| Understanding the evolution of defects in materials under irradiation is important for the design and simulation of radiation-resistant materials.Although experiments and simulations at the micro or macro scales have been extensively studied,a cross-scale continuum model linking different scales remains challenging.In this paper,through multi-scale analysis,the separability of scale in the evolution concerning point defects is derived.With this feature,a three-scale model for the absorption effect of grain boundaries on point defects is established.By analytically solving equations concerning point defects at different scales,and asymptotic matching between the three scales,an equivalent boundary condition for capturing the role of the grain boundary is obtained.This model uncovers the partial absorption of grain boundaries on point defects.Through this model,the sink strength of polycrystalline with respect to its grain size is estimated;meanwhile,with the equations in continuous dislocation dynamics and the grain boundary model represented by dislocations,this paper presents the simulation for the migration of grain boundary,where the asymmetric deformation under irradiation conditions is shown.In addition,a multi-scale model of the interaction between voids/bubbles and point defects in the irradiated materials is set up.In this model,the evolution of voids/bubbles is completely decoupled into a homogenised model which evolves and a micro-evolution model with quasistatic characteristics.In the micro model,the key parameters and mathematical formulas are derived while a machine learning model is trained based on the results of microscale simulation.In the macro level,by establishing equivalent homogenized terms concerning micro-evolution,the evolution equations of voids/bubbles under long-term irradiation is presented.Based on this model,a detailed analysis of the influence of the interface,the external load and the irradiation dose on the growth of voids/bubbles is given. |
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