A hierarchical multi-scale model for hexagonal materials taking into account texture evolution during forming simulation
Due to the absence of sufficient number of slip systems in hexagonal close packed (hcp) metals to accommodate arbitrary plastic deformation, mechanical twinning occupies an important role in the mechanical behavior of these metals. Twinning causes a significant and abrupt change in the orientation of crystals, whilst simultaneously affecting the hardening and plastic flow behavior of the material considerably. Modeling of forming processes of hexagonal close packed metals thus requires accounting for the evolution of texture and texture induced anisotropy, especially due to twinning. Additionally, the computational framework for the simulation of forming processes must be reliable and efficient in order to guarantee results in realistic time frames. In the present work, a phenomenological constitutive model consisting of an anisotropic yield function, associate flow rule and isotropic hardening, is coupled with the viscoplastic self-consistent polycrystal model in order to capture the slip and twinning activity, texture evolution and the evolving anisotropy during plastic deformation of hcp materials, similar to a hierarchical multi-scale modeling framework proposed by Van Houtte et al.  for cubic metals. To account for texture evolution during plastic deformation, the parameters involved in the anisotropic yield function are regularly updated based on mechanical test data obtained from the polycrystal model at the micro-scale. The parameter update is performed at discrete steps instead of every increment. The developed model is applied to describe the behaviors of pure zirconium at liquid nitrogen temperature. The results of the numerical simulations were found to be good agreement with experimental results, and at acceptable computation time.