tested at different displacement rates. 1) 5.0 mm/min blue line, 2) abor ted, 3) 0.05 mm/min aqua line, 4) 0.5 mm/min red line and 5) 10 mm/min r ecommended ASTM rate-pink line

PAGE 43

43 Table 4-2: Three point bend SENB fracture toughness values tested at different crosshead rates Sample rate (mm/min) Width (cm) Thickness (cm) Peak Load (kN) Ultimate tensile strength (MPA) Modulus (MPA) Energy at Break (N*mm) KIC chevron (MPA m 1/2 ) 1 5.0 0.6 0.3 0.08 47.7 5902.1 15.1 1.7 3 0.05 0.6 0.3 0.07 47.5 7217.2 9.3 1.6 4 0.5 0.7 0.3 0.06 40.0 6060.2 8.5 1.3 5 10.0 0.6 0.3 0.06 39.9 6655.4 7.2 1.3 Figure 4-4: Fracture features fo r a 0.05 mm/inch crosshead rate Figure 4-5: Twist/hackle (arrows) fracture featur es observed at a 0.5 mm/inch crosshead rate

PAGE 44

44 Figure 4-6: Secondary crack fo rmation (arrow) evident at a 5.0 mm/min crosshead rate Figure 4-7: Innovative pre-crack fixt ure designed to hold a straight edge razor bl ade and attach directly to the Instron Dynamight load cell. Now that the applied pre-crack load could be controlled, a consistent pre-crack depth could be made along the entire length of the SENB macro notch. Table 4-3: Standard SENB KIC with acetone and evaluated pe r standardized SENB method Sample Width (mm) Thickness (mm) Peak Load (kN) KIC ideal SENB (MPA m 1/2 ) KIC ideal SENB corrected (MPA m 1/2 ) 2 6.5 3.0 0.052.21.1 3 6.4 3.0 0.041.70.9 4 6.4 3.2 0.052.11.1 5 6.5 3.2 0.062.51.3 6 6.5 3.1 0.052.11.1 Mean 6.5 3.1 0.052.11.1 Std. Dev. 0.03 0.06 0.010.30.2

PAGE 45

45 Table 4-4: Alternative SENB KIC with acetone and evaluated per standardized SENB method Sample Width (cm) Thickness (cm) Peak Load (kN) KIC ideal SENB (MPA m 1/2 ) KIC ideal SENB corrected (MPA m 1/2 ) 1 1.3 0.3 0.1 2.1 1.3 2 1.3 0.3 0.1 2.1 1.1 4 1.3 0.3 0.1 2.4 1.3 5 1.3 0.3 0.1 2.1 1.1 6 1.3 0.3 0.1 3.0 1.6 7 1.3 0.3 0.1 3.5 1.8 Mean 1.3 0.3 0.1 2.6 1.4 Std. Dev. 0.0 0.0 0.0 0.6 0.3 20 microns 20 microns Figure 4-8: Quantitative fractography images of localized flaws on the failed SENB samples (arrows mark boundaries of flaw origin)

PAGE 46

46 Table 4-5: Fracture toughness, KIC, values when quantitative fr actography was applied to the fracture features for the failed alternativ e SENB samples prepared with acetone Sample (max) (MPA) c= (ab)1/2 (m) KIC = (1.26)*( corrected )* (c)1/2 (MPa m1/2 ) 1 42.6 1.E-041.3 2 45.3 8.E-051.2 4 47.4 6.E-051.0 5 46.1 4.E-050.8 6 64.1 9.E-051.7 7 71.7 6.E-051.5 Mean 52.9 7.E-051.2 Std. Dev. 12 3.E-050.3 Table 4-6: Mean KIC for various techniques KIC SENB ideal KIC SENB corrected QF KIC SENB ( corrected) (MPA m 1/2 ) (MPA m 1/2 ) (MPA m 1/2 ) Alternative SENB no acetone 3.0 1.6 1.5 Alternative SENB acetone 2.6 1.4 1.2 Standard SENB no acetone 2.01.1 0.6 Standard SENB acetone 2.1 1.1 0.7 Figure 4-9: Fracture toughne ss for the SENB techniques

