A dislocation density-based viscoplasticity model for cyclic deformation: Application to P91 steel

To describe the viscoplastic behavior of materials under cyclic loading, a dislocation density-based constitutive model is developed based on the unified constitutive theory in which both the creep and plastic strain are integrated into an inelastic strain tensor. The stress evolution during cyclic deformation is caused by the mutual competition and interaction between hardening and recovery. To incorporate the physical mechanisms of cyclic deformation, the change of mobile dislocation density is associated with inelastic stain in the proposed model. The evolution of immobile dislocation density induced by strain hardening, dynamic recovery, static recovery and strain-induced recovery are simulated separately. The deterioration of yield strength following the hardening in tension (or compression) and subsequently in compression (or tension) is described by the Bauschinger effect and reduction of immobile dislocation density, the latter is induced by static- and strain-induced recovery. A kinematic hardening law based on dislocation density is proposed, both isotropic hardening and softening are described by determining the evolution of hardening parameters. The experimental data of P91 steel under different strain rates and temperatures are adopted to verify the proposed model. In general, the numerical predictions agree well with the experimental results. It is demonstrated that the developed model can accurately describe the hardening rate change, the yield strength deterioration and the softening under cyclic loading.