Role of Initial Crack Tip Shape, Plastic Compressibility and Strain Softening on Near-Tip Stress-Strain State in Fatigue Cracks during Simulation of a Finite Deformation based Elastic-Viscoplastic Constitutive Model

Deformation and Stress-Strain Fields under Fatigue Loading

Abstract

This paper deals with the effect of initial crack tip shape, plastic compressibility, and strain softening on near-tip stress-strain fields for a mode I crack subjected to fatigue loading under plane strain and small scale yielding. A finite strain-based elastic-viscoplastic constitutive equation with bilinear hardening and hardening-softening-hardening hardness functions is taken up for simulation. It is observed that plastic compressibility and strain softening have a significant impact on crack tip opening displacement (CTOD) and tip propagation. Furthermore, it has been viewed that the initial shape of a crack tip can significantly influence both the CTOD and the crack tip extension for the bilinear hardening material; however, with identical conditions for the hardening-softening-hardening material, the initial crack tip shape affects the fatigue crack growth much lesser though the CTOD is influenced considerably. In comparison to the crack growth in the plastically incompressible hardening-softening-hardening solids, the variation of the crack growth (with respect to the tip curvature radius) is more and peculiar in the corresponding plastically compressible solid. To explain and to get a better insight of the crack tip deformation, the near-tip plastic strain and hydrostatic stress have been illustrated.