PAGE 47

47 Figure 4-10: Ideal (A) vs. corre cted (B) fracture toughness, KIC, for alternative SENB samples treated with acetone Figure 4-11: Ideal (A) vs. corre cted (B) fracture toughness, KIC, for the standard SENB samples treated with acetone

PAGE 48

48 Figure 4-12: Alternative SENB samples trea ted with acetone (A) vs. without (B) Figure 4-13: Standard SENB samples tr eated with acetone (A ) vs. without (B)

PAGE 49

49 Figure 4-14: Standard (A) vs. alternative (B) SENB samples treated with acetone Figure 4-15: Top view of an empty flexure fixt ure and side view with a loaded sample Table 4-7: Test results for the chev ron sample fractured in 4-point bend Sample Width (mm) Thickness (mm) Peak Load (N) Tensile strength (MPA) Modulus (MPA) Yield Stress (MPA) strain at break (%) Energy at Break (N*mm) Break stress (MPA) A 6.4 3.2 54.0 25.0 943 7.9 25.0 0.3 8.6 25.0 B 6.4 3.2 53.3 24.7 958 0.7 24.7 0.3 8.8 24.7 C 6.5 3.1 42.2 20.9 939 1.4 20.9 0.2 6.1 20.9 A = No preload was applied to sample B = A 20N preload was applied per the standard 4-pt bend test position shown before testing C = Sample was first inverted and the 20N preload was applied per the chevron ASTM method

PAGE 50

50 Table 4-8: Chevron fl exure fracture toughness Sample Width (mm) Thickness (mm) Peak Load (N) Y min KIC chevron (MPA m 1/2 ) A 6.4 3.2 53.5 2.8 1.9 B 6.4 3.2 54.0 2.9 1.9 C 6.4 3.2 53.3 2.8 1.8 D 6.5 3.1 42.2 2.8 1.5 0 10 20 30 40 50 60 0.0000.0020.0040.0060.0080.0100.0120.014 Load (N) Crosshead (in) [1] 2 F Y B M Figure 4-16: Load vs. displacement behavior typica lly observed for a tested chevron sample. The line of best fit (red line) is a pplied to each curve for analysis.

PAGE 51

51 a) b) c) d) e) f) g) h) Figure 4-17: Chevron fracture features due to a 500N load cell and 0.05 mm/min displacement rate.

PAGE 52

52 Figure 4-18: Higher magnification of catastrophic failure at chevron notch tip (red arrow) Table 4-9: Test data for chevron sample s tested with acetone and no pre-load Sample Width (mm) Thickness (mm) Peak Load (N) Tensile Strength (MPa) Modulus (MPa) Energy At Yield (N*mm) Energy At Break (N*mm) Stress At Break (MPa) 1 6.6 3.1 47.7 22.7 8452.8 0.3 8.1 22.5 2 6.6 3.1 54.5 26.0 9261.5 0.3 9.2 26.0 3 6.7 3.1 34.2 16.0 7492.1 0.3 4.4 16.0 4 6.6 3.1 56.0 26.7 8769.6 0.4 10.0 26.7 5 6.7 3.1 53.6 25.7 8917.5 **** 9.0 25.7 Mean 6.6 3.1 49.2 23.4 8578.7 0.3 8.1 23.4 St. Dev. 0.1 0.0 9.0 4.4 673.4 0.0 2.2 4.5

PAGE 53

53 0 10 20 30 40 50 60 0.0000.0050.0100.0150.020 Load (N) Crosshead (in) [1] 2 3 4 5 F Y B M Figure 4-19: Load vs. displacement curves for chevron samples tested with acetone Table 4-10: Standard chevron fr acture toughness for samples tested with acetone and no pre-load Sample Width (mm) Thickness (mm) Peak Load (N) Stress At Break (MPa) Peak Load (kN) Y min chevron Chevron KIC (MPA m 1/2) 1 6.6 3.1 47.7 22.5 0.05 2.7 1.6 2 6.6 3.1 54.5 26.0 0.05 2.7 1.8 3 6.7 3.1 34.2 16.0 0.03 2.6 1.1 4 6.6 3.1 56.0 26.7 0.06 2.7 1.8 5 6.7 3.1 53.6 25.7 0.05 2.7 1.7 Mean 6.6 3.1 49.2 23.4 0.05 2.7 1.6 St. Dev. 0.1 0.0 9.0 4.5 0.01 0.0 0.3

