Prediction of in-plane anisotropy of bendability based on orientation distribution function for polycrystalline face-centered cubic metal sheets with various textures

Abstract

Bendability of sheet metals is strongly affected by crystallographic orientation, and it was recently found that the bendability had a correlation with the Taylor factor in Al-Mg-Si and Cu-Ni-Si alloy sheets. This paper has proposed an analytical method for predicting in-plane anisotropy of bendability in polycrystalline face-centered cubic metal sheets by using the mean value of Taylor factors for all orientations in the space of the Euler angles. The calculation was performed on the assumption that a strain condition at the convex surface during bending deformation is close to plane strain tension. Using various ideal orientations with Gaussian distribution or various real textures of annealed aluminum or copper alloys, the normalized Taylor factor, which was defined as a ratio of the mean Taylor factor for a textured material to that for a randomly oriented one, was compared with some known experimental data on bendability at directions of 0° and 90° to the rolling direction. The results clearly showed that bendability was better at the bending direction with a lower normalized Taylor factor. Since the formation of shear bands at the sheet surface causes deterioration of bendability, the present analytical method based on the normalized Taylor factor has an advantage in predicting the bendability at arbitrary directions in a sheet, if textures of metal sheets are measured on the surface without polishing by means of X-ray diffraction.