Constitutive modeling of commercial pure titanium sheet based on non-associated flow rule and differential hardening

Abstract

The commercial-pure titanium (CP-Ti) sheet has attracted a great interest from biomedical and aerospace industries because of its strong mechanical advantages such as lightweight, high strength, good formability, and corrosion-resistance. However, strong anisotropic features, such as evolutionary yield surface and strength difference in tension and compression, of the CP-Ti require advanced constitutive modeling compared to standard advanced high strength steel sheets. This study took into account the differential hardening behavior and the changing R-value of CP-Ti sheet observed during the uniaxial tensile and bulge tests in developing a material model. The observed behaviors are modeled by Hill48 quadratic function based on non-associated flow rule with equivalent plastic work dependent evolutionary parameters. The developed material model was then implemented into a user material subroutine (VUMAT) for ABAQUS/EXPLICIT and used to simulate a circular deep drawing to verify the developed model. Simulation results are compared with those of a material model coupling Yld2000–2d yield function with associated flow rule. The comparison shows that the developed material model provides not only a good agreement with the experiment for yield and potential surfaces but also accurate predictions in forming simulations.