An enhanced Francois distortional yield model: Theoretical framework and experimental validation

A distorted yield surface with a higher curvature in the preloading direction and a rather flat curve in the reverse direction has been observed in numerous materials that experience a preloading process. To describe such distorted yield surfaces, a novel distortional yield model was proposed. The model involves the distorted stress extended from the original version defined by Francois, and can be theoretically applied to any quadratic or nonquadratic yield functions. The original Hill48 and Barlat91 yield criteria were adopted as representatives in this work, for describing the behavior of different steel and aluminum sheets in a two-stage loading experiment. The experimental outcomes obtained from previous publications were employed for the validation of the model. A case of application in a deliberately designed two-stage loading experiment with annealed 6061 aluminum sheet was presented as well. Distinct yield surface distortion has been observed in the second loading stage at small deformation levels with the prestrained sheet metals, and the surface distortion gradually recovers and stabilizes within a small range of strain thereafter. Additionally, initial distortion is positively correlated with the prestrain level. Associated with a novel evolution rule of back stress, the distorted yield surface, as well as the transient phenomena including the Bauschinger effect, orthogonal softening and permanent softening effects in the second loading stage, was successfully described by the proposed model.