A discrete–continuous model of coupled plasticity and fracture

Understanding the interplay between plasticity and fracture is the basis for the prediction and design of materials and structures, which is controlled by the concurrent dynamics of discrete dislocations and cracks. However, till now, how to directly capture the co-evolution of a three-dimensional (3D) discrete dislocation network and arbitrary crack remains challenging due to their intrinsic complex interactions and different modeling frameworks. To overcome these issues, we proposed a discrete–continuous coupled plasticity–fracture model in a thermodynamic consistent framework, which can not only reproduce the discrete crack–dislocation interdependence dynamics, but also demonstrate capability and flexibility in handling complex boundary value problems by simultaneously considering the co-evolution of continuous plasticity and fracture field. This model offers many advantages, including accurately capturing the image force of the crack surface on dislocation, the shielding and anti-shielding effect of 3D dislocation on crack propagation, as well as reproducing arbitrary crack propagation without reliance on a predefined crack path. As a representative example, a notched microbeam bending problem is studied and compared with experiments, yielding new insights regarding the 3D co-evolution of collective defects and their influence on mechanical response.