Delamination Analysis of Composite Laminates
Wei Ding
A thesis submitted in conformity with the requhments for the degree of Doctor of Phiiosophy Graduate Department of Chemical Engineering and Appiied Chemistry University of Toronto
@ Copyright by Wei Ding 1999 National Library BiMiothèque nationale 14 dan, du Canada Acquisitions and Acquisitions et Bibliographie Senrices services bibliographiques 395 Wellington Street 395, rue Wellington OttawaON K1AON4 Ottawa ON K1A ON4 Canada Canada
The author has granted a non- L'auteur a accordé une licence non exclusive licence allowing the exclusive permettant à la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, distribute or sell reproduire, prêter, àistribuer ou copies of this thesis in microform, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/film, de reproduction sur papier ou sur format électronique.
The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimes reproduced without the author's ou autrement reproduits sans son permission. autorisation. Delamination Analysis of Composite Laminates
Wei Ding
Doctor of Phiiosophy, 1999 Department of Chernical Engineering and Appüed Chemietry University of Toronto
Abstract
A combined theoretical and experimental study has been conducted on the delamination of fibre reinforced polymenc composites. The main objectives were to gain a better understanding of the physical orîgin of delamination fhcture toughness and to develop theoretical models to predict the critical strain energy release rates of delamination in composite materials.
Of the many energy dissipation mechanisms present in the delamination process, crack tip plastic deformation was determined to be the most critical one. Two analytical beam models, based on the double cantilever beam @CB) specimen and the end notched flexure (ENF) specimen, were developed. A frsicture criterion, based on the skof the crack tip plastic zone, was incorporated into thae beam models so that the mode 1 and mode II cntical strain energy release rates of composites can be predicted using the corresponding resin and fibre properties as well as composite structural parameters. A complete set of mechanical tests were perfiormed on five polymeric composite systems, including both thermoset and thennoplastic systems, and on their correspbnding neat polymer resins. The theoretical predictiom for delamination kture toughness nom the present anaiytical models agreed very well with the data obtained in the present experiments and those in the literature over a wide range of composite laminates. Acknowledgments
1 am especiaily gratefiù to my supervisor, Professor M.T. Kortschot, for his support,
encouragement and guidance throughout this work. Special thanks go to Professor M.R.
Piggott for allowing the use of his labomtory facilities and for his insightfd advice and
discussion on composite materiais. 1wouid aiso like to thank Professor D.E. Cormack for
taking tirne fiom his busy schedule to be the chair of the reading cornmittee, giving me
valuable advice and guidance.
1greatly appreciate the assistance and helpfidness of Mr. S. Law and Mr. S. Dai in
my experimental work. 1 would like to thank dl rny fiends and colleagues, Chengjie
Zhang, Ning Yan, Gus Trakas, Saeed Douroudiani, Dennis Cicci and the present MTK
group for their interesthg and inspiring conversations and discussion.
The hcial assistance fiom the Govemment of Ontario in term of Ontario
Graduate Scholarships (OGS) and the National Science and Engineering Research
Council of Canada (NSERC) is also greatly appreciated. ,
Finally, 1 would like to thank my wife, Yigping, for her patience, understanding and support. Table of Contents
Abstract Acknowledgments Table of Contents Nomenclature viii List of Tables xii List of Figures 1 Introduction 2. Literature Review 2.1 Delambation Testing 2.1.1 Mode1 2.1.2 Mode II 2.1.3 Mode III 2.1.4 Mixed Mode 2.2 MaterialEffects 2.3 Fractography 2.4 Summary Theoretical Modelling 3.1 Introduction 3.1.1 Delamination Mechanisms 3.1.2 Present Work 3.2 Mode 1 Delamination Model 3.2.1 Introduction 3.2.2 Mathematical Development 3.2.3 Failure critenon 3.3 Mode II Delamination Model 3.3.1 Introduction 3.2.2 Mathematical Development 3.2.3 Failure criterion 4. Experimental Studies 4.1 Testing and Equipment 4.1.1 Polymer Tensile Test 4.1.2 Single-edge Notched Bend Test (SENB) 4.1.3 Mode 1 Delamination Test 4.1.4 Mode II Delamination Test 4.1.5 Fractography 4.2 Materials and Sample Preparation 4.2.1 Materials Selection 4.2.2 Preparation of Tensile Specimens 4.2.3 Preparation of SENB Specimens 4.2.4 Preparation of Mode 1 and Mode II Specimens 4.2.5 Preparation of Specimens for Microscopie Studies 5. Experimental Results 5.1 Introduction 5.2 Experimental redts 5.2.1 PolymerTensileTest Results 52.2 SENB Test Results 5.2.3 Mode 1 and Mode II Test Resuits 5.2.4 Fractography 6. Model Application and Discussion 6.1 Introduction 6.2 Mode 1 Mode1 Application 6-2-1 Model Evaluation 6.2.2 Theoretical Predictions and Discussion 6.3 Mode II Mode1 Application 6.3,l Model evaluation vii
6.3.2 Theoretical prediction and discussion 6.4 Conclusions 7. Conclusions
8, Recommendations 123
9, References 124
Appendices
A Mathematical details of mode 11 beam model --- Elastic /plastic case 133
B Mathematical development for mode II beam model - Elastic case 138 Nomenclature
Sym bol Definition
crack length
the dope of a plot of normalized crack length (ah)vs. the cubic
root the compliance the MCC method
specimen width
constants in the solutions of goveming differential equations
compliance
compliance of the EM: specimen calculated by the mode II mode1
compliance of the ENF specimen calculated by the classical beam
theory
constants in the solutions goveming differential equatiom
constants in the solutions goveming differential equations
Young's modulus
Young's modulus of fibres
Young's modulus of ma&
Young's moduius of the composite beam in the fibre direction
Young's modulus of the composite beam perpendicuiar to the fibre
direction
shear modulus of the composite beam shear modulus of fibres
shear modulus of matrix
strain energy release rate
seain energy release rate of mode 1, II, and III
strain energy release rate caiculated by classical beam theory
cntical strain energy release rate
critical strain energy release rate of mode 1, II and III
half thickness of the barn specimen
stifiess of the elastic foundation in the mode 1 mode1
stress intensity factor
critical stress intensity factor
length of the crack tip plastic zone
critical lengths of the crack tip plastic zone in mode 1 and II
half length of the ENF specimen the slope of a least square regression line used in compliance calibration in ENF test foundation spring constants in mode 1 and II models bending moment the dope log compliance vs. log crack length in the CC method ratio between the critical sizes of the crack tip plastic zone in the mode 1 delamination and in the resin fiacture ratio between the cntical sizes of the crack tip plastic zone in
the mode II delamination and in the resin kture
extemal Ioad
extemal load at the onset of plastic deformation
radius of the crack tip plastic zone in resin hcture
cntical radius of the crack tip plastic zone in resin kture
glas-transition temperature extemal energy
interna1 energy including both elastic and plastic energy fibre volume fiaction deflections of the beams work of hcture length of the elastic shear spring foundation correction coefficients for large deflection and transverse shear deflection of the beam deflection of the beam at the onset of plastic defiornation the x-intercept of a plot of the cube root of the specimen cornpliance vs. the mck length in the MBT method the area of the crack surface parameter used in the mode 1model shear correction coefficient in the mode II model
Poisson's ratio density of composite material density of fibres density of matrices
Yield stress of the spring foundation shear stress on the center surface of the ENF specimen
Yield shear stress of the spring foundation xii
List of Tables
Table 5.1 Tensile strengths of al1 neat resins
Table 5.2 Tensile moduli of al1 neat resins
Table 5.3 SENB test results of neat resin materials
Table 5.4 Mode 1 and mode II delamination test redts
Table 6.1 Comparisons of GKof the present composite systems
Table 6.2 Matenal properties of the reshs and fibre volume fiactions of the
composite systems
Table 6.3 Comparisons of G,of previous composite systems
Table 6.4 Materials properties of three typical composite laminates
Table 6.5 Comparisons of C, and G, values between the finite element
results and the present solutions
Table 6.6 Comparisons of C, and G,,values between the present results and
the finite element solutions
Table 6.7 Cornparisons of C, and G, values between the present results and
the finite element solutions
Table 6.8 Cornparisons of the cornpliance and the G, of ENF specirnens
Table 6.9 Comparisons of G, of the present composite systems
Table 6.10 Comparisons of Gnc of the previous composite systems List of Figures
Figure 1.1 Basic delamination modes
Figure 2.1 Mode 1 delamination test method
Figure 2.2 Mode II delamination test method
Figure 2.3 Mode III delamination test methods
Figure 2.4 Mixed-mode delamination test methods
Figure 3.1 An optical micrograph of a petrographic thin section of a rubber-
toughened AS4lpolycarbonate composites. The plastic zone is
observed using cross polarized light. (after Parker and Yee [1989])
Figure 3.2 Classical beam solution of DCB specimen
Figure 3.3 Beam on the elastic-plastic foundation
Figure 3.4 The elastic-plastic load-deflection curve of the DCB specimen
Figure 3.5 Illustration of constraînt effect of adherend on the crack tip plastic
zone in adhesive (after Kinloch and Shaw [1981])
Figure 3.6 Iliustration of the relationship between adhesive bond fhcture
toughness, G,and bond thickness, h.
(&et Kinloch and Shaw [l98 11)
Figure 3.7 Beam on the elastic-plastic shear spring foundation
Figure 3.8 Energy dissipation mechanisms in mode 11 delamination
Figure 4.1 Specimen configuration of polymer tensile test
Figure 4.2 Specimen configuration of single edge notched bending test xiv
Figure 4.3 Specimen configuration of mode I delamination
Figure 4.4 Specimen configuration of mode II delamination
Figure 5.1 Mode 1 hturesurface of S2-glass/Epon-815 (curing cycle 1)
Figure 5.2 Mode U kturesdace of S2-glass/Epon-8 15 (curing cycle 1)
Figure 5.3 Mode 1 hcture surface of S2-glass/Epon-8 15 (curing cycle 2)
Figure 5.4 Mode II kturesurface of S2-glasd'pon-8 15 (curing cycle 2)
Figure 5.5 Mode 1 fracture surface of E2-glass/Polypropylene
Figure 5.6 Mode II firicture surface of E2-glass/Polypropylene
Figure 5.7 Mode 1 hcture surface of E2-glass/Nylon-12 (oven dry)
Figure 5.8 Mode II fhcture surface of E2-glass/Nylon-12 (oven dry)
Figure 5.9 Mode I frsicture surface of E2-glass/Nylon-12 (saturated)
Figure 5.10 Mode II fhcture surface of E2-glasdNylon-12 (saturated)
Figure 5.1 1 Cross-section of S2-glass/Epon-8 15 composites
Figure 5.12 Cross-section of E2-glass/polypropylene composites
Figure 5.13 Cross-section of E2-glass/Nylon- 12 composites
Figure 6.1 Comparison of strain energy release rate vs. force relation between
the present analysis and the finite element method
(Yamada [l9881)
Figure 6.2 Comparison of strain energy release rate vs. deflection relation
ôetween the present analysis and the finite element method
Or- [19881)
Figure 6.3 Comparisons of mode I criticai strain energy release rates Figure 6.4 Comparisons of cornpliance predictions as a fùnction of a/L
Figure 6.5 Comparisons of strain energy release rates as a function of a&
Figure 6.6 Comparison of cornpliance predictions as a hction of a/L
Figure 6.7 Comparison of strain energy release rates as a function of a/L
Figure 6.8 Comparison of current analysis with other analytical and finite
element analyses of the ENF specimen
Figure 6.9 Comparison of G, between the cwent analysis and the finite
element analysis over a wide range of E,,/G,, ratios
Figure 6.10 Comparisons of the mode II cntical strain energy release rates Introduction
Failure nnalysis of laminated composite structures has atüacted a great deal of interest in recent years due to the increased application of composite materials in a wide range of high-performance structures. Intensive experimental and theoretical studies of failure analysis and prediction are being conducted. Delamination, the separation of two adjacent plies in composite laminates, represents one of the most critical failure modes in composite laminates. In fact, it is an essential issue in the evaluation of composite laminates for durability and damage tolerance.
Histoncally, the short-beam shear (SBS) test method (ASTM D-2344)was the only experimental technique commonly used to measure the interlaminar strength of composites. However, when the short-beam shear test was used in conjunction with advanced composites, such as graphitelepoxy, considerable dificulty was encountered in interpreting experimental data because of the complexity of faüure modes observed in the
SBS spechens. New interlaminar test methods have been developed because of a general dissatisfaction with the short-beam shear test and the need for a more complete characterization of delamination fhcture. Most of these methods are based on a fracture mechanics approach with the critical stniin energy release rate king the characterizing parameter. Generally speakhg, delamination in laminated composites may develop in any one of or any combination of three basic modes of interla.kture. These modes are mode 1, the opening mode, or peel mode, mode II, the in-plane shear mode or sliding shear mode, and mode III, the out of plane shear mode or twisthg shear mode, as shown in figure 1.1.
Figure 1.1 Basic delamination modes
The criticai strain energy release rate is the generally accepted measure of total energy required to initiate a delamination in the material, and is denoted by the symbol
G,. This value has ken found to depend on the mode of delamination. Thus there are three G, values: G, ,Ga, and Gmcfor mode 1, mode II and mode III respectively. Many aspects of delamination have been studied, including various test methods
for mode 1, mode II, mode III and mixed-mode loading, experimental data reduction
methods, material effects, environmental effects, and effiects of various testing
parameters, fibre orientation, stacking sequence, and so on. Scanning electron
microscopy (SEM) has been widely used to describe the delamination process and to
search for characteristic features associated with different delamination modes. There
exist detailed descriptions of characteristic surf'hce features of the delaminated specimens.
Although there are a few efforts to explain and mode1 the delamination process, most of
the work has ken done in the attempt to obtain values for Gc rather than to seek the
physical origin of the delamination and to develop appropriate models to predict these
cntical strain energy release rates, G,c,G ,and G,.
From both materials science and engineering design standpoints, the understanding of the physical origin of composite delamination and the theoreticai modelling for delamination hcture toughness are necessary. It is not dEcient to measure G, and to use it in the design unless the test configurations are identical to the end use situations. Since reai failures ofien occur in complicated situations, many factors, such as delamination mode, ply orientation, stacking sequence and specimen thichess, need to be investigated. A complete experimental data set of delamination toughness for design purposes of a particuiar materiai would be rather large. The understanding of the nature of delamination kture and the theoretical modelling based on the fundamental understanding would greatly reduce the number of delamination experiments required.
Also, the theoretical modelling can help us to understand Merthe finicture mechaaisms Introduction 4 and materials parameters that are most important in controlling hcture properties so that we know how to improve materials hture toughness and how to develop new materials with high hture properties.
The critical strain energy release rate, Gc , can be affected by many factors, including composite structurai parameters such as fibre volume fraction and ply orientation, and materials properties of the constituent materials such as tensile strength and elastic modulus of the resin and the fibre. Gc should probably be treated as a structural property rather than a material property. Therefore, based on a fundamental understanding of the physical mechanisms involved in the delamination process, it shouid be possible to develop a general mode1 to relate the cntical strain energy release rate, Gc , to the materiais properties of the constituent matenais and the basic composite structurai properties.
The objectives of the present research were to gain a better understanding of the physical origin of delamination fhcture toughness in composite materials, and to develop mathematical models to predict the critical strain energy release rates associated with different delamination modes, especially mode 1 and mode II. Emphasis was placed on the plastic deformation around the crack tip which was believed to be a critical factor in determinhg the delamination fracture toughness, and on the relatiomhip between the extent of crack tip plastic zone or damage zone and the critical strain energy release rate.
A combined experimental and theoretical study was conducted to determine the role of crack tip plastic deformation and other microfailures, and finally to achieve the goal of predicting the dependence of the critical strain energy release rate on delamination mode, material properties of fibre and ma&, and composite structural properties. Speciaily, two enalytical beam models dong with a fracture cnterion based on the size of crack tip plastic zone were developed for predicting the critical sitrain energy release rates of mode
1 and mode II. A complete set of mechanical tests was performed on five composite material systems and their corresponding neat resins. Both thennoset and thermoplastic composite systems were included in the experhents in order to obtain a wide range of materials properties to test the present theoretid models. The theoretical predictions for delamination fiacture toughness nom the present theoretical analysis agreed very favorably with the data in the present experiments as well as those in the literature. Literaiure Review 6
2. Literature Review
Numerous studies have been conducted on many aspects of delamination in composite
laminates. Some studies concenirated on reporting delamination toughness data of new
composite materials; others dealt with various delamination test methods and
experimental data reduction methods. There were also studies of hctography, materials
effects, environmental effccts and so on. Unfortunately, not many studies have been devoted to obtaining a fundamental understanding of delamination fhcture mechanisms and to developing theoretical models to predict the critical strain energy release rates.
The following literature review focuses on three important aspects of delamination that are directly related to the present study: delamination testing, materials effects and fractography.
2.1 Delamination Testing
2.1.1 Mode 1
The mode 1 delamination test has traditionally been treated as the most important form of delamination characterization. The double cantiiever beam (DCB) test, as show schematically in Figure 2.1, is the most commonly used mode 1 delamination test and is the ody test of delamination characterization of composite laminates that has been standardized by the ASTM @5528-94a). Figure 2.1 Mode 1 delamination test method
The concept of the DCB test was originated fkom the cleavage test used in hcture mechanics. In the 1930s, Obreimoff [1930] used the cleavage technique to evaluate the fkcture surface energy of mica. In the early 1960s, Berry [1963] introduced the cleavage technique to measure the fkcture sudace energy of PMMA. Based on the cleavage test, the DCB test was origiaally developed for evaluating the mode 1 hcture toughness of adhesive bonded joints. Ripling et al. [1964] deterrnined that a DCB specimen consisting of an adhesive bond line between metal arms was well-suited for such a purpose.
