Sheet metal formability analysis for anisotropic materials

Sheet metal formability is conventionally assessed in a two dimensional plot of principal strains or stresses in comparison to a forming limit curve. This method implicitly assumes that the forming limit is isotropic in the plane of the sheet, an assumption that is intrinsically inconsistent with the use of material models that are anisotropic. Since the trend today is to utilize models with full anisotropy in order to more accurately capture the physics of material behavior, the issue of anisotropy of forming limits must also be addressed. The challenge is that the forming limit is no longer defined by a curve but requires the definition of a surface in strain or stress space, and therefore it is no longer appropriate to view these limits with the convenience of the conventional two dimensional diagrams. Furthermore, recent developments in the characterization of sheet forming limits under nonproportional loading suggest that is advantageous to view forming limit behavior in terms of stresses rather than strains, a view that is adopted in this paper. A solution to the challenge of assessing formability for an anisotropic material is proposed and illustrated using an analysis of the 2-Stage Forming Benchmark highlighted in the Numisheet '99 Conference