Plastic flow localization resulting from yield surface vertices: crystal plasticity and corner theories of plasticity

This article describes the fundamentals and importance of the yield surface vertex effects in plastic flow localization predictions. The yield surface vertex effects are inherent in crystal plasticity based on Schmid law and have been elaborated in phenomenological corner plasticity theories. First, the theoretical importance, experimental evidence and modeling strategies of the yield surface vertices are presented. Next, plastic flow localization analyses using the yield surface vertex effects in previous studies are reviewed. Both full-field analyses by the finite element method and simplified analyses (i.e., Marciniak–Kuczynski-type of approach) are considered. It is also to be noted that conventional plasticity theories (including both phenomenological and crystal plasticity theories) do not involve any intrinsic material length-scale effects. This could lead to drawbacks in applications and plastic flow localization analyses, because these theories do not enable to predict shear bands with width of finite size. We conclude with the presentation and review of recent developments of gradient-enhanced vertex-type plasticity and crystal plasticity theories.