Frictional interface crack in anisotropic bimaterial under combined shear and compression.
This paper is devoted to the problem of a frictionally sliding interface crack embedded in an infinite anisotropic bimaterial subjected to remote shear and normal compression load. By sliding of the crack surfaces in its own plane, the frictional coefficient is assumed to be constant over the sliding zone. The remote compressive force is applied so that crack faces perpendicular to the sliding direction are assumed to be completely closed. The investigation of this frictional crack problem is carried out by modeling the crack by a continuous distribution of dislocations, and by the superposition technique. The unknown densities of dislocations are chosen so that the boundary conditions of original problem are satisfied. To formulate the above problem, the fundamental solution due to a single concentrated dislocation acting on the crack-free bimaterial is constructed. The problem is reduced to a set of singular integral equations, where the unknowns in the equations are the dislocation densities. Before solving these singular integral equations for the dislocation densities, the stress singularities at the interface crack tip are discussed by adopting the common approach of near-tip expansion method. The characteristic equation for the frictional cracks for general anisotropic bimaterial is obtained. The particular cases of bimaterials (anisotropic, monoclinic and isotropic) are considered to analyse the stress singularity. Then, before the discussion of the general case for bimaterial, the authors consider a homogeneous solid when the crack faces are frictionless, or are not frictionless. It is shown that the satisfaction of the homogeneous anisotropy condition allows the material to transmit normal stress across the crack faces without any interference, even if the surfaces have the roughness property. Finally, the results are obtained in analytic form for monoclinic bimaterial. In this case, the orders of singularities depend on the material constant, frictional coefficient and the direction of the frictional force.
scientific article; zbMATH DE number 2067559