Quasi-statically growing crack tip fields in plastically compressible hardening-softening-hardening solid

Abstract

Purpose As the normality concept for frictional dilatant material has a serious drawback, the key feature in this numerical study is that the material here is characterized by elastic-viscoplastic constitutive relation with plastic non-normality effect for two different hardness functions. The paper aims to discuss this issue. Design/methodology/approach Quasi-static, mode I plane strain crack tip fields have been investigated for a plastically compressible isotropic hardening–softening–hardening material under small-scale yielding conditions. Finite deformation, finite element calculations are carried out in front of the crack with a blunt notch. For comparison purpose a few results of a hardening material are also provided. Findings The present numerical calculations show that crack tip deformation and the field quantities near the tip significantly depend on the combination of plastic compressibility and slope of the hardness function. Furthermore, the consideration of plastic non-normality flow rule makes the crack tip deformation as well as the field quantities significantly different as compared to those results when the constitutive equation exhibits plastic normality. Originality/value To the best of the authors’ knowledge, analyses, related to the constitutive relation exhibiting plastic non-normality in the context of plastic compressibility and softening (or softening hardening) on the near tip fields, are not explored in the literature.