Strain-rate potential based elastic/plastic anisotropic model for metals displaying tension–compression asymmetry

Theoretical description of plastic anisotropy requires the definition of either stress potentials or plastic strain-rate potentials. In general, strain-rate potentials are more suitable for process design. Existing strain-rate potentials (phenomenological or texture-based) are applicable only to the description of the plastic behavior of materials with cubic crystal structure. Very recently, Cazacu et al. [9] have developed an orthotropic strain-rate potential applicable to metals that display tension–compression asymmetry when subjected to monotonic loading (e.g. hexagonal metals). This strain-rate potential is the exact work-conjugate of the anisotropic stress potential of Cazacu et al. [8]. In this paper, an elastic/plastic formulation based on the proposed strain-rate potential and a fully implicit time integration algorithm for this potential are presented. Finite-element tube bending simulation results demonstrate the capabilities of the model to represent the effects of the anisotropy and tension–compression asymmetry of the material on its mechanical response. If a material has the same yield in tension and compression, the strain-rate potential reduces to that proposed by Hill [17]. Further, validation of the robustness and accuracy of the integration algorithm is performed by using this new model and Hill [17] to simulate a circular cup drawing test of a steel plate.