- Email: [email protected]
Characterisation of pure and mixed mode fracture in composite laminates
Theoretical and Applied Fracture Mechanics 7 (1987) 115-123 North-Holland
115
CHARACTERISATION OF PURE AND MIXED M O D E FRACTURE IN C O M P O S I T E LAMINATES T.E. TAY, J.F. WILLIAMS Deparmwnt of Mechanical and Industrial Engineering, University of Melbourne, Australia
R. JONES Structures Division, Department of Defence, Defence Science and Technolo~Iv Organisation, Melbourne, A ustraha
The extensive use of advanced fibre composite materials for aircraft construction has necessitated the development of a damage tolerance methodology for aircraft components. Such a methodology would facilitate the design of more efficient and reliable composite structures and their maintenance in service. Therefore, it is necessary, to characterize and understand the complex failure modes of fibre composites, including the influence of temperature, moisture and various defects arising from manufacture or service conditions. This paper briefly discusses the present status of some approaches to the experimental characterization of pure and mixed-mode fracture of composite laminates.
1. Introduction
Apart from providing high specific strength and stiffness, considerable weight reduction can be achieved in aircraft components constructed from graphite-epoxy composites. These composites are also highly resistant to corrosion and fatigue cracking. Often there is significant improvement in the durability of components constructed from composites compared to those manufactured from aluminium alloys. However, significant degradation in compressive strength can arise due to the presence of defects. Various types of defects can occur in composite laminates during both manufacture and service, but sub-surface delaminations (i.e., single or multiple internal cracks whose planes are parallel to the surface of a component) arising in service are of particular interest since they can easily escape detection while adversely reducing the residual strength. Multiple delaminations close to the surface of the component can frequently occur in service due to impact from dropped tools or stones thrown up from the runway. This type of damage is often difficult to detect since there may be little or no visible indication of damage at the surface of the component (BVID). In view of the significant influence of delamination-type defects on the structural be-
haviour of composites, a great deal of interest has been focused on investigating and characterizing delamination behaviour in composite materials. In recent years, the principles of Linear Elastic Fracture Mechanics (LEFM) and the concept of Energy Release Rate during crack propagation have been applied with some success to the problem of fracture in composite laminates. Delamination growth in these materials is often a complex mixed-mode process and many research efforts have focused on establishing general failure criteria and the understanding of the mechanics of delamination growth. It is the purpose of this paper to discuss these investigations and to make appropriate compariSOILS.
2. Characterisation of delamination resistance
Delamination in composite laminates is often a mixed-mode fracture process since in the laminates, both interlaminar tension and shear stresses are present at the delamination front. The interlaminar tensile stresses give rise to a Mode I component (with the associated energy release rate GI), and the interlaminar shear stresses give rise to a Mode II component (with energy release rate GH). When using the energy release rate approach
0167 8442/87/$3.50 c~ 1987, Elsevier Science Publishers B.V. (North-Holland)
116
T.E. Tav et aL / Characterisatton of pure and mixed moae fracture
P
2P I
-
L
ao__.~
-
Fig. 4. End Notched Flexure (ENF) test for Glt c. Fig. 1. Double Cantilever Beam (DCB) test for G to. Pu
P
P
L
-
i-
2hf
L
I AsI2
Pt Fig. 2. Mixed-Mode Flexure test (MMF) for GLIlc.
Fig. 5. Asymmetrically loaded split laminate for Gl.ll c.
to characterise delamination, it must be remembered that the growth will be both mixed-mode and non-serf-similar. In attempting to formulate suitable failure criteria based on the energy release rate method. m a n y researchers have designed a variety of experiments of laminated plates with the intention of isolating and characterizing pure Mode I. pure Mode II and mixed-mode failure (see Figs. 1-11).
ing on the matrix material and the nature of the fibre-matrix interface. In interpreting the values of Gtc from DCB specimens, attention should be given to the surface morphology of the delaminated area, since extensive fibre bridging [10] or intraply cracking [14] can influence the value of energy release rate obtained so that it is higher
J
3. M o d e I characterisation There has been considerable success in characterising Mode I delaminations. The methods most popularly used are the Double Cantilever Beam (DCB) test and the free-edge delamination tensile (EDT) test. The results of these tests on comparable material systems by various researchers are briefly summarized in Table 1A. It can be seen that the values of G rc are fairly consistent within the type of test method employed, varying between 80 to 240 J / m E, depend-
L
P-
l
~l-
L i
~ gouge
Fig. 3, Cracked Lap Shear (CLS) test for Oi.ii ¢, Gnc.
. 2/i
J
cl
Fig. 6. Edge Delamination Tensile (EDT~ test for Gt,n¢, Gt¢.
-_
I i
-P
T, E. Tay et al. / Characterisation of pure and mixed mode fracture
P
than the value that would have been obtained if the delamination was entirely confined within the matrix-rich region and the plane of initial delamination. Table 1B briefly describes some of the experi-
fflt
I
/
-o- ' : - o - N d
///,/ L
. . . .
\\\-k /
] 17
\4
4 - -
\\
....
]
-----I
-
cloth r e i n f o r c e d area Fig. 10. Modified Three Rail Shear test for G,, c.
"/ "/ "/ '/
o
15° Fig. 7. Off-Axis Tensile test for Gni[c, Glc.
~x
~
3,8 mm notches
5× Fig. 8. Double Edge Notched tensile test for G l nc Glc-
Fig. 11. Sing edge notch specimen in the modified arcan test fixture for G~c, G[,lic and Guc.
2P
64 ply L_
I
r~
~--defect .
I
F 76,2 127-
~j,
Fig. 9. Three Point Bend test for Gnc.
76,2
-I 127
mental and data analysis techniques used by researchers in estimating the value of Gtc. For the DCB tests, three methods of analysis are commonly used: they are an analysis based on beam theory [1,2,6,10,11], the area under load displacement curve method [13] and a semi-empirical compliance method [14]. All three methods give reasonable results. The edge delamination tensile specimen has received quite a lot of attention, notably from O'Brien [8,9]. Laminated plate theory and the simple rule of mixtures to compute
118
T.E. Tay et al. / Characterisation of pure and mixed mode fracture
the stiffness loss due to delaminations have been used to obtain an expression relating the critical energy release rate Gc to the critical strain e measured at the onset of delamination. The values of Gc so obtained are often only slightly higher than the value obtained through DCB specimens [13]. This is not surprising, since in E D T specimens. the delaminations initiate at the free-edge where high peel stresses are present, essentially resulting in predominantly Mode I fracture. A disadvantage of EDT-type tests is that they often produce intraply cracking as welt as delamination~ resulting in complex fracture surface morphologies rather than the "clean" delamination surfaces encountered in undirectional DCB tests. An attempt to modify the E D T specimen by introducing starter delaminations in the form of inserts has resulted in considerable lowering of the value of Gic [12]. Furthermore. it has also been shown that G k obtained through EDT specimens is sensitive to
differences in specimen widths [12] (see Table 1A). The 90 o Centre N o t c h specimen has also been used by a number of researchers [5,13]. This method relies on the computation of the stress intensity factor K~c which is. in turn. related to G k through an expression involving material constants. Although the experimental and analytical procedures of the 90 ° CN test are very different from those of the E D T or DCB tests, the values of G~c obtained through these methods agree reasonably well. perhaps indicating that at least for Mode I behaviour, the test methodologies are acceptable.
