In this paper, a new full-field numerical framework is proposed to model large strain phenomena in polycrystals. The proposed framework is based on the elasto-viscoplastic (EVP) fast Fourier transform (FFT) formulation presented by Lebensohn et al. (2012) and the rate dependent crystal plasticity framework developed by Asaro and Needleman (1985). In this implementation, the full-field solutions of micromechanical fields are computed on a regular, voxelized representative volume element (RVE) in which either a single or multiple grid points represent a single grain. The Asaro and Needleman (1985) formulation coupled with a semi-explicit, forward gradient time-integration scheme (Peirce et al., 1983) is used to compute local stresses and the FFT-based method is used to find local strain fluctuations at each grid point. The proposed model is calibrated using experimental uniaxial tensile test results of aluminum alloy (AA) 5754 sheet and then used to predict texture evolution and stressstrain response for balanced biaxial tension and plane-strain tension along rolling (RD) and transverse (TD) directions. The predicted stress-strain and texture results show a good agreement with experimental measurements. The CPU time required by the proposed model is compared with the original EVP-FFT model for two separate cases and the proposed model showed significant improvement in computation time (approximately 100 times faster).

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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 Kuczyński 1967 Int. J. Mech. Sci. 9 609–20) framework to predict the forming limit diagrams (FLDs) of face-centered cubic polycrystals. The RTCP-FFT 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-FFT-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.