Damage tolerance of composite cylinders

Damage tolerance of composite cylinders

Composite Structures 4 (1985) 75--91 Damage Tolerance of Composite Cylinders Michael J. Graves* and Paul A . L a g a c e t Technology Laboratory for...

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Composite Structures 4 (1985) 75--91

Damage Tolerance of Composite Cylinders

Michael J. Graves* and Paul A . L a g a c e t Technology Laboratory for Advanced Composites, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

ABSTRACT The fracture of pressurized graphite~epoxy cylinders was investigated and their damage tolerance assessed. The cylinders were 610 mm long and 305 mm in diameter and were fabricated from Hercules A370-5H/3501-6 prepreg fabric in quasi-isotropic four-ply configurations: (0,45)s and (45, O)s. The cylinders were slit in the longitudinal direction and the critical notch sizes for three pressure levels were determined. Experiments on coupons of similar construction loaded in tension were previously conducted. The critical flaw sizes for the cylinders were well predicted from the flat coupon data corrected for the effects of curvature. In addition, circumferentially wrapped unidirectional plies of Hercules AS1/3501-6 tape of various stacking sequences were used as selective reinforcement on several (0, 45)~ cylinders. These reinforcing plies did change the path of damage but did not prevent catastrophic failure.

1 INTRODUCTION

One of the important considerations in the design of an aircraft is structural integrity and the life of the structure. Life design for an aircraft structure can be based on the fail-safe concept or the safe-life approach. More recently, the concept of damage tolerant design has come into use. *Present address: Boeing Military Airplane Company, Seattle, Washington 98124 USA. tTo whom all correspondence should be addressed. 75 Originally presented at SAE Business Aircraft Meeting, Wichita, KS, April, 1983. Reprinted with permission O 1983 Society of Automotive Engineers, Inc.

76

Michael J. Graves, Paul A. Lagace

Damage tolerance of aircraft structures is defined in MIL-STD-1530A (USAF) as, 'The ability of the airframe to resist failure due to the presence of flaws, cracks, or other damage for a specified period of unrepaired usage'. 1The concepts of redundant structures and the use of linear elastic fracture mechanics have given the designer of metal aircraft the tools with which to meet current damage tolerance criteria. 2.3 These methods are not easily extended to composite materials whose high specific strength and specific stiffness, as well as other advantages, make them desirable for use in aircraft structures. The USAF military specification MIL-A-83A.A.A.regarding airplane damage tolerance requirements contains the phrase, ' . . . not intended to be directly applicable to advanced composite structures'. There are similar concerns expressed by the F A A in their Advisory Circular 20-107 for civilian composite aircraft structures. 4 Previous studies have addressed the damage tolerance characteristics of composites. ~8 These investigations include experimental work and the development of analytical tools to assess and predict the fracture behaviour of composites. Unlike the fracture of metals, which is well characterized by the principles of linear elastic fracture mechanics (LEFM), the fracture of composites involves a complex interaction of fiber breaks, matrix cracks and interply delaminations. 9..~ Many of the previous studies in the fracture of composites have limited themselves to the use of uniaxial loading, generally tensile, of flat coupons. The consensus of these studies is that LEFM does not provide a good criterion for the fracture behavior of composites in the presence of notches." Some investigators ~2-~4have performed biaxial tests on composites generally in the form of tubular specimens to study the fracture behavior. The difficulties in the testing procedure involved in this work have limited the scope of these studies. Further work, both experimental and analytical, is required to characterize the behavior of composites in the presence of notches under biaxial, as well as uniaxial, loads.

2 OBJECTIVES This study is concerned with the fracture behavior of pressurized graphite/epoxy cylinders under the presence of longitudinal slits. There were three main objectives of the investigation: (1) to examine the effect of notch size and stacking sequence on the fracture stress (pressure) and failure mode for composite cylinders under internal pressure; (2) to

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develop a means to predict the fracture stresses of pressurized composite cylinders using coupon (fiat plate) data; and (3) to determine the effects of selective reinforcement of composite cylinders on the fracture stresses and failure modes of these cylinders. These factors are important in a number of areas, especially that of a pressurized aircraft fuselage during high altitude flight. The experiments were designed such that the stress levels in the test articles were similar to those in the fuselage of a wide-body jet under cruise conditions.

