Kinetics of evolution of radiation induced micro-damage in ductile materials subjected to time-dependent stresses

• Evolution of radiation induced damage under mechanical loads in solids is investigated.
• Clusters of voids generated by irradiation and subjected to inelastic fields are described.
• Two kinetic laws of damage evolution are compared: Rice & Tracey and Gurson models.
• Additive formulation for radiation induced and mechanical damage fields is applied.
• Closed form analytical solutions for damage evolution under cyclic loads are obtained.

The present paper aims at predicting evolution of radiation induced damage in the solids subjected to mechanical loads beyond the yield stress. Moreover, the evolution of radiation induced damage is combined with the evolution of mechanically induced damage within the common framework of Continuum Damage Mechanics (CDM). An additive formulation with respect to damage parameters (tensors) has been postulated. Multiscale constitutive model containing strong physical background related to the mechanism of generation of clusters of voids in the irradiated solids has been built. The model is based on the experimental estimation of concentration of lattice defects (interstitials, di-interstitials, interstitial clusters, vacancies, di-vacancies, vacancy clusters) in Al as a function of dpa (displacement per atom), and comprises the relevant kinetics of evolution of radiation induced damage under mechanical loads. Two kinetic laws of damage evolution were taken into account: the Rice & Tracey model and – for comparison – the Gurson model. As an application, estimation of lifetime of a cylindrical shell (coaxial target embedded in a detector of particles) subjected to combination of irradiation and mechanical loads, has been carried out. It is demonstrated that the number of cycles to failure depends strongly on the accumulation of micro-damage due to irradiation. The lifetime of irradiated components has been expressed as a function of two parameters: maximum dpa and axial stress amplitude on cycle.