Atomic mixed-mode cohesive-zone dual constitutive laws of impurity-embrittled grain boundaries in polycrystalline solids via nanoscale field projection method

Abstract

Atomic-scale mixed-mode intergranular fracture, featured by non-local non-linear discrete atomic debonding processes near a crack tip along a grain boundary (GB), is modeled with a cohesive zone in a continuum scale controlled by cohesive-zone dual constitutive relations, a balanced traction-separation relationship, i.e., a conventional cohesive-zone law (CZL), and an unbalanced traction (UT)-centerline displacement (CD) relationship. In order to bridge two different scales, we developed a nanoscale field projection method (nano-FPM) based on atomic-scale interaction J and M integrals, for which asymptotic anisotropic elastic fields near an interfacial crack with balanced and unbalanced crack-face tractions are used as probing fields of the CZL and UT-CD relationship, respectively. Cracking phenomena along a GB in nickel with segregated sulfur impurity atoms under mixed-mode loadings are simulated with molecular dynamics. Embrittlement by sulfur impurity atoms is quantitatively estimated with the mixed-mode CZL of the GBs in nickel via the nano-FPM developed in this study. UT-CD relationship, a special feature of atomic fracture, representing the micromechanical change of surface stress between GB and cracked surfaces, is also obtained by the nano-FPM. New functional relationships for CZL, UT-CD relationship, and decohesion potential obtained by the nano-FPM are proposed to facilitate the implementation of them into mesoscale or continuum-scale analysis on mixed-mode intergranular fracture.