3 THE EXPERIMENT The material used for the construction of the cylinders is Hercules A3705H/3501-6 graphite/epoxy fabric prepreg provided in rolls 1 m in width. The use of fabric composites has received increased attention in recent years because of their handling characteristics and potential for reducing fabrication costs. The fabric was found to have advantages in the fabrication of curved surfaces due to its drapeability and resistance to shearing deformation during the handling process. The cylinders were laid up by hand on an aluminium mandrel. A release layer of 'guaranteed' nonporous teflon was placed between the mandrel and the composite material to aid in mandrel removal after cure. The individual plies of graphite/epoxy fabric were carefully laid on the assembly with special care taken at 'ply joints'. Peel-ply was applied to the outer layer of graphite/epoxy to give the cured material the desired finish. Other curing materials (porous teflon, paper bleeder and fiberglass air breather) were then wrapped around the assembly. These materials were drawn tight to prevent any wrinkles. The assembly was then vacuumbagged with care taken to avoid bag wrinkles. The entire curing assembly is represented in Fig. 1. The material was cured in an autoclave under 0-59 MPa pressure and a full vacuum according to the standard cure cycle for AS1/3501-6 prepreg. There was a 1 h hold at 116°C and a 2 h hold at 177°C under these conditions. After removal from the mandrel, the composite cylinder was post-cured for 8 h at 177°C. A total of 19 cylinders were fabricated, seven of these were of the (45, 0)s* configuration and the other 12 were of the *The ply angle refers to the angle of the warp fibers in the fabric. The fill fibers are at a 90 ° angle to this. Thus a 0 ° ply has fibers at 0 ° and 90°. In this study, the 0 ° direction is along the h o o p axis of cylinders.

Michael J. Graves, Paul A. Lagace

78

1

2

3 4 5

6

7

l~g. 1. Diagram of curing assembly. 1--Aluminium mandrel with a coat of mold release; 2 q g u a r a n t e e d nonporous teflon, T C G F - - E H V 0.003, premium; 3---graphite/epoxy layup; 4 - - p e e l ply no. 3921; 5--porous teflon, TCGF 0.001-P porous; 6--paper bleeder; 7 - - HS-6262 vacuum bagging, 2 mils thick.

(0, 45)s configuration. Of these latter 12 cylinders, six were constructed with reinforcing belly bands of unidirectional graphite/epoxy plies 76 mm in width. Two such reinforcing bands were placed 305 mm apart (measured center-to-center) in three different configurations (Table 1). The overall cylinder dimensions were 610 mm in length, 305 m m in diameter, and approximately 1.4 rnm in thickness. A typical cylinder is illustrated in Fig. 2. The cylinders were sealed with aluminium endcaps bonded to each end. The endcaps were 25.4 mm thick and had an outside diameter of 330 ram. A circular groove 12-7 mm deep and 3.175 mm wide was cut into the

TABLE 1

Reinforcement Types

Type

Description Four unidirectional plies on the outer surface. Two unidirectional plies on the inner surface. Two unidirectional plies on the outer surface. A symmetric layup with the reinforcement interweaved. The laminate cross-section is: 0° ply--fabric unidirectional tape; 45 ° ply-fabric unidirectional tape--symmetric

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Fig. 2. Characteristics of cylinder specimen. P = internal pressure.

cap. A two-part potting epoxy was used to bond the endcaps to the cylinder. The epoxy was an Epon 815 resin and V40 hardener manufactured by the Miller-Stephenson Company. The resin-to-hardener mixing ratio was 100: 60 and this mixture was cured for 5 h at 82°C. The object of the tests was to provide a fail/no-fail criterion for the cylinders. The cylinder was placed horizontally in the test setup shown in Fig. 3 located in a blast chamber. Pressure was provided from bottled nitrogen which was secured outside the chamber. The cylinder was pressurized to a predetermined level (three such levels were used) and was then punctured by a blade of a known size with the use of a guillotine mechanism, also shown in Fig. 3. If the cylinder did not fail, it was allowed to depressurize. The region where the slit was made by the blade was patched by laminating two pieces of 181 fiberglass cloth with a quick-cure epoxy. Such a completed patch can be seen towards the bottom of the cylinder in Fig. 3. The cylinder was then repressurized. The next largest blade was used to puncture the cylinder in a region away from the original puncture. This procedure was continued until the cylinder failed. The blades were made of oil hardened steel with a nominal thickness of 0.8 m m and in widths from 10.05 to 69.85 m m in intervals of 6.35 ram. It is important to note that the test was not intended to be a dynamic or impact test but was intended to provide an instantaneous slit of length equal to the blade width. If the fracture of the cylinder did occur, it was due to the slit reaching or surpassing the critical notch size. After failure, photographs of the specimens were taken and the fracture paths were traced.