4. Mode II characterization The situation with Mode II delamination is unfortunately very different. There is wide variability of results of Gnc in the literature for corn-
Table 1A Comparison of experimental values of Glc from literature Material
Reference
Test method
G 1, (J/m2 )
T300/5208 T300/5208 T300/5208 T300/5208 T300/5208
Wilkins. et al. [1] Ramkumar. Whitcomb [2] Chai [14] O'Brien [8] Byers [33]
DCB (Double Cantilever Beam} DCB DCB EDT (Edge Delamination Modified width-tapered DCB
87.6 102.6 86_+8 137 160-241
GY70/5208
Russell. Street [6]
DCB
AS1/3501-6 AS1/3501-6
Russell. Street [3,6] Jurf. Pipes [15]
DCB Modified Arcan Test
110 79
AS4/3501-6
Aliyu, Daniel [11]
DCB
198-232
AS1/3502 AS1/3502 AS1/3502 AS1/3502 AS1/3502 AS1/3502
Bradley, Cohen [10] Whitney, Browning [13] Nicholls, Gallagher [16] Bradley, Cohen [10] Whitney, Browning [13] Whitney, Browning [13]
DCB DCB DCB CT (Compact Tension I 90 o CN (Centre Notch} EDT
155 140 105-175 225 154 267
AS4/3502
Bradley, Cohen [10]
DCB
225 Extensive fibre bridging observed.
AS4/3502 AS4,/3502 AS4,/3502 AS4/3502 AS4/3502
Bradley, Cohen [10] Whitney, Knight [12] Whitney, Knight [12] Whitney, Knight [12] Whitney, Knight [12]
CqEDT 50.8 mm wide specxmen EDT 25.4 mm wide specimen EDT Modified with inserts DCB
120 103 238 81-96 158
T300/1034C
Donaldson [5]
90 o CN
T300/934
O'Brien [9]
EDT
216
T300/934
Wang, et al. [17]
DEN. Double Edge Notched Coupon
157
83
77.9
12.E. Tar et al. / Characterisation of pure and mi.~ed mode fracture
119
Table 1B Description of analysis and experiment for determining Gic Reference
Test method Description
Wilkins, et al. [l]
DCB
Compliance method of test procedure employed, i.e., G = p 2 ( d C / d a ) / 2 W . Load-displacement curve monitored for static loading. Relationship between compliance and crack length was obtained, C = 2a3/3E1 = Ala 3. Also. relationship, between critical load P~ and crack length was derived as P~. - (G~.WEI)I/2/a = A z / a . The value of G~. can then be calculated. Both experimental curves of C vs. a and P~ vs. a were obtained via a least-squares-fit routine to obtain A 1 and A2.
Ramkumar, Whitcomb [2]
DCB
Similar data analysis as in [l].
Russell Street [6]
DCB
Similar data analysis as in [1].
Bradley, Cohen [10]
DCB
Analysis based on linear beam theory. G a = 8P,Z / L 2 / W E I , where P, was the applied load, L~ was length of the split laminate. The analysis was essentially similar to Wilkins [1].
Aliyu, Daniel [1]
DCB
Beam analysis method used. The analysis extended to include transverse shear deformation and kinetic energy effects on the energy release rate. A semi-empirical method based on assumption of partial elastic foundation support beyond the crack tip was proposed. Effect of crack velocity on energy release rate studied. GI,. found to increase with crack velocity.
Whitney, Browning [13]
DCB
Glc obtained through the relationship Gl~ = 1/26 Ac (P162- p231), where PI and P2 are the loads before and after crack extension, 31 and 32 the deflections before and after crack extension, and Ac the increment in crack extension. The analysis was based on area between the loading and unloading curves.
Chai [14]
DCB
Semi-empirical method of analysis used. An empirical relationship between compliance C and crack length l, C = al", where a, n were constants, was used to obtain n P3 GI 2b l "
Jurf and Pipes [15]
Modified Arcan test on Single Edge Notch Specimens. The aluminium fixtures enabled mixed-mode loading of the specimen by varying the angle of loading, a. For pure Mode I loading, a = 90 o and the applied stress normal to the crack plane was o = P/A, where P the applied load and A the area of specimen on which the load was applied. There was some scatter in the values of K ~ obtained. Glc was obtained via the expression
where Sll , $33 , $1:~ and Ssf were terms of the compliance tensor. Byers [331
DCB
Width-tapered specimens for comparison of interlaminar fracture toughness of composites with different resin systems. However, the aluminium tabs were actually half inch thick plates adhesively bonded to the entire top and bottom surfaces of the laminated specimen. The values of GIc obtained were much higher than those obtained by others using normal DCB specimens, probably due to increased stiffness introduced by the aluminium plates. The expression Gtc = 1 2 p 2 / ( E h ) ( a / b ) 2 was used, where P the crack initiation load, and ( a / b ) the specimen taper ratio.
Donaldson [5]
90 ° CN
Gh: was obtained through calculation of KI~ = arqc v ~ a , where a was the half crack length, and ONC the far-field stress normal to the crack. G t was associated with K 1 via an equation containing the orthotropie material properties.
T.E. Tay et a L / Characterisation of pure and mixed mode fracture
120 Table 1B (continued) Reference
Test method
Description
Whitney, Browning[13]
90 ° C N
Gic obtained through calculation of Kte = o ~ / ~ r ( a + a0~':-~, where a 0 was an inherent flaw determined from the average stress criterion, o ~ the notch strength of plate of infinite extent, on°° was obtained from on, the strength of a tensile coupon with finite width, via an isotropic width correction relationship. Gic related to KI~ through
+ aL---~-2~LTE--~]' Gl¢ obtained was higher t h a n values obtained through 0 ° DCB tests. Wang, et al. [17]
DEN
Gj available at notch-tip calculated by a two-dimensional plane-stress finite element routine.
Bradley, Cohen [10]
CT
Displacement-Load relationship monitored. Tests conducted in displacement control to allow stable crack growth. Standard linear fracture mechanics relationship G I = ( P 2 / 2 B X O C / ~ a ) used.
O'Brien [8,9]
EDT
Laminated plate theory and simple rule of mixture for stiffness loss due to delaminations were used to derive
G¢ = --~---(ELAM -- E * ) , where ELAM stiffness of plate calculated from laminated plate theory, E * stiffness of partially delaminated laminate, e¢ critical strain at the onset of delamination, and t was the laminate thickness. Whitney, Knight [12]
Modified EDT
Specimens h a d free-edge starter cracks of length a embedded in the centre plane of specimens. Classical laminated plate theory invoked to obtain GI~ = he2c(E~,- E * ), where h was half thickness of laminate, e¢ the critical strain. E~ and E * modified inplane stiffness terms. E* here is not the same as O'Brien's E * . Values of G ~ obtained slightly lower than those from unmodified EDT's.
