A constitutive framework for steady-state creep in coarse-grained zirconium alloys under irradiation

A constitutive framework for steady-state creep in polycrystalline zirconium alloys under neutron irradiation is elaborated. The framework combines a two-scale description with internal variables. The structure of the local constitutive laws within individual grains follows from a thermodynamical formulation accounting for freely migrating defects nucleated by radiation and for deformation produced by dislocation glide and climb, while the structure of the overall constitutive relations for the polycrystalline aggregate follows from homogenisation. The resulting description is thermodynamically consistent and conforms to the generalised standard material model. A special class of constitutive laws is generated using convex dissipation potentials reproducing the mean-field reaction rate theory. The relations are nonlinear and reflect an inherent coupling between irradiation creep and growth; however, they admit partial linearisation even for moderate stress levels. Some implications for mechanistic creep models of common use are discussed.