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Michael J. Graves, Paul A. Lagace

Fig. 3. Experimental set-up showing guillotine mechanism with blade and patch on cylinder.

4 M O D E L I N G THE CYLINDER Previous work had been conducted on coupon specimens manufactured from (0, 45)~ and (45, 0)~ fiat fabric laminates.IS A typical specimen is represented in Fig. 4. Specimens were manufactured with various sized holes or slits in the center and tested under uniaxial load in order to determine the sensitivity of the composite to various sized notches. The

Damage toleranceof composite cylinders TOP VIEW

81

SIDE VIEW

/EPOXY ~B

RAPHITE/EPOXY

20 ITE/EPOXY

FM-125 FILM ADHESIVE

;/EPOXY

ASS/EPOXY

5 0 mm

Fig. 4. Characteristicsof coupon specimen.

data were correlated using the method suggested by Mar and Lin. 16Mar and Lin have proposed that the fracture stress of a notched composite laminate can be correlated by an equation which resembles the linear elastic fracture mechanics equation: o'f = Hc(2r) -~

(1)

where Hc is the composite fracture toughness, trf is the fracture stress, and 2r is the size of the notch. The value of the exponent m is determined by calculating the stress singularity caused by a crack at a bimaterial interface, in this case fiber and matrix. For graphite/epoxy this value is calculated to be 0-28.17 Lagace18 has shown that this correlation works well for many laminates if there is no delamination. 19 The experimental data from the investigation by Graves 15 correlate well using the M a r L i n equation. The values of m determined by a linear regression of the experimental data are 0-276 for the (0, 45), laminate and

Michael J. Graves, Paul A. Lagace

82

0.284 for the (45, 0)s laminate compared to the theoretical value of 0.28. The values for the composite fracture toughness are 765 MPa (mm) °2s for the (0, 45)s laminate and 761 MPa (ram) °28 for the (45,0)s laminate. In addition, this investigation demonstrated several other important results: (1) as suggested by Mar and Lin and other investigators, the size of the flaw, and not its shape, determines fracture stress since specimens with holes or slits of the same size failed at the same stress; (2) the composite is insensitive to slight irregularities in slit manufacture as coupons with slits

PR

°'22 = T

~

~...~/~-

~

~,w

~

~

_

PR

°]' - ~ -

-,....

Fig. $. Membrane model of biaxial state of stress in cylinder.

made by impact with a blade or carefully manufactured by a jeweler's saw, failed at the same stress for a given slit size; (3) the composite is insensitive to a slit parallel to the loading direction as the specimen failed at the unnotched fracture stress in this case. Each of the above considerations was important in modeling the pressurized cylinders so that fracture data from coupon tests could be used to predict cylinder failure. First, the region where the slit is introduced is assumed to behave as a membrane. That is, the material is subjected to a biaxial state of stress due to the internal pressure and the sealed ends. This is illustrated in Fig. 5. Then, by using the fact that the composite is insensitive to a slit parallel to the loading direction, the longitudinal stress, o.11, can be ignored and only the hoop stress, o'22, applied perpendicular to the slit, is considered in determining the far-field stress responsible for fracture. The second step of modeling involves the

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slit manufacture. As described, the slits were created by a blade attached to a guillotine device. This does not represent a dynamic impact test but is modeled as the appearance of an instantaneous slit. In addition, since the composite is insensitive to notch type and manufacture method, the blade size can be used as the slit size in correlating the data.

