A fracture criterion for finitely deforming crystalline solids—The dynamic fracture of single crystals

The major objective of this work has been to develop, within a continuum framework, a microstructurally-based computational theory to investigate dynamic failure in metals. To model the nucleation and propagation of failure surfaces at the microstructural scale, under large deformations and dynamic loading conditions, general finite-deformation theory, as relating to the decomposition of the deformation gradient, was tailored to monitor displacement incompatibilities and fracture in crystalline solids subjected to large deformations. Based on this proposed decomposition, a general fracture criterion for finitely deforming crystals, using the integral law of incompatibility, was developed. The analyses indicate that this newly proposed fracture formulation and criterion can be validated with experimental results, and can be used to accurately predict brittle and ductile failure modes for the large deformation of single crystals. As part of the newly proposed decomposition of the deformation gradient, sub-problems can also be solved for lattice distortions, such as twinning and geometrically necessary dislocation (GND) densities. Accordingly, the interactions of GND densities with cracks were investigated for single crystals. GND densities were shown to form as loops for stationary crack tips, but no loops formed for propagating cracks.