Prediction of hardening effect by irradiation-induced vacancy clusters with dislocation dynamics

Abstract

Development of irradiation hardening models attracts extensive attention in designing nuclear materials. Dislocation dynamics (DD) method is a powerful tool in this field for its advantages of predicting mechanical response with microstructural changes such as dislocation evolution, and its extendibility by incorporating the hardening mechanisms, i.e., the dislocation motion impeded by irradiation-induced defects such as vacancy/interstitial clusters, dislocation loops, precipitates etc. Focusing on the hardening effect contributed by vacancy cluster (VC) that is of high number density even at low irradiation dose, this work develops a VC-dislocation interaction model based on Eshelby's equivalent inclusion method. Specifically, a VC is treated as an inclusion with a certain eigenstrain that gives zero stress inside the VC at the presence of dislocation. By adding the interaction force between VC and dislocation derived using the eigenstrain to dislocation force, we implement this model in open-source DD software ParaDiS. Further, we apply the model to investigate the hardening effect by VCs with varying size and number density. Simulation results show that the hardening by VCs of different sizes is all proportional to the 2/3 power of total number density. To further quantify the hardening effect of VCs, we propose a hardening model which modifies the previous Frediel-Kroupa-Hirsch (FKH) model by making the hardening coefficient in linear relation with VC diameter and introducing an effective diameter that account for size distribution of VCs. The MFKH (modified FKH) model with no free parameter shows good accuracy in predicting VC induced hardening in tungsten comparing with experiments.