Whitney, Browning [13]
EDT
Laminated plate theory used to derive GI~ = h e ~ ( 1 - E ~ ' / E 1 ) f f , I~ where h was half laminate thickness, e, the critical strain at delamination. E~ laminate m o d u l u s in the load direction, El* an effective laminate modulus for detaminated composite, and /~1 was the experimentally determined value o f E 1. Both E 1 and El* were calculated from laminated plate theory. If E1 = El, then the expression for GI¢ would be the same as O'Brien's expression.
parable composite systems. Table 2 shows the variation of G m obtained ranges from 154 to 1200 J / m 2. The experiments designed to m e a s u r e G I I c are often derived from tests to determine shear strength. Although the cracked lap shear specimen has been used to determine GIIc, it is essentially a mixed-mode specimen. The proportion of GII present in this test has been determined, through finite element analyses, to be between 75% and 80% of the total system energy release rate [1,2]. Since the cracked lap shear specimen is a mixedmode specimen, the value of G1k is dependent on the failure criterion used [2] and the accuracy of the finite element analysis in determining the proportions of G I and G H. Some researchers have attempted to obtain G~I~ more directly through pure Mode II tests. Russell
and Street [3,6] have used an edge delaminated laminate specimen simply loaded as a beam specimen. Chatterjee's [4] three-point bend test was similar except that two delaminations were introduced instead of one and were located in the flexural compressive region of the specimen. Chatterjee however, reported values of GIIc about twice the value of those obtained by Russell and Street. Jurf and Pipes [15] modified the Arcan test fixtures and used them to test a single edge notch specimen. Because of the nature of the geometry required, this specimen had to be about 90 plies thick and bonded to an aluminium fixture. The main advantage of the Arcan test was that it enabled Mode I, Mode II and Mixed-Mode testing on a single specimen type. However, therewas also a tendency for s o m e specimens to fail at the
121
72E. Tay et al. / Characterisation of pure and mixed mode fracture Table 2 Comparison of experimental values of Gnc from literature Reference
Description of test method and analysis
Material
Gllc ( J / m 2 )
Wilkins et al. [1]
CLS (Cracked Lap Shear) specimens: Relative proportions of G I and G u obtained through finite element analysis. Proportion of Mode II, G found to be approximately 75% of total energy release rate.
T300/5208
154
R a m k u m a r and Whitcombe [2]
CLS (Cracked Lap Shear) specimens. The embedded delamination did not always propagate along the midplane, but crossed over to the adjacent interface. A simple strength-of-materials analysis of the CLS specimen to account for the change in stiffness due to the crossover was used to compute the change in compliance with crack length, dC/da. A geometrically non-linear finite element analysis was performed to determine the relative proportions of G 1 and Gjl at the critical load. G~ was obtained experimentally. Values of Gl, G n and Glc were substituted into three failure criteria and Gn¢ obtained: (a) GI/GIc + Gn/Gnc =1, (b) (G1/GIc) 2 + ( G n / G n c ) 2 =1, (c) ( G I / G k ) 2 +(GH/Gnc) 2 +(GI/GI¢)(GII/GH¢ ) = 1 .
T300/5208
876, if criterion (a) used 456, if criterion (b) used 643, if criterion (c) used
Russell and Street [3,6]
ENF (End Notched Flexural) specimens. Specimens were subjected to three point flexural loading. The Teflon starter notch tip was placed midway between two loading pins. Beam theory analysis was used to obtain d C / d a to be substituted into the expression for Gll~, yielding GI1c = 9aZPzCb/2b(2 L 3 + 3a3), where C b was the compliance due to bending.
AS1/3501-6 HMS/3501-6 AS4/2220-3
452+6 152_+ 11 750 4_ 25
Chatterjee et al. [4]
Three Point Bend Test specimens. Implanted defects in the form of two-ply Teflon delaminations were located in the region of compressive flexural stress. A computer code was used to solve the problem of disbonds between two plies. Some of the specimens were fatigued to produce sharp crackfronts.
AS1/3501-6
1042 _+214 Blunt crack tips. 950_+ 175 Sharp crack tips.
Donaldson [5]
Modified Three Rail Shear Test. This was not a delamination test, but an inplane crack was cut into a unidirectional laminate parallel to the fibre direction. Earlier finite element analysis by Lakshminarayana [30] showed a uniform state of in-plane shear stress throughout the central region of the specimen. This shear stress was computed via % = P~/2tl, where Pc the critical applied load, t and l the specimen thickness and length respectively. The stress intensity factor
T300-1034C
506
ASI/3501-6
670
Knc = % ~ a , where a the half crack length, was computed and substituted into
KIIc~/2EL ,SF V V /2'T where EL, ET, PLT and Jurf and Pipes [15]
b'LT + 2GLT '
GLT w e r e material properties.
Modified Arcan Test on Single Edge Notch specimens. The fixtures enabled mixed-mode loading of the specimen by varying the angle of loading, a. The stresses applied to specimen were simply o = ( P sin a)/A, for the normal stress. and ~-= ( P cos a)/A for the shear stress, where A was the area of specimen through which the load was transmitted. The specimens were 91 ply thick, with teflon inserts, and were adhesively bonded to the ahiminium Arcan fixtures. For Mode II loading, a = 0 o. Some specimens failed at the metal-composite adhesive bond. Kn¢ was obtained and related to GII c via the expression
122
T.E. "Fayet al. / Characterisation of pure and mixed mode fracture
Table 2 (continued) Reference
Description of test method and analysl~
IV2 Sl1_ /
3~33
Gllc="tlcf2 VV~ll-
Materi',d
Gnu,(j/m2)
2S13- $55
2S~s
where SH, $33, $13 and $55 were terms of the compliance tensor.
fixture-specimen adhesive bond. thus rendering the test invalid. Donaldson [5] investigated Mode II failure of a notched in-plane crack through a modified three-rail shear test arrangement. It may be argued that since both the growth of delaminations and in-plane along-the-fibre cracks in unidirectional laminates are matrix-dominated, the three-rail shear test should yield a Gnc that is dependent only upon the matrix material.
Conclusion Much work remains to be done to properly characterize delaminations in composite laminates. particularly their Mode II and Mixed-Mode behaviour. Various failure criteria proposed have met with only limited success in explaining mixed-mode failure. Much evidence suggests that Gnc is much higher than GIc. In mixed-mode fracture, the contributions of Mode I and Mode II components to the total energy release rate are complicated and not readily apparent. In particular, the individual quantities of G: and GI: cannot necessarily be simply added together to obtain the total energy release rate. This is because, in threedimensional delamination propagation, the growth of the crackfront is often non-self-similar, and furthermore .the contribution of Mode II may become significant. The analyses and expenments carried out to date have concentrated mainly on the first two modes of failure, although for thicker non-unidirectional laminates, the contributions of Modes II and III become increasingly more significant than that of Mode I. Clearly a failure surface in three-dimensional (a failure envelope in two-dimensional) stress space needs to be developed. This goal is presently not yet attainable since there does not appear to be a set of consistent data for mixed-mode fracture from different investigations. In proposing failure criteria.
expressions often used are of the form ( Gl ~clc I
m
l Gu w-
--)Giic
n = 1.
