Slip system-resolved GNDs and SEDs: A multi-scale framework for predicting crack nucleation in single-crystal metals

Scalar forms of geometrically necessary dislocation (GND) and stored energy density (SED) are commonly used to capture localized strain gradients and damage in metals. However, these scalar approaches fail to provide detailed information at individual slip systems, thereby diminishing the slip system-dependent features critical to understanding plasticity and damage behavior. Here, we develop methods to resolve GNDs and SEDs onto individual slip systems through experimental techniques including multi-scale digital image correlation (DIC) and electron backscatter diffraction (EBSD), together with multi-scale simulation approaches including crystal plasticity finite element (CPFE) and discrete dislocation plasticity (DDP). These methods are applied to single-crystal (SX) plates with a circular hole, eliminating the interference from grain boundaries. In contrast to the scalar GNDs, the resolved GNDs show pronounced slip system-dependent and asymmetric distributions around the hole circumference. In addition, the resolved GNDs migrate along with the extension of slip band boundaries, with the growth rate accelerating in the later stages of deformation. Furthermore, under the CPFE framework, the GNDs-mediated SEDs successfully capture the asymmetric cracking behavior and crystallographic planes of crack nucleation observed in the in-situ DIC tests, which cannot be reflected in conventional scalar SEDs. Moreover, compared with micro-DIC (μDIC) results, the resolved SEDs in the DDP framework accurately capture the slip trace-induced crack nucleation at the micro-scale. The GND-mediated resolved SEDs demonstrate strong potential as a universal damage indicator for metallic materials, enabling accurate prediction of crack nucleation at the micro-scale.