Practical fracture limit function considering data flexibility under plane-stress conditions in Lagrangian formulation

Ductile fracture limits have been extensively studied from the perspectives of material science and mechanics. While these studies have provided scientifically significant insights into ductile fracture limits, the influence of the evolution of anisotropy observed in actual experimental data suggests a need to account for diversity in the experimental data. To address this, it may be possible to further develop the model by investigating more influences from the field of materials science. However, from an engineering perspective, it can be effective to represent the diversity of acquired experimental data as practical functions for use, rather than solely focusing on the material science aspect. This paper presents mathematical formulations representing the strain- and stress-based fracture limit surfaces of ductile materials, to consider diverse data set for the evolution of anisotropy, under plane-stress conditions within the framework of the Lagrangian formulation. The model introduces a strain-based fracture limit surface (FLS), which has an additional anisotropic profile function based on the commonly used two-dimensional strain-based fracture limit curve (FLC). The anisotropic profile function is capable of capturing the evolving anisotropic profile based on the deformation mode and principal loading direction to represent more flexible shapes. With this function, a three-dimensional strain-based FLS, which can present the variation in fracture strains in the space of the deformation mode and principal loading direction, can be constructed. Then, the proposed model transformed this strain-based FLS into a stress-based FLS by converting the presented state vector in the former into the corresponding vector in the latter in the Lagrangian formulation. To achieve this, this study developed a formulation that considers the nonlinear evolution of stress anisotropy independent of the strain anisotropy during stress evolution. The two proposed models were validated by experimental results on a dual-phase steel. These models provide flexible fracture limit functions for ductile materials under varying stress and strain conditions in engineering applications.