t}
where m and n are constants. Although useful in curve-fitting the experimental data. such expressions lack feasible physical interpretations. Indeed the extension of such a law to three dimensional failure, besides needing the value Gmc, has no physical backing. Any acceptable failure criteria based on energy release rates must have a sound physical basis and for the case of two-dimensional, self-similar growth, eq. (1) must reduce to the form Gtot = G1 + Gir This philosophy has the following implications: (1) A consistent test methodology must be developed for both Guc and Gmc. (2) Less emphasis must be given to the curve fitting approach for mixed-mode fracture. (3) A detailed three-dimensional analysis should be undertaken for each test method in order to determine the relative contributions due to G t, G~1 and GI1 I. References [1] D.J. Wilkins. J.R. Eisenmann. R.A. Canfin. W.S. Margolis and R.A. Benson, "Characterizing Delamination Growth in Graphite-Epoxy", Damage m Composite Materials. ASTM STP 775. 168-183 (1982). [2] R.L. Ramkumar and J.D~ Whitcomb. "Characterization of Mode I and Mixed-Mode Delamination Growth in T300/5208 Graphite Epoxy", Delamination and Debonding of Materials, ASTM STP 876, 315-335 (1985], [3] A.J. Russell and K.N. Street, "The Effect of Matrix Toughness on Delamination: Static and Fatigue Fracture under Mode II Shear Loading of Graphite Fibre Composites", Paper presented at NASA/ASTM Symposium on Toughened Composites, Houston, 13-15 March 1985 [4l S.N. Chatterjee. R.B, Pipes and R.A. Blake Jr. "Criticality of Disbonds in Laminated Composites". Effects of Defects in Composite Materials. ASTM STP 836. 161-174 I.984).
T.E. Tar et al. / Charaeterisation of'pure and mixed mode fracture
[5] S.L. Donaldson, "Fracture Toughness Testing of Graphite/Epoxy and Graphite/PEEK Composites", Composites 16(2), 103-112 (1985). [6] A.J. Russell and K N . Street, "Factors Affecting the Interlaminar Fracture Energy of Graphite/Epoxy Laminates", Progress in Science and Engineering of Composites, ICCM-IV, Tokyo, Japan Society of Composite Materials (1982). [7] A.J. Russell and K.N. Street, "Moisture and Temperature Effects on the Mixed-Mode Delamination Fracture of Unidirectional Graphite/Epoxy", Delamination and Debonding of Materials, ASTM STP 876, 349-370 (1985). [8] T.K. O'Brien, "Analysis of Local Delaminations and Their Influence on Composite Laminate Behaviour", Delamination and Debonding of Materials, A S T M STP 876, 282-297 (1985). [9] T.K. O'Brien, "Characterization of Delamination Onset and Growth in a Composite Laminate", Damage in Composite Materials, A S T M STP 77.5, 140-167 (1982). [10] W.L. Bradley and R.N. Cohen, "Matrix Deformation and Fracture in Graphite-Reinforced Epoxies", Delamination and Debonding of Materials, A S T M STP 876, 389-410 (1985). [11] A.A. Aliyu and I.M. Daniel, "Effects of Strain Rate on Delamination Fracture Toughness of Graphite/Epoxy", Delamination and Debonding of Materials, A S T M STP 876, 336-348 (1985). [12] J.M. Whitney and M. Knight, "A Modified Free-Edge Delamination Specimen", Delamination and Debonding of Materials, ASTM STP 876, 298-314 (1985). [13] J.M. Whitney and C.E. Browning, "Materials Characterization for Matrix-Dominated Failure Modes", Effects of Defects in Composite Materials, A S T M S T P 836, 104-124 (1984). [14] H. Chai, "The Characterization of Mode I Delamination Failure in Non-Woven, Multidirectionat Laminates", Composites 15 (4), 277-290 (1984). [15] R.A. Jurf and R.B. Pipes, "Interlaminar Fracture of Composite Materials", Composite Materials 16, 386 (1982). [16] D.J. Nicholls and J.P. Gallagher, "Determination of Gl~ in Angle Ply Composites using a Cantilever Beam Test Method", J. Reinforeed Plastics and Composites 2, 2 (1983), [17] A.S.D. Wang, N.N. Kishore and W.W. Fong, "On Mixed-Mode Fracture in Off-Axis Unidirectional Graphite/Epoxy Composites", Progress in Science and Engineering of Composites, ICCM-IV, Tokyo, Japan Society for Composite Materials (1982). [18] W.D. Bascom, J.L. Pointer, R.J. Moulton and A.R. Siebert, "The Interlaminar Fracture of Organic-Matrix, Woven Reinforcement Composites", Composites, Jan. 9-18 (1980). [19] T.K. O'Brien, "Mixed-Mode Strain-Energy-Release Rate Effects on Edge Delamination of Composites", Effects of
123
Defects in Composite Materials, A S T M STP 836, 125 142 (1984). [20] F.X. de Charentenay, J.M. Harry, Y.L Pre] and M.L. Benzeggagh, "Characterizing the Effect of Delamination Defect by Mode I Delamination Test", Effects of Defects in Composite Materials, ASTM STP 836, 84-103 (1984). [21] D.F. Devitt, R.A. Schapery and W.L. Bradley~ "A Method for Determining the Mode 1 Delamination Fracture Toughness of Elastic and Viscoelastic Composite Materials", J. Composite Materials 14, 270 285 (1980). [22] G.E. Law, "A Mixed-Mode Fracture Analysis of ( +_25/90,~)~ Graphite/Epoxy Composite Laminates", Effects of Defects in Composite Materials. ASTM STP 836, 143-160 (1984). [23] A.S.D. Wang and F.W. Crossman, "Imitation and Growth of Transverse Cracks and Edge Delamination in Composite Laminates Part 1: An Energy Method". J. Composite Materials 14, Supplement, 71-87 (1980). [241 A.J. Kinloch, "Workshop on Damage Tolerance of Fibre-Reinforced Composites", Glasgow, Scotland (1985). [25] AJ. Russell and K.N. Street, "On the Development of a Mixed-Mode Tensile-Shear Interlaminar Fracture Criterion for Graphite/Epoxy Composites", Presented to Tenth Canadian Fracture Conference CFCIO "Modelling Problems in Crack Tip Mechanics", August 24-26, 1983, Waterloo, Ontario. [26] W.T. Chester, S.E. Fielding and P.D. Hihon, "'Predictive Modelling of Damage in Composite Materials", March 1985. [27] T.K. O'Brien, "Interlaminar Fracture of Composites", J. Aeronautical Soc. India 37 (1), 61-69 (1985). [281 S.S. Wang, "Delamination Crack Growth in Unidirectional Fibre-Reinforced Composites under Static and Cyclic Loading", Composite Materials: Testing and Design (Fifth Conference) A S T M STP 674, 642-663 (1979). [29] F.X. de Charentenay and M. Benzeggagh, "'Fracture Mechanics of Mode I Delamination In Composite Materials", Advances in Composite Materials, Proc. Third Internat. Conf. Composite Materials, Paris, 186-197 (1980). [30] H.V. Lakshminarayana, "A Symmetric Rail Shear Test for Mode II Fracture Toughness (GII~) of Composite Materials--Finite Element Analysis", J. Composite Materials 18, 227-238 (1984). [31] D.H. Morris and H.T. Hahn, "Mixed-Mode Fracture of Graphite/Epoxy Composites: Fracture Strength", J. Composite Materials" 11, 124-38 (1977). [32] E.F. Rybicki, D.W. Schmueser and J. Fox, "An Energy Release Rate Approach for Stable Crack Growth in the Free-Edge Delamination Problem", J. Compagite Materials tl, 470-487 (1977). [33] B.A. Byers, "Behaviour of Damaged Graphite Epoxy Laminates Under Compression Loading", NASA-CR159293, Final Report, Jan. 1978-Dec. 1979, (1980).
