Slip-band propagation at the tip of an edge crack during plastic deformation

Abstract

Experimental investigations indicate that in many cases under plane deformation, the initial plastic strains in the vicinity of a separation crack are localized along two narrow bands at an angle of approximately 45° to the line of the crack [9]. Methods of solving elastoplastic problems in which these plasticity bands (slip bands) are modeled by fracture lines of tangential displacements have been developed in fracture mechanics; in that case, tangential stresses equal to the yield point in shear τ_y are assigned to these lines [2]. The problem of the development of slip bands then reduces to solution of the plane problem of the theory of elasticity for a branched notch; in that case, the dimensions and orientation of lateral branching corresponding to plasticity bands are determined during the solution. A series of results [1, 5, 6, 8, 10–16] for an infinite plane with a separation crack, where the slip bands are located symmetrical bout the line of the crack, have been obtained in this segment. In our study, we solve the plane elastoplastic problem (plane deformation) for a half space with an arbitrary oriented edge crack under an arbitrary load. Numerical results are obtained for a constant pressure on the crack or tensile forces at infinity.