Sheet metal formability analysis for anisotropic materials under non-proportional loading

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 of assessment implicitly assumes that the forming limit is isotropic in the plane of the sheet. While the assumption of isotropy in the forming limit is perhaps a good engineering approximation, it 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 two-dimensional diagrams. Furthermore, recent developments in the characterization of sheet forming limits under non-proportional 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 that rescales the stresses by a factor so that the scaled stresses have the same relationship to a single forming limit curve in a 2D plot in stress-space, as the actual stresses have to the true anisotropic forming limit in 3D space. The rescaling enables engineers to accurately view the formability of all the elements at the same time for a given finite element analysis of an application. This paper also discusses other challenges of using stresses in the assessment of formability, focusing on an analysis of the 2-Stage Forming Benchmark highlighted in the Numisheet '99 Conference. Stresses are found in this application to unload to non-critical values after reaching critical levels earlier in a forming process, which suggests that a full integration of the stress-based forming limit criterion with FE simulation is required to detect critical states that may temporarily occur during the forming process. (c) 2005 Elsevier Ltd. All rights reserved.