115
CHARACTERISATION OF PURE AND MIXED M O D E FRACTURE IN C O M P O S I T E LAMINATES T.E. TAY, J.F. WILLIAMS Deparmwnt of Mechanical and Industrial Engineering, University of Melbourne, Australia
R. JONES Structures Division, Department of Defence, Defence Science and Technolo~Iv Organisation, Melbourne, A ustraha
The extensive use of advanced fibre composite materials for aircraft construction has necessitated the development of a damage tolerance methodology for aircraft components. Such a methodology would facilitate the design of more efficient and reliable composite structures and their maintenance in service. Therefore, it is necessary, to characterize and understand the complex failure modes of fibre composites, including the influence of temperature, moisture and various defects arising from manufacture or service conditions. This paper briefly discusses the present status of some approaches to the experimental characterization of pure and mixed-mode fracture of composite laminates.
1. Introduction
Apart from providing high specific strength and stiffness, considerable weight reduction can be achieved in aircraft components constructed from graphite-epoxy composites. These composites are also highly resistant to corrosion and fatigue cracking. Often there is significant improvement in the durability of components constructed from composites compared to those manufactured from aluminium alloys. However, significant degradation in compressive strength can arise due to the presence of defects. Various types of defects can occur in composite laminates during both manufacture and service, but sub-surface delaminations (i.e., single or multiple internal cracks whose planes are parallel to the surface of a component) arising in service are of particular interest since they can easily escape detection while adversely reducing the residual strength. Multiple delaminations close to the surface of the component can frequently occur in service due to impact from dropped tools or stones thrown up from the runway. This type of damage is often difficult to detect since there may be little or no visible indication of damage at the surface of the component (BVID). In view of the significant influence of delamination-type defects on the structural be-
haviour of composites, a great deal of interest has been focused on investigating and characterizing delamination behaviour in composite materials. In recent years, the principles of Linear Elastic Fracture Mechanics (LEFM) and the concept of Energy Release Rate during crack propagation have been applied with some success to the problem of fracture in composite laminates. Delamination growth in these materials is often a complex mixed-mode process and many research efforts have focused on establishing general failure criteria and the understanding of the mechanics of delamination growth. It is the purpose of this paper to discuss these investigations and to make appropriate compariSOILS.
2. Characterisation of delamination resistance
Delamination in composite laminates is often a mixed-mode fracture process since in the laminates, both interlaminar tension and shear stresses are present at the delamination front. The interlaminar tensile stresses give rise to a Mode I component (with the associated energy release rate GI), and the interlaminar shear stresses give rise to a Mode II component (with energy release rate GH). When using the energy release rate approach
0167 8442/87/$3.50 c~ 1987, Elsevier Science Publishers B.V. (North-Holland)
116
T.E. Tav et aL / Characterisatton of pure and mixed moae fracture
P
2P I
-
L
ao__.~
-
Fig. 4. End Notched Flexure (ENF) test for Glt c. Fig. 1. Double Cantilever Beam (DCB) test for G to. Pu
P
P
L
-
i-
2hf
L
I AsI2
Pt Fig. 2. Mixed-Mode Flexure test (MMF) for GLIlc.
Fig. 5. Asymmetrically loaded split laminate for Gl.ll c.
to characterise delamination, it must be remembered that the growth will be both mixed-mode and non-serf-similar. In attempting to formulate suitable failure criteria based on the energy release rate method. m a n y researchers have designed a variety of experiments of laminated plates with the intention of isolating and characterizing pure Mode I. pure Mode II and mixed-mode failure (see Figs. 1-11).
ing on the matrix material and the nature of the fibre-matrix interface. In interpreting the values of Gtc from DCB specimens, attention should be given to the surface morphology of the delaminated area, since extensive fibre bridging [10] or intraply cracking [14] can influence the value of energy release rate obtained so that it is higher
J
3. M o d e I characterisation There has been considerable success in characterising Mode I delaminations. The methods most popularly used are the Double Cantilever Beam (DCB) test and the free-edge delamination tensile (EDT) test. The results of these tests on comparable material systems by various researchers are briefly summarized in Table 1A. It can be seen that the values of G rc are fairly consistent within the type of test method employed, varying between 80 to 240 J / m E, depend-
L
P-
l
~l-
L i
~ gouge
Fig. 3, Cracked Lap Shear (CLS) test for Oi.ii ¢, Gnc.
. 2/i
J
cl
Fig. 6. Edge Delamination Tensile (EDT~ test for Gt,n¢, Gt¢.
-_
I i
-P
T, E. Tay et al. / Characterisation of pure and mixed mode fracture
P
than the value that would have been obtained if the delamination was entirely confined within the matrix-rich region and the plane of initial delamination. Table 1B briefly describes some of the experi-
fflt
I
/
-o- ' : - o - N d
///,/ L
. . . .
\\\-k /
] 17
\4
4 - -
\\
....
]
-----I
-
cloth r e i n f o r c e d area Fig. 10. Modified Three Rail Shear test for G,, c.
"/ "/ "/ '/
o
15° Fig. 7. Off-Axis Tensile test for Gni[c, Glc.
~x
~
3,8 mm notches
5× Fig. 8. Double Edge Notched tensile test for G l nc Glc-
Fig. 11. Sing edge notch specimen in the modified arcan test fixture for G~c, G[,lic and Guc.
2P
64 ply L_
I
r~
~--defect .
I
F 76,2 127-
~j,
Fig. 9. Three Point Bend test for Gnc.
76,2
-I 127
mental and data analysis techniques used by researchers in estimating the value of Gtc. For the DCB tests, three methods of analysis are commonly used: they are an analysis based on beam theory [1,2,6,10,11], the area under load displacement curve method [13] and a semi-empirical compliance method [14]. All three methods give reasonable results. The edge delamination tensile specimen has received quite a lot of attention, notably from O'Brien [8,9]. Laminated plate theory and the simple rule of mixtures to compute
118
T.E. Tay et al. / Characterisation of pure and mixed mode fracture
the stiffness loss due to delaminations have been used to obtain an expression relating the critical energy release rate Gc to the critical strain e measured at the onset of delamination. The values of Gc so obtained are often only slightly higher than the value obtained through DCB specimens [13]. This is not surprising, since in E D T specimens. the delaminations initiate at the free-edge where high peel stresses are present, essentially resulting in predominantly Mode I fracture. A disadvantage of EDT-type tests is that they often produce intraply cracking as welt as delamination~ resulting in complex fracture surface morphologies rather than the "clean" delamination surfaces encountered in undirectional DCB tests. An attempt to modify the E D T specimen by introducing starter delaminations in the form of inserts has resulted in considerable lowering of the value of Gic [12]. Furthermore. it has also been shown that G k obtained through EDT specimens is sensitive to
differences in specimen widths [12] (see Table 1A). The 90 o Centre N o t c h specimen has also been used by a number of researchers [5,13]. This method relies on the computation of the stress intensity factor K~c which is. in turn. related to G k through an expression involving material constants. Although the experimental and analytical procedures of the 90 ° CN test are very different from those of the E D T or DCB tests, the values of G~c obtained through these methods agree reasonably well. perhaps indicating that at least for Mode I behaviour, the test methodologies are acceptable.
