On plastic crack driving force in crystal-plasticity phase-field fracture model

Abstract

Coupled crystal-plasticity phase-field (CPPF) fracture models could potentially forecast short crack propagation, but there is no consensus on the crack driving force (CDF) from the plastic contribution among existing CPPF fracture models. Herein, we systematically investigate CPPF fracture models with four types of plastic CDFs and identify these models’ capability in simulating crack propagation in single crystal. These models comprehensively account for various CDFs arising from plastic dissipated energy (${\psi }^{\text{p,diss}}$), plastic locking energy (${\psi }^{\text{p,lock}}$), defect energy (${\psi }^{\text{p,defect}}$), and ${\psi }^{\text{p,diss}}$ combined with critical energy release rate ($G_{\text{c}}$) reduction. The objective is to assess the rationality and distinctions among different CPPF fracture models in simulating the fracture of single crystal and analyze the change of plastic strain and plastic energy during crack propagation. It is found that in a single-edge notched face-centered cubic single-crystal copper subjected to tension along [001] direction, the CPPF fracture models with CDF from ${\psi }^{\text{p,diss}}$ and ${\psi }^{\text{p,defect}}$ can only reproduce the brittle-like type-I cracking with crack path perpendicular to [001] axis. This is attributed to that both ${\psi }^{\text{p,diss}}$ and ${\psi }^{\text{p,defect}}$ are much lower than elastic energy (${\psi }^{\text{e}}$) and thus ${\psi }^{\text{e}}$ dominates the cracking behavior. In contrast, CPPF fracture models with CDF from ${\psi }^{\text{p,lock}}$ and ${\psi }^{\text{p,diss}}$ with $G_{\text{c}}$ reduction can replicate the ductile cracking with crack path along the slip direction (45 ° to [001] axis), agreeing with experimental observations. The model with ${\psi }^{\text{p,lock}}$ is further demonstrated rational in predicting both brittle and ductile fracture. In addition, the model is utilized to simulate the crack propagation in polycrystalline copper, further validating its potential applicability in polycrystalline materials. Our work has clarified the role of different types of plastic CDFs in CPPF fracture model and could shed light on the CPPF modeling of short crack propagation in metals.