5 RESULTS A N D DISCUSSION As previously stated, the object of the tests was to provide a fail/no-fail criterion for the cylinders. Thus the results of the tests are fail/no-fail regions at the pressure levels tested. These are summarized in Table 2. These pressure data are plotted against slit length in Fig. 6. The M a r L i n correlation from the coupon data is also plotted in Fig. 6 using the relation: 0"22 - -

pR h

(2)

where R is the cylinder radius, h is the thickness and p is the internal pressure. The experimental data for the cylinders fall significantly below the predicted behaviour via the extrapolation of the flat plate data using the Mar-Lin equation. There are two major differences between the coupon tests and the pressurized cylinder tests. The first difference is the biaxial state of stress. However, the o-,, component of the stress can be discounted as discussed in the last section. The second difference is that the cylinder is curved and is therefore a shell. According to Folias,20 at a notch in a shell the inherent consequences of initial curvature are the presence of an interaction between bending and stretching and the presence of higher stress levels than those found in a similarly loaded flat plate. Thus the apparent reduced resistance to fracture initiation of a curved panel is due to local bending caused by this bending-stretching coupling. The data therefore need to be corrected for the effects of curvature. Folias was able to obtain solutions for the stress field around a slit in an isotropic cylindrical shell in an asymptotic form. The solution is dependent on a shell parameter, h, defined as: X2 = a2[12( 1 - v2)]'/2 Rh

(3)

63.50 57-15 44.45 44-45 31-75 31- 75 38.10 38-10 50-80 44~45 44-45 50-80

69-85 63-50 50-80 50-80 38-10 38-10 44-45 44-45 57-15 50-80 50-80 57-15

0-896 0-896 1.170 1-170 1-450 1.450 1-170 1-170 1-170 1-170 1-170 1-170 B1 B2 B3 B4 B5 B6 B7

Cylinder number 50-80 57-15 44.45 44-45 44-45 31.75 31-75

57-15 63-50 50.80 50-80 50-80 38.10 38-10

0-896 0.896 1.170 1.170 1.170 1.450 1-450

Pressure at failure (MPa)

aThe letter R followed by a number indicates that the cylinder had circumferential reinforcements of the type indicated.

A1 A2 A3 A4 A5 A6 A7-R1 ~ A8-R1 A9-R2 A10-R2 A1 l - R 3 A 12-R3

Cylinder number

Largest blade size which Blade size did not cause which caused failure failure (ram) (mm)

Largest blade size which Blade size did not cause which caused failure failure (mm) (mm) Pressure at failure (MPa)

(45, O)s

(0, 45)s

TABLE 2 Results of Pressurized Cylinder Tests

p,

¢5

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where a is the half-slit length, v is the Poisson's ratio, R is the cylinder radius and h is the cylinder thickness. Composite materials are generally anisotropic, however, so that the isotropic solution will not apply for most laminates. Erdogan e t al. 21"22 have expanded the analysis of cracks in cylindrical shells to include

54~ s)On(4d5D 0')A sTA EXPERIMENTAL

(3_ o

. hi 131 :::D

5

~

~

N

CORRELATION

2--

-PLATE

u') ua rF

/ ~ y F O L I A SFOLA IS

a-

CORRECTION

KRENK CORRECTION SHELL I

0

20

I

I

40 60 SLIT LENGTH 2A, mm

I

I

80

I00

l~g. 6. Plot of experimental data for unreinforced cylinders and M a r L i n failure predictions: both uncorrected (plate) and corrected (shell) for curvature effects.

material with a special orthotropy, such as titanium. A material is defined as specially orthotropic if it satisfies the condition: (ELET) 1/2

GLT

=

211 + (VLTVTL)1/2]

(4)

where the subscripts L and T represent the properties in the longitudinal and transverse directions, respectively, q3ais special orthotropy is an in-plane condition and should not be confused with the special orthotropy of bending problems where the bending-stretching coupling terms are zero. Materials satisfying the in-plane special orthotropy must also satisfy the out-of-plane special orthotropy for the analysis to apply. Krenk 23was

Michael J. Graves, Paul A. Lagace

86

able to obtain an asymptotic solution with a shell parameter incorporating this special orthotropy: k2 = a2[12(1 - vLrv-rL)(ET/EL)] ~/2 Rh

(5)

in order to determine the stresses around the crack. This solution includes the effects of transverse shear. This solution is not explicit in the param e t e r h, but involves integrals which must be evaluated numerically depending upon the value of h. However, this parameter is very important in that shells with the same value of h will have the same stress field at slits. Elastic analysis of the laminates used in this investigation was carried out via classical laminated plate theory with the elastic constants determined in Ref. 24: EL = 72"0 GPa ET = 72.0 GPa VLT = 0"06 V~ = 0"06 GLT = 4"5 GPa /ply -- 0-35 mm w h e r e the subscripts L and T refer to the longitudinal (warp) and transverse (fill) directions, respectively, of the basic fabric ply, and tp~yis the ply thickness. The two laminates used in this investigation satisfy the condition of special orthotropy expressed in eqn (4). Thus, the solution of Krenk can be used to correct for the effects of curvature. These laminates are also quasi-isotropic. Thus both the isotropic correction from Folias and the correction from Krenk have been applied to the flat plate data correlation and plotted in Fig. 6. It can be seen that both the isotropic and specially orthotropic corrections coupled with the M a r L i n equation yield an excellent correlation for the cylinder data. The specially orthotropic correction by Krenk does yield some improvement over the isotropic solution by Folias for these composite cylinders. However, in order to apply this method to general laminated cylinders, the generally orthotropic stress state must be known for the slit in a

