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

Abstract

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.

A Review of Characterization and Modelling Approaches for Sheet Metal Forming of Lightweight Metallic Materials

“…CP modelling can track the plastic anisotropy of sheet metals by considering textures changes during non-proportional loading [ 238 ]. Thus, researchers employed CP modelling to predict the FLDs of such sheet metals [ 414 , 415 , 416 , 417 , 418 , 419 , 420 , 427 , 428 , 429 , 430 , 431 ] by coupling the M-K model with crystal plasticity. Their new framework was based on the RVE, representing a single material point on the metallic sheet.…”

Multiscale modeling of discontinuous dynamic recrystallization during hot working by coupling multilevel cellular automaton and finite element method

“…Recently, this approach was further improved by Zhang et al (2020), who modeled the thermal interface grooving and deformation anisotropy of titanium alloys with a lamellar colony by a combination of the Monte Carlo (MC) methodand CPFEM. Lately, Nagra et al (2020) creatively improved the rate-tangent-crystal plasticity-fast Fourier transform framework proposed by Nagra et al (2017Nagra et al ( , 2018 to model the DRX behavior of hexagonal closed-packed (HCP) AZ31 alloys and further investigated the formability of the alloys by coupling the M-K approach with the CA method. The improved numerical framework has the advantage of quantifying the intrinsic characteristics, including macro stress, strain, twining volume fraction, micromechanical fields, texture evolution, and local dislocation density of HCP alloys.…”