A single crystal constitutive law for multiple slip and twinning in single-phase hexagonal close-packed materials was developed. For each slip-mode, a dislocation population was evolved explicitly as a function of temperature and strain-rate via thermally-activated recovery and debris formation. The associated hardening included stage-IV. A stress-based hardening law for twin activation accounted for temperature effects via its interaction with slip dislocations. For comparison with macroscopic measurements, this single-crystal law was implemented into a visco-plastic-self-consistent polycrystal model which accounted for texture evolution and contained a sub-grain micro-mechanical model for twin reorientation and morphology. Slip- and twinning-dislocations interacted with the twin boundaries via a directional Hall–Petch mechanism. The model was adjusted so as to predict the plastic anisotropy of clock-rolled pure Zr for 3 different deformation paths and at 4 temperatures ranging from 76 to 450K (at a quasi-static rate of 10−3/s). The model captured the transition from slip-dominated to twinning-dominated deformation as the temperature decreased, and identified microstructural mechanisms, such as twin nucleation and twin–slip interactions.

A Dislocation-Based Constitutive Law for Pure Zr Including Temperature Effects. I.J.Beyerlein, C.N.Tomé: International Journal of Plasticity, 2008, 24[5], 867-95