Computationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database. (April 2018) - Gupta, Akash; Ben Bettaieb, Mohamed; Abed-Meraim, Farid; Kalidindi, Surya R.
Abstract: The present investigation focuses on the development of a fast and robust numerical tool for the prediction of the forming limit diagrams (FLDs) for thin polycrystalline metal sheets using a Taylor-type (full constraints) crystal plasticity model. The incipience of localized necking is numerically determined by the well-known Marciniak–Kuczynski model. The crystal plasticity constitutive equations, on which these computations are based, are known to be highly nonlinear, thus involving computationally very expensive solutions. This presents a major impediment to the wider adoption of crystal plasticity theories in the computation of FLDs. In this work, this limitation is addressed by using a recently developed spectral database approach based on discrete Fourier transforms (DFTs). Significant improvements were made to the prior approach and a new database was created to address this challenge successfully. These extensions are detailed in the present paper. It is shown that the use of the database allows a significant reduction in the computational cost involved in crystal plasticity based FLD predictions (a reduction of about 96% in terms of CPU time). Highlights: A computationally efficient tool is developed for predicting Forming Limit Diagrams. Rate-dependent crystal plasticity model using the DFT spectral database is used. A more accurate new spectral DFT database was created and validated. This new tool resulted in 96% reduction in the computational cost for FLD predictions.