Geometrical relationships between side necking and plastic zone size near a crack tip in ductile metals. Part I: Modified boundary layer solutions

Abstract

ABSTRACTThe plastic zone size is regarded as the measure of a material's resistance, and it also determines the fracture behaviour. Recently, stereo digital speckle photography (SDSP) has been found to be useful for measuring in‐situ the side necking developed on the lateral surfaces of a specimen during a standard fracture test procedure for JIC. Because plastic deformation occurs without any volume change, the in‐plane plastic zone developed around a crack tip should be accompanied by out‐of‐plane deformation, that is, side necking. With the aid of the new measurement technique, side necking is expected to act as a gauge for indicating the plastic zone size. As a preliminary study, the geometrical relationships between side necking and the plastic zone size near a crack tip in ductile metals are explored by using a finite element model with modified boundary conditions. As parameters representing the geometrical similarity between side necking and the plastic zone, the shapes of each region, the distances from the crack tip to the boundaries of each region, rp and rs and the areas of each region, Ap and As are examined for their sensitivities to variables such as mode mixity, hardening exponent and so on. Among them, the areas, Ap and As seem to be the best for application because an excellent linearity between them is maintained in a wide range of mode mixity and load level regardless of the hardening exponent, specimen thickness and yield stress.