A non-associated constitutive model considering anisotropic hardening for orthotropic anisotropic materials in sheet metal forming

An anisotropic constitutive model based on the non-associated flow rule that is combined with non-quadratic and quadratic functions was developed for orthotropic anisotropic sheet metals. The non-quadratic Barlat's YLD91 function was applied for the description of the anisotropy in the yield stresses, and the classical quadratic Hil148 function was adopted to describe the anisotropy in the plastic deformation. A continuous scheme for capturing the anisotropic hardening based on the implicit YLD91 function was proposed for higher modeling accuracy. The anisotropic parameters can be obtained from three directional uniaxial tensile tests and a hydraulic bulge test. The developed model can be applied under a general three-dimensional condition. The developed model was implemented into the finite element code ABAQUS as a user material subroutine (UMAT). To evaluate the capability of the developed model, directional uniaxial tension and prediction of the yield surface were considered, and a circular hole expansion process with the JSH59OR sheet were simulated using different material models. A suitable static-implicit analysis and solid elements were applied. The comparison between the experimental and simulation results indicates that the modeling accuracy can be improved by applying the developed model. Furthermore, the simple formulations can also contribute to cost saving in the parameter acquisition process and computation. It is concluded that the developed anisotropic model can be used as an alternative and user-friendly method in solving the common industrial problems with large plastic deformation.