This paper deals with the influence of initial crack-tip shape, plastic compressibility and material or strain softening on near-tip stress-strain fields for mode I crack when subjected to fatigue loading with an overload event under plane strain and small scale yielding conditions. A finite strain elastic-viscoplastic constitutive equation with a hardening-softening--hardening hardness function is taken up for simulation. For comparison, a bilinear hardening hardness function is also considered. It has been observed that the near-tip crack opening stress σ yy , crack growth stress σ xx , and hydrostatic stresses are noticeably controlled by the initial crack tip shape, plastic compressibility, material softening as well as the overload event. The distribution pattern of different stresses for a plastically compressible hardening--softening-hardening solid appears to be very unusual and advantageous as compared to those of traditional materials. Therefore, the present numerical results may guide material scientists/engineers to understand the near-tip stress-strain fields and growth of a crack in a better way for plastically compressible solids, and thus may help to develop new materials with improved properties.

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.