4. Mode II characterization The situation with Mode II delamination is unfortunately very different. There is wide variability of results of Gnc in the literature for corn-
Table 1A Comparison of experimental values of Glc from literature Material
Reference
Test method
G 1, (J/m2 )
T300/5208 T300/5208 T300/5208 T300/5208 T300/5208
Wilkins. et al. [1] Ramkumar. Whitcomb [2] Chai [14] O'Brien [8] Byers [33]
DCB (Double Cantilever Beam} DCB DCB EDT (Edge Delamination Modified width-tapered DCB
87.6 102.6 86_+8 137 160-241
GY70/5208
Russell. Street [6]
DCB
AS1/3501-6 AS1/3501-6
Russell. Street [3,6] Jurf. Pipes [15]
DCB Modified Arcan Test
110 79
AS4/3501-6
Aliyu, Daniel [11]
DCB
198-232
AS1/3502 AS1/3502 AS1/3502 AS1/3502 AS1/3502 AS1/3502
Bradley, Cohen [10] Whitney, Browning [13] Nicholls, Gallagher [16] Bradley, Cohen [10] Whitney, Browning [13] Whitney, Browning [13]
DCB DCB DCB CT (Compact Tension I 90 o CN (Centre Notch} EDT
155 140 105-175 225 154 267
AS4/3502
Bradley, Cohen [10]
DCB
225 Extensive fibre bridging observed.
AS4/3502 AS4,/3502 AS4,/3502 AS4/3502 AS4/3502
Bradley, Cohen [10] Whitney, Knight [12] Whitney, Knight [12] Whitney, Knight [12] Whitney, Knight [12]
CqEDT 50.8 mm wide specxmen EDT 25.4 mm wide specimen EDT Modified with inserts DCB
120 103 238 81-96 158
T300/1034C
Donaldson [5]
90 o CN
T300/934
O'Brien [9]
EDT
216
T300/934
Wang, et al. [17]
DEN. Double Edge Notched Coupon
157
83
77.9
12.E. Tar et al. / Characterisation of pure and mi.~ed mode fracture
119
Table 1B Description of analysis and experiment for determining Gic Reference
Test method Description
Wilkins, et al. [l]
DCB
Compliance method of test procedure employed, i.e., G = p 2 ( d C / d a ) / 2 W . Load-displacement curve monitored for static loading. Relationship between compliance and crack length was obtained, C = 2a3/3E1 = Ala 3. Also. relationship, between critical load P~ and crack length was derived as P~. - (G~.WEI)I/2/a = A z / a . The value of G~. can then be calculated. Both experimental curves of C vs. a and P~ vs. a were obtained via a least-squares-fit routine to obtain A 1 and A2.
Ramkumar, Whitcomb [2]
DCB
Similar data analysis as in [l].
Russell Street [6]
DCB
Similar data analysis as in [1].
Bradley, Cohen [10]
DCB
Analysis based on linear beam theory. G a = 8P,Z / L 2 / W E I , where P, was the applied load, L~ was length of the split laminate. The analysis was essentially similar to Wilkins [1].
Aliyu, Daniel [1]
DCB
Beam analysis method used. The analysis extended to include transverse shear deformation and kinetic energy effects on the energy release rate. A semi-empirical method based on assumption of partial elastic foundation support beyond the crack tip was proposed. Effect of crack velocity on energy release rate studied. GI,. found to increase with crack velocity.
Whitney, Browning [13]
DCB
Glc obtained through the relationship Gl~ = 1/26 Ac (P162- p231), where PI and P2 are the loads before and after crack extension, 31 and 32 the deflections before and after crack extension, and Ac the increment in crack extension. The analysis was based on area between the loading and unloading curves.
Chai [14]
DCB
Semi-empirical method of analysis used. An empirical relationship between compliance C and crack length l, C = al", where a, n were constants, was used to obtain n P3 GI 2b l "
Jurf and Pipes [15]
Modified Arcan test on Single Edge Notch Specimens. The aluminium fixtures enabled mixed-mode loading of the specimen by varying the angle of loading, a. For pure Mode I loading, a = 90 o and the applied stress normal to the crack plane was o = P/A, where P the applied load and A the area of specimen on which the load was applied. There was some scatter in the values of K ~ obtained. Glc was obtained via the expression
where Sll , $33 , $1:~ and Ssf were terms of the compliance tensor. Byers [331
DCB
Width-tapered specimens for comparison of interlaminar fracture toughness of composites with different resin systems. However, the aluminium tabs were actually half inch thick plates adhesively bonded to the entire top and bottom surfaces of the laminated specimen. The values of GIc obtained were much higher than those obtained by others using normal DCB specimens, probably due to increased stiffness introduced by the aluminium plates. The expression Gtc = 1 2 p 2 / ( E h ) ( a / b ) 2 was used, where P the crack initiation load, and ( a / b ) the specimen taper ratio.
Donaldson [5]
90 ° CN
Gh: was obtained through calculation of KI~ = arqc v ~ a , where a was the half crack length, and ONC the far-field stress normal to the crack. G t was associated with K 1 via an equation containing the orthotropie material properties.
T.E. Tay et a L / Characterisation of pure and mixed mode fracture
120 Table 1B (continued) Reference
Test method
Description
Whitney, Browning[13]
90 ° C N
Gic obtained through calculation of Kte = o ~ / ~ r ( a + a0~':-~, where a 0 was an inherent flaw determined from the average stress criterion, o ~ the notch strength of plate of infinite extent, on°° was obtained from on, the strength of a tensile coupon with finite width, via an isotropic width correction relationship. Gic related to KI~ through
+ aL---~-2~LTE--~]' Gl¢ obtained was higher t h a n values obtained through 0 ° DCB tests. Wang, et al. [17]
DEN
Gj available at notch-tip calculated by a two-dimensional plane-stress finite element routine.
Bradley, Cohen [10]
CT
Displacement-Load relationship monitored. Tests conducted in displacement control to allow stable crack growth. Standard linear fracture mechanics relationship G I = ( P 2 / 2 B X O C / ~ a ) used.
O'Brien [8,9]
EDT
Laminated plate theory and simple rule of mixture for stiffness loss due to delaminations were used to derive
G¢ = --~---(ELAM -- E * ) , where ELAM stiffness of plate calculated from laminated plate theory, E * stiffness of partially delaminated laminate, e¢ critical strain at the onset of delamination, and t was the laminate thickness. Whitney, Knight [12]
Modified EDT
Specimens h a d free-edge starter cracks of length a embedded in the centre plane of specimens. Classical laminated plate theory invoked to obtain GI~ = he2c(E~,- E * ), where h was half thickness of laminate, e¢ the critical strain. E~ and E * modified inplane stiffness terms. E* here is not the same as O'Brien's E * . Values of G ~ obtained slightly lower than those from unmodified EDT's.