PAGE 54

54 CHAPTER 5 CONCLUSIONS Critical fracture toughness, KIC, for the various tested techniques are summarized in Table 5-1. The student t-test, t(11) = 0.36, P < 0.05 (two tail), executed at a 95% confidence level in Figure 5-2 verified the uniaxial tensile test to evaluate qu antitative fractography fracture toughness (Instron) was not st atistically different fr om the standardized chevron flexure method. The student t-test, t(11) = 0.90, P < 0.05 (two tail), executed at a 95% confidence level in Figure 5-3 verified that the uniaxial tensile test to evaluate quantitative fractography fracture toughness was not statistically different from the standardized SENB method. The ANOVA analysis, F( 5, 27) = 3.89, P >0 .05, executed at a 95% confidence level in Figure 5-4 determined no statistical diffe rence between fracture toughness comparisons measured with the standardized techniques. The load vs. displacement behavior of the te sted chevron samples revealed unstable crack extension due to catast rophic failure from the chevron notch tip. Fracture toughness results were therefore higher than those from chevron tests w ith stable crack extension, however, the mean critical chevron fracture toughness was not statistically different from the other standardized techniques. The ANOVA analysis, F( 9, 52) = 9.5, P >0. 05, executed at a 95% confidence level for all tested fracture techniques is provided in Figure 5-5. For quantitative fractography applied to failed SENB surfaces, the KIC average was reported based on the stress concentration factor that ranged from 1.7 (low) to 2.7 (high). In summary, at a 95% confidence level, the stude nt t-test verified that the determination of fracture toughness using quantitative fractography from fracture surfaces of uniaxial tensile specimens was not statistically different from the standardized SENB or chevron flexure

PAGE 55

55 methods. At a 95% confidence level, the student t-te st verified that acetone did not affect the KIC measurements regardless of techni que.At a 95% confidence level, the student t-test also verified that the alternative vs. standard SENB samples yielded similar KIC results. For the same SENB technique, different W/B sample ratios did not change the KIC calculations. An ANOVA analysis performed at a 95% confidence level determined th at there is not statis tical difference between fracture toughness measured with standardized techniques. When applying quantitative fractography to th e failed SENB fracture features, a stress concentration factor must be used to account for the effect of crack geom etry on the local cracktip stress level due to the SENB pre-crack at the base of the SENB macro notch. A stress correction factor that ranged fr om 1.7 to 2.7 was selected based on literature. ANOVA analysis performed at a 95% confidence level determined a statistical difference in the fracture toughness evaluated with the standardized techniques vs those measured when quantitative fractography was applied to the failed SENB fracture features. When quantita tive fractography was applied to the failed SENB features, the lower fracture tou ghness shown for standard SENB sets G and H in Figure 5-5 resulted from a lower break stress. Be cause the measured flaw sizes between samples were similar, this lower break stress was unexp ected and due to some other effect not being measured. The load vs. displacement behavior of the te sted chevron notch samples showed unstable crack extension due to catastrophic failure fr om the chevron notch tip. Although the fracture toughness results were greater than results that would have genera ted had stable crack extension occurred, the mean critical chev ron fracture toughness was not sta tistically different from the other standardized techniques. Future work coul d investigate different ratios or chevron notch

PAGE 56

56 angles to promote stable crack propagation but wa s not deemed necessary for the scope of this study. This study demonstrated the importance of qua ntitative fractography as a failure analysis tool to accurately identify intrinsic material fl aws and failure origin. Quantitative fractography on the failed SENB fracture featur es revealed that the crack assumed to occur along the entire length of the SENB macro notch by the SENB standa rdized technique seldom occurs in reality. In contrast, failure in the tested samples typical ly resulted from semi-elliptical flaws, which suggests the flaw size assumed by the standardiz ed techniques is not appropriate. Modeling methods such as finite element analysis, should be used to combine independently notch, precrack, and semi-elliptical elements to model the observed behavior more effectively.

