Mechanical response of zirconium—I. Derivation of a polycrystal constitutive law and finite element analysis

Simulating the forming of anisotropic polycrystals, such as zirconium, requires a description of the anisotropy of the aggregate and the single crystal, and also of their evolution with deformation (texture development and hardening). Introducing the anisotropy of the single crystal requires the use of polycrystal models that account for inhomogeneous deformation depending on grain orientation. In particular, visco- plastic self-consistent models have been successfully used for describing strongly anisotropic aggregates. As a consequence, using a polycrystal constitutive law inside finite element (FE) codes represents a considerable improvement over using empirical constitutive laws, since the former provides a physically based description of anisotropy and its evolution. In this work we develop a polycrystal constitutive description for pure Zr deforming under quasi-static conditions at room and liquid nitrogen temperatures. We use tensile and compressive experimental data obtained from a clock-rolled Zr sheet to adjust the constitutive parameters of the polycrystal model. Twinning is accounted for in the description. The polycrystal model is implemented into an explicit FE code, assuming a full polycrystal at the position of each integration point. The orientation and hardening of the individual grains associated with each element is updated as deformation proceeds. We report preliminary results of this methodology applied to simulate the three-dimensional deformation of zirconium bars deforming under four-point bend conditions to maximum strains of about 20%. A critical comparison between experiments and predictions is done in a second paper (Kaschner et al., Acta mater. 2001, 49(15), 3097-3107). Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.