Exploration of subsequent yield surfaces through unit cell simulations

Subsequent yield surfaces of ductile solids, pre-strained in shear and/or tension, exhibit various characteristic features that depend on the proof strain used to detect yield. These features include kinematic hardening when the proof strain denoting yield is low, isotropic hardening when it is high, formation of a ‘nose’ in the loading direction and flattening of the rear part of the yield surface. With the aid of a computational homogenisation scheme that allows application of arbitrary macro stress or macro deformation gradient to a unit cell, we show that essential features of the subsequent yield surfaces owe their origin to the extent of plasticity accumulated within the unit cell. For instance, a simple unit cell containing a spherical void, where the void serves to create a heterogenous distribution of plastic strain, suffices to computationally reproduce the experimentally observed features. Moreover, in contrast to experiments which generally allow plotting of the yield surface in a normal stress – shear stress plane, the computational scheme allows fuller exploration of the subsequent macro yield surface in the macro stress space. We find that what seems to be a translation and distortion of the yield surface in experiments, is actually most pronounced near some critical octahedral planes characterised by levels of triaxiality induced by the pre-straining process. The evolution of the yield surface in regions where the triaxiality is higher is considerably different. Moreover, as homogeneous yielding is approached with loading of the unit cell, the material seems to forget the nature of the pre-straining process and undergoes isotropic hardening.