Constitutive modeling of plastic anisotropy and strength differential effect of commercially pure titanium and its application to finite element analysis of circular cup drawing

Owing to its strong corrosion resistance, moderate mechanical properties, and excellent biocompatibility, commercially pure titanium (CP Ti) has been widely applied in the fields of marine sciences, aerospace, and biomedicine. To reduce the trial-and-error production of CP Ti components and optimize the forming processes, an advanced constitutive model for accurate forming simulation of CP Ti was developed in this study based on the non-associated flow rule. The developed non-associated constitutive model can capture the orthotropic flow stress anisotropy, tension–compression strength differential (T-C SD) effect, and planar deformation anisotropy of CP Ti, and it was validated using material characterization data of a hot-rolled CP Ti plate. The developed constitutive model was implemented in Abaqus/Standard via the user subroutine UMAT and achieved an accurate finite element (FE) analysis of the circular cup drawing for the CP Ti sheet. All the material properties considered in the developed constitutive model affect the FE analysis results, which indicate the necessity of considering the orthotropic flow stress anisotropy, T-C SD effect, and in-plane deformation anisotropy during the sheet metal forming simulation of CP Ti.