Whitney, Browning [13]
EDT
Laminated plate theory used to derive GI~ = h e ~ ( 1 - E ~ ' / E 1 ) f f , I~ where h was half laminate thickness, e, the critical strain at delamination. E~ laminate m o d u l u s in the load direction, El* an effective laminate modulus for detaminated composite, and /~1 was the experimentally determined value o f E 1. Both E 1 and El* were calculated from laminated plate theory. If E1 = El, then the expression for GI¢ would be the same as O'Brien's expression.
parable composite systems. Table 2 shows the variation of G m obtained ranges from 154 to 1200 J / m 2. The experiments designed to m e a s u r e G I I c are often derived from tests to determine shear strength. Although the cracked lap shear specimen has been used to determine GIIc, it is essentially a mixed-mode specimen. The proportion of GII present in this test has been determined, through finite element analyses, to be between 75% and 80% of the total system energy release rate [1,2]. Since the cracked lap shear specimen is a mixedmode specimen, the value of G1k is dependent on the failure criterion used [2] and the accuracy of the finite element analysis in determining the proportions of G I and G H. Some researchers have attempted to obtain G~I~ more directly through pure Mode II tests. Russell
and Street [3,6] have used an edge delaminated laminate specimen simply loaded as a beam specimen. Chatterjee's [4] three-point bend test was similar except that two delaminations were introduced instead of one and were located in the flexural compressive region of the specimen. Chatterjee however, reported values of GIIc about twice the value of those obtained by Russell and Street. Jurf and Pipes [15] modified the Arcan test fixtures and used them to test a single edge notch specimen. Because of the nature of the geometry required, this specimen had to be about 90 plies thick and bonded to an aluminium fixture. The main advantage of the Arcan test was that it enabled Mode I, Mode II and Mixed-Mode testing on a single specimen type. However, therewas also a tendency for s o m e specimens to fail at the
121
72E. Tay et al. / Characterisation of pure and mixed mode fracture Table 2 Comparison of experimental values of Gnc from literature Reference
Description of test method and analysis
Material
Gllc ( J / m 2 )
Wilkins et al. [1]
CLS (Cracked Lap Shear) specimens: Relative proportions of G I and G u obtained through finite element analysis. Proportion of Mode II, G found to be approximately 75% of total energy release rate.
T300/5208
154
R a m k u m a r and Whitcombe [2]
CLS (Cracked Lap Shear) specimens. The embedded delamination did not always propagate along the midplane, but crossed over to the adjacent interface. A simple strength-of-materials analysis of the CLS specimen to account for the change in stiffness due to the crossover was used to compute the change in compliance with crack length, dC/da. A geometrically non-linear finite element analysis was performed to determine the relative proportions of G 1 and Gjl at the critical load. G~ was obtained experimentally. Values of Gl, G n and Glc were substituted into three failure criteria and Gn¢ obtained: (a) GI/GIc + Gn/Gnc =1, (b) (G1/GIc) 2 + ( G n / G n c ) 2 =1, (c) ( G I / G k ) 2 +(GH/Gnc) 2 +(GI/GI¢)(GII/GH¢ ) = 1 .
T300/5208
876, if criterion (a) used 456, if criterion (b) used 643, if criterion (c) used
Russell and Street [3,6]
ENF (End Notched Flexural) specimens. Specimens were subjected to three point flexural loading. The Teflon starter notch tip was placed midway between two loading pins. Beam theory analysis was used to obtain d C / d a to be substituted into the expression for Gll~, yielding GI1c = 9aZPzCb/2b(2 L 3 + 3a3), where C b was the compliance due to bending.
AS1/3501-6 HMS/3501-6 AS4/2220-3
452+6 152_+ 11 750 4_ 25
Chatterjee et al. [4]
Three Point Bend Test specimens. Implanted defects in the form of two-ply Teflon delaminations were located in the region of compressive flexural stress. A computer code was used to solve the problem of disbonds between two plies. Some of the specimens were fatigued to produce sharp crackfronts.
AS1/3501-6
1042 _+214 Blunt crack tips. 950_+ 175 Sharp crack tips.
Donaldson [5]
Modified Three Rail Shear Test. This was not a delamination test, but an inplane crack was cut into a unidirectional laminate parallel to the fibre direction. Earlier finite element analysis by Lakshminarayana [30] showed a uniform state of in-plane shear stress throughout the central region of the specimen. This shear stress was computed via % = P~/2tl, where Pc the critical applied load, t and l the specimen thickness and length respectively. The stress intensity factor
T300-1034C
506
ASI/3501-6
670
Knc = % ~ a , where a the half crack length, was computed and substituted into
KIIc~/2EL ,SF V V /2'T where EL, ET, PLT and Jurf and Pipes [15]
b'LT + 2GLT '
GLT w e r e material properties.
Modified Arcan Test on Single Edge Notch specimens. The fixtures enabled mixed-mode loading of the specimen by varying the angle of loading, a. The stresses applied to specimen were simply o = ( P sin a)/A, for the normal stress. and ~-= ( P cos a)/A for the shear stress, where A was the area of specimen through which the load was transmitted. The specimens were 91 ply thick, with teflon inserts, and were adhesively bonded to the ahiminium Arcan fixtures. For Mode II loading, a = 0 o. Some specimens failed at the metal-composite adhesive bond. Kn¢ was obtained and related to GII c via the expression
122
T.E. "Fayet al. / Characterisation of pure and mixed mode fracture
Table 2 (continued) Reference
Description of test method and analysl~
IV2 Sl1_ /
3~33
Gllc="tlcf2 VV~ll-
Materi',d
Gnu,(j/m2)
2S13- $55
2S~s
where SH, $33, $13 and $55 were terms of the compliance tensor.
fixture-specimen adhesive bond. thus rendering the test invalid. Donaldson [5] investigated Mode II failure of a notched in-plane crack through a modified three-rail shear test arrangement. It may be argued that since both the growth of delaminations and in-plane along-the-fibre cracks in unidirectional laminates are matrix-dominated, the three-rail shear test should yield a Gnc that is dependent only upon the matrix material.
Conclusion Much work remains to be done to properly characterize delaminations in composite laminates. particularly their Mode II and Mixed-Mode behaviour. Various failure criteria proposed have met with only limited success in explaining mixed-mode failure. Much evidence suggests that Gnc is much higher than GIc. In mixed-mode fracture, the contributions of Mode I and Mode II components to the total energy release rate are complicated and not readily apparent. In particular, the individual quantities of G: and GI: cannot necessarily be simply added together to obtain the total energy release rate. This is because, in threedimensional delamination propagation, the growth of the crackfront is often non-self-similar, and furthermore .the contribution of Mode II may become significant. The analyses and expenments carried out to date have concentrated mainly on the first two modes of failure, although for thicker non-unidirectional laminates, the contributions of Modes II and III become increasingly more significant than that of Mode I. Clearly a failure surface in three-dimensional (a failure envelope in two-dimensional) stress space needs to be developed. This goal is presently not yet attainable since there does not appear to be a set of consistent data for mixed-mode fracture from different investigations. In proposing failure criteria.
expressions often used are of the form ( Gl ~clc I
m
l Gu w-
--)Giic
n = 1.