The simplicity and pure mode 1 nature of the DCB test have made it a nahiral candidate for characterizhg mode 1 delamination in advanced composite materials. In early 1980s, a number of researchers used the DCB specimen to study the interlaminar ktureof continuous fibre reinforceci composite materials. Bascom et al. [1980] applied
a tapered DCB specimen to evduate delamination in woven fabnc composites. Wilkins
et al. [1980] used a straight sided DCB specimen to study graphite/epoxy composites.
Devitt et al. [1980] employed the DCB test to study the delamination fracture of
glasdepoxy composites. Whitney et al. [1982] thoroughly assessed the viability of the
DCB test in characterizhg mode 1 delamination in composites laminates and determined
that the DCB test was capable of discriminating between matenals of different
interlaminar toughness, and could be used as a matend screening tool.
Further studies on many aspects of the DCB test were perfonned. For example,
Chai [1984] studied the effects of constituent matenals on the interlaminar fkacture toughness using the DCB test. He concluded that the interlaminer hcture energy of composite laminates depended on the matrix constituent only, not on fibres or their orientations. A detailed study of fibre bridging in DCB specimens was perfonned by
Johnson md Mangalgiri 119871. Much less fibre bridging was observed when the delaminahg halves were placed at a slight angle (1SO, 3') to each other.
Several researchers investigated the methods of load applications in the DCB test.
Srniley [1985] used small smws to fix the loading hinges to the carbodPEEK specirnens since the adhesive bonding was unreliable for themioplastic matrix composites. Glessner
[1989] reported that instead of using loading hinges, load can be applied by driving a wedge between the two DCB am. Other than the piano-hinge type tabs, as shown in A-- A-- Litera e Review 9
Figure 2.1, load may also be applied by T type tabs which were studied in great length by
Naik et al. [1990].
The experimentai data reduction and the stress analysis of the DCB specimen
were performed by many researchers. The strain energy release rate, G, , is basically a
hction of the load, the displacement, the crack length and other material and stnichiral
panuneters used in the delamination test. It is very important to develop appropriate
expressions to calculate G, based on these data. The most comrnonly used data reduction
methods have been the compliance rnethod (CC) proposed by Berry [1963], the modified
beam theory @EST) proposed by Hashemi et al. [1989] and modified compliance (MCC)
method proposed by Kageyarna and Hojo [1990]. Many analytical and finite element
analyses for the crack tip stress and the mode 1 strain energy release rate, G, , of the DCB
specimen have dso been conducted, including Kanninen [1973], Wang et al. [1978],
Whitney [1985], Yamada [1987, 19881 and Williams [1989]. Details will be discussed
in Chapter 3.
O'Brien and Martin [1993] reported the draft DCB standard which was based on the 'round robin' test results of mode 1 interlaminar &tue toughness. To create an artincial crack, the use of PTFE (Teflon? based inserts, rather than polyimide, of thiclmess 13 pm or less was recommended. The modified beam theory (MBT) method was recommended for data reduction since it yielded the most consemative results.
Recently, the DCB test has been installed as a fodASTM standard, D5528-94 (1994), for characterizhg mode I interlaminar fhcture for fibre reinforced polymer matrk composites.
2.1.2 Mode II
Mode II delamination involves sliding two crack sufaces to propagate a crack, as shown in Figure 1.1. Many mode II delamination tests have ken proposed and there is disagreement over which one is the easiest to perforxn, and debate as to which method yields the best (Le. pure mode II) results. Nevertheless, the end notched flexure (ENF) test, as shown schematically in Figure 2.2, has emerged as probably the most widely wd test configuration for mode II delamination since it is easy to perfom and does produce pure mode II failure.
End Notched Flexure @NF) (RUssmIl and Street, 1982)
Figure 2.2 Mode II delamination test method The ENF test was first proposed by Russell and Street [1982] for characterizhg
mode II delamination. It shares the same specimen design as the DCB test, allowing the
use of beam theory for data reduction, and it also demonstrates a sufnciently large
compliance, ailowing the use of experimental compliance calibration methods as well.
The shplest expression for the compliance, C, ,and the mode II strain energy release
rate, GBT, of the ENF specimen were obtained by Russell and Street [1982] using the
classical beam theory,
where P, a, b and E, ,I are the load, the crack length, the width and the bending stiffhess of the ENF specimen, respectively.
The evaluation of mode II strain energy release rate and the stress analysis of ENF test has ken extensively studied by several researchers, both analytically and numerically. In the late 1970s, Barrett and Foschi [1977] performed a fhite element analysis to evaluate mode II stress intensity factors in cracked wood beams. In the 1980s,
Mail and Kochhar [ 19861, Gillespie et al. [1986], and Salpekar et al. [1988] ali conducted two-dimensionai finite element analysis of the ENF specimen for composite rnaterials. Lirerature Review 12
Murthy and Chamis 119881 and Valisetty and Chamis LI9881 carried out three-
dimensional finite element analysis to evaluate the stralli energy release rate for the ENF
and other mixed-mode specimens. Furthemore, He and Evans [1992] analyzed the ENF
test and several other delamination tests using the finite element method. The ENF
specimen was dso analyzed by several researchers using the analytical approach,
including Carlsson et al. [1986a], Carlsson et al. [1986b], Whitney et al. [1987], Whitney
[1988], Chattejee [199l], Wang and Williams [1992] and Corleto and Hogan [1995].
Timoshenko beam theory, plate theory, higher-order beam theory were used in their
studies. Details will be discussed in Chapter 3.
Comparable to the case of the DCB test, many aspects of the ENF test have been
studied. For example, in the study by Carlsson et al. [1986a], the size of the ENF
specimen was analyzed to minimize geometric nonlinear response and to avoid nonlinear material behaviour. The effect of the fiction between the two crack surfaces of the upper and lower beams was also shidied in their study. Murri and Guyun [1988] studied the loading scheme of ENF test. They conducted a cornparison between three-point bend, four-point bend and end clamped center loaded test rnethods. Three different lay-ups,
[90,/0/&45], [!JO& 1, and [903/O/f451, of T3OO/S208 graphitdepoxy were tested. Similar
Gc results for all three lay-ups and test configuratiom were obtained.
It is worth mentionhg that in ENF tests, especialiy for brittle epoxy based composites, the crack growth is sudden and unstable, accompanied by a large drop in the Literatwe Review 13 load. This leads to a large difference between the maximum load and the crack-arrest load, i.e., the load when the crack propagation speed reduces to zero. Therefore, which load should be used to calculate delamination hcture toughness became a debatable issue. In a study by Vu-Khanh [1987], tests were carried out on lamuiated specimens to generate unstable crack growth and subsequent crack-arrest It was shown that the crack- arrest hcture toughness (the material's resistance to penetration by a ninnllig crack) was equivalent to that at initiation, contrary to what has been observed in mode 1 crack propagation where hcture energy during unstable, fast crack growth is much lower than that at initiation and during stable propagation. On the other hand, Kageyama et al.
[1991] proposed a stabilized ENF test. Using a special displacement gage, tests were carried out under a constant crack shear displacement (CSD)rate, Le., the relative shear displacement between the upper and lower halves of the specimen at the delaminated end.
This approach resuited in a stable crack growth. The G, during stable crack growth is almost constant, and about 15% to 20% higher than that at crack initiation.
In general, the ENF test provides a straightforward method for determining Gnc.
It is now the focus of ASTM standardization efforts [ASTM ciraft protocol, 19901.
2.1.3 Mode III
Mode III delamination test has been the greatest challenge in chanicterization of the three basic fracture modes. Ensuring a pure mode III delamination is extremely dif£icult. Two commonly used test mettiods for characterizhg mode III, the split cantilever beam (SCB)
test and the edge crack torsion (ECT) test, are shown schematically in Figure 2.3.
Donaidson [1988] first proposed the SCB test for mode III delamination
characterization, which shared the same type of specimen as the DCB test in mode I and
the ENF test in mode II. Similar beam theory equations could therefore be used for data
reduction. However, Mermidies on the SCB test by Martin [1991] and Donaldson et
al. [1991] ciiscovered that the SCB test did not yield a 'pure' mode III delamination, and a
substantial mode II component at the edges of the specimen existed. These conclusions were supported by fractographic evidence dong with finite element analyses.
Split Canülever Bearn (SCB) (Donaldson - 1988)
Figure 2.3 Mode III delamination test methods
To eliminate the mode II component, SMet al. [1993] and Robinson and Song
[1992, 19931 simultaueously proposed a new loading scheme in the SCB test. Their modification consisted of two sets of loads on each arm, with one being twice the magnitude of the other at one-half of the distance hmthe crack tip. The new loading regime eliminated the moment at the crack trip, in tum eliminating the mode II
component The true value of G, could therefore be detemnined. Their Gmc resuits
were verified by finite element analyses.
The latest test for mode III delamination charactenzation is the edge crack torsion
method proposed by Lee [1993]. The mode III edge delamination was achieved by
twisting a laminated plate. Date reduction was simple and was derived nom a J-integral
analysis. The ASTM D30 standardkation comfnittee is currently studying this test
method.
2.1.4 Mixed Mode
It is believed that delaminations in service seldom occur in pure mode 1, II or III, but
rather in a mixture of the three modes. However, most studies of mixed mode
delamination have ken limited to a mixture of modes 1 and II. This is probably due to the extreme difficulty and complexity that may arise when devising test methods
including the mode III component.
Various tests for characterizing mixed mode kture such as the Arcan, the cracked lap shear (CLS), the edge delamination test (EDT), the asymmeûic DCB, the mixed mode flexure (MMF), the variable ratio mixed mode 0and the mked mode bending (MMB), are shown schematically in Figure 1.4. Mixed-Mode Bending(MME)) C (Remder & C~WS- 1990)
Test Fixhira et a. - 1978)
1 MixedModr Fhxure WMF) Variable Ratio Mixed-Mode (VRMM) (Ruridl & Street - lm) (Hashemi et ai. - lm
(Bradley & Cohen - lm)
Cncked Lap Sheu (CLS) (Wilkins et al. - 1982)
Figure 2.4 Mixed-mode delamination test methods
Of the many tests, the mixed mode bending (MMB), proposed by Reader and
Crews [1990], appears to be the most promising one. It is easy to perfonn and has the same type of specimen as the DCB test in mode 1, the ENF test in mode II and the SCB test in mode III. The use of one type of specimen to perform any delamination test,
including mode 1, II, III, and mixed-mode tests, would be advantageous because it would
aiiow for mass production of specimens for hi&-volume testing, and similar theories could be used for data reduction.
Mer and Crews [1990] anaiyzed the MME3 specirnen using a simple superposition of the stress analyses of the DCB and the ENF specimens. A wide range of ratios of mixed mode 1 and II can be achieved simply by moving the loading point on the lever. Beam theory equations sirnilar to those used in the DCB and the ENF tests and finite element method were used to determine the strain energy release rate G, and Gu, good agreement was obtained.
Mixed mode failure criteria have always been the focus of the mixed mode hcture shidies. Many researchers, such as Jurf and Pipes [1982], Hahn and Johannesson
[1983], Law [1984], Donaldson [1985] and Yoon and Hong [1990], investigated mixed mode failure critena; however, Meagreement between researchers was achieved. In a
Mer study of the MMB test, Reeder [1993] evaluated many mixed mode failure criteria, and concluded that due to the greatly dflerent responses of different composite systerns, no single failure critenon based only on the pure mode I and II toughness values of a matenal would be able to mode1 all laminated composite materials. He niggested that mixed mode toughness testing be included during the chatacterization of the delamination resistance of a composite material. It seems that a more fiuidarnental approach is needed to obtain a universal failure criterion.
Material Effects
When attempting to characterize delamination in composite laminates, it is important to understand the behaviour of constituent materiais. in particular, the behaviour of the matrix is generally believed to play a key role in deteminhg the delamination resistance.
The most commonly used matrix material for composite laminates is epoxy, a brittle thermoset polyrner, which generally does not yield much defoxmation and plasticity during failure. However, in studies conducted by Bascom et al. [1985, 19871, the fhcture surfaces of delaminated mode 1 specimens of AS4/3501-6,a brittle epoxy system, were carefûlly examined. When the surfaces were heated to a temperature above the matrix glass transition temperature Tg,they found considerable relaxation (30050%) of the matrix, indicating that extensive shear yielding of the ma& as weli as plastic deformation did occur even in brittle epoxy systems.
Toughened, rubber-rnodined epoxies and several thennoplastic matrices such as
PEEK generaüy exhibit greater plasticity and also offer better resistance to delamination.
Russell and Street [1987] studied the effect of matrix toughness on both the static and fatigue delamination behaviour of a variety of composite systems. They reported that as a result of increasing the matrk toughness, the increase in interlaminar hture toughness
is significantly higher under mode 1 loading than under mode II loading. Hunston et al.
[1987] hvestigated numerous laminate systems in an attempt to correlate the
delamination GIc and the resin Gc values. Brittle polyrner composites gained a much
greater benefit fiom the improvement of the neat resin G, than tougher resin composites.
Jordan et al. [1989] found that an increase in the neat resin fiacture toughness yielded an
increase in the delarnination fiachire toughness of the laminate, but the rate of increase
dropped off sharply for epoxy resins with values of Gc in excess of 700 J/m2.
These studies show that toughened matrices do lead to a limited increase in G,
values. This is probably due to the combined effect of both the higher amount of matrix
plasticity associated with delamination in these materials and the constraint of fibres on
the size of the plastic zone at the tip of the advancing crack. Piggott [1988] noted that
with ductile matrices, irnprovements in the delamination resistance of composite
laminates depended on increasing the matrix yielding stress, rather than increasing the
matrix toughness, due to the effect of fibre constraints on the plastic zone at the crack tip.
However, Bradley and Cohen [1985] found that for toughened resin laminates,
microcracks can be seen in a region of 3 to 5 fibre diameters both above and below the
plane of the delamination. Jordan and Bradley [1987] also reported that a very smd
damage zone of 5pm existed for untoughened composite systems (AS4/3 502) while
tougher systems had much larger damage zones measuring between 10 and 35p. Parker and Yee [1989] also observed that the plastic zone extended weil beyond a single fibre Literaîure Review 20
layer in their rubber-modified AS4/polycarbonate composites. So whiie it would appear
that the plastic zone is constrained by adjacent fibres, somehow it may still be able to
penetrate fibre layers.
Compared to thennoset matenal systems, the studies of thermoplastic polymer
matrices are very limited except for PEEK. Several researchers have studied
delamination properties of AS4/PEEK composites (Russell and Street [1987], Leach et al.
[1987], Prel et al. [1989], O'Brien et al. [1989], Martin and Murri [1990], Russell
[1991]). Even though the reported values of mode 1 and mode II bcture toughness of
PEEK composites varied greatly, they were certainly much higher than those of bnttie epoxy composites, indicating that thermoplastic matrix composites generally offer a better delamination resistance. Nevertheless, it is certain that more research should be conducted on other thermoplastic rnatrix composites due to theù prornising firture in engineering applications.
2.3 Fractography
Fractography is an extremely important tool in the study of composite delamination. The study of fiachue surfaces rnay explain the physical nature of strain energy release rate to a great extent. In earlier studies, fractography was used by Moms [1979]to study characteristic
feahues of notched graphite/epoxy specimens. He found 'hackles' on the hture
surfaces, which correlated well with the direction of hcture. Moms speculated that
hackles were the direct result of the tension cracking in specimens. However, in
delamination testing, hackles are usually associated with mode II loaduig of brinle
composite systems. It is now known that hackles in mode II delamination are caused by
the principai tensile stresses in the pure shear stress state. Two in-depth studies of hackle
formation and the micromechanimis of delamination were performed by Hibbs and
Bradley [1987] and Corleto and Bradley [1989], both of which used ENF tests to
charactenze mode II delamination. Real-time bcture observations were made in their
studies. The SEM pictures clearly showed the hackle formation process in brittle resin
systems. It seems that hackles are the result of coalescence of sigrnoidal-shaped
microcracks, rather than the results of ma& yielding and plastic deformation.
Furthemore, as Hibbs and Bradley [1987]reported, hackles were absent for ductile resin
systems such as AS4/Dow-Q6 due to extensive yielding and ductile hcture. This was
probably the cause of the fact that the increase fiom G, values to correspondhg Gnc
values in brittle resin systems was much larger than that in ductile resin systems. Their
report was supported by Russell and Street [1987]in their study of the mode I and mode
II delamination toughness and the fkctography of AS4/FlSS and AS4PEEK.
With respect to mode 1 delamination, Bascom et al. [1985, 1987 examined the mode 1 delamination fkture daces of AS4/3501-6 and other composite systems and reported that the major features observed were fibre pull-out, hackle markings, and smooth resh fracture. However, Hibbs and Bradley [1987] found a surfiace similar to a
'co~gatedroof structure, and identified the primary mechanism of hture to be
interfacial debonding of the fibre and the matrîx.
Udortunately, few fractographic studies of mode III hcture surfies have been
performed. Lee [1993] noted that the hcture surfaces of mode III specimens were
rough, and exhibited 'hackle-like' formations, as well as river-markings. Shdet al.
[1993] found a unique feature, 'shear crevices', on the hcture surfaces of their mode III
specimens. They noted that these crevices could be used to identify mode III failure where delamination is propagating parallel to the fibre direction.
There have also ken a number of fraftographic studies of off-axis delamination.
Johannesson and Blikstad [1985] studied angle-ply laminates of graphitelepoxy which were loaded in tension. Before the final tende failure, edge delamination occurred under mixed-mode state. They found that the kture surfaces contained resin-rich and resin- poor regions, and there were dense populations of hackles and imprints of fibres.
Purslow [1988] studied cross-ply and mutidirectionai graphite/PEEK composite laminates loaded in tension, compression, and flexure. He noted that failure was chmterized by pulied out fibres, chevron markings, and ductile matrix failure.
