Cracks occurring at arbitrary orientations in lamellar composites are studied. The associated boundary value problem is formulated in terms of dual integral equations in which the kernels are found in series form. This series representation of the kernels is shown to converge quite rapidly. Variation of the stress intensity factors with the constituent elastic moduli is presented, and a comparison of calculated values with a Mohr's circle approximation of the stress intensity factors at arbitrary orientations is made. This comparison results in the conclusion that the Mohr's circle approximation is accurate as long as the crack tip is far enough from the bimaterial interface.
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References
1.
Chou, Y.T., "Linear Dislocation Arrays in Heterogeneous Materials,"ACTA Met.,13, 1965, p. 779
2.
. Kaung, J. and Mura, T., "Dislocation Pile-Up in Two Phase Materials,"J. App. Physics, 39, 1968, p. 109
3.
. Kaung, J. and Mura, T., "Dislocation Pile-Up in a Half Space,"J. App. Physics ,40, 1969, p. 5017
4.
. Chou, W.T. and Tetelman, A.S., "Dislocation Arrays and Elastic-Plastic Cracks in a Two-Phase System,"J. Composite Matls.,4, 1970 , p. 222
5.
. Cook, T.S. and Erdogan, F., "Stresses In Bonded materials with a Crack Perpendicular to the Interface,"Int. J. Engrg. Sci., 10, 1972, p. 677.
6.
Erdogan, F. and Gupta, G.D., "The Stress Analysis of Multi-Layered Composites with a Flaw,"Int. J. Solids & Struc.,7, 1971, p. 39
7.
. Erdogan, F. and Gupta, G.D., "Layered Composites with an Interface Flaw,"Int. J. Solids & Struct., 7, 1971 , p. 1089
8.
. Hilton, P.D. and Sih, G.C., "A Laminate Composite with a Crack Normal to the Interface,"Int. J. Solids & Struct.,7, 1971, p. 913
9.
. Tamate, O., and Iwasaka, N., "An Arbitrarily Oriented Crack in a Semi-Infinite Medium with a Surface Layer under Tension,"Int. J. Solids & Struct. , 11, 1975, p. 1257
10.
. Bilby, B.A. and Eshelby, J.D., "Dislocations and the Theory of Fracture," Fracture, Vol. 1, edited by H. Liebowitz, Academic Press , 1968, p. 99.
11.
Vitek, V., "Yielding on Inclined Planes at the Tip of a Crack Loaded in Uniform Tension,"J. Mech. and Phys. Solids, 24, 1976, p. 263
12.
. Riedel, H., "Plasic Yielding on Inclined Slip-Planes at a Crack Tip,"J. Mech. and Phys. Solids, 24, 1976, p. 277
13.
. Vilmann, C.R. , and Mura, T., "Fracture Related to a Dislocation Distribution,"J. Appl. Mech.,46, 1979, p. 817
14.
. Tanaka, K., and Mura, T., "A Dislocation Model for Fatigue Crack Initiation,"J. Appl. Mech. , 48, 1981, p. 97
15.
. Dundurs, J. and Mura, T., "Interaction Between an Edge Dislocation and a Circular Inclusion,"12, 1964 , p. 177
16.
. Atkinson, K.E. , "The Numerical Solution of Fredholm Integral Equations of the Second Kind", SIAM J. Num. Anal.,4, 1967 p. 337
17.
. Atkinson, K.E. , "A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind", SIAM, Philadelphia, 1976
18.
. Bogy, D.B., "On the Plane Elastostatic Problem of a Loaded Crack Terminating at a Material Interface", J. Appl. Mech.1971 , p. 911.