t}
where m and n are constants. Although useful in curve-fitting the experimental data. such expressions lack feasible physical interpretations. Indeed the extension of such a law to three dimensional failure, besides needing the value Gmc, has no physical backing. Any acceptable failure criteria based on energy release rates must have a sound physical basis and for the case of two-dimensional, self-similar growth, eq. (1) must reduce to the form Gtot = G1 + Gir This philosophy has the following implications: (1) A consistent test methodology must be developed for both Guc and Gmc. (2) Less emphasis must be given to the curve fitting approach for mixed-mode fracture. (3) A detailed three-dimensional analysis should be undertaken for each test method in order to determine the relative contributions due to G t, G~1 and GI1 I. References [1] D.J. Wilkins. J.R. Eisenmann. R.A. Canfin. W.S. Margolis and R.A. Benson, "Characterizing Delamination Growth in Graphite-Epoxy", Damage m Composite Materials. ASTM STP 775. 168-183 (1982). [2] R.L. Ramkumar and J.D~ Whitcomb. "Characterization of Mode I and Mixed-Mode Delamination Growth in T300/5208 Graphite Epoxy", Delamination and Debonding of Materials, ASTM STP 876, 315-335 (1985], [3] A.J. Russell and K.N. Street, "The Effect of Matrix Toughness on Delamination: Static and Fatigue Fracture under Mode II Shear Loading of Graphite Fibre Composites", Paper presented at NASA/ASTM Symposium on Toughened Composites, Houston, 13-15 March 1985 [4l S.N. Chatterjee. R.B, Pipes and R.A. Blake Jr. "Criticality of Disbonds in Laminated Composites". Effects of Defects in Composite Materials. ASTM STP 836. 161-174 I.984).
T.E. Tar et al. / Charaeterisation of'pure and mixed mode fracture
[5] S.L. Donaldson, "Fracture Toughness Testing of Graphite/Epoxy and Graphite/PEEK Composites", Composites 16(2), 103-112 (1985). [6] A.J. Russell and K N . Street, "Factors Affecting the Interlaminar Fracture Energy of Graphite/Epoxy Laminates", Progress in Science and Engineering of Composites, ICCM-IV, Tokyo, Japan Society of Composite Materials (1982). [7] A.J. Russell and K.N. Street, "Moisture and Temperature Effects on the Mixed-Mode Delamination Fracture of Unidirectional Graphite/Epoxy", Delamination and Debonding of Materials, ASTM STP 876, 349-370 (1985). [8] T.K. O'Brien, "Analysis of Local Delaminations and Their Influence on Composite Laminate Behaviour", Delamination and Debonding of Materials, A S T M STP 876, 282-297 (1985). [9] T.K. O'Brien, "Characterization of Delamination Onset and Growth in a Composite Laminate", Damage in Composite Materials, A S T M STP 77.5, 140-167 (1982). [10] W.L. Bradley and R.N. Cohen, "Matrix Deformation and Fracture in Graphite-Reinforced Epoxies", Delamination and Debonding of Materials, A S T M STP 876, 389-410 (1985). [11] A.A. Aliyu and I.M. Daniel, "Effects of Strain Rate on Delamination Fracture Toughness of Graphite/Epoxy", Delamination and Debonding of Materials, A S T M STP 876, 336-348 (1985). [12] J.M. Whitney and M. Knight, "A Modified Free-Edge Delamination Specimen", Delamination and Debonding of Materials, ASTM STP 876, 298-314 (1985). [13] J.M. Whitney and C.E. Browning, "Materials Characterization for Matrix-Dominated Failure Modes", Effects of Defects in Composite Materials, A S T M S T P 836, 104-124 (1984). [14] H. Chai, "The Characterization of Mode I Delamination Failure in Non-Woven, Multidirectionat Laminates", Composites 15 (4), 277-290 (1984). [15] R.A. Jurf and R.B. Pipes, "Interlaminar Fracture of Composite Materials", Composite Materials 16, 386 (1982). [16] D.J. Nicholls and J.P. Gallagher, "Determination of Gl~ in Angle Ply Composites using a Cantilever Beam Test Method", J. Reinforeed Plastics and Composites 2, 2 (1983), [17] A.S.D. Wang, N.N. Kishore and W.W. Fong, "On Mixed-Mode Fracture in Off-Axis Unidirectional Graphite/Epoxy Composites", Progress in Science and Engineering of Composites, ICCM-IV, Tokyo, Japan Society for Composite Materials (1982). [18] W.D. Bascom, J.L. Pointer, R.J. Moulton and A.R. Siebert, "The Interlaminar Fracture of Organic-Matrix, Woven Reinforcement Composites", Composites, Jan. 9-18 (1980). [19] T.K. O'Brien, "Mixed-Mode Strain-Energy-Release Rate Effects on Edge Delamination of Composites", Effects of
123
Defects in Composite Materials, A S T M STP 836, 125 142 (1984). [20] F.X. de Charentenay, J.M. Harry, Y.L Pre] and M.L. Benzeggagh, "Characterizing the Effect of Delamination Defect by Mode I Delamination Test", Effects of Defects in Composite Materials, ASTM STP 836, 84-103 (1984). [21] D.F. Devitt, R.A. Schapery and W.L. Bradley~ "A Method for Determining the Mode 1 Delamination Fracture Toughness of Elastic and Viscoelastic Composite Materials", J. Composite Materials 14, 270 285 (1980). [22] G.E. Law, "A Mixed-Mode Fracture Analysis of ( +_25/90,~)~ Graphite/Epoxy Composite Laminates", Effects of Defects in Composite Materials. ASTM STP 836, 143-160 (1984). [23] A.S.D. Wang and F.W. Crossman, "Imitation and Growth of Transverse Cracks and Edge Delamination in Composite Laminates Part 1: An Energy Method". J. Composite Materials 14, Supplement, 71-87 (1980). [241 A.J. Kinloch, "Workshop on Damage Tolerance of Fibre-Reinforced Composites", Glasgow, Scotland (1985). [25] AJ. Russell and K.N. Street, "On the Development of a Mixed-Mode Tensile-Shear Interlaminar Fracture Criterion for Graphite/Epoxy Composites", Presented to Tenth Canadian Fracture Conference CFCIO "Modelling Problems in Crack Tip Mechanics", August 24-26, 1983, Waterloo, Ontario. [26] W.T. Chester, S.E. Fielding and P.D. Hihon, "'Predictive Modelling of Damage in Composite Materials", March 1985. [27] T.K. O'Brien, "Interlaminar Fracture of Composites", J. Aeronautical Soc. India 37 (1), 61-69 (1985). [281 S.S. Wang, "Delamination Crack Growth in Unidirectional Fibre-Reinforced Composites under Static and Cyclic Loading", Composite Materials: Testing and Design (Fifth Conference) A S T M STP 674, 642-663 (1979). [29] F.X. de Charentenay and M. Benzeggagh, "'Fracture Mechanics of Mode I Delamination In Composite Materials", Advances in Composite Materials, Proc. Third Internat. Conf. Composite Materials, Paris, 186-197 (1980). [30] H.V. Lakshminarayana, "A Symmetric Rail Shear Test for Mode II Fracture Toughness (GII~) of Composite Materials--Finite Element Analysis", J. Composite Materials 18, 227-238 (1984). [31] D.H. Morris and H.T. Hahn, "Mixed-Mode Fracture of Graphite/Epoxy Composites: Fracture Strength", J. Composite Materials" 11, 124-38 (1977). [32] E.F. Rybicki, D.W. Schmueser and J. Fox, "An Energy Release Rate Approach for Stable Crack Growth in the Free-Edge Delamination Problem", J. Compagite Materials tl, 470-487 (1977). [33] B.A. Byers, "Behaviour of Damaged Graphite Epoxy Laminates Under Compression Loading", NASA-CR159293, Final Report, Jan. 1978-Dec. 1979, (1980).