Shikhmanter et al. [1991] examined the fkcture dace morphologies of multi- directional composites subjected to tension, compression, in-plane shear, and three-point bending, and confïnned that the fiactography of each ply in a multidirectional lay-up is very similar to that in a unidirectional specimen of the same orientation Trakas and Literature Review 23
Kortschot [1995] made a cornparison between the mode II and mode III ktographic
results. They found that kture surfaces of mode II 0°/00 and mode III 90°/900
specimens exhibit very similar shear hackles, and fracture surfaces of mode II 90°/900and
mode III 0"/0° specimens exhibit similar shear crevices. This indicated that no
characteristic surface exists for either mode II or mode III, and that the relationships
between the direction of crack propagation and both mode and ply orientation are
important. Their fractographs also showed that shear crevices penetrate into the matrix
and run vertically dong the fibres.
2.5 Summary
It has been show that the delamination mechanism of composite laminates is very complicated, and that many factors influence the failure process. Although many methods of measuring delamination resistance have been developed, and materials effects, fracography and many other aspects have studied in great detail, the physical origin of the delamination process is still not well understood.
Surprisingly, there are very few theoretical models that can predict delamination f'racture toughness. For metal hcture, Stuwe [1980] developed a mode1 to estimate KK by caiculating the plastic energy needed to form a ductile hcture dace. For mode 1 delamination of composites, Lee [1984, 19881 midied in detail the failure process of composite delamination. The crack tip plastic zone that developed between fibre layers was identifïed as the major energy dissipation mechanism. An in situ failure model was
Merproposed to estimate the critical strain energy release rate of laminates, GIc , based
on several resin properties, which gave usefil insights into the relative influence of resin
properties on the GIc . He concluded that resin modulus and yield stress were at least as
important as resin GK in controliing the G, of the composite laminate. The physical
implication of this model that the crack tip plastic zone was the most critical factor in
composite delamination was quite sound, and the quantitative predictions of G,were
reasonable. Nevertheless, Lee's predictions were very sensitive to a fitting parameter in
the approxirnate crack tip stress distribution used in the model. In mode 11 delamination,
Lee [1997] again analyzed matrix microcracks and shear hackles in the mode II
delamination process. The microcrack initiation shear stress was found on the basis of
kture mechanics, and the regular spacing between shear hackles was predicted utikg the shear lag theory. As a result, a quantitative relationship was denved relating the critical strain energy release rate of mode II delamination, Gnc, and several resin properties. This model reveais the important influence of resin fhcture and yielding properties on the mode II delamination toughness; the numerical predictions of GE generally foilow the trend of the experimental G, for several carbodepoxy systems studied but are again very sensitive to a cuve fitting parameter.
In conclusion., the need to understand the physical nature of kture and to develop theoretical models predicting delamination fkcture toughness is obvious. A fiindamental understanding and suitable theoretical models cm suggest what materials parameters are the most important factors in controlling fiacture properties so that Literaiwe Review 25 methods can be developed to improve delamination kture toughness and to develop new composites with high fracture properties. Also, theoretical modelling based on the funchmental understanding might eliminate some unnecessary experiments and greatly reduce the work for experimental characterization of delamination.
It is the purpose of the present study to understand the fiacture mechanisms in the delamination process, and to develop quantitative relationships between the critical strain energy release rates and material properties of the constituent materials and other composite structurai parameters. 3. Theoretical Modelling
3.1 Introduction
3.1.1 Delamination Mecbanisms
The criticai strain energy release rate, G,, of composite delamination hcture can be affected by many factors. The major energy dissipation mechanisms in the delamination process include fibre-matrix debonding, fibre breakagelbridging, mat& microcracWcraze and crack tip plastic deformation.
where y is the area of the delarninated surface.
These energy dissipation rnechanisms should be carefûlly analyzed in order to determine the contributions of different kinds of damage. Firstly, as discussed by
Chakachery and Bradley [1 987, fibre-rnatrix debonding generally decreases the delamination fhctuxe toughness, especially in mode 1 where there is a large normal stress on the fibre-matrix interface. Madhukar and Drzal [1992] also studied the interfacial
strength of the interface between the fibres and the matrix and found that simple sUTf'ace
treatment of fibres greatly increased the interfacial strength and that this led to increases
in G, and Gu, values and even caused less fibre bndging. Since most commercial fibres
have sUTface treatments that significantly increase the fibre-matrix interfacial mgth,
fibre-matrix debonding phenornenon is not extensive in the delamination process in spite of the fact that there are some clan fibres on the delamination surface. As a result, the main crack generally propagates within the matrix material between the plies of the composite laminates.
Secondly, previous studies, such as those of Johnson and Mangalgiri [1987], Lee et al. [1989] and Nilsson [1993], showed that fibre breakage and bridging has little effect during in the initial stage of delamination; these factors mainly account for the difference between the initial and propagation delamination toughness. For unidirectional specimens, the mode 1 propagation fraction toughness is usually much higher than the initial one. Johnson and Mangalgin [1987] also reported that the fibre bridging could be significantly reduced by "misaligaing" the prepregs by a smaii amount (1.5' and 34 during the lay-up. In their tests of such laminates, there was alrnost no clifference between initiation and propagation fkture toughness values. Since most delamination in real structures normally nins between mis-aligned plies or off-axis plies, fibre bridging is not an important issue. Therefore, the initiation values of fkture toughness are of more interest because they exclude the effect of fibre bridging. In the ASTM mode I standard, the use of initiation values is also recornmended. There is experimental evidence that a long and nmw plastic/damage zone
around the crack tip exists, indicating either extensive plastic deformation or numerous
microcracks. Bascom et al. 11985, 19871 studied a brittle epoxy system, AS4/3501-6.
They found significant relaxation in the epoxy ma& aer the delaminated specimens
were heated to a temperature above the ma& Tg,indicating plastic yieldhg did occur
even in the brinle epoxy matrk. Jordan and Bradley [1987] reported the sizes of crack
tip damage zones in brittle and toughen epoxy matrices. Parker and Yee [1989] also
observed plastic zones in the matrix using cross polarized light when studying the carbon
fibre reinforced composites with rubber-toughened polycarbonate ma&. On the other han& compared to the total stxain energy spent on the delatnination fracture, the strain energy spent on creating the cleavage of a main crack with virtually no plasticity during the failure is trivial, only about 50 m.J/m2. Therefore, the major energy dissipation mechanisms in the composite delamination fracture could be either significant surface and subsurface plastic deformations or a fairly large number of microcracks within the crack tip plastic/damage zone.
3.1.2 Present Work
In the initial stage of the present research, considerable effort was expended to find the evidence of microcracks within the damage zone and to measure accurately the crack tip plastic deformations. Four experimental techniques were chosen for these purposes. X-ray radiography and laser thermography were used for microcrack detection, and video image correlation method (MC)and shadow opticd method of caustics were
used for local plastic strain measurement.
In the X-ray radiography test, specirnens with a small amount of delamination
growth were first immersed in a zinc iodide solution for several hours. The specimens
were then taken out and washed with water to clean the zinc iodide on the surfaces. Only
the zinc solution in the cracks remained. X-ray radiography tests of the penetrated
specimens were then conducted. However, the X-ray films of mode 1, II and III
specimens did not reveal any trace of microcracks. Either the microcracks were too tiny
to be penetrated by the zinc iodide solution, or there were no microcracks at dl.
Laser thermography was used to detennine if there were diffuse microcracks too small to be detected by radiography. The presence of large amount of tiny microcracks would change the thermal coefficient of the composites. Therefore, the microcracks could be detected by cornparhg the thermographs of the delaminated specimen and the undelaminated specimen. In this experiment, a laser beam was directed at the delaminated specimen, and both reflection and transmission thermographs were recorded and anaiyzed. The same procedure was perfonned on the undelaminated specirnen as well. However, no signincant sign of microcracks showed up on the laser thermographs.
The digital video image correlation method (WC) is an experimental technique to determine the deformation of objects subjected to loading. In this method, a video camera is used to capture and digitize an image of a random pattern printed on the dace of a specimen. In practice, two digital images, one for the undeformed object, and the
other for the deformed object, of the same surface are obtained, and a computer program
is used to analyze and compare these two images. By mapping the defodimage to the
original undeformed one, the pro- is able to obtain the displacement and strain fields.
The rnethod can be used with images taken through a scanning electron microscope, and
hence is wful for tracking the highly localized strain field near the tip of a delamination.
This technique was used to measure the plastic deformation at the delamination crack tip.
However, due to complexity of the delamination crack fiont area, it was very difficult to find the real crack tip once the specimen was unloaded, and thus it is very hard to interpret the data obtained. As a result, the measurement of plastic deformation at the delamination cmck tip was not successful.
The shadow optical method of caustics is one of the primary experimental tools in fiachire mechanics. Optical patterns of the crack tip, obiained either by reflection or by transmission, are analyzed to obtain the stress intensification at the crack tip. It has been successfùlly applied to both transparent and non-transparent isotropie materials.
However, in the case of composite materials, it was very hard to get a clear optical pattern due to the presence of fibres that complicated the whole situation.
The scaaning electron microscope was also extensively used to examine the fracture daces of the delaminated specirnens in the hope that evidence of plastic deformation and microcracks couid be found. Numerous delaminated specimens were examined at the nano-meter scale; however, w significant number of tiny microcracks were found around the crack tip. This again suggested that either there were no
microcracks at all or the microcracks were too small to be observed. Another possibility
was that the tiny microcracks closed when the specimens were unloaded. Nevertheless,
there was not any significant evidence that showed the presence of tiny rnicrocracks.
In contrast, as discussed in previous studies, the crack tip plastic deformation was
evident even though no one has been able to measure accurately the crack tip plastic
strains. Figure 3.1 is an optical rnicrograph, fiom Parker and Yee [1989], that shows
direct evidence of a plastic zone area extending several fibre diameters below the fracture
surface. Based on these observations, it is believed that the large plastic deformation
around the crack tip is the most probable energy dissipation source.
Figure 3.1 An optical micrograph of a petrographic thin section of a rubber-toughened
AS4/polycarbonate composite. The plastic zone is observed using cross
polarized light. (after Parker and Yee [1989]) The following theoretical work is based on the premise that the large plastic
deformation in the crack tip plastic/damage zone accounts for most of the energy
dissipation in delamination fracture. Two analyticd beam models dong with a fhcture
criterion have been developed for predicting the critical stmh energy release rates for
mode 1 and mode II delamination.
3.2 Mode 1Delamination Mode1
3.2.1 Introduction
The most commonly used mode 1 delamination test is the double cantilever beam (DCB) test, which was installed as a formal ASTM standard in 1994. The present mode 1 delamination mode1 is based on the DCB conf~guration.
The simplest and most comrnon way to analyze the DCB specimen is to apply simple cantilever beam theory. In this approach, the two amis of the DCB specimen are treated as cantilever beams, assuming that the ends of beams, i.e. the crack fiont cross section, are rigidly fixeci, which means the cross section has no deformation at ali as shown in Figure 3.2.
However, it is obvious that the material ahead of the crack fiont is not iiifinitely rigid, especially in the case of composite materials where the transverse and shear Theoretical Mode fiing 33 stiffness are very low compared to the longitudinal stiffness. The beams do have shear deformation and end rotation.
Figure 3.2 Classical beam solution of DCB specimen
The effect of end rotation was first studied in detail by Kanninen [1973] for isotropie materials. The uncracked part of the DCB specimen was replaced by a beam on an elastic foundation, the so called Winkler foundation (Other foundation models were discussed by Ken [1964]). Kaminen's model yields excellent agreement with well- established numerical and experimentai data, and has ken wideiy accepted. Williams
[1989] extended this method to deal with orthotropic composite materials. The effects of both end rotation and transverse shear deformation were included in Williams' study. In the meantime time, Yamada [1987, 19881 extended Kanninen's model by introducing plastic deformation at the crack tip. The Winkler foundation was parily replaced by an elastic and perfectly plastic zone near the rrack tip. The modined mode1 with partly Theoretical Mode11 ing 34
elastic and partly plastic foudation is more representative of the real situation in the
DCB specimen in which there is a plastic/damage zone at the crack tip. However, al1 of
the previous efforts have ken focused on getting a more accurate relationship between
the strain energy release rate G, and the applied load, so that the critical load Pc cm be
used to compute an accurate value of the cntical strain energy release rate, G,. No one
has made an effort to predict the cntical strain energy release rate of mode 1 delamination,
G,utilizing this type of model based on materials properties of matrix and fibres as well as other composite structurai parameters.
In the present study, a failure criterion, similar to that used by Lee [1984], relating the critical plastic zone sue ahead of the crack tip in the DCB specimen to the cnticai plastic zone size of the correspondhg neat resin, was incorporated into the modified DCB model with an elastic and plastic foundation. The critical strain energy release rate of mode 1 delamination, G, , has ken successfully related to the critical seain energy release rate of the neat resin, Gc ,the yield stress of the neat resin, q ,and other elasticity constants of the neat resin and the composite laminates.
322 Mathematical Development
The DCB specimen and the model used for upper haif of the beam are show in Figure
3.3. The uncracked part of the half beam is treated as a beam on an elastic-plastic foundation. The foundation material is assumed to be linear elastic and perfectly plastic, Theoretical Matelling 35
which results in a uniformiy distributed yield stress, o, , in the plastic region of the
foundation.
III
Figure 3.3 Beam on the elastic-plastic foundation
The displacement of the half beam on the elastic-plastic foundation, as shown in
Figure 3.3b, is govemed by the following differential equations, for OSxll,
where w, ,w, and w, are the deflections of the beam in the regions 1, II, and III; $ and le
are the lengths of the plastic region and the elastic region, respectively; q is the yield
stress of the foundation material, which is the yield stress of the neat resin when the beam
is made of composite laminates; 1 is moment of inertia of the beam; E,, is the elastic
modulus in the fibre direction of the composite beam, which can be obtained by the de
of mixtures,
in which V, is the fibre volume hction of the composites, and E, and E, are the elastic modulus of the fibre and the resin, respectively; and finally the panuneter h is defined as
in which k is the stifEiess of the elastic fomdation. It shouId be noted that l/h has a dimension of length and is called characteristic length which govems the decay of the tende stress in the elastic fomdation. Foliowing Williams' suggestion, k can be modeled as Theoretical ModeIIing 37
(3.2.6)
where m, is a foudation spring constant, and E, is the transverse modulus of the
composite beam which is defined as,
For isotropic beams, m, was set to 1/2 and was well justified by Kanninen [1973]in the excellent agreement with numerical and experimental results. For orthrotropic beams, both Yamada [1987] and Williams [1989] used % for m, and obtained good agreement with their finite element results even though Williams suggested that m, value might be
Mermodified to reach even better agreement.
The boundary conditions and continuity conditions are Theoretical M&hg 3 8
---d3wl - P (sr3 E,, I Theoretical Mdlling 39
(3.2.16)
The continuity condition, Equation (3.2.18), implies that the maximum possible stress in the elastic foundation is the same as the yield stress in the plastic foundation and occurs at the interface with the plastic region.
Foiiowing Yarnada's approach, solutions for the haif beam are readily obtained as foiIows, under the condition that Alil, is rather large (>2ir), which is true for most DCB specimens with the ASTM D5528 configuration. where Theoretical ModeZIing 4 1
The strain energy release rate, G,, of the DCB specimen can be defhed as,
where U, is the extemal work, and U, is the intemal energy of the beam incluchg both elastic and plastic energy. It would become extremely complicated if the exact solution for G, were pursued.
Instead, Yamada [1987] turned to a numerical differentiation method to calculate G,.
However, in the present research, a new and relatively simple analfical approach is used to calculate G,. As iilustrated in Figure 3.4, since only smd and moderate crack tip yielding is considered, the plastic deformation is genedy very dl. Therefore, it is acceptable to approximate the load-deflection curve, fiom the onset of the yielding to the tinai Ioading point, by a straight line AB.
load
Figure 3.4 The elastic-plastic load-deflection curve of the DCB specimen
The interna1 energy, U, ,can then be calcuiated by the area under the lines OA and AB. Thus, Theoretical Modelling 43
(3.2.36)
With -duut = P-d6 ,the solution for G, is finally obtained as follows, da da
where P and 6 are the force and deflection at the free end of the beam; P, and 6, are the force and deflection at the free end of the beam at the onset of plastic yielding of the beam, and
2 (Z, + -)' a,"b A P= 1 da P dl, dB, ---- (a+1J2-BI(l+-)-- (a+[,)+=dB2 da E,,I da da
---dB, cyb ,dlp -+-2dl, 1 2 --c,--dCl 4 dC2 da - E,,z'~-+G'P&da y* da Ipda It is worth noting that by making use of Equation (3.2.38) and other equations,
fiom Equation (3.2.39) to Equation (3.2.50), the final expression for the strain energy
release rate, G, , is only related to $, a,, , and other geometric and material constants of the DCB specimen.
3.23 Faiïure Criterion
The crack tip inelastic material deformation, including plasticity in metals and crazing in polymers, is critical in the hcture of rnaterials, and the size of the crack tip plastic zone Theoretical Mdlling 46
can be directly related to the stress intensity factor or the strain energy release rate. Since
simple estimation of the size of the crack tip plastic zone by the linear elastic kture
mechanics (LEFM) is increasingly inaccurate as the inelastic region at the crack tip
grows, many corrections to the LEFM have been proposed. For srnall and moderate
crack tip yielding, the two most noted corrections are the Irwin approach [1960], which is
based on a simple force balance at the crack tip, and the strip yield mode1 by Dugdale
[1960], which is a classical application of the principle of superposition. The Irwin
approach is utilized here. In a state of plane strain, the radius of the crack tip plastic zone,
r,, ,is defined by Irwin [1960] as,
where K is the stress intensity factor and a, is the yield strength of the material; or
where E, v and G are Young's modulus, Poisson ratio and the strain energy release rate of the material, respectively.
It is obvious that when K or G reaches the criticai value K, or Gc ,the relevant critical plastic zone size, r, , can be obtained using Equations (3.2.51) and (3.2.52).
Therefore, it is appropriate to view r, as a material characterizhg parameter in the limit of small and moderate yielding. This relationship is comparable to the one between the
crack tip opening displacement (CTOD), proposed by Wells [1961], and the J integral,
proposed by Rice [1968], when large amount of crack tip plasticity occurs.
