In the present study, the crack tip shape effect on near-tip deformation and fields is numerically investigated for a mode I crack under plane strain and small-scale yielding conditions. We explore here the quasi-static deformations of solids characterized by finite strain elastic-viscoplastic material model with bilinear hardening and hardening-softening-hardening hardness functions. For comparative analyses, both plastically incompressible and plastically compressible solids have been considered. It has been observed that the crack tip shape can have great consequence on the near-tip deformation and plastic fields. As the crack tip radius is increased, the plastic strain and stresses advance more to the tip of a crack as compared to the crack surface. It has also been revealed that the combination of crack tip curvature radius, material softening and plastic compressibility provides some useful and fundamental information for the near-tip deformation and plastic fields.

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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.