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cylinder in order to use a generally orthotropic correction for the effects of curvature. At present, this solution does not exist.

6 FAILURE MODES In all cases, the failure of the cylinders was catastrophic, often leaving the cylinder in several pieces. The specimens were 'reconstructed' after failure and the damage path and mode observed. For the cylinders made of the (0, 45)s laminate, the primary fracture path proceeded axially from each end of the slit in a symmetric manner. After reaching a length of approximately 250 mm, the fracture path branched at ---45° angles and continued to the endcaps. This is represented schematically in Fig. 7(a). The cylinders made of the (45, 0)s laminate showed a primary fracture path which extended roughly along the axial direction. There was a tendency for these specimens to shatter into smaller pieces than the (0, 45)= specimens. Only one specimen of the (45, 0)~ type exhibited the (cI~

(b)

1~. 7. Failure modesof (a) (0,45)~and (b) (45,0)~unreinforeedcylinders.

88

Michael J. Graves, Paul A. Lagace

j

J4

76ram

J 76mm

Fig. 8. Failure modes of (0,45), cylinders with (a) reinforcement types 1 and 2 and (b) reinforcement type 3.

significant branching observed for the (0, 45)~ specimen. Any branching which occurred in the (45, 0)~ cylinder was restricted to an area near the endcaps, as illustrated in Fig. 7(b). The fracture modes observed for both laminates were independent of the notch size which was introduced. The reinforcements in six (0, 45), cylinders were not successful in arresting fracture. However, in two of the three reinforcing arrangements (refer to Table 1) the fracture path was significantly altered. For the reinforcement type 3 of tape interleaved with the fabric the fracture mode was the same as in the unreinforced case (Fig. 7(a)). This is represented in Fig. 8(b). For reinforcement types 1 (four plies of tape on the outer surface) and 2 (two plies of tape on the outer surface, two on the inner surface), the fracture path did not branch and continue to the endcaps. For these cases, the fracture path branched at 90° angles just before reaching the reinforcement band and ran around the cylinders approximately along the reinforcements extending slightly into these bands as

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illustrated in Fig. 8(a). It is important to note that these reinforcements did not alter the critical blade size for a given pressure level. This can be seen by examining the data for the unreinforced cylinders and those for the reinforced cylinders in Table 2.

7 CONCLUSIONS An analysis method has been presented by which the failure of pressurized graphite/epoxy cylinders with slits can be predicted using the data from fiat plate tests. This involves the use of a correction to take into account the local stress intensification due to curvature at the slit. The data from the cylinder tests correlate well using this procedure. However, this procedure can only be used for a small subset of possible composite laminates, those which are specially orthotropic. It is recommended that further study be undertaken to produce similar methods by which to correct for curvature effects in generally anisotropic cylinders. The failure modes of the tubes were also observed to change with laminate stacking sequence. In addition, the path of fracture was altered by placing circumferential reinforcements of certain stacking sequences. These reinforcements did not, however, prevent the catastrophic failure of the cylinders. Further work should also concentrate on developing methods by which the fracture process can be arrested thereby resulting in damage tolerant designs. The experiments conducted herein used a guillotine mechanism with various blade sizes at predetermined pressure levels. Although this method did work well, the data obtained are in terms of a region of notch sizes where the pressure is critical rather than a specific critical notch size at a given pressure. Future investigators should develop a means to introduce a slit into the cylinder, seal this slit without structurally reinforcing the cylinder, and then pressurize the cylinder. 'Point' data could be obtained in this manner.

ACKNOWLEDGMENT The authors wish to acknowledge the support of the United States Air Force, AFSC/Aeronautical Systems Division, Wright-Patterson Air Force Base under Contract No. F33615-77-C-5155. Dr Stephen W. Tsai was the contract monitor.