In the case of composite delarnination fkture, plastic defonnation does occur at
the delarnination crack tip, as reported by Bascom et al. [198S, 19871, even in the brittle
epoxy system, AS4/35O 1-6. Jordan and Bradley [l987] also reported sizes of crack tip
damage zones for several composite systems. However, the stress and strain fields at the
delarnination crack tip are more complicated than those in metals and polymers due to the
presence of fibres in the matrix. Although matrix plastic deformation may sometimes
develop around fibres to penetrate certain nurnber of fibre layers, the adjacent fibre layers
still impose a significant constraint on the development of the crack tip plastic/damage zone, especially in ductile resin systems (Piggott [1988] and Parker and Yee [1989]). As a result, the crack tip plastiddamage zone is generally long and narrow.
This fibre constraint eEect is quite similar to the adherend constraint effect on the adhesive plastic defodon in adhesive bonds. A brief review of the adhesive bond kture would be beneficial here. Bascom et al. 119751, Bascom and Cottington [1976] and Hunston et al. [1980] studied the effect of the bond thickness on the bture toughness of adhesive bonds. Their experiments showed that the kture toughwss of the adhesive bond was greatly &êcted by the bond thickness when the bond thickness was rather small. This was due to constraint in the development of the crack tip plastic defodon zone, which is imposed by the adherend matenals. Their studies were supported by a nu&cal analysis of the adhesive DCB specimen by Wang et al. [1978].
Wang et al. found that the tensile stress in the adhesive layer would decay more slowly than that in the pure adhesive matenal, as the bond thickness is decreased. Kinloch and
Shaw [1981] further stated that when the bond thickness was reduced, the crack tip plastic zone was first constrained and elongated, and increased in volume. Then the crack tip plastic zone would decrease in volume when the bond thickness became too small and the crack tip plastic zone was highly constrained, as illustrated in Figure 3.5. As a resuit, the fiacture toughness of the adhesive bond would first increase and reach its maximum when the bond thickness was approximately eqd to the diameter of the cntical plastic zone in the pure adhesive hcture. The toughness of the adhesive bond would graduaily decrease when the bond thickness was merreduced, as illustrated in Figure 3.6.
Illustration of constraint effect of adherend on the crack tip plastic
zone in adhesive (after Woch and Shaw i198 11) Gc, (adhesiot bond)
Bond 'hckness
Figure 3.6 Illustration of the relationship between adhesive bond Facture toughness, Gc,
and bond thickness, h. (after Kinloch and Shaw [ 198 11)
The relationship between the strain energy release rates of pure resins and composites is analogous to that between pure adhesives and adhesive bonds. It is quite reasonable to postdate that the crack tip plastic zone in a composite laminate is constrained and elongated by adjacent fibre layea, and the cntical length of the plastic zone is proportional to the critical radius of the plastic zone in the fracture of the relative pure min. Lee [1984] also made a similar argument in his in-situ failure model. Thus,
where 1, is the cntical length of the plastic zone in the mode I delamination hcture; n, is a proportionality constant which could be detemiined experimentdy, and is the ody fitting parameter in the mode 1 delamination model; and r, is the critical radius of the plastic zone of the pure resin material, which can be calculated by Equations (3.2.51) or
(3.2.52) with K, and Gc replacing K and G, respectively.
Substituting Equation (3.2.53) into the final expression for G, ,Equation (3.2.37), we finally obtain the expression for the cntical strain energy release rate of mode I delamination, G, ,which is a fhction of the matenal properties of the resin and the fibre in the composite system only, illustrated as follows,
Once the yield stress, a, , tensile modulus, E, , and the critical sealli energy release rate,
Gc , of the resh, the tensile modulus, E, , of the fibre and the fibre volume fraction, V, , are known, the mode 1 critical strain energy release rate cm then be predicted by the
Equation (3.2.54). The oniy fitthg parameter, n, , can be determined either experimentally through observation of sizes of the crack tip plastic zones in both resins and composite laminates or empincaliy through curve fitting among different composite systems, 3.3 Mode II Delamination Mode1
33.1 Introduction
The present mode II delamination mode1 is based on the end notched flexure (ENF) test
configuration, which is probably the most widely used mode II delamination test and is
the focus in the ASTM standardization process.
The ENF test was proposed by Russell and Street [1982], who developed the
simplest expression for the mode 11 strain energy release rate, G, ,based on the classical
beam theory. However, since the crack tip shgularity and the transverse shear
defornation were neglected in their analysis, theu expression can significantly
underestimate G,. Finite element andysis of the ENF specimen has been performed by
several researchers, including Mal1 and Kochhar [1986], Gillespie et al. [1986], Saipekar
et al. [1988], He and Evans [1992] and Wang and Williams [1992]. These finite element
studies show that there is a significant departure fiom the classical beam solution for G,.
In the meantime, many analytical corrections have ken carried out. Carlsson et
ai. [1986a] used the fïrst order beam theory, the so called Timoshenko beam theory, to
incorporate the effcct of the transverse shear deformation Carlsson et al. [l986b] and
Whitney et al. Cl9871 considered the stress singularity at the crack tip using a shear deformation plate theory. Whitney [1988] Meranalyzed the ENF specimen by using higher-order beam theory (HOBT)and Reissner's variational principle. Chatterjee [199 11
studied the ENF specimen by applying the principle of superposition and Irwin's virtual
crack closure technique. Wang and Williams [1992] adjusted the Gn expression by
introducing a correction factor to the crack length, a, which is a sirnilar correction
procedure to the G, of the DCB specimen by Wiiam [1989]. Each of these studies
attempted to provide a more accurate analytical model. Success was usually judged by
comparing the analytical results to well-known finite element solutions, such as those of
Salpekar et al. [1988] and Wang and Williams [1992].
More recently, Corleto and Hogan [1995] evaluated the G, of the ENF specimen
by superposing the solution of a beam on a gewralized elastic foundation to incorporate
the effect of the crack tip deformation, and the solution of the ENF based on the
Timoshenko beam theory to incorporate the effect of the transverse shear deformation.
They found that the G, is only Bected by the crack tip deformation, and is actually
independent of the transverse shear deformation. This is consistent with the discussion
by Carlsson and Gillespie [1989] that their plate theory solution for the G, is independent
of the transverse shear deformation if the crack tip singularity is removed from this
solution. Thus, the crack tip deformation seems to be the most critical factor in the
evaluation of the GD.
As is the situation in the analysis of the DCB specimen, all previous efforts have ken focused on getting a more accurate calculation of the strain energy release rate G,.
Few have made the effort to predict the critical strain energy release rate of mode II delamination G,. To the best of the author's knowledge, the only a-pt is the model
proposed by Lee [1997] as discussed in Chapter 2. Lee [1997] analyzed the failure
mechanisrns in mode II delamination, and a quantitative relationship between the mode II
critical strain energy release rate and the properties of the matrix materiai was proposed.
In the present model, since the strain energy release rate is independent of the
transverse shear deformation, classical beam theory rather than Timoshenko beam theory
is applied to the ENF specimen to produce a simplified solution for G, . The crack tip
defonation of the ENF specimen is incorporated into the Gusolution by assuming that
certain length of the bearn near the crack tip is rested on a linear elastic and perfectly
plastic shear spring foundation. The beam model is straightfoward and highly accurate.
Excellent agreement between the present solution for the G, and the finite element
solutions is obtained. Furthemore, for the first the, the length of the plastic zone at the
mode II delamination crack tip can be calculated. Combined with a failure criterion
similar to the one used in the model 1 model, the current model gives fairly good
prediction for the cntical strain energy release rate, G, , on the basis of the matrix and
fibre material properties.
333 Mathematical Development
The ENF specimen and the model for half of the beam are shown in Figure 3.7.
Assuming that each half of the beam carries the same load, the loads at the two ends of the upper hdf of the beam are, P/4, and the load at the central point is Pl2. For the uncracked part of the ENF specimen away fiom the crack tip region, only shear stress, t, , exists on the center surface due to the anti-symmetric nature about the center line of the
ENF specimen. The shear stress, r, ,can be easily found using Timoshenko beam theory,
where P is the force applied on the ENF specimen and h is the thickness of the half beam.
The region close to the crack tip is treated as a beam on an elastic-plastic shear spring foundation. The foundation materid is assumed to be linear elastic and perfectiy plastic, which results in a unifody distributed yield shear stress, r, , in the plastic region of the foundation.
The displacement of the half beam, as show in Figure 333, is governed by the following differential equations,
for -(a+lp)Sx 5 -lp (3.3.2) Theoreticai Modelling 55
Figure 3.7 Bearn on the elastic-plastic shear sp~gfoundation
for OSxSx, (3.3.4)
for x, Sx 51-a-l, (3.3.5)
for 1-a-1, Sx52l-a-Z, (3.3.6)
where w, ,w, , w, ,w, and w, are the deflections of the beam in the regions 1, II, III, IV and V; $ and x, are the lengths of the plastic region and the elastic region of the shear spring fouadation, respectively; r, is the yield shear stress of the foundation material, which is the yield stress of the pure resin when the beam is made of composite laminates;
1 is moment of inertia of the beam; El, is the elastic modulus in the fibre direction of the composite bearn, which cmbe determined by the deof mixtures, as show in Equation
(3.2.4); G,, is the shear modulus of the beam, which cmbe determineci as follows,
where V, is fibre volume fraction; Cif and G, are the shear moduius of fibre and matrix, respectively; u and m, are the shear correction factor and the shear spring constant, respectively, which can be detemüned by comparing the results of the present mode1 with finite element results.
Considering the boundary conditions at the two ends of the beam, Le., both bending moments are zero and both shear forces are P/4, the solutions for the displacements can be solved as follows, in which a is defined as,
and the constants fiom C, to Cl, , as well as $ and x, can al1 be detemiined by the following fifieen continuity conditions,
The continuity conditions, Equation (3.3.20) and Equation (3.3 .BI),imply that the maximum possible shear stress in the elastic foundation is the same as the yield shear stress in the plastic foudation and at the interface with the plastic region, and the minimum shear stress in the elastic foundation is the same as r, .
By applying above boundary and continuous conditions, we have,
(3.3 .go) and the two constants $ and x, can be solved fiom the following two equations when C,,
C, and C, are substituted in,
Following the approach used for the calculation of G, in the mode 1 beam model, the strain energy release rate, G, ,can again be defined as, where P and 6 are the force and deflection at the center of the haif beam; P, and 6, are the force and deflection at the center of the half beam at the onset of plastic yielding of the beam, and
8[5b (m,h)](a 1, sinh a, + cosh a,) P= 2a(a +l,)sinhax, +2coshmo -(2-3m,)
in which C,, , C, , C,, and Cl, have the same expressions as C, , C, , C,, and C,, but with $ king set to zero; x, can be solved fiom the foilowing equation,
and Theoretical Mocteling 63
dS 1 P(a + IJ2 dl, dC, (l+-)--(a+lp)-C,(l+-) dI, --da- 2EJ 4 da da da
dC2 2-- dlp dC,, +-- (1 +-)+-(a Z) (3.3.51) da 16 d(a da - CI2(l+-) dl, +-]del, da da
where the expressions for dCi/da, i = 1,2, .. . 13, dlJda and duda, as well as dCiJda, i =
1,2, .. . 13, dx,Jcia, Y and R, are al1 provided in Appendix A.
Analogous to the mode 1 model, by making use of Equations (3.3.44), and other
Equations, fiom Equation (3.3.45) to Equation (3.3.5 I), the final expression for the strain energy release rate, G, , is only related to 4, r, , and other geometric and material constants of the ENF specimen.
It should be pointeci out that if the foundation material is assumed to be totally elastic, an elastic solution for G, cm dso be obtaiwd, which is provided in detail in
Appendix B. As will be shown in Chapter 5, the elastic solution is also fairly accurate for G, calculations even though it can not give predictions for the lengths of crack tip plastic zones. Theoretical Modeling 64
333 Failure Criterion
Fractographic deson mode U delamination surface have been performed by many
researchers. In brittle epoxy ma& systems, there are extensive "shear hackle"
phenornena on the delamination surface; Hibbs and Bradley [1987] and Corleto and
Bradley [1989] showed the microcrack initiation aad coaiescence process that led to the
formation of the "shear hackles". It is generally believed that ahead of the main mode II
delamination crack tip, a senes of matrix mode 1 microcracks develop approximately in
the direction of 45' degree with an almost regular spacing; the main mode II crack
propagates when these mode 1 microcracks start to coalesce. Even though the plastic deformation is generally srnall in brittle epoxy systems, it is still a critical factor when it happens at the crack tips of the matrix mode 1 microcracks and in the coalescence process, or in general, in the vicinity of the main mode II crack, as illustrated in Figure
3.8a
On the other hand, in toughened epoxy and ductile thennoplastic matrix systems, no "shear hackles" are observed on the mode II delamination suface. Instead, Davies and de Charentenay [1987] and Jordan et al. [1989] both observed extensive matrix yielding without microcracking, in the AS4/PEEK and the T3T145IF185 systems, respectively. Thus, it can be poshilated that when the rnatrix materiai becomes more and more ductile, plastic deformation plays a greater role and leads to a larger and larger spacing between the mode 1 microcrackS. EvenWy plastic deformation becomes the dominant mechanism that totally suppresses the matrix microcracking process, as
illustrated in Figure 3.8b.
>aaa (a) Mode II delamination in brittle mat*
Mode II delamination in ductile matrbc
Figure 3.8 Energy dissipation mechanisms in mode II delamination
In conclusion, the energy dissipation in mode II delamination can be directly related to the matrix yielding which happens during the formation of matrix mode 1 microcracks at the crack tip and their coalescence process. Therefore, it is still reasonable to assume that the critical length of the mode 11 crack tip plastiddamage zone is proportional to the critical radius of the plastic zone in the mode I fnicaire of the relative pure matrix materials, Le. , where lpnc is the critical length of the plastic/damage zone in the mode II delamination
hcture; n, is the proportion constant which could be detemllned experimentally or
empiricaily; and r, is the critical radius of the plastic zone in the mode 1 hcture of the
pure matrix matenal, which can be calculated by Equations (3.2.50) and (3.2.5 1) with K,
and G, replacing K and G, respectively.
Substituthg Equation (3.2.52) into the final expression for G, ,we finally obtain
the expression for the critical strain energy release rate of mode II delamination, G, ,
which is again a fùnction of the matenal properties of the resin and the fibre in the
composite system ody, illustrated as follows,
Once the yield stress, r, ,tensile modulus, E, , shear moduius G, and the critical strain energy release rate, Gc ,of the resin; the tensile modulus, E, ,and shear modulus G, of the fibre; and the fibre volume Mon, V, , are known, the mode II cntical strain energy release rate can then be predicted by the above equation. The only fining parameter, n, , can be determined either experimentally through observation of sizes of the crack tip plastic zones in both resins and composite laminates or empiricaliy through cwefitting among different composite systems. Experimental Studies 67
Experimental Studies
Most previous experimental studies of composite delamination have been focused on collecting accurate delamination toughness values. Although many studies also included ktography and matenals effects, there has been little emphasis on the origin of delamination toughness and the relative ma& material properties were usually not measured. However, it is the matrix material properties that largely control the composite delamination toughness. In this study, the experimental work was designed to investigate the critical factors that control the delamination hcture toughness of composite materials and to evaluate the present theoretical models. A complete set of experimental tests were perfonned on the selected composite systems and their corresponding matrix materials.
Al1 the mechanical properties involved in the theoretical models were measured so that the validity of the postuiated mode 1 and mode II models could be assessed. A detailed description of the experimental work is presented in the following sections.
Testing and Equipment
A series of mechanical tests were performed on a wide range of composite laminates and their corresponding neat resin materials. For neat resin materials, a tende test and a single edge notched bend (SENB)test were carried out to obtain the yield strength, the tensiie modulus and the resin hcture toughness. For composite laminates, both mode 1 and mode II delamination tests were conducted to obtain the delamination fkctm toughness. AU mechanical tests were performed at room temperature on a Sintech 20
testing machine, hooked up to a 486 computer ninning Teshvorks v2.10 and equipped
with an MTS load cell (model 3 132-146; 1000 lbs capacity).
The hture surfaces of both mode I and mode II delaminated specimens were also studied using a Hitachi Scanning Electron Microscope (SEM) (model S-2500).
Pictures of the cross-sections of the composite specimens were also acquired using the
SEM to detemiine the volume f'raction of fibres in the composites.
4.1.1 Polymer Tensile Tests
Tensile tests were performed on every matrix material used in the present composite systems. The tests were conducted in accordance with the ASTM standard test method for tensile properties of plastics D638M-93.The major purpose of the tensile test was to obtain the elastic modulus, the yield strength andlor the ultimate strength of these materials. The specimen configuration is shown in Figure 4.1. A typicai tensile specimen was 150 mm in overall length and 3 mm in thickness; the length and the width of the test section of the specimen were 100 mm and 12.75 mm, respectively. For polypropylene, dog-bone specimens were used For nylon and epoxy, long rectanguiar specimens were used to simple the specimen manufacture and to conserve materials.
The tensile tests were carried out in two steps. Firstly, the specimen was loaded at a speed of 5 mm/min to a load within the elastic limit of the materiai. The load and displacement were used to calculate the elastic modulus. An MTS extensometer (Model
632.25B-50 with 2 inches gauge length) was used for accurate measurnent of
displacement during the elastic modulus test. The specimen was then unloaded and the extensometer removed. Secondly, the same spechen was loaded again at the same speed until its breaking point. The yield stress and strain as well as ultimate stress and strain were recorded.
