Shear banding in strain hardening polycrystals during rolling

Initiation and development of shear band (SB) in f.c.c. strain hardening polycrystals during rolling are modelled in terms of crystallographic texture. The constitutive law of the material is expressed in terms of the texture-dependent normalized yield surface and the critical shear stress which evolves with strain. The normalized yield surface is predicted by the Taylor model as a function of rolling texture. It is shown that a rounded vertex (RV) develops at the loading point as the rolling texture becomes more and more marked. A detailed characterization of the RV is carried out. It is found that the normalized curvature radius of the RV decreases from unity towards zero at very large strain. This allows for a small stress perturbation to induce a shear strain perturbation with a large orientation deviation of deformation. By linearized stability analysis, the condition for initiation of SB from the shear strain perturbation is obtained. Development of SB is analysed by solving the established governing equations of shear banding. It is shown that the conditions for SB initiation and saturation of shear localisation depend strongly on the texture. Based on this model problem, a long discussion is carried out which allows a better understanding of the basic physical origin and saturation of SB in strain-hardening polycrystals, as well as the effects of yield surface curvature and yield surface rotation whose general form is derived.