anongba, p.n.b. université félix-houphouët-boigny de cocody - u f r sciences des structures de la matière et de technologie, côte d’ivoire

INTERFACE CRACK UNDER MIXED MODE I+II LOADING AND INTERNAL SHEAR STRESS DUE TO POISSON EFFECT: THEORY AND CONFRONTATION WITH EXPERIMENTS

31481

In this study, we analyse an interface crack loaded in mixed mode I + II with an additional internal shear stress that originates from a difference in the magnitudes of the Poisson s contractions present on both sides of the interface. The presence of such an internal shear stress is common in composites under load. The crack is represented by a continuous distribution of two families of edge dislocations with infinitesimal Burgers vectors. The distribution functions of the dislocations at equilibrium satisfy a system of two integral equations with Cauchy-type singular kernels. A solution is given to a class of singular integral equations which, when applied to our modelling, permits to derive closed-form expressions for the dislocation distribution functions and corresponding relative displacements of the faces of the crack, the crack-tip stresses, and the crack extension force. We then proceed to a comparison of theory with experiments with special attention to the work of Liechti and Chai (Journal of Applied Mechanics, 1992) with edge-cracked bi-material epoxy/glass strip specimens in bi-axial loading experiments. Reasonable agreement with experiment is obtained.

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linear elasticity , poisson effect , dislocations , interface crack , singular integral equations , brittle fracture mechanics

Revue Ivoirienne des Sciences et Technologie

44