Figure 4.1 Specimen configuration of polymer tensile test
4.1.2 Single-edge Notched Bend Test (SENB)
Because of its accuracy in evaluating the fhcture toughness and its relative ease of use, the single-edge notched bend test was chosen to obtain the kture toughness of al1 matrix materials. The tests were performed in accordance with the ASTM standard test method for plane-strain fkture toughness and strain energy release rate of plastic materials, D5045-93. The specimen configurations are as shown in Figure 4.2. A three-point bend fixture was used in the SENB fiachire tests. The specimens were loaded at a speed of 10 mmhin until their final fracture. Indentation tests were also performed on uncracked calibration specimens in such a way tbat the loading thes were the same as those in the hcture tests. Lower test speeds were usually involved in the indentation tests since the indentation specimens were stiffer. The displacement and energy fiom the indentation tests were used to correct the displacement and energy in the hture tests. In some cases, such as polypropylene and nylon, specimens with different thichess, B, were tested to make sure that the requirement for plain strain condition was satisfied, i.e., the thickness, B, must be greater than 2.5(&hJ2 .
Figure 4.2 Specimen configuration of single edge notched bending test
The K, calculations were based on the data reduction method specified in the
ASTM standard using the critical load, P, ,the initiai crack length, a, and other specimen dimensions. Generaiiy, the maximum load, P,, ,was taken as the critical load, P, ,if the
P, P, feii within the range of the line with the initial compliance and the line with a compliance 5% greater than the initial one; othenvise, the intersection of the line with a
5% greater compliance and the load-displacement curve was taken as the critical load. The exact crack length, a , was measured on the kturd specimen surface after the fracture test.
Two kinds of critical strain energy release rates were calcdated in the tests. One was obtained by the following relationship derived fkom fkacture mechanics,
where the elastic modulus was taken fkom the corresponding tensile test. The other was obtained fiom directly fiom the energy derived fiom integration of the apparent load- displacement curve up to the load point as used for the K, calculation. Since the elastic moduius, E , in the hcture test may not be the same as the one obtained fiom the tensile test because of the viscoelastic effects of polymers, it is preferable, as suggested by the
ASTM standard, to use the G, obtained fiom the energy calculation.
4.1.3 Mode 1Delamination Test
Mode 1 delamination tests were perfonned on the unidirectional laminated specimens of aU composite systems using the double cantilever beam (DCB) specimen. The test procedures generally followed the ASTM standard test method for mode I interiamuiar fiachue toughness of unidirectional fibre-reinforcecl polymer maeix composites D552&
94a. Ody the test speed was increased fiom 0.5 mm/& to 2.5 mm/min to avoid excessively long testing time and the corresponding viscoelastic behaviour. The
specimen configurations are show in Figure 4.3. The dimensions of each specimen were
125 mm in length, 20 mm in width. The thickness varied f?om 3 mm to 5 mm, and the
insert length was about 62.5 mm.
Figure 4.3 Specimen configuration of mode 1 delamination
Loading hinges were used in the mode 1 delamination test. In the case of thennoset epoxy systems, the hinges were bonded to the delaminated end of each arm of the specimen with epoxy glue. Before applying the epoxy, surfaces of both the hinge and specimen were sanded ushg sandpaper (400 Mt) and cleaned with acetone. When the surfaces were dry, the hinge and the specimen were bonded and a C-clamp was used to hold hem in place for at least 24 hours, after which they were tested. In the case of thennoplastic systems, a screw based method was used to attach the loading hinge to the mode 1 specimen because it is difficult to obtain sufncient adhesive strength with these thermoplastic polymers. Two srnail holes were drilied on the delaminated end of each arm of the specimen, and the hinge was fastened onto the specimen with two small screws. Al1 the hinges were 12.5 mm long and 20 mm wide, resulting an initial crack
length of 50 mm when they were attached to the specirnens.
Before the delamination test, one edge of the specirnen was marked with an extra-
fine permanent market in intervais of O, 1,2, 3,4, 5, 10, 15,20,25 mm starting fiom the
nominal location of the end of the insert. In some cases, the marking intervals were
changed to 0,2,4,6,8,10, 15,20,25 mm, and no signifïcant eeffects were observed in the
data reduction due to the interval changes. During the test, the crack propagation was
observed using a travelling microscope or a magnifjhg glass. When the crack reached
each interval mark, the corresponding load and displacement were recorded. The loading
was stopped and the specirnen was unloaded when the crack finally reached 25 mm. The specirnen was then opened manually and the original crack length was adjusted based on the measured position of the insert.
Three data reduction methods are specified in the ASTM mode 1 standard, Le., the modified beam theory (MBT)method, the compliance calibration (CC) method and the modified compliance cdibration (MCC)method. The MBT rnethod is based on a modified beam theory expression for G, developed by Hashemi et al. [1989], where A is the x-intercept of a plot of the cube root of the specimen compliance vs. the
crack length. The CC method is based on the following expression proposed by Berry
[19631,
where n is determined fiom the dope of a plot of log compliance vs. log crack length.
The MCC method was onginally proposed by Kageyama and Hojo [1990]. The O, is
calculated as folIows,
where A, is the dope of a plot of normalized crack length (ah)vs. the cube root of the
compliance.
Although dl three data reduction method generated close results in most cases, the results fiom the MBT method, as suggested by the ASTM standard, were used to represent the values of G, because the MBT method usually gives the most conservative results. 4.1.4 Mode II Delamination Test
As is in the mode 1 tests, mode II delamination tests were carried out on unidirectional
specimens of all materials systems using the end notched flexure (ENF) specimen in accordance with the ASTM test protocol for mode II interlaminar kture testing. The test speed was again increased fiom 0.5 rnmlmin to 2.5 rnm/min to reduce the testing time. The specimen dimensions were 150 mm in length, 20 mm in width. The thickness varied fiom 3 mm to 5 mm, and the insert length was nominally 50 mm.
Figure 4.4 Specimen configuration of mode II delamination
A three-point bend fixture was used in the mode II test. The specimen was marked on its upper sudace with a permanent marker in [en& of 0, 15, 20, 25, 30, 35 and 50 mm fiom the end of the insert. A compliance calibration test was perfbmed for each specimen by testing the compliance of the specimen with different crack lengths as marked. The specimen was fht placed at zero crack length position and loaded in the kture to a small load within the elastic limit and then unloaded. The load and the displacernent of the center point of the specimen were used to calculate the specimen compliance corresponding to the crack length. The specimen was then shifted in the
fixhire to the next marked position to repeat the compliance test. AU the compliance data
were used in the fiaal compliance calibration. Mer the compliance test, the specimen
was placed at the 25 mm crack length position to perfom the delamination test. In
general, when the load reached the onset of delamination, there was a sudden and
significant drop in the load. The specimen was then unloaded, and the peak load and
corresponding displacement were recorded and used in delamination calculation.
Three data reduction methods are specified in the ASTM protocol. The first method is the experimental compliance calibration (ECC) method that uses the following expression for G,,
where m is obtained tiom the compliance calibration, Le., a lest square regession of the form, C = Co + ma3 . The second method is the direct beam theory (DBT)method.
Values of G, are determined using the following expression, This method does not account for factors such as large displacement effect, etc. The third
method is the corrected beam theory (CBT)method in which the Gu values are comcted
if necessary to account for the large displacement effect and the transverse shear effect.
The expression for Gu is,
where a, and a, are the correction parameters for the effects of large deflection and transverse shear, respectively; E,, is the specimen moduius measured during the compliance calibration when a = 0.
In the present expehent, the experimental compliance calibration (ECC)method is used in the final report.
4.1.5 Fractography
Digital images of the delamination kture sdaces of mode 1 and mode II delaminated specirnens were taken using Hitachi S-2500 sc&g electron microscope. The images were then imported into Corel photo-~aint@and edited to obtain the best resolution.
Pictures of the cross-sections of the composites were ais0 acquired using the SEM.
Image dysis software (OptimasQ6 0) was used to determine the fibre volume fiaction of the composites by analyzing the pictures of the cross-section. In the case of thennoplastic composites, the fibres were not uniformly distributed in the composites,
and thus a density measurement method was also used to con6.m the fibre volume
ktion determined by the pictures of the cross-section. Densities of neat resin and their
composites were measured using method described in the ASTM standard test method for
density and specific gravity (relative density) of plastics by displacement (D792-9 1). The
fibre densities were obtained fkom Piggott [1994]. The fibre volume hction was then
obtained fiom the densities using the following expression,
where V, is the fibre volume, p,, , p,,, and p, are densities of the composites, the matrix resin and the fibre, respectively.
4.2 Materials Selection and Sample Preparation
4.2.1 Materials Selection
In order to test the theoretical models for delamination kture, composite materiais with a wide range of properties were selected. The experimental study included five composite systems; three thennoplastic systems and two thermoset systems. E2-glass fibre/Polypropylene
E2-glass fibre/NyIon- 12 (oven dry)
E2-glas fibre/Nylon- 12 (water saturated)
S2-glas fibre/Epoxy (Epon-8 15) with curiog cycle one
curing cycle one: cure at 130°C for 2 hours and pst cure at 180°C for 1 hour
S2-glass fibre/Epoxy (Epon-8 15) with curing cycle two
curing cycle two: cure at 140°C for 4 hours and post cure at 280°C for 1 hour
For thermoplastic systems, the prepregs of E2 glass-fibre/polypropyleneand E2 glass-fibre/nylon-12 as well as neat polypropylene and nylon-12 powders were al1 donated by BAYCOMP. For thermoset systems, the S2-glass fibre was donated by
FIBERITE, Texas; the epoxy resin, Epon-8 15, was puchased fiom SHELL, Texas; and the curing agent, Anchor 1115, was donated by Air Products and Chernicals, Inc.,
Pennsy Ivania.
Two kinds of Teflon* sheets with different thickness, 12.5 pm and 25 pm, were supplied by Chemfab Corporation of Merrimack, New Hampshire. They were used as the insert for the artincial delamination in the delamination specimens. In general, thinner insert materials usually result in lower f'racture toughness. However, it shouid be pointed out that no significant variations of delamination kture toughness is expected due to the present smail thickness change of the Teflon inserts, as discussed by Murri and
Martin [1993]. 4.23 Preparation of Tensiie Specimens
The dog-bone shaped polypropylene tende specimens were made using an Engle injection moulding machine (mode1 ES28/82). The preparation of nylon- 12 tensile specimens was a bit more complicated. The nylon powder was first dried in an aluminurn open container in a vacuum oven at lM°C for 24 hours. The tempenrhw was then increased to about 240°C to melt the nylon powder; after that the nylon was cooled down naturally to fonn a plate which subsequently was machined iato long rectangular shaped tensile specimens on a milling machine. To create water saturated nylons, the specimens were boiled in water until they reached the saturated state.
The epoxy tensile specimens were made by curing the epoxy in the oven using two different curing cycles. Two rectangular glas panels were clamped together with long narrow rubber strips of 3 mm in thickness placed in between them dong three edges to form a container. The epoxy, Epon 8 15, and the curing agent, Anchor 11 15, were mixed together at 100 to 5 ratio and then poured into the glas panel container and cured in the oven. Mer curing, the epoxy plates were cut into long rectanpuiar tensile specimens using a diamond-tipped water-cooled rotary saw.
4.23 Preparation of SEM3 Specimens
The polypropylene SENB specimens were also made in the oven by melting the polypropylene powder at about 200°C under vacuum in an aluminum container and then cooling it naturally to fonn a plate which was subsequently machined into SENB
specirnens on a rniliing machine- For each specimen, a sharp notch of about half the
specimen width was created using a hacksaw, and the crack was sharpened by sliding a
fiesh razor blade in the notch. The nylon-12 and epoxy SENB specirnens were made
using a similar procedure to that used to make the corresponding tensile specimens. The notch and the naturai crack were created on each nylon-12 and epoxy SENB specimens in the same way as that used on polypropylene specimens.
4.2.4 Preparation of Mode 1 and Mode U Specimens
The thermoplastic unidirectional mode 1 and mode II specimens were made fiom the prepregs donated by the manufacturer. The prepregs were cut using scissors and carefully placed on top of one another with a Teflona sheet inserted in between the midde two layers to create an artificiai delamination crack. The total lay-up consisted of
18 plies aligned with the 0' direction for al1 thermoplastic mode 1 and mode II specimens, except for mode II nylon satunited specimens where 24 plies were used to increase the bending stifniess of the specimens. The prepregs were placed in a steel hot press mould together with aluminum spacers and a thermocouple. The aluminum spacers were used to maintain the laminate thickness and prevent over-pressing; and the thermocouple was used to monitor the press temperature accurately. The mould was covered with aluminum foi1 and then sprayed with a tetrafîuoroethylene (TFE) based release agent,
MS-122N supplied by Miller-Stephenson Chernicd Company, Inc., Connecticut, for easy removal of the laminates and cleaning of the mould. The whole steel modd was then
placed in a Wabash 50-ton hot press machine (mode1 50-1818-2TM), and composite
laminates were made in accordance with manufacturer suggested curing cycles. For
polypropylene composites,
a) 20 psi at 2 10°C for 3 minutes b) 90 psi at 2 1O°C for 1 minute
C) 90 psi at room temperature for two minutes
For nylon composites,
a) 20 psi at 260°C for 5 minutes b) 90 psi at 260°C for 1 minutes
c) 90 psi at room temperature for 5 minutes
The final thickness was about 5 mm for 18-layer polypmpylene laminates; 4 mm
for 18-layer nylon laminates and 5 mm for 24-layer nylon laminates. FWythe water-
cooled diamond saw was used to cut the laminates into appropriate sizes of mode 1 and
mode II specimens.
For thermoset epoxy systems, since the commercial glasdepoxy prepregs were not avdable, the prepregs were made using filament winding machine with S2 glas fibre and the mixed solution of epoxy Epon 815 and curing agent Anchor 11 15 at 100 to 5 ratio. The prepregs were then cut using a standard scissors, placed into the steel mould
with a Teflone sheet in between the middle two layers, and pressed to make composite
laminates using the hot press in a similar way as that used in the thennoplastic
composites case. Two different curing cycles were used, Le.,
a) 130°C for 2 hours and post cure at 180°c for 1 hour
b) 140°C for 4 hours and post cure at 280°C for 1 hour
Al1 epoxy laminates had 18 layers and the final thickness were about 3.5 mm.
Again, a water-cooled diamond saw was used to cut the laminates into appropriate sizes
of mode 1 and mode II specimens.
42.5 Preparation of Specimens for Microscopic Studies
Specimens for fiactographic studies were cut using the diamond rotary saw to a size of
approximately 2cm by 2cm. Specimens for cross-section observation were also cut using
the diamond saw, and the surfaces of the cross-section were polished on a very fine sand
wheel (2400 grit). AU the specimens were cleaned with ethanol and mounted on special
specimen holders ushg a glue gun. The glue was left to cool for a few minutes after
king applied. The specimens were then placed in the gold sputter coater made by
Polaron and coated with a 10 A layer of gold, after which a srnail amount of carbon based paint was applied onto the edge of the specimen and the holder. The paint was used to make a connection between the specimen, the glue, and the holder, making the entire arrangement conductive. The conductive carbon paht was supplied by Structure Probe
Inc. of Chester, Pennsylvania The specimens were ready to be studied under the scanning electron microscope when the paint became dry. S. Experimental Results
5.1 Introduction
Although many researchea have reported the values of delamination fkcture toughness of vanous composite systems, there are not many reports that include the properties of the corresponding matrix matenals. In this chapter, a complete set of materials properties of resins and composites is reported. These results give a fairly clear picture of the fiacture behaviour of the five thennoplastic and thermoset composite systems and their corresponding polymer resins. Theoretical predictions of delamination hcture can be made based on these experimental results.
5.2 Experimental Results
5.2.1 Polymer Tensile Test Results
The yield stresses, or ultirnate stresses in the case of brittle resins, of the neat resins used in this snidy are presented in Table 1. The tensile moduli are presented in Table 2.
Nylon resins were tested in both dry and water satunited states and the water content did have an effect on the tensile pmperties. The water sahiraed nylon resin became more ductile with lower yield strength and elastic modulus than the oven dry nylon resin. In the case of epoxies, a higher pst curing temperature had little effect on tensile strength but increased elastic modulus by 30%. In general, thermoset epoxy resins were stronger,
and had larger tende strengths and higher elastic moduli than those of thennoplastic
resins tested.
I Resins -or s (MW SD (MPa) 95% CI (MPa) Polypropylene 31 0.6 0.7 Nylon4 2 (oven dry) 49 3.3 2.7 Nylon-1 2 (sahirated) 41 2.3 1.9 Epoxy (curing cycle 1) 58 9.8 4.9 Epoxy (curing cycle 2) 59 6.1 6.4
Table 5.1 Tensile strengths of dl neat resins
5.2.2 SENB Test Results
The plain-strain hcture toughness and the critical strain energy release rates of the neat
resin materials are show in Table 5.3. As expected, the thennoplastic resins were
generally much tougher than the epoxy resins. Also, higher water content made the nylon
resin even more ductile and improved the toughness. However, it was surprishg to find
that higher the pst curing temperature did not lead to more brittle epoxy for the
temperature range of the current tests. On the contrary, a higher post curing temperature
moderately increased the epoxy fhture toughness. This indicated that higher post cliring temperature resulted in greater cross-link density but did not produce significant degradation of the epoxy resin. Resins E (GPa) SD (GPa) 95% CI (GPa) Polypropy lene 1.7 O. 1 O. 1 Nylon- 12 (oven dry) 1.8 0.2 O. 1 Nylon- 12 (sahiraed) 1.1 O. 1 O. 1 Epoxy (culing cycle 1) 3.2 0.5 0.2 Epoxy (curing cycle 2) 4.2 1.1 0.9
Table 5.2 Tensile moduli of al1 neat resins
Resins
1 I KK Waml'? 1.9 Fracture SD O. 1 toughness 95%CI 0.1 Gr via KI, 0d/m2) 1.9 SD 0.2 Strain energy 95% CI 0.3 release rate G, via energy @J/m2) 2.4 SD 0.7 95% CI 1.1 Specimen thickness (mm) 18 Thickness requir. [2. S(K,~/~J~](mm) 10
Table 5.3 SENB test results of neat resin materials Experimenral RmIts 88
5.23 Mode I and Mode II Delamination Test ResuIts
The mode 1 and mode II cntical stmh energy release rates of the five composite systems
are shown in Table 5.4. Both mode I and mode II critical strain energy release rates of
the thermoplastic systems were much higher than those of the brittie thermoset epoxy
systems. A close look at Table 5.4 also revealed that ratio between the critical strain
energy release rates of the thermoplastic systems G&GIC was smaller than the
correspondhg ratio in the brinle epoxy-based systems. Furthennore, water content did
have an effect on the fracture toughness of the nylon composites. Both mode 1 and mode
II hcture toughness of the water sahirated nylon composites were slightly higher than
those of the oven dry nylon composites. On the other hand, the epoxy post curing
temperature af5ected the mode Il fkacture toughness more than the mode 1 fiachire
toughness.
