Brittle to quasi-brittle transition and crack initiation precursors in crystals with structural Inhomogeneities

Crack initiation emerges due to a combination of elasticity, plasticity, and disorder, and it displays strong dependence on the material’s microstructural details. The characterization of the structural uncertainty in the original microstructure is typically empirical and systematic characterization protocols are lacking. In this paper, we propose an investigational tool in the form of the curvature of an ellipsoidal notch: As the radius of curvature at the notch increases, there is a dynamic phase transition from notch-induced crack initiation to disorder-induced crack nucleation. We argue that the this transition may unveil the characteristic length scale of structural disorder in the material. We investigate brittle but elastoplastic metals with continuum, microstructural disorder that could originate in a manufacturing process, such as alloying. We perform extensive and realistic simulations, using a phase-field approach coupled to crystal plasticity, where microstructural disorder and notch width are systematically varied. We identify the brittle-to-quasi-brittle transition for various disorder strengths in terms of the damage and stress evolution. Moreover, we investigate precursors to crack initiation that we quantify in terms of the expected stress drops during displacement control loading.