Multi-scale finite element analyses of sheet metals by using SEM-EBSD measured crystallographic RVE models

In this study, two multi-scale analyses codes are newly developed by combining a homogenization algorithm and an elastic/crystalline viscoplastic finite element (FE) method (Nakamachi, E., 1988. A finite element simulation of the sheet metal forming process. Int. J. Numer. Meth. Eng. 25, 283–292; Nakamachi, E., Dong, X., 1996. Elastic/crystalline viscoplastic finite element analysis of dynamic deformation of sheet metal. Int. J. Computer-Aided Eng. Software 13, 308–326; Nakamachi, E., Dong, X., 1997. Study of texture effect on sheet failure in a limit dome height test by using elastic/crystalline viscoplastic finite element analysis. J. Appl. Mech. Trans. ASME(E) 64, 519–524; Nakamachi, E., 1998. Elastic/crystalline viscoplastic finite element modeling based on hardening–softening evaluation equation. In: Proc. of the 6th NUMIFORM, pp. 315–321; Nakamachi, E., Hiraiwa, K., Morimoto, H., Harimoto, M., 2000a. Elastic/crystalline viscoplastic finite element analyses of single- and poly-crystal sheet deformations and their experimental verification. Int. J. Plasticity 16, 1419–1441; Nakamachi, E., Xie, C.L., Harimoto, M., 2000b. Drawability assessment of BCC steel sheet by using elastic/crystalline viscoplastic finite element analyses. Int. J. Mech. Sci. 43, 631–652); (1) a “semi-implicit” finite element (FE) code and (2) a “dynamic explicit” FE code. These were applied to predict the plastic strain induced yield loci and the formability of sheet metal in the macro scale, and simultaneously the crystal texture and hardening evolutions in the micro scale. The isotropic and kinematical hardening laws are employed in the crystalline plasticity constitutive equation. For the multi-scale structure, two-scales are considered. One is a microscopic polycrystal structure and the other a macroscopic elastic plastic continuum. We measure crystal morphologies by using the SEM-EBSD apparatus with a unit of about 3.8 μm voxel, and define a three dimensional (3D) representative volume element (RVE) for the micro polycrystal structure, which satisfy the periodicity condition of crystal orientation distribution. A “micro” finite element modeling technique is newly established to minimize the total number of finite elements in the micro scale. Next, the “semi-implicit” crystallographic homogenization FE code, which employs the SEM-EBSD measured RVE, is applied to the 99.9% pure-iron uni-axial tensile problem to predict the texture evolution and the subsequent yield loci in the various strain paths. These “semi implicit” results reveal that the plastic strain induced anisotropy in the micro and macro levels can be predicted by our FE analyses. The kinematical hardening law leads a distinct plastic strain induced anisotropy. Our “dynamic-explicit” FE code is applied to simulate the limit dome height (LDH) test problem of the mild steel DQSK, the high strength steel HSLA and the aluminum alloy AL6022 sheet metals, which were adopted as the NUMISHEET2005 Benchmark sheet metals (Smith, L.M., Pourboghrat, F., Yoon, J.-W., Stoughton, T.B., 2005. NUMISHEET2005. In: Proc. of 6th Int. Conf. Numerical Simulation of 3D Sheet Metal Forming Processes, PART A and B(Benchmark), pp. 409–451) to estimate formability. The “dynamic explicit” results reveal that the initial crystal orientation distribution has a large affects to a plastic strain induced texture and anisotropic hardening evolutions and sheet formability.