Composite systems E2Mylon E2Mylon E2PP S2Epoxy S2fEpoxy (saturated) (oven dry) (CI) (c2) GIC(kJ/m2) 1.4 1.O 0.8 0.25 0.23 Mode 1 1 SD I 0.3 0.2 I 0.1 0.05 0.03
Gnc Wm2) 2.8 2.3 1.8 1.7 0.9 Mode II SD 0.3 0.4 0.2 0.2 O. 1 95% CI 0.4 0.3 O. 1 0.2 O. 1
Table 5.4 Mode 1and mode II delamination test dts 5.2.4 Fractography
Figures 5.1 to Figure 5.4 are typical pictures of mode 1 and mode II fracture surfaces of
S2-glasdEpon-8 15 composites with two different curing cycles. As expected, similar surfaces are observed for the two epoxy-based composites in mode 1 and mode II cases.
Mode 1 surfaces are generally clean and smooth, indicating low delamination fracture toughness. The general features on the mode 1 suffies are a cleaved matrix, tiny serrations on the fibres indicating tende cracks, and some fibre lifting. Mode II surfaces are more coarse; and the typicai features of brittle composite materials in mode II delamination, Le., the "shear hackles", are present on both mode II surfaces of the S2- glass/Epon-8 15 composites.
Figure 5.1 Mode 1fracture suffixe of S2-glass/Epon-815 (curing cycle 1) Fractographs of mode 1 and mode II delamination of E2-glass/polypropylene, E2-
glassMylon-12 (oven dry) and E2-glasdNylon-12 (satunited) are shown in Figure 5.5 to
Figure 5.10. In con- to the brittle epoxy composites, extensive plastic defonnation
was observed on both mode 1 and mode II fiace surfaces of these composite systems.
For these more ductile composites, the difference between the mode 1 and mode II fbcture surfaces was not pronounced. The ductility explains why thennoplastic composite systems have a higher fiachue toughness than brittle thermoset composite systems. The sirnilarity of the hcture surfaces of these materials suggests that the difference between mode I and mode II f'racture toughness should be smaller than that of bride epoxy composite systems, as measured in practice.
Figure 5.2 Mode II kturesurface of S2-glasdEpon-8 15 (curing cycle 1) Figure 5.3 Mode 1 hcture surface of S2-giass/Epon-8 15 (curing cycle 2)
Figure 5.4 Mode II fracture surface of S2-glass/Epon-8 15 (curing cycle 2) Figure 5.5 Mode 1 fi-acture surface of E2-glass/Polypropylene
Figure 5.6 Mode II hturedace of E2-glass/Polypropylene Figure 5.7 Mode 1 fkcture surface of E2-glassMylon-12 (oven dry)
Figure 5.8 Mode II fiachire surface of E2-glass/NyIon-12 (oven dry) Figure 5.9 Mode 1 kturesurface of E2-glass/Nylon-12 (saturated)
Figure 5.10 Mode II hture daceof E2-glasdNylon-12 (saturated) Figure 5.1 1 to Figure 5.13 are some typicai pictures of the cross-sections of the
composite systems studied. By loading these digital images hto Optimase 6.0, the
diameters of S2 glass fibre and E2 glass fibre were determined to be approximately 8 to
12 p and 14 to 18 p,respectively. Also, the fibre volume fiactions were detennined
to be approximately 65% for S2-glasslEpon-815 and 35% for E2-glass/Polypropylene
and E2-glassNylon-12. As discussed previously in the experimental section 4.1.5, since
the fibres were not unifonnly distributed in the thermoplastic composite systems, the
density measurement method was also used to decide the fibre volume fiactions for thennoplastic systems, and confïrmed the V, to be about 35%.
Figure 5.1 1 Cross-section of S2-glass/Epon-8 15 composites Figure 5.1 2 Cross-section of E2-glass/polypropylene composites
Figure 5.13 Cross-section of E2-glass/Nylon-12 composites M&f Application lmd Discussion 97
6. Mode1 Application and Discussion
6.1 Introduction
The objectives of this study were to understand the kture mechanisms in composite delamination, and to develop appropriate models to predict the delamination fiacture toughness. The theoretical models presented previously have predicted that the delamination frsicture toughness is controlled mainly by the properties of the resin and the structurai constants of the composite laminate. Once the properties of the resins and the fibres, and the structural properties of the composites were obtained in experirnents,
Equations (3.2.54) and (3.3.53) were used to predict the criticai strain energy release rates, Gr and G,, respectively. The theoretical predictions for GE and Gnc were then compared with the experimental values.
The present theoreticai models were also used to predict Glc and Gu, for other composite systems studied in the Literature. Because few previous studies included the properties of the matrix materials, experimental data for only six composite systems in the literature were selected to test the present theoretical models. The theoretical predictioas were also compared with the experimental results in previous studies. MALApplication and Dkcussion 98
Very good agreement has been achieved between the theoretical predictions and
the experimental data from both the present experiments and the literature. Details are
discussed in the following sections.
6.2 Mode I Model Application
6.2.1 Model Evaluation
The validity of calculations of the stress, cornpliance, and the strain energy release rate,
G,, in the mode 1 beam model had been venfied by Yamada [1987,1988] by applying the
model to an adhesive joint problem and cornparhg the results of the model with the
elastic-plastic finite element solutions. Excellent agreement was obtained.
However, in the present analysis, the calculation of the G, is different from that
used by Yamada [1988]. Rather than using a numerical differentiation, a simple linear
approximation was used to calculate the change in total strain energy in the DCB
specimen. Therefore, in order to test the accuracy of the present model, it is necessary to
apply the present analysis to the example used in Yamada's study and to compare the present solution for G, with the elastic-plastic finite element solution. Note that at this stage, only the relationship between applied load and strain energy release rate is king discussed. The computation of the critical strain energy release rate is presented later
(section 6.1.2). MdefApplication and Discussion 99
The DCB specimen in the example had a crack Iength of 12.7 mm; the width and the thickness of the half beam were 0.635 mm and 1 .O1 mm, respectively; and the thickness of foundation was 0.254 mm. The Young's moduli of the beam and the foundation were 117 GPa and 27.6 GPa, respectively; the yield stress of the foundation was 34.5 MPa The Poisson's ratios were 0.3 for both materials.
Figure 6.1 and 6.2 show the cornparisons of the resdts for G, by the present anaiysis and the fhite element rnethod. Nearly identical results were obtained. This proved that the present linear approximation used in the G, calcdation is accurate enough for DCB specimens with small and moderately large crack tip plastic defornation.
Figure 6.1 Cornparison of strain energy release rate vs. force relation between
the present analysis and the finite element method (Yamada [1988]) Mo& Application and Discussion 100
O 0.2 0.4 0.6 O. 8 1 Ooiiecüon (mm)
Figure 6.2 Cornparison of strain energy release rate vs. deflection relation between
the present analysis and the finite element method (Yarnada [1988])
6.1.2 Theoretical Predictions and Discussion
By applying the failure cntenon, as discussed in the theoretical section 3.2.3, to the mode
1 beam model, predictions of the cntical strain energy release rate, GK , of composite systems can be obtained using Equation (3.2.54). The only fitthg parameter in the current mode I delamination model is the proportion constant n, which is the ratio between the sizes of the critical crack tip plastic zone in the mode 1 delamination and in the neat resin hture. It was detennined to be 1.25 by trial and error. This gave a reasonable indication that the cntical length of the plastic zone at the mode 1 delamination crack tip is a little longer than that at the mode 1 resin hcture crack tip. M& AppZication and Discussion 10 1
Comparisons of the theoretical predictions and the experimental results for the mode 1 cnticd strain energy relerw rates of the present five composite systems are shown in Table 6.1. Fibre properties used in the calculation were obtained fiom Piggott [1994].
The standard deviations for the theoretical predictions were obtained by propagating the experimentai standard deviaîions of the properties of component materials through
Equation (3.2.54). Very reasonable agreement is reached. The average error in the prediction is about 27%. Further comparisons of the theoretical predictions and previous experhental results for other composite sy stems were dso performed. The material properties of the corresponding resins and the fibre volume fractions in the composite laminates are show in Table 6.2. Table 6.3 shows the comparisons of the cntical strain energy release rates. Again, very good agreement is obtained. The average error is about
24% in this case. Figure 6.3 shows the comparisons of al1 the composite systems studied.
The total average error between the theoretical predictions and experimental results is about 25%.
Composite Systems G, (Experimentai) (kJ/m2) GE (Theoretical) (W/mZ) E2/Nylon- 12 (saturated) 1.4H.3 1=8 E2/Nylon-12 (dry) 1-0k0.2 1.1 E2Rolypropylene 0.8H.1 0.6 S2Epn-8 15 (curing cycle 1) Om25I0.O5 0.36 S2Epon-815 (curing cycle 2) 0.23iû.03 0.30
Table 6.1 Comparisons of G,of the present composite systems Modd AppIication and DiSmsion 102
Composite Resin a, or q Resin E Fibre volume S y stems fiaction V, (%) AS4/35O 1-6 0.12 69 (Johnston et al., (Present) Sehitoglu, 1996) Sehitoglu, 1996) 1991) AS4/3502 41.4 4.28 62 (Jordan et ai., (Hercules, 1990)
T3T/F155 54 (Jordan et al., (Jordan et al., (Jordan et al., (Jordan et al., 1989) 1989) 1989) 1989) T3T/F185 72.9 3.56 0.46 58 (Jordan et al., (Jordan et al., (Jordan et al ., (Jordan et al., 1989) 1989) 1989) 1989) AS4/PEEK IO0 3.6 2.0 61 (Johnston et al., (Johnston et al., (Johnston et al., (Leach et al., 1991) 1 1991) 1991) 1987) AS4PEKK 1.O 58 (~han&1988)1 (Chang, 1988) (Chang, 1988) (Chang, 1988)
Table 6.2 Materiai properties of the resins and fibre volume
fiactions of the composite systems
Composite Systems G, (Experi.) @lm2) G, (Theor.) (k.J/m2) AS4/350 1-6 (Trakas & Kortschot, 1995) 0.f 3îO.04 0.1 9 AS4/3502 (Jordan et al., 1989) 0.19 0.12 T3T/F155 (Jordan et al., 1989) 0.34 0.32 T3TE 185 (Jordan et al., 1989) 0.46 0.52 AS4/PEEK (O'Brien, 1997, average) 1.4 1.O AS4PEKK (Chang, 1988) 1.O 0.9
Table 6.3 Cornparisons of GK of previous composite systems Mode1 Application and DUcussion 1O3
These comparisons show that the present mode 1 model predicts the trend of
delamination toughness reasonably well. This suggests that the kture mechanisms of
delamination fkture have been reasonably characterized by the crack tip plastic zone
model. The mode 1 delamination fracture toughness, GIc, is largely controiled by the
resin yield stress, a, and the elastic modulus, E, dong with the resin fiacture toughness,
Gc . The fibre volume hction, V, , also has an important effect on the G, since it
controls the resin content in the composites. Generally speaking, the larger the a, and Gc,
the larger the G, ; while the smaller the E and V, , the larger the GIc. In brittle
composites, and E plays a more important role than Gcin detemiining G, , while in
some ductile composites, the effect of Gc becomes greater.
An important feature of the mode I model is that only one fitting parameter, nt, is adjusted in the model, and yet a reasonably good prediction of delanilnation hcture toughness has been made for a variety of composite materiais. The n, may be experimentally measured if a technique can be developed to measure accurately the size of the crack tip plastic zone. Although the mathematical terms Uivolved in Equation
(3.2.54) are complicated, all the calculations can be easily performed in a simple spreadsheet using Excel or any data processing software.
The success of this model does not exclude the possibility that a better micromechanical stress analysis dong with a more sophisticated failure criterion based on experimentally detemiined crack tip plastic or craze/darnage zone might provide a better prediction of delamination fkture toughness. Mode1 Application and Discussion 104 Modd Application und Dkcussion 105
6.3 Mode II Model Application
63.1 Model Evaluation
Before applying the mode II delamination model to composite systems to predict G,
values, the validity of the cornpliance and the G, calculations in this model should be examuied.
First of dl, the two foundation parameters, K and m, , in equation (3.3.4) must be determined. The K is the shear correction coefficient and the m, is the shear spring constant. The former is used to compensate the non-dom distributions of the shear stress and strain over the beam cross-section, and the Iatter is related to the thickness of the beam foundation. As a htstep, let us consider the case where the shear spring foundation is totally elastic. For isotropie materiais, Kanninen [1974] set m to be 0.5 in his spring foundation model for mode I DCB specimen, assuming that the foudation spring panuneter was related to the thickness of the half beam section, and used the following expression given by Cowper [1966] for r ,
with v ,the Poisson's ratio, equai to 3/11. Thus, IC was about 0.848 which is very close to the traditional value 5/6, used by Roark [1954]. Even though the selections of these Model Application and Dismssion 106
values are somewhat arbitrary, they were well justified by the excellent agreement with
finite element results. For orthotropic mateds, while these values still provide good
results, Williams [1989] suggested that they might be Mermodified to get a more
accurate fit. Corleto and Hogan [1995] also evaluated these two parameters by fitting
their predictions of the compliance and the strain energy release rate of the ENF with
previous fmite element results. They eventually found that setting m, = 0.5 and K = 12
yielded the best agreement for their model. It is worth noting that sûictly speaking, when
K and m, are changed to fit fuiite element results, they should no longer be treated as the
traditional shear correction coefficient and the traditional foundation sprlng parameter.
In the present approach, the values of K and m, were determined by setting the
shear correction coefficient K equal to the traditional value of 96, and then changing the
shear spring constant m, until the best agreement was reached between the current predictions for the compliance and the SMenergy release rate and those of previous biteelement results.
Figure 6.4 shows comparisons of the compliance predictions between the finite element results fkom Saipekar et al. [1988] and the present elastic results with different m valws. While the best agreement is obtained setting m, = 1, the maximum ciifference is only 5.2% when m = 1.75 . Figure 6.5 shows similar comparisons of the strain energy release rate predictions. The best agreement is reached when m, = 1.75, and the maximum ciifference is ody 1.68% . In both figures and ail that follow, C, and GBT Model Application and Discussion 1O7 represent the results of the compliance and the strain energy release rate of the ENF specimen from the classical beam theory solution by Russeil and Street [1982].
Figure 6.4 Comparisons of compliance predictions as a function of a/L
Figure 6.5 Comparisons of strain energy release rates as a fûnction of a/L Modd Application and Dkcslssion 1O8
Aw 1.05 -- Aw un
Y wiI
I 1 +Wang and Williams [1992]
0.95 -- 1 -?:~t:~ 1l -m= 1 0.9 , 0.2 0.4 0.6 0.8
Figure 6.6 Cornparison of compliance predictions as a hction of aR.
Other tests of the foundation panuneters are shown Figure 6.6 and 6.7, where the curent elastic results for C, and G, are compared with the nnite element results of Wang and Williams [1992]. For compliance, setting m, = 1 gives the best prediction; but for strain energy release rate, the best overall agreement is observed when m, = 1.75. For m,
= 1.75, the maximum difference in both compliance and strain energy release rate are
1.5 , 1.45 .,- +Wang and Williams [1993 1.4 .- / / 1.35 -.
1.05 -- 1, 0.2 0.4 0.6 O. 8
Figure 6.7 Cornparison of strain energy release rates as a function of dL Moclei Application and Discussion 109
In general, these cornparisons suggest that mu = 1.75 is the best choice for the
shear spring constant; dong with the shear correction coefficient K = 5/6, the shear spring
constant mu provides a very good approximation of the foundation parameters.
Materials E, , (GPa) E, (GPa) G,, (GPa) v,, 1 115.1 9.65 4.48 0.3 2 43 .5 2 7.24 4.14 0.25 3 146.4 10.34 4.62 0.3 7
Table 6.4 Materials properties of three typical composite laminates
Based on these foundation parameters, the present elastic analysis was compared
with a series of analyses in the literature. The first example was taken fiom Salpekar et al. [1988], in which three kinds of typicd composite materiais were analyzed by the finite element method. Matenal 1 is a classical test problem, which has also been analyzed by severd other researchers; while materials 2 and 3 represent the typical properties for
S2/SP250 glasdepoxy and AS4/PEEK, respectively. The three sets of material properties are show Table 6.4. The ENF specimen has a hed haMength L equal to 38. lmm, and a fked half-thickness h equal to 1.7mm. Detaiied compdsons of C, and Gubetween the current results and those of Salpekar et al. [1988] are shown Table 6.5. Excellent agreement is obtained for all three types of typical composite matenals over a wide range of a/L, i.e., crack-length/beamamlengthratio. Mode1 Application and Dt3cussion 1 1O
Saipekar Percentage Salpeka. Percentage et al. Present DifTereace et al. Present Difference
Material 1 0.2 1.O6 1.O05 -5.2 1.305 1.298 -0.6 0.4 1.O69 1.O2 -4.6 1.142 1.16 1.6 0.6 1.O76 1.O38 -3.5 1 ,O9 1.108 1.7 0.8 1.O76 1.O52 -2.2 1.O64 1.O82 1.7 0.9 1.O73 1 .O56 -1.6 1.O5 1.O73 2.1 Material 2
Table 6.5 Cornparisons of C, and G, values between the finite element results and the
present solutions Model Application and Discussion 1 11
As depicted in Figure 6.8, G, of material 1 fiom several analyses are aiso compared with the current elastic results. Chatterjee's [1991] solution and the higher- order beam solution of Whitney [1988], as weli as the present analysis, provide the best approximations of G, when compared with the finite element results of Salpekar et al.
