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

The 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 J_IC . 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, r_p and r_s and the areas of each region, A_p and A_s are examined for their sensitivities to variables such as mode mixity, hardening exponent and so on. Among them, the areas, A_p and A_s 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.