Generalized distortional hardening modeling for nonlinear strain paths in sheet forming

Abstract

In sheet metal forming process, a material is subjected to a nonlinear strain path where it shows complex hardening behaviors including Bauschinger effect, permanent softening, nonlinear transient behavior, yield surface contraction, and overshooting behavior. It is possible to describe these behaviors by using distortional hardening model in which yield surface is contracted and rotated according to the loading path changes. However, the conventional distortional hardening models are limited to use for industry application because of its complex form of equation and significant simulation time. In addition, material behaviors under nonlinear strain path are known to be strain rate dependent. However, there has not been reported any strain rate dependent distortional hardening model. Therefore, in this study, a new distortional hardening model has been proposed with simpler form of equation than the conventional distortional hardening model while preserving the same level of accuracy as the conventional model. In addition, by introducing rate dependent term to the proposed model, the rate dependent material behaviors under nonlinear strain path are accurately described. The accuracy of the proposed model was verified from predicting material behaviors under three path changes: tension followed by compression, tension along the rolling direction followed by tension along the diagonal or transverse direction. For strain rate dependency, it was predicted the rate dependent tension followed by compression behavior. In order to apply the proposed models for finite element simulation, it was implemented into finite element software ABAQUS by using User-MATerial (UMAT) subroutine through stress integration algorithm based on finite difference method. The single element and high-speed U-bending forming and springback prediction simulations were conducted for the verification of the developed UMAT.