[1988]. Even though Chatterjee's solution is the closest to the finite element solution, the largest difference between the current analysis and the finite element results is oniy about
2.9% ,which venfies the accuracy of the current adysis.
-Salpekar et al. (FE-7
Figure 6.8 Cornparison of current analysis with other analyticai and finite
element analyses of the ENF specimen M'del Application and Discussion 1 12
The second exsmple was taken fiom Wang and Williams [1992], in which the
finite element method was applied to two sets of composites. AU ENF specimens had a
half-length of 5Omm and a half-thickness of 1.Sm.m. In Table 6.6, the present elastic
results of C, and Gu for the fïrst set of composites over a wide range of a/L ratios are
compared with those of Wang and Williams [1992]. The solutions are within 3.6% difference in both cases of C, and G, . Similar cornparisons of Cuand G, for the second set of composites are listed in Table 6.7. Once again, very close agreement is reached.
CIIG GdG, Wang & Percentage Wang & Percentage a/L Williams Present Difference Williams Present Difference [1992] . (%) [ 19921 (%) 0.2 1 .O41 1 .O04 3.6 1.272 1.235 2.9 O .4 1 .O5 1 1.015 3.4 1.164 1.123 3.6 0.6 1 .O61 1 .O29 3 .O 1.121 1 .O82 3.5 0.8 1 .O64 1 .O4 2.3 1 .O87 1 .O62 2.3
Table 6.6 Cornparisons of C, and G, values between the present results and the finite
element solutions ( E,, = E, = 130 GPa, G,,= 4 GPa, v = 0.3 ) Model Application and Disctlssiun 1 13
WG, Wang & Percentage Wang & Percentage a/L Wiiliams Present Difference Williams Present DiEerence [1992] (%) 119921 (%> 0.2 1.O8 1 1.O04 7.1 1.332 1.29 3.2 1.215 1.155 4.9
Table 6.7 Cornparisons of C, and G, values between the present results and the finite
element solutions (El, = 147.1 GPa, E, = 7.8 1 GPa, G,,= 2.76 GPa, v = 0.3)
1.5 -. 1.4 - j 'Wang and Williams [1992]j i +Present 3 - L l P A w
I
Figure 6.9 Cornparison of G, between the current analysis and the finite
element analysis over a wide range of E,,/G,, ratios
A Merverification of the present analysis is demo~l~tratedin Figure 6.9, where the current results of G, are again compared with those of the fhite element solutions in
Wang and Williams [1992] over a wide range of E,,/G,, ratios. The present solution M&f Application and Discussion 1 14
ciiffers fiom the finite element solution by only 6.2% even when the E,,/G,, ratio becomes
as large as 106.46 .
Adopting the same values of the foundation parameters K and m, used in the
elastic dysis, the elastic-plastic model was used to calculate the compliance, C, , and
the seain energy release rate, G, , of uniâirectional ENF specimens of two widely used
composite systems, AS4/35016 and AS4REEK. The load P in the elastic-plastic
solution was set to be 5% greater than P, , the load correspondhg to the omet of plastic
yielding of the ENF specimen. In Table 6.8, the present results for C, and G, are
compared with those obtained by Chatejee's equation. As expected, the results of the
elastic-plastic solution are slightly greater than those of the elastic solution and
Chatterjee's solution.
CdC, WG, Composite Elastic- Elastic Elastic- Elastic Chetterjee system plastic plastic [199 11 AS4/350 1-6 1.2136 1.2131 1,093 1 1.O928 1,0855 AS4PEEK 1.O252 1.O252 1.1 110 1.1 106 1.1027
Table 6.8 Cornparisons of the compliance and the Guof ENF specimens
All these cornparisons prove that both elastic and elastic-plastic models provide accurate evaluations for G, and C, of the ENF specimen. Compared to previous analytical solutions, this model used the classical beam theory instead of more Md1Application and Dt3ctlssion 1 15
complicated beam theory or plate theory, and thus the solution is relatively simple and
straight forward. AU the calculations can be performed in a simple spreadsheet using
Excel or any other data processing software. Also, for the first the, the plastic zone ske
at the mode II delamination crack tip can be estimated.
63.2 Theoretical Predictions and Discussion
Applying the failure cnterion, as discussed in section 3.3.3, to the mode II beam model,
predictions for the critical strain energy release rate, G,, , of composite systems can be
made using Equation (3.3.53). Since the two foundation parameters, K and m,, are fit
comparing the elastic solution for cornpliance and strain energy release rate with the
finite element solutions and are not adjusted based on those data, the only fitting
panuneter in the current mode II delamination model is the proportion constant n, which
is the ratio between the sizes of the cntical crack tip plastic zone in the mode II
delamination and in the neat resin hcture. It was determined to be 2.0 by tnal and error.
This indicates that the crack tip plastic zone in mode II delamination is even longer than those in mode I delamination and in resin fracture.
The cornparisons of the theoretical predictions and the present experimental results are shown in Table 6.9. Very reasonable agreement was reached. The average emr in prediction was about 23% . Fibre properties were again obtained fiom Piggott
[1994], and the standard deviatiom for the theoretical predictions were obtained using the Model Application and Dismrsion 1 16 same procedure as in the mode 1 model predictions. Theoretical predictions for G, of other composite systems were also made and compared with experimental results in the literature, as shown in Table 6.10. The fibre volume ktions of these composite systems and the material properties of the correspondhg resins were the same as used in the mode
1 model application, which were shown in Table 6.3. Again, The theoretical predictions were in good agreement with the experimental data in the literahue. The average error was about 32% in this case. Figure 6.10 illustrates the cornparisons of ali composite systems studied. The total average error between the theoretical predictious and experimental results was about 28%. Note that in al1 the calculations, resin ry and G, were obtained nom yield strength and modulus E using the relations ry = oJ(3)lRand
G = E/(l+v) where v is the Poisson's ration (-0.3).
Composite Systems G, (Experimental) (kJh2) G, (Theoretical) (kJ/m2)
E2/Nylon-12 (satmted) 2.8k0.3 3.7
E2Mylon- 12 (dry) 2.3k0.4 2.8
E2/Polypropylene 1.8f0.2 1.S
S2Epon-8 15 (curing cycle 1) 1.7H.2 1wO
SZIEpon-8 15 (curing cycle 2) 0.WO. 1 0.8
Table 6.9 Cornparisons of G, of the present composite systems Modd Application and Discussion 1 17
Composite Systems G, (Experi.) (J/m2) Ga, (Predicted) (J/m2)
AS4/350 1 (Trakas & Kortschot, 1995) 0.7f0.1 0.5
AS4/3502 (Jordan et al., 1989) 0.6 0.3
T3TF 155 (Jordan et al., 1989) 1.7 0.9
T3T/F 185 (Jordan et al., 1989) 1 .l 1.4
AS4PEEK (O'Brain, 1997, average) 2.6 2.7
Table 6.10 Cornparisons of Ga, of the previous composite systems
As is the case in mode 1 delamination model, the mode II delamination model
provide reasonably good predictions for the mode iI delamination toughness over a wide
range of composite materials, although only one fitting parameter, nn,, is adjusted in the
model. The physical implication in this model that the crack tip plastic deformation is the major energy dissipation mechanism appears to be quite sound. Sirnilar to mode 1 delamination, the mode II delamination fkcture toughness, G, ,is also largely controlled by the resin yield stress, a, and the elastic modulus, E, dong with the resin fhcture toughness, G, . The fibre voiume hction, V, , also has an important effect on the G, since it controls the resin content in the composites. Generally speaking, the larger the a, and Gc ,the larger the Gnc ;while the smder the E and V, ,the larger the G, . In brittle composites, oyand E plays a more important role than Gc in determining Ga, , while in Mode1 Application and Discussion 1 18 some ductile composites, the effect of Gc becomes greater. This is in conformity with the fractographic findings that the ductile matrix systems produces more plastic deformation.
AU the calculations for Gnc can be easily perfonned in a simple spreadsheet wing
Excel or any data processing software, although the mathematicai terrns involved in
Equation (3.3.53) seems to be complicated. The fitting parameter, n, , may be experimentally measured if a technique can be developed to measure accurately the size of the crack tip plastic zone. At present, there does not appear to be a good technique available for such a measurement in a real composite system. Further experimental work on large scale model systems might be of benefit in this regard.
This model can be applied to a variety of composite systems. Nevertheless, a better prediction of the mode II delamination fkachire toughness might be obtained by
Merinvestigation on micromechanical stress analysis and fkcture mechanisms.
Md1Application and Discussion 120
Conclusions
Close agreement was reached between the predictions of delamination hture toughness by the present theoretical models and the experimental results, nom both the present experimentai tests and other tests reported in the literahue. This clearly shows that the crack tip plastic/darnage zone is a critical factor in delamination of composite laminates and that the present models are successful in predicting the critical strain energy release rates using the resin and other laminate properties. The models can, at least, be employed as useful techniques for scaling the delamination fracture toughness of composite matenais. 7. Conclusions
Delamination is one of the most common and dangerous failure modes in composite
laminates. In recent years, extensive research has ken conducted on many aspects of
delamination failure. However, few studies have been devoted to examining the physical
nature of composite delamination and to deriving quantitative relationships between
delamination process and the cntical seain energy release rate. In this study, a
comprehensive experimental and theoreticai program of research was canied out to
establish the correlation between the cntical strain energy release rates and materiai properties of the resins and composite structural properties. The crack tip plastic deformation was detemiined to be the most important energy dissipation mechanism involved in composite delamination, and two theoreticai models were successfully developed to predict the delamination hcture toughness in mode 1 and mode II delamination.
The two andyticai beam models were based on the double cantilever beam @CB) specimen and end notched flexure (ENI?) specimen. A fhcture critenon relating the sizes of the crack tip plastic zones in the delamination and in the corresponding neat resin fiacture was hcorporated into these two beam models so that predictions for the critical strain energy release rates can be made for mode 1 and mode II delaminations. Conclusions 122
A complete set of mechanical tests was conducted on five composite systems and their corresponding neat resins. Both thermoset and thennoplastic composite systems were chosen so that a wide range of material properties can be obtained to test the theoretical models.
The present theoretical predictions for mode 1 and mode II delamination fracture toughess agreed very favorably with the present experirnental data as well as those in literature over a wide range of composite systems. This indicates that not only the present theoretical models can be used as usefùl tools for predicting mode 1 and mode II delamination hcture toughness, but also the assurnption on which these models are based, i.e., the crack tip plastic deformation is the most cntical energy dissipation mechanisrn, is correct. 8. Recommendations
1) More experimental approaches should be developed to measure either the extent
of crack tip plastic/damage zone quantitatively or other new parameters that are uniquely
related to the crack tip plastic deformation. These experiments would help us to
undentand not only the delamination process in composite materials but also the general
kture phenomena in materials. Perhaps large scale mode1 matenals should be employed.
2) Further theoretical models could be developed for mode III and mixed mode delamination hcnires to predict the critical stmh energy release rates. These models would give usefùi information to both matends scientists and design engineers and greatly reduce the need for unnecessary fhcture tests.
3) Due to their relatively low cost and recyclable nature, thermoplastic composites have a very promising future. More studies should be conducted on the thermoplastic composite matenals to enhance their mechanical properties. 9. References
Anderson, T.L., (1991) 'Fracture mechanics: Fundamentals and applications', CRC Press, Florida, USA.
Annual Book of ASTM Standard 8.01, 'Standard test method for tensile properties of plastics (metric)', D638M-93 (1993).
Annuai Book of ASTM Standard 8.01, 'Standard test method for density and specific gravity (relative density) of plastics by displacement', D792-9 1 (1 99 1).
Annual Book of ASTM Standard 15.01, 'Test method for apparent interlamiiiar shear strrngth of parallel fibre composites by short-beam method', D2344-84 (1 984).
Annual Book of ASTM Standard 8.01, 'Standard test methods for plane-strain hcture toughness and strain energy release rate of plastic matenals', D5045-93, (1993).
Annual Book of ASTM Standard 15.03, 'Standard test method for mode 1 interlaminar fiachire toughness of unidirectional fibre-reinforced polymer matrix composites', D5528- 94a (1 994).
Arcaa, M., Hashin, Z., and Voloshin, A., (1978) 'A method to produce uniform plane- stress States with applications to fibre reinforced materials', Experirnental Mechanics, Vol. 8, ~141-146.
ASTM protocol for mode1 II interlaminar fircture testing (1990).
Barrett, J.D. and Foschi, RO., (1977) 'Mode II stress intensity factor for cracked wood beams' ,Engineering Fracture Mechanics, Vol. 9, p3 7 1-3 78.
Baacom, W.D., Cottington, RL., Jones, EL., (1975) 'The fkacture of epoxy and elastomer-modifïed epoxy polymers in buik and as adhesives', Journal of Appled Polymer Science, Vol. 19, ~2545-2562.
Bascom, W.D., Cottington, RL., (1976) 'EEect of temperature on the adhesive fhcture behaviour of an elastomer-epoxy resin', Jomal of Amiesion, Vol. 7, p333-346.
Bascom, W.D., Bitner, M.,Moulton, RJ., Siebert, AR (1980) 'The interlaminar btureof organic-ma& woven reinforced composites', Composites, January, p9. Bascom, W.D.9 Bo& D.J., Fuller, B., Phillips, P.J., (1985) 'Fractography of the interlaminar f'racture of carbon-fibre epoxy laminates', Joudof Materials Science, Vol. 20, p3 184-3 190.
Bascom, W.D., BOU, D.J., Hunston, D.L., Fuhr, B., Phillips, PJ., (1987) 'Fractographic analy sis of interlamintu Fracture? ,ASTM STP 93 7, p 13 1- 149.
Berry, JoP* (1963) 'Detennination of kture energies by the cleavage technique', Journal of AppZied Physics, Vol. 34, p62-68.
Bradley, W.L., Cohen, RN. (1985) 'Matrix Deformation and Fracture in Graphite- Reidorced Epoxies' ASTM STP 876, p3 89-4 10.
Broek, D., 'Elementary engineering fkcture mechanics', 4th edition, Kltnver Acadernic Publishers, The Netherlands.
Carlsson, LA., Gillespie Jr., J.W., Pipes, RB. (19868) 'On the Analysis and design of the End Notched Flexure (ENF) Specimen for Mode II Testing' Journal of Composite MateriuZs, Vol. 20, p594-604.
Carisson, L.A., Gillespie Jr., J.W., Wbitney, JoM.9 (1986b) 'Fracture mechanics analysis of the end notched flexure specimens', Proceedings of the first Confeence on Composite MuteriaZs, Lancaster, Pennsylvania.
Carlsson, L.A., Gillespie Jr., JmWm, (1989) 'Mode II interlaminar fiacture of composites', Application of Fracture Mechanics to Composite Materiais, Elsevier, New York, USA, pl 13-158.
Chai, H. (1984) 'The Characterization of Mode I Delamination Failure in Non-Woven Muitidixectional Laminates' Composites Vol. 1 5, No 4, p277-290.
Chakachery, E., Bradley, W., (1987) 'A cornparison of the crack tip damage zone for fracture of Hexcei FI85 neat resin and TdT145F185 composite', Pol'er Science and Engineering, Vol. 23, p33-40.
Vaiisetty, RR, Chah, C.C., (1988) 'Composite interlaminar fhcture toughness: Three-dimensional fhite-element modeling for mixed mode 1, II and fracture', ASTM STP 972, p23.
Chang, I.Y., (1988) 'PEKK as a new themioplastic matrix for high performance composites', SAMPE Quarterly, Vol. 19, No. 4, p29-34.
Chatterjee, S.N., (1991) 'Analysis of test specimens for interlaminar mode II fhcture toughness', Part 1 & Part 2, Joumai of Composite Maierds, Vol. 25, p 470-493 & p494- 51 1. Corleto, CR, Bradley, W.L. (1989) 'Mode II delamination fracture toughness of unidirectionai graphite/epoxy composites', ASTM STP 1012, p20 1-22 1.
Corleto, COR,Hogan, &A., (1995) 'Energy release rate for the ENF specimen using a beam on an elastic foundation', Jounial of Composite Materiais, Vol. 29, p1420-1436.
Cowper, G.R (1966) 'The shear coefficient in Timoshenko's beam theory', Journal of Applied Mechanics, Vol. 33, p3 35-340.
Davies, P., de Chareiitenay, FX, (1987) 'The effect of tempurature on the interlamuiar Facture of tough composites', Proceedings of the SLxth International Conference on Composite MateriaZs, Vol. 3, p284-294.
Devitt, D.F., Schapery, RA., Bradley, W.L. (1980) 'A Method for Detennining the Mode 1 Delamination Fracture Toughness of Elastic and Viscoelastic Composite Matenals' Journal of Composite Materiais, Vol. 1 4, p270-285.
Donaldson, S.L. (1985) 'Fracture Toughness Testing of GraphitelEpoxy and GraphiteIPEEK Composites' Compoistes Vol. 16, pl 03- 1 12.
Donaldson, SL. (1988) 'Mode III Interlaminar Fracture Characterization of Composite Materials' Composites Science and Technology, Vol. 32, p225-249.
Donaldson, S.L., MaII, S., Lingg, C. (1991) 'The Split Cantilever Beam Test for Characterizing Mode [II Interlaminar Fracture Toughness' JCTRER, Vol. 13, p41-47.
Dugdal, D.S., (1960) 'Yielding in steel sheets containing slits', Journal of the Mechanics and Physics of Solids, Vol. 8, p 100- 104.
Gillespie Jr, J.Wq Carlsson, LmAq Pipw, RB. (1986) 'Finite element analysis of the end notched flexure specimen for measuring mode II hcture toughness', Composite Science and Technology, Vol. 27, p 177- 197.