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MichaelJ. Graves, PaulA. Lagace REFERENCES

1. Military Standard 1530A (USAF), Air structural integrity program, airplane requirements, August 1, 1975. 2. Swift, T., Damage tolerant analysis of redundant structures, Fracture mechanics design methodology, AGARD Lecture Series Number 97, 1978. 3. Swift, T., Design of redundant structures, Fracture mechanics design methodology, A G A R D Lecture Series Number 97, 1978. 4. FAA Advisory Circular, Composite aircraft structure, AC20-107, July 10, 1978. 5. Olster, E. F. and Roy, P. A., Tolerance of advanced composites to ballistic damage, Composite materials: testing and design (third conference), ASTM STP 546, 1974, pp. 583-603. 6. Ghatia, N. M. and Verette, R. M., Crack arrestment of laminated composites, Fracture mechanics of composites, ASTM STP 593, 1975, pp. 200-14. 7. Sendeckyj, G. P., Concepts for crack arrestment in composites, Fracture mechanics of composites, ASTM STP 593, 1975, pp. 215-26. 8. Konishi, D. Y. and Lo, K. H., Flaw criticality of graphite/epoxy structures,

Nondestructive evaluation and flaw criticality for composite materials, ASTM STP 696, 1979, pp. 125 4A.. 9. Almard, E. Q., Emburg, J. D. and Wright, E. S., Fracture in laminated materials, Interfaces in composites, ASTM STP 452, 1968, pp. 107-29. 10. Mullin, J. W., Berry, J. M. and Gatti, A., Some fundamental fracture mechanisms applicable to advanced filament reinforced composites, Journal of Composite Materials, 2 (1968) 82-103. 11. Mar, J. W. and Lagace, P. A., Tensile fracture of graphite/epoxy laminates with holes, Advances in composite materials, Vol. 1, Ed. by A. R. Bunsell, Oxford, Pergamon Press, 1980, pp. 130--45. 12. Daniel, I. M., Biaxial testing of graphite/epoxy composites containing stress concentrations--Part I, AFML-TR-76-244, December, 1976. 13. Soden, P. D., Leadbetter, D., Griggs, P. R. and Eckold, G. C. The strength of a filament wound composite under biaxial loading, Composites (October, 1978) 247-50. 14. Daniel, I. M., Liber, T., Vanderby, R. and Killer, G. M., Analysis of tubular specimen for biaxial testing of composite laminates, Advances in composite materials, Vol. 2, Ed. by A. R. Bunsell, Oxford, Pergamon Press, 1980, pp. 900-13. 15. Graves, M. J., The catastrophic failure of pressurized graphite~epoxy cylinders, PhD thesis, M.I.T. Department of Aeronautics and Astronautics, September, 1982. 16. Mar, J. W. and Lin, K. Y., Fracture of boron/aluminium composites with discontinuities, Journal of Composite Materials, 11 (1977) 405-21, 17. Fenner, D. N., Stress singularities in composite materials with an arbitrarily oriented crack meeting an interface, International Journal of Fracture, 12 (1975 ) 705-21.

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18. Lagace, P. A., Notch sensitivity and stacking sequence of laminated composites, ASTM Seventh Conference: Composite Materials Testing and Design, Philadelphia, Pennsylvania, April, 1984. 19. Lagace, P. A., Delamination failure under tensile loading, Proceedings of the sixth conference on ]ibrous composites in structural design, AMMRC MS 83-2, November, 1983. 20. Folias, E. S., Asymptotic approximations to crack problems in shells, Mechanic's of fracture, Vol. 3, Leyden, Noordhoff International, 1977, pp. 117--60. 21. Erdogan, F., Ratwani, M. and Yuceoglu, U., On the effect of orthotropy in a cracked cylindrical shell, International Journal of Fracture, 10 (1974) 369-74. 22. Erdogan, F., Crack problems in cylindrical and spherical shells, Mechanics of fracture, Vol. 3, Leyden, Noordhoff International, 1977, pp. 161-99. 23. Krenk, S., Influence of transverse shear of an axial crack in a cylindrical shell, International Journal of Fracture, 14 (1978) 123-43. 24. Chang, Y. P. and deLuis, J., Determination of the mechanicalproperties of graphite~epoxy fabric composite, Technology Laboratory for Advanced Composites Report 82-5, M. I. T., May, 1982.