A concise fracture model for ductile metals: Integration of symbolic regression and strength theory

An ideal fracture model for engineering applications should accurately predict fracture behavior across various ductile metals while maintaining a concise formulation with minimal fitting parameters. By comparing the roles of weak constraints (derived from microscopic mechanism analysis) and strong constraints (based on strength theories) in symbolic regression, two fracture models are proposed: the theory and symbolic regression-based fracture model (TSR-F model) and the extended symbolic regression-based fracture model (ESR-F model). Symbolic regression, when applied under strong constraints, is able to effectively derive generalized fracture model for various ductile metals using limited experimental data. The effectiveness and accuracy of the models are validated through experiments on 26 types of metals, demonstrating their applicability across a wide range of materials and over a broad range of stress triaxiality and Lode angle parameters, where the ESR-F model shows superior performance. Moreover, the performance of the TSR-F model is close to that of the ESR-F model, which indicates the critical importance of incorporating appropriate constraints in symbolic regression. Furthermore, while the strong constraints are introduced through the generalization of the von Mises and Maximum Mohr-Coulomb criteria for isotropic metals, one may be compelled to neglect anisotropy induced under low-triaxiality ductile fracture to avoid overly complicated expressions. This study demonstrates the potential of symbolic regression methods with suitable strong theoretical constraints to develop universal expressions of mechanical models using limited experimental data.