Glensser, AL., Takemori, M.T., VaUwce, M.A. and Cinord, S.K. (1989) 'Mode 1 interlaminar fracture toughness of unidirectionai carbon fibre composites using a novel wedge driven delamination design', ASTM STP IOIZ, p 18 1-200
Hahn, H.T., Johaanesmn, T. (1983) 'A correlation Between Fracture Energy and Fracture Morphology in Mixed-Mode Fracture of Composite' Proceedings of 4th International Conference on the Mechanical Behavior of Materials, Stockholm, Sweden, p431-438.
Hashemi, S., Kinloch, A.J., Williams, G. (1987) 'Interlaminar hcture of composite materials', Proceedings of lCCM 4th internutional confrence, Vol. 3, London, pp254- 264. Hashemî, S., Kinloch, A.J., Williams, G. (1989) 'Corrections needed in double cantilever beam tests for assessing the interlaminai failure of fibre-composite', Journal of Mizterials Science Letters, Vol. 8, p 125- 129.
He, M.Y., Evans, AmGa,(1992) 'Finite element dysis of beam specimens used to measure the delamination resistance of composites', Journal of Composite Technology and Research, Vol. 14, p23 5-240.
Hercules (1990) 'Product literature' ,Magna, Utah, USA.
Hibbs, M.F., Bradley, W.L. (1987) 'Correlations between micromechanical failure processes and the delamination toughness of graphite/epoxy systems', ASTM STP 948, p68-97.
Hunston, D.L., Bitner, J.L., Rushford, J.L., Oroshnik, Je, Rose, W.%, (1980) 'Fracture of rubber-toughened adhesive: viscoelastic effects', Journal of EZastomers und Plastics, Vol. 12, p133.
Hunston, D.L., Moulton, RJ., Johnston, N.J, Bascom, WB. (1987) 'Ma& Resin Effects in Composite Delamination: Mode 1 Fracture Aspects' ASTM STP 93 7. p74-94.
Irwin, COR,(1960) 'Plastic zone near a crack and fracture toughness', Sagamore research Conference Proceedings, Vol. 4, p63
Johannesson, T., Bükstad, M. (1985) 'Fractography and Fracture Critena of the Delamination Process', ASTM STP 876, p 4 1 1-423.
Johnson, W.S., Mangalgiri, P.DO,(1987) 'Investigation of fiber bridging in double cantilever beam specimens', Journal of Composites Technol~gyand Research, Vol. 9, p10-13.
Johnston, NJ., Towell, T.W., Hergenrother, P.M., (1991) 'Physical and mechanicai properties of high-performance thermoplastic polymers and their composites', Thermoplastic composite materials, Elsevier, New York, USA, p27-72.
Jordan, W.M., Bradley, W.L. (1987) 'Micromechanisms of hcture in toughened graphite-epoxy laminates', ASTM STP 93 7 p 95- 1 14.
Jordan, W.M., Bradley, W.L., Moulton, RJ. (1989) 'Relating resin mechanicai properties to composite delamination hcture toughness', Joml of Composite Materials, Vol. 23, p 923-943.
Jurf, RA., Pipes, RB. (1982) 'Interlaminar Fracture of Composite Materials' Journal of Composite MateriaZs, Vol. 1 6, p3 86-394. Kageyama, K. and EIojo, M., (1990) 'Proposed methods for interlaminar kture toughness tests of composite laminates', Proceedings of the 5th CI.S./Japanconference on composite materials, Tokyo, p227-234.
Kageyama, K., Kikuchi, M., Yanagisawa, N. (1991) 'Stabilized End Notched Flexure Test: Characterization of Mode II Interlaminar Crack Growth' ASTM STP 11 IO, p2 10- 225.
Kanninen, M.F., (1973) 'An augmented double cantilever beam mode1 for studying crack propagation and arrest', Internatiod Journal of Fracture Vol. 9, No. 1, p83-91.
Kanninen, M.R, (1974) 'A dynamic anaiysis of unstable crack propagation and arrest in the DCB test specimen' ,International Journal of Fracture Vol. 10, No.3, p4 15-43 0.
Karayaka, M., Sehitoglu, H., (1996) 'Failure behavior of unidirectional AS4/35016 carbon/epoxy laminates', Journal of Composite Materials, Vol. 30, No. 10, pl 150-1 176.
Kerr, A.D., (1964) 'Elastic and viscoelastic foundation models', Journa2 of Applied Mechanics, Vol. 3 1, p49 1-498.
Kinloch, A.J., Shaw, SmJm,(1981) 'The fiachire resistance of a toughened epoxy adhesive' Journal of Adhesion Vol. 12, p59-77.
Law, G.E. (1984) 'Mixed-Mode Fracture Analysis of (&25/90,,), GmphiteEpoxy Composite Laminates' ASTM STP 836, p 143- 160.
Leach, D.C., Curtis, D.C., Tambiin, D.R (1987) 'Delamination behavior of carbon fibre/poly(etheretherketone)(PEEK) composites', ASTM STP 93 7, p3 58-3 80.
Lee, S., Gaudert, P.C., Dainty, RC., Scott, RF., (1989) 'Chanicterization of the fkcture toughness property (G,3 of composite laminates using the double cantilever beam specimen', Pol'er Composites, Vol. 1 O, p 305-3 12.
Lee, S.M., (1984) 'Correlation between resin materials variables and transverse cracking in composites', Journal of Materials Science, Vol. 19, ~2278-2288.
Lee, SM., (1988) 'Failure mechanism of delamination kture', ASTM STP 972, p356- 365.
Lee, S.M. (1993) 'An Edge Crack Torsion Method for Mode III Delamination Fracture Testing' Journal of Composites Technology and Resemch Vol. 15, No 3, p 193-201.
Lee, SM., (1997) 'Mode II delamination failure mechanism of polymer matrix composites', Journal of Material Science, Vol. 32, p 1287- 1295. Madhukar, M.S., Dnal, LeTe, (1992) 'Fiber-rnatrix adhesion and its effect on composite mechanical properties: N. Mode 1 and mode II fracture toughness of graphitelepoxy composites', Journal of Composite Materiais, Vol. 26, p93 6-968.
Md, Sm, Kochhar, K.N., (1986) 'Finite element analysis of end-notch flexture specimens' ,Journal of Composite Technology Resemch, Vol. 8, p54-5 7.
Martin, RH., Mum, C.B. (1990) 'Characterization of mode 1 and mode II delarnination growth and thresholds in AS4REEK composites', ASTM STP 1059, p25 1-270.
Martin, RH. (1991) 'Interlaminar Fracture Characterization: A Current Review' NASA Contractor Report No 1 87573.
Martin, RH. (1991) 'Evaluation of the Split Cautilever Beam For Mode III Testing' ASTM STP 11 10, p243 -266.
Morris, C.E. (1979) 'Determinhg Fracture Directions and Fracture Ongins on Failed GraphitelEpoxy Surfaces' ASTM STP 696, p274-297.
Mum, G.B., Guynn, F.G. (1988) 'Analysis of Delamination Growth From Ma& Cracks in Laminates Subjected to Bending Loads' ASTM STP 972 p322-339.
Mum, G.B., Martin, RH. (1993) 'Effect of initial delamination on mode 1 and mode 11 interlaminar bctwe toughness and fatigue f'racture threshold', ASTM STP 1156, p239- 256.
Murthy, P.L.N., Chamis, C.C., (1988) 'Sublaminate- or Ply-level anaiysis of composites and strain energy release rate of end-notched and mixed mode hcture specimens', ASTM STP 972, p4 1.
Naik, RA., Crews, J.H. Jr., Shivakumar, K.N. (1991) 'Effects of T-Tabs and Large Deflections in Double Cantilever Beam Specimen Tests', ASTM STP 11 IO, p 169-1 86.
Nilsson, K-F. (1993) 'On growth of crack fionts in the DCB test', Composites Engineering, Vol. 3, p527-546.
Obreimoff, J.W., (1930) Proc. R Soc. London A 127, p290.
O'Brien, T.K., Jobston, NmJq Morris, D.H., Simmonds, RA., (1983) 'Determination of interlaminar fracture toughness and fkcture mode dependence of composites using the edge delamination test', Proceedings of the international conference on testing, evaluation and quaiity control of composites, University of Surrey, England, p223-232.
O'Brien, TeK, Murri, CeBe, Sdpekar, S.A., (1989) 'Interlaminar shear kture toughness and fatigue thresholds for composite matenals', ASTMSTP 1012, p222-250. O'Brien, T.K., Martin, RH. (1993) 'Round Robin Testing for Mode 1 Interlaminar Fracture Toughness of Composite Matenals' Journal of Composites Technology und Research, Vol. 15, No 4, p269-28 1.
O'Brien, T.K, (1997) 'Composite interlaminar shear hcture toughness, GD,: shear measurement or shear myth ? ', NASA Technical Memorandum 1 10280.
Parker, D.S., Yee, AF., (1989) 'Factors influencing the mode 1 interlaminar fhcture toughness of a rubber toughened thermoplastic matrix composite', Jownai of Thermoplastic Composite Materiais, Vol. 2, p2- 18.
Piggott, M.R (1988) 'The effect of constraints due to fibres on the delamination of composites', Journal of Materials Science Vol. 23, p 3778-378 1.
Piggot, MA, (1994) 'Load bearing fibre composites' Merpec Press, Toronto, Canada.
Prel, Y.J., Davies, P., Benzeggagh, M., de Charentenay, FOX,(1989) 'Mode 1 and mode II delamination of themosetting and thermoplastic composites', ASTM STP 10 12, p25 1-269.
Punlow, D. (1988) 'Fractography of Fibre-Reinforced Thennoplastics, Part 3. Tensile, Compressive and Flexural Failures' Composites. Vol. 19, No 5, p 358-366.
Reeder, J.R, Crews, J.H. Jr., (1990) 'Mixed-Mode Bending Method for Delamination Testing' AMJournal Vol. 28, No 7, p 1270-1276.
Reeder, J.R (1993) 'A Bilinear Failure Criterion for Mixed-Mode Delamination' ASTM STP 1206, ~303-322.
Rice, J.R, (1968) 'A path independent integral and the approximate analysis of strain concentration by notches and cracks', Journal of Applied Mechanics, Vol. 35, p3 79-3 86.
Ripling, E.J., Mostovoy, S. and PatricL, RL. (1964) Materials Research and Standards, p 129.
Robinson, P., Song, D.Q. (1992) 'A New Mode III Delamination Test For Composites' AhComp. Letfers Vol. 1, No 5, pp 160-164.
Robinson, P., Song, D.Q. (1993) 'Development of a Mode III Delamination Test For Composites' 2nd hi. Conference on Defornation & Fracture of Composites.
Ruueii, Al, Street, K.N. (1982) 'Factors affécting the interlaminar Facture energy of graphite/epoxy laminates', Progress in Science and engineering of composites (ICCM- IV), Tokyo, ~279.286. Russell, A.J., Street, KNw (1985) 'Moistute and Temperature Effects on the Mixed- Mode Delamination Fracture of Unidirectional GraphitelEpoxy' ASTM STP 876. p349- 370.
Russell, AJ. and Street, K.N. (1987) 'The EEect of Ma& Toughness on Delmination: Static and Fatigue Fracture Under Mode II Shear Loading of Graphite Fiber Composites' ASTM STP 93 7 p275-294.
Russell, AwJw (1991) 'Initiation and growth of mode II in toughened composites', ASTM STP 1110. ~226-242.
Salpekar, SeAm, Ftaju, I.S., O'Brien, T.K., (1988) 'Strain energy release rate analysis of the end notch fiemire specimen ushg the Eteelement method', Joudof Composites Technology and Research, Vol. 1 0, p 13 3- 13 9.
Sharif, F., Kortschot, MwT, Martin, RH. (1993) "Mode III Delamination Using a Split Cantilever Beam' 5th Symposium of Composite Materiais: Fatigue and Fracture.
Sbikhmanter, Lw,Cina, B., Eldror, 1. (1991) 'Fnictography of Multidirectional CFRP Composites Tested Statically' Composites, Vol. 33, No 6, p437-444.
Smiley, AJ., (1985) 'Master of mechanical and aerospace thesis', University of DeIaware, Newark, DE
Stuwe, &P., (1980) 'The work necessary to form a ductile fiachire surface', Engineering Fracture Mechanics, Vol. 1 3, p23 1-23 6.
Tirkas, K., Kortschot, M.T. (1995) 'The relationship between critical strain energy release rate and delamination Mmde in mutidirectional carbon-fibre/epoxy laminates', ASTM STP 1285, p283-304.
Vu-Khanh, Tm (1987) 'Crack-Arrest Study in Mode II Delamination of Composites', Polymer Composites Vol. 8, No 5, p3 3 1-34 1.
Wang, S.S., Mandeli, J.F., McGarry, FwJ., (1978) 'An analysis of the crack tip stress field in DCB adhesive hcîure specimens', Intematiowl Journal of Fracture, Vol. 14, p3 9-58.
Wang, Y., Wim,J.G., (1992) 'Corrections for mode II hcture toughness specimens of composite materials' ,Composite Science and Technologv, Vol. 43, pz5 1-256.
Weiis, AA, (1961) 'Unstable crack propagation in metals: Cleavage and fast kture', Proceedings of the Crack Propagation Symposium, Vol. 1, Crdeld, UK. Whitney, J.M., Browning, C.E., Hoogstedan, W. (1982) 'A Double Cantilever Beam Test for Chanicterizing Mode 1 Delaaination of Composite Materials' JomaI of Reinforced Plastics and Composites, Vol. 1, p297-330.
Whitney, AM., (1985) 'Stress analysis of the double cantilever beam specimen', Composite Science & Technology, Vol. 23, p20 1-2 19.
Whitney, LM., Gillespie Jr., J.W., Carlsson, L.A.,(1987) 'Singularity approach to the end notched flexure specimen', Proceedings of the Second Conference on Composite Materials, Lancaster, Pennsy lvania
Whitney, J.M., (1988) 'Analysis of the end notch flexure specimen using a higher order beam theory based on Reissner's principle', Proceedings of Americun Society for Composites, 3rd Technicul Conference, Lancaster, Pennsylvania
Wilkins, D.J., Eisenmann, J.R., Camin, RA., Margoiis, W.S., Bensoi, RA. (1982) 'Characterizhg Delamination Growth in Graphite-Epoxy ' ASTM STP 775, p 1 68- 183.
Wüliams, J.G., (1989) 'End corrections for orthotropic DCB specimens', Composite Science and Technology Vol. 35, p367-376.
Wüliams, J.G., (1993) 'A review of the determination of energy release rates for strips in tension and bending. Part I - Static solutions', Joudof Spain Anuiysis Vol. 28, No. 4, p23 7-246.
Yamada, S.E., (1987) 'Elastic/plastic hcture analysis for bonded joints', Engineering Fracture Mechanics Vol. 27, No. 3, p315-328.
Yamada, S.E., (1988) 'The J-Integral for augmented double cantilever bearns and its application to bonded joints', Engineering Fracture Mechanics Vol. 29, No. 6, p673- 682.
Yoon, S.H., Hong, C.S. (1990) 'Interlaminar Fracture Toughness of Graphite/ Epoxy Composites Under Mixed-Mode De formations' Experinzental Mechanics, ~234-239. Appendix A
Mathematical details of mode II beam mode1 - Elastic /plastic case (A. 10)
(A. 1 1)
dC12 P -- - -(l-a-lp)(z+-)+- dl, Go (A. 12) da 8 da da
(A. 14)
(A*1 5) (A. 16)
(A. 17)
(A. 18)
(A. 19)
a2 a 1 1 Y = -(x, + a){[-cosh(m,, ) + -sinh(m,,fl - -(x, + a)) 2 4 4a 16 a f 1 - 3(1- 2q,)[-*a*sinh(ar,) + -cosh(ax,,) - -(2 - 34,)] 4 4 8 Appendix B
Mathematical development for mode II beam model - Elastic case
In this section, the mode II beam model is solved assuming that the foundation material is
linear elastic, as shown in Figure B. 1. Yield stress, t, is not involved in the model, and ail
other parameters are defined as the same as those in Chapter 3.
Figure B. 1 Beam on the elastic shear spring foundation
The displacements of the half beam in different regions, as shown in Figure B. 1b, are govemed by the following differential equations, d3w2 I P mu, -- - -f-+nG,,b-(-)-(m,Ih)] for OSxSx, rbc3 ElII 4 clk
for I-aSxS2l-a
where E,,I is the bending stiffhess of the composite beam; G,, is shear modulus of the beam; w, ,w, ,w, and w, are the deflections of the beam in regions 1, II, III and IV; x,, is the length of the elastic shear spring foundation; K is the shear correction coefficient and m, is the shear spring constant.
Considering the boundary conditions at the two ends of the bearn, i.e., both bending moments are zero and both shear forces are P/4, the solutions for the displacements can be readily obtained as follows, I p 3 P w, = -(--X +-(21 -a)x2 + C,x + CIO) E,, I 96 32
in which a is defined as,
and the constants fiom C, to C,, , as well as x, can al1 be determined by the continuous conditions, i.e., the deflection, the slope and the bending moment are continuous at
x =O, x, and (1 -a). The shear stress of the foundation is also contiauous at
3P x = x0 , Le., r(xo)= ro = - . In addition, the deflection is set to zero at x = I - a as a 8h reference point to the whole beam.
As shown in Figure 2, the displacement, 6 , at the central loading point may be calculated fiom where 6, and G, can be calcuiated fiom w,(x) and w,(x) when x = -a and x = 21 - a ,
respectively .
Figure 2 Illustration of vertical displacements for the ENF specimen
The compliance of the ENF specimen is defined as,
(B.11)
and the strain energy release rate is based on the change in compliance with crack extension, Finally the stmh energy release rate of the ENF specimen can be expressed as,
where the expressions of Ci and dCi/da ,i = 1,2, .. . 10, are given as follows, Note: constants C, and x, can be detemüned numencally by equations (B.17) and
(B. 18). dC, P ,di, I dC6 Ca, dC- ca, de8 -- - x,+-- xo +c;- +- th 32 da 2 da xo +C6% =+da- da da