Function of cleavage strength for symmetrical tilt grain boundaries

Abstract

The cleavage strength for grain boundaries (GBs) plays a crucial role in understanding the GBs' behavior and microstructure evolution during deformation. However, its universal discipline remains uncertain, and a quantitative description is currently unavailable. Here we propose the theoretical models to systematically quantify the strength of symmetrical tilt GBs in the discrete atomic perspectives. Specifically, based on the interaction of metallic atomic pairs, the interaction between the arbitrary parallel planes is expressed by considering the atomic pair distribution on both sides of the separated planes. On this basis, the function of GBs’ cleavage strength is proposed by considering that the interaction at GBs is composed of the interaction of the interfaces that make up GBs and the interaction between mirror atomic pairs at both sides of the symmetry plane. Furthermore, the theoretical prediction of the critical energy release rate Gc for the sharp crack extension is proposed based on the present cleavage strength function. All the theoretical models are validated by the ab initio simulations or citations. This work quantitatively proposes the cleavage strength function of symmetrical tilt GBs, predicts the critical energy release rate for cleavage, and provides a new methodology for studying mechanical properties of materials in the discrete atomic perspectives.