Two-scale finite element analyses for bendability and springback evaluation based on crystallographic homogenization method

• Sheet metal formability and crystal texture analyses using two-scale finite element method.
• Bendability and springback properties of copper alloy sheet metals.
• V-bending processes analyses of single-crystal and polycrystal sheet metals.

In this study, a relationship between the sheet metal formability, such as the bendability and springback property, and the crystal texture was investigated by using our two-scale finite element (FE) analysis code based on the crystallographic homogenization method (Nakamachi et al., 2010 [1]). Our code employed a two-scale finite element model, such as the microscopic polycrystal structure and the macroscopic elastic plastic continuum, which can predict the anisotropic plastic deformation of sheet metal in the macro-scale, and the crystal texture and hardening evolutions in the micro-scale. The macro-FE model consisted of the die, punch and sheet metal. The die and punch were modeled as the rigid bodies for “V-bending” process analyses. The measured crystal orientation distribution was adopted as the initial texture in the microscopic polycrystal FE model, which corresponded to the three-dimensional representative volume element (RVE). RVE model was featured as 3×3×3 equi-divided solid finite elements, totally 27 FEs with 216 crystal orientations assigned at the integration points of micro-finite elements. The bendability was evaluated by the surface wrinkle growth index and the strain localization – the shear band formation – by using two-scale FE results. On the other hand, the springback property was defined by the angular difference between before and after the punch and die removing process – the post-process. At first, we investigated the bendability of single crystal sheets, which have typical preferred orientations of the copper alloy sheet, to elucidate the fundamental mechanism of shear band formation and wrinkle growth in the V-bending process. Next, we analyzed V-bending processes of four copper alloy polycrystal sheets to evaluate the bendability and springback property. The Cube-dominant texture sheet of the Corson series copper alloy and the {001}〈110〉-dominant texture sheet of the phosphor-bronze alloy show a high-bendability. On the other hand, the S-dominant texture sheet of the Corson series copper alloy and the Brass-dominant texture sheet of the phosphor-bronze alloy show a low-bendability. By contraries, the Cube-dominant and {001}〈110〉-dominant texture sheets have a low-springback property, and the S-dominant and Brass-dominant textures sheets have a high-springback property. Our two-scale FE results of four copper alloy sheets in the V-bending and the post-process were compared with experimental results, and finally the validity of our two-scale FE code was confirmed.