(untitled) (Advances in Applied Mathematics and Mechanics, 2025)
Plastic instability is an inherent property of metal materials, and enhancing the formability of sheet metal can be attributed to the retardation of plastic instability. In this study, we revisited the tensile instability of dual-phase (DP) steel by introducing a novel damage evolution model. Leveraging the theory of plastic instability and continuum damage mechanics (CDM), the instabilities of DP1180 steel sheet were investigated by examining the rotation angle of the uniaxial tensile specimen, which serves as an indicator for the onset of localized necking instability. Based on the hypothesis of elastic modulus equivalence, the damage evolution equation in uniaxial tension was derived mathematically, and the implicit and explicit expressions of the damage evolution were proposed. Furthermore, the relationship between effective stress and equivalent strain in the process of uniaxial tensile test was obtained. It was found that the sharp increase of effective stress was the direct factor leading to the fracture of DP1180 steel sheet. Finally, the mechanism of damage evolution was studied by scanning electron microscopy (SEM), including the nucleation, growth, and coalescence of voids. This study elucidates the mechanisms of tensile instabilities in DP steel sheets and provides a potential damage criterion for localized instability.