Prediction of DP600 and TRIP780 yield loci using Yoshida anisotropic yield function

Abstract

The continual demand for vehicle weight reduction, improved fuel efficiency and crashworthiness has driven the automotive industry to increasingly fabricate automotive body parts from advanced high strength steel (AHSS) sheet, such as dual phase (DP) and transformation induced plasticity (TRIP) steels. It is therefore essential to carefully investigate the forming behaviour of these sheet materials under various forming conditions. In this work, the quasi-static tensile flow behaviour of DP600 and TRIP780 sheet specimens was obtained in three orientations (RD, DD, and TD) with respect to the