Prediction of forming limits for anisotropic materials with nonlinear strain paths by an instability approach

Abstract

An effective perturbation approach is extended with Hill'48 yield criterion and Hosford's yield criterion to forecast the forming limits of metallic sheets with nonlinear strain paths. The phenomenon of localized necking is treated as a process that develops over a period of time during the deformation, rather than an event, which occurs in an instant at some point of instability or bifurcation. When the perturbation growth accumulation reaches a certain value, the necking is assumed to be well developed and become observable and the strain level in the homogeneous region will be the limit strain. It is found that the preferred orientation of the perturbation (POP) at necking coincides with the orientation for the necking predicted by traditional approach very well. The influences of strain rate sensitivity index m on the forming limit have been illustrated by the proposed method. This method is also used to validate the equivalent plastic strain (EPS) based Forming Limit Diagram (epFLD) (Zeng et al., 2009) for different bilinear strain paths. Investigations demonstrate that if the strain path changes before the EPS at the onset of deformation instability of plane strain deformation, the predicted forming limits will be the same as those predicted by original epFLD. However, the predicted forming limits will deviate from those predicted by original epFLD if the strain path changes after the EPS. Compared with the test data (Brunet and Morestin, 2001; Wang et al., 2017), the predicted FLDs with Hill'48 yield criterion are quite satisfactory for both steel Fep04 and AA5754-O.