A strain components-based Mohr–Coulomb fracture criterion for proportional loading

Abstract

Ductile fracture criteria are crucial in the application of elastoplastic materials like advanced high-strength steels, particularly due to their tendency to fail without significant localized necking. It is aimed to figure out the unified mechanism for ductile fracture and accurately describe it with phenomenological criteria. In this study, the effect of the stress triaxiality and the Lode parameter is analyzed mathematically. The maximum shear strain and the normal strain to fracture are emphasized in the proposed strain components-based Mohr–Coulomb fracture criterion particularly designed for plane stress states, and it is assumed that fracture occurs when the combination of the maximum shear strain and the normal strain reaches the critical value. It is then extended to describe fracture with the equivalent plastic strain and the normal strain to fracture. The experimental fracture data of AA 2024-T351 and the additively manufactured Ti-6Al-4V titanium alloy are used to verify the proposed models. A fracture forming limit diagram comprising forming limit curves calibrated from stress states under different stress triaxialities is proposed based on the proposed fracture criteria for plane stress states. This study shows that a strong correlation between the maximum shear strain and the normal strain to fracture has been observed, and it can be described piecewise-linearly. Besides, the orientation of the fracture surface under both tension (including plane strain tension) and compression (including plane strain compression) can be qualitatively explained by the Mohr’s strain circles. The results provide a new insight into the intrinsic deformation and fracture mechanism of materials that fail without severe localized necking.