An efficient full-field crystal plasticity-based M-K framework to study the effect of 3D microstructural features on the formability of polycrystalline materials

In this paper, the new rate tangent-fast Fourier transform-based elasto-viscoplastic crystal plasticity (CP) constitutive framework (RTCP-FFT) developed by Nagra et al (2017 Int. J. Plast. 98 65-82) is implemented in the so-called Marciniak-Kuczynski (M-K) (Marciniak and Kuczynski 1967 Int. J. Mech. Sci. 9 609-20) framework to predict the forming limit diagrams (FLDs) of face-centered cubic polycrystals. The RTCP-FFI approach that accounts for 3D grain morphologies and grain interactions is used to compute the FLDs for aluminum alloys (AAs). The model employs two statistically representative volume elements with identical initial microstructures, one inside the imperfection band region (required for M-K analysis) and other outside the imperfection band region of the sheet metal. The proposed RTCP-FFI -based M-K model is a full-field, mesh-free and efficient CP formulation that enables a comprehensive investigation of the effects of 3D microstructural features on the FLDs with extremely small computational times. The new model is validated by comparing the predicted FLDs for AA5754 and AA3003 AAs with experimental measurements. Furthermore, the predicted FLDs are compared with the well-known Taylor-type homogenization scheme-based M-K model (MK-Taylor) predictions. Furthermore, the effects of different grain shapes as well as local grain interactions on the FLD predictions are studied. The study reveals that among the various microstructural features, the grain morphology has the strongest effect on the predicted FLDs and the FLD predictions can be significantly improved if the actual grain structure of the material is properly accounted for in the numerical models.