The effect of dislocation density on the forming limit curve predicted with the crystal plasticity method

One of the most important and widely used tools to predict the behavior of sheets is the Forming Limit Diagram (FLD). The m-k model is one of the prediction methods, which can be combined with the phenomenological or the crystal plasticity equations to achieve the desired results. In this research, to predict the forming limit diagram, the direct combination of the m-k method with the crystal plasticity has been applied. The direct method is chosen due to the particular state of the mathematical equations associated with FLD. A Face-Centered Cubic (FCC) polycrystalline metal has been used here, so, the Taylor method for the polycrystals can be used. Although this method ignores the interactions between the crystals to describe plasticity, it can also reduce the computational cost by simplifying of the strain uniformity theory. In this study, polycrystal plasticity and dislocation method have been merged with a new way. Only the hardening process is modeled based on the dislocation density and its modifications, and the entire analysis is based on the rate-dependent crystal plasticity. For the first time, the forming limit diagram is plotted to take into account the effect of dislocation density, and the results have shown that considering the effect of the dislocation density on the shear strength changes, the forming limit diagram formulation becomes nearer to the experimental values.