Crystal plasticity model for UO2: Introduction of the dislocation climbing and coupling with the thermally activated gliding

Abstract

Modelling of viscoplastic behaviour of $U{O}_2$ nuclear fuel at high temperature is of major interest to analyze the risk of cladding failure in power transient condition where pellet to cladding mechanical interaction occurs. In this study, we investigate the impact of dislocation climbing on the viscoplastic behaviour of $U{O}_2$ single crystal at high temperature where climbing mechanism is activated by vacancy diffusion. The modelling framework is that of an existing crystal plasticity law devoted to thermally activated gliding for lower temperatures. The constitutive equation of the crystal plasticity model are modified in order to add dislocation interaction hardening and stored dislocation recovery. The latter is assessed with dynamic recovery induced by cross slip and static recovery induced by dislocation climbing. A phenomenological model is proposed to compute the dislocation climbing velocity and the associated dislocation density recovery rate. The dislocation gliding velocity law is also improved with a physically based formulation introducing the activation energy for a double kink mechanism. The complete model, for low and high temperatures, is built with a harmonic coupling function enabling a more physically based formulation of the constitutive equations devoted to each mechanism. An implicit numerical implementation of the resulting model is proposed with a finite strain formulation in the framework of the MFront open source tool. A first validation of the complete model has been done with experiment/simulation comparisons for single crystal creep compression tests. In this first step, the validation is limited to orientations where only the modes 1 and 2 (soft and hard slip modes) are suspected of having a major contribution to the viscoplastic behaviour. Thanks to the contribution of dislocation gliding, interaction and climbing we can explain the evolution of the compression flow stress as a function of the temperature from 800 °C to 1600 °C in good agreement with experimental results. The physically based formulation gives also a justification of the temperature dependency of the apparent thermal activation energy and of the strain rate sensitivity.