On the Effect of Anisotropy and Inertia on Shear Banding: Instability of Biaxial Stretching

The instability of biaxial stretching leading to the development of shear bands in viscoplastic materials with both isotropic hardening and kinematic hardening is examined. The main issues are to evaluate the effect of anisotropy and inertia on the onset of instability and to examine the development and evolution of an inhomogeneous deformation structure, using both a linear analysis and a nonlinear finite element analysis. It is shown that the back stress and plastic spin, modeling deformation induced anisotropy and texture development, have a significant influence on the critical state at which the first instability occurs. The corotational rate of the back stress and its relation to the spin of the substructure produces apparant softening, causing instability at positive strain hardening (in the absence of back stress and corotational rates instability occurs at zero hardening). When decreasing the magnitude of the spin of the substructure by varying the plastic spin parameter the critical value of the hardening parameter decreases towards zero, illustrating again the softening effect of the spin. It is also shown that at the onset of instability, the linear analysis predicts the development of a periodic structure of square cells, implying that although the deformation has become inhomogeneous it is far from being localized. The nonlinear finite element analysis also predicts the formation of a square cell pattern at the onset of instability. This pattern however evolves into localized shear bands far into the post localization regime as shown by the nonlinear analysis.