Modeling and simulation of induced anisotropic hardening and springback in sheet metals during non-proportional loading

Sheet metal forming processes invariably involve non-proportional loading and changes in deformation/loading direction, resulting in a very complex material and structural behaviour. Much of this complexity can be traced back to the reaction of the material microstructure to such loading. In the case of hardening behaviour, for example, the interplay between the direction of inelastic deformation, the orientation of dislocation structures, and the current deformation/loading direction, plays an important role. The purpose of the current work is the formulation, numerical implementation and application of a thermodynamically-consistent material model for anisotropic hardening in such materials taking this interplay into account. Direction- and orientation-dependent quantities are represented in the model with the help of evolving structure tensors. These include the strength of dislocation structures, dislocation polarization, and kinematic hardening. Together with the initial texture-based inelastic flow anisotropy, these govern the evolving anisotropic response of the model to changes in loading direction. To exemplify this, the behaviour of the model subject to typical two-stage loading histories involving monotonic, reversing and orthogonal changes in loading/deformation direction are investigated for various parameter values. These simulations demonstrate clearly the effect of severe and abrupt changes in deformation/loading direction on the hardening behaviour and so on the resulting springback process