Scattering on a square lattice from a crack with a damage zone

A semi-infinite crack in infinite square lattice is subjected to a wave coming from infinity, thereby leading to its scattering by the crack surfaces. A partially damaged zone ahead of the crack-tip is modeled by an arbitrarily distributed stiffness of the damaged links. While the open crack, with an atomically sharp crack-tip, in the lattice has been solved in closed form with help of {the} scalar Wiener-Hopf formulation (SIAM Journal on Applied Mathematics, 75, 1171--1192; 1915--1940), the problem considered here becomes very intricate depending on the nature of damaged links. For instance, in the case of partially bridged finite zone it involves a $2\times2$ matrix kernel of formidable class. But using an original technique, the problem, including the general case of arbitrarily damaged links, is reduced to a scalar one with the exception that it involves solving an auxiliary linear system of $N \times N$ equations where $N$ defines the length of the damage zone. The proposed method does allow, effectively, the construction of an exact solution. Numerical examples and the asymptotic approximation of the scattered field far away from the crack-tip are also presented

HR-EBSD analysis of in situ stable crack growth at the micron scale

Understanding the local fracture resistance of microstructural features. such as brittle inclusions, coatings, and interfaces at the microscale under complex loading conditions is critical for microstructure-informed design of materials. In this study, a novel approach has been formulated to decompose the J-integral evaluation of the elastic energy release rate to the three-dimensional stress intensity factors directly from experimental measurements of the elastic deformation gradient tensors of the crack field by in situ high (angular) resolution electron backscatter diffraction (HR-EBSD). An exemplar study is presented of a quasi-static crack, inclined to the observed surface, propagating on low index {hkl} planes in a (001) single crystal silicon wafer