PAGE 57

57 Table 5-1: Average Fracture Toughness, KIC, for the various techniques tested Technique SENB KIC corrected (standardized method) (MPA m 1/2 ) KIC with QF applied to SENB ( corrected) (MPA m 1/2 ) Alternative SENB no acetone 1.61.5 Alternative SENB with acetone 1.41.2 Standard SENB no acetone 1.10.6 Standard SENB with acetone 1.10.7 Chevron 1.6 Quantitative Fractography method 1.5 Figure 5-1: Fracture to ughness vs. technique

PAGE 58

58 Figure 5-2: Fracture toughness for the tensile quantitative fract ography (A) vs. chevron flexure technique (B) Figure 5-3: Fracture toughness for the tensile Instron quantitative fr actography (A) vs. alternative SENB acetone (B)

PAGE 59

59 Figure 5-4: Statistical comparis on of fracture toughness evaluated wi th standardized techniques for an ANOVA analysis at a 95% confidence level Where A = Corrected alternative SENB KIC no acetone B = Corrected alternativ e SENB KIC with acetone C = Corrected standard SENB KIC no acetone D = Corrected standard SENB with acetone E = Instron KIC F = Chevron KIC

PAGE 60

60 Figure 5-5: Statistical compar ison of fracture toughness evalua ted with standardized and quantitative fractography techniques for an ANOVA analysis at a 95% confidence level where A = Corrected alternative SENB KIC no acetone B = Corrected alternative SENB KIC with acetone C = Corrected standard SENB KIC no acetone D = Corrected standard SENB with acetone E = Instron KIC F = Chevron KIC G = Quantitative Fractogra phy KIC for failed standa rd SENB no acetone H = Quantitative Fractography KIC for fa iled standard SE NB with acetone I = Quantitative Fractography KIC fo r failed alternative SENB acetone J= Quantitative Fractography KIC for failed alternative SENB no acetone

PAGE 61

61 CHAPTER 6 FUTURE WORK The effect of sharp vs. blunt cracks on pol ymer fracture toughness could be evaluated by repeating these fracture toughness te sts using acetone on a brittle th ermoplastic polymer such as poly (methyl methacrylate). Since all tested chevron samples revealed unstable crack extensi on due to catastrophic failure from the chevron notch tip, future work could investigate different chevron geometries or chevron notch angles that promote stable crack propagation but was not deemed necessary for the scope of this study. Quantitative fractography on the failed SENB fr acture features revealed that the crack assumed to occur along the entire length of th e SENB macro notch by th e standardized SENB technique seldom occurs in reality. Therefore, in the future more effective modeling methods, such as finite element analysis, should be deve loped and utilized to combine independent notch, pre-crack, and semi-elliptical elements to more effectively model the observed crack propagation behavior.

PAGE 62

62 CHAPTER 7 LIST OF REFERENCES 1. A. A. Griffith: Philos. Trans R. Soc ., 1920, 221,163-198. 2. L. Plangsangmas, J. Mecholsky, Jr., and A.B. Brennan: J. Appl. Polym. Sci., 1999, 72, 257268. 3. G. Medri, C. Cali, and R. Ricci: Plastics, Rubber and Composites Processing and Applications, 1995, 23(4), 260-268. 4. R.Y Ting and R.L Cottington: Journal of Applied Polymer Science, 1980, 25(9), 18151823. 5. E.J. Oborn: Fracture Toughness of a Liquid Crystalline Epoxy Department of Materials Science and Engineering, University of Flor ida, Gainesville, Florida 32611, 2000, p. 18-53. 6. M. Sakai and M. Inagaki: J. Am. Ceram. Soc., 1989, 72, 388-394. 7. A. A. Griffith: Philos. Trans R. Soc ., 1920, 221,163-198. 8. F.I. Baratta: The Effect of Crack Inst ability/Stability of Fr acture Toughness of Brittle Materials," Fatigue and Fracture Mechanics: 28th Volume, ASTM STP (1321), J.H. Underwood, B.D. Macdonald, and M.R. Mitchell, Eds., American Society for Testing and Materials, Philadelphia, PA, 1997, p. 577601. 9. ASTM Designation: E1823-96E1, Standard Terminology Relating to Fatigue and Fracture Testing, Annual Book of ASTM Standards American Society for Testing and Materials, Philadelphia, PA, 1996, p. 1027-1044. 10. M. Sakai and M. Inagaki: J. Am. Ceram. Soc., 1989, 72, 388-394. 11. L. Ewart and S. Suresh: J. Mater. Sci. Lett., 1986, 5, 774-778. 12. T. Nose and T. Fuji: J. Am. Ceram. Soc., 1988, 71, 328-333. 13. A. Meyers and K. Chawla: Mechanical Behavior of Materials, Prentice-Hall, Inc., Upper Saddle River, NJ, 1999, p. 363-364. 14. S. Bandyopadhyay: Materials Scienc e and Engineering 1990, A125, 158-165. 15. J.E. Ritter, M.R. Lin, and T.J. Lardner: Journal of Materials Science, 1988, 23, 2370-2378. 16. S.R. Choi and J.A. Salem: J. Mater. Res ., 1993, 8, 3210-3217. 17. J. Chia: Institute of Materials Research and Engineering, 2004, 4, 1-4.

