Forming Limit Diagram Of Metal Sheet In Actual Strain Path With Respect To Forming Process

Abstract

Sheet metal forming is generally limited by plastic instability in the form of diffuse necking followed by localized necking and final failure.The forming limit diagram (FLD) is dependent upon the material properties such as strain hardening exponent (n), strain rate sensitivity parameter (m), Anisotropy parameter (r), grain size as well as strain path. Since the actual strain path in the sheet metal forming is not always linear, thus the FLDs that are obtained throughout linear strain path do not have good agreement with experiments. In this paper the FLD of sheet is obtained throughout actual strain path (nonlinear) in both theoretical and experimental approaches. In the theoretical analysis, a localized necking model is used and a many slices approach is introduced to assess the FLD. In solving the theoretical formulations, the loading path is considered nonlinear confirming the actual strain path of sheet in the cup drawing. The experimental study is carried out using a special design biaxial tension machine which can produce any strain path on the samples. It is concluded that the limit strains in the actual strain path, near the punch radius in cup drawing, are lower than obtained throughout linear path, the theoretical results show good agreement with experimental results.