PAGE 63

63 18. R.Y Ting and R.L Cottington: Journal of Applied Polymer Science, 1980, 25(9), 18151823. 19. G. W. Irwin: Trans. ASME J. Appl. Mech., 1957, 24, 361-364. 20. G. W. Irwin: Trans. ASME J. Appl. Mech., 1962, 29, 651-654. 21. P. N. Randall: ASTM STP 410 1967, 88-126. 22. J. J. Mecholsky, S. W. Freiman, and R.W. Rice: J. Am. Ceram. Soc. 1977, 60, 114-117. 23. C. E. Inglis: Transactions of the Institute of Naval Architects, 1913, 55, 219-241. 24. A. A. Griffith: Phil. Trans. Roy. Soc., 1921, A221, 163-198. 25. E. Orowan: Repts. Prog. Phys. 1948, 12, 185. 26. J. Mecholsky Jr.: Quantitative Fracture Surface A nalysis of Glass Materials ; Simmons, C. J. and El-Bayoumi, O. H., Ed.; American Ceramic Society, Westerville, Ohio, 1993. 27. L. Plangsangmas, J. Mecholsky Jr., and A.B. Brennan: J. Appl. Polym. Sci., 1999, 72, 257268. 28. A. C. Roulin-Moloney: Fractography and Failure Mechanisms of Polymers and Composites Elsevier Science Publis hers Ltd., New York, 1989. 29. L. Engel, H. Klingele, G. W Ehrenstein, and H. Schaper: An Atlas of Polymer Damage Prentice-Hall, Inc., Englewood Cliffs, NJ, 1981. 30. ASTM Designation: C1322-96a, Standard Pr actice for Fractography and Characterization of Fracture Origins in Advanced Ceramics, Annual Book of ASTM Standards American Society for Testing and Material s, Philadelphia, 1996, p 421-465. 31. ASTM Designation: D5045-99, Standard Test Methods for Plane-Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials, Annual Book of ASTM Standards, American Society for Testing and Ma terials, Philadelphia, 1999, p. 347-355. 32. ASTM Designation: C1421-99, Standard Test Methods for Determination of Fracture Toughness of Advanced Ceramics at Ambient Temperature, Annual Book of ASTM Standards American Society for Testing and Ma terials, Philadelphia, 1999, p. 641-669. 33. R. Hertzberg: Deformation and Fracture Mechanics of Engineering Materials; 3rd ed.; John Wiley & Sons, Inc., New York, 1989.

PAGE 64

64 BIOGRAPHICAL SKETCH Stephanie DiFrancesco graduated from Villanova University in 1997 with a bachelors degree in chemical engineering and a minor in chemistry. Stephanie DiFrancesco is employed by Motorolas Advanced Product Technology Center in Fort Lauderdale, FL. Technical skills include thermal, mechanical and rheological material characterization techniques. As the Plastic Lab Administrator, Stephanie s upports global product development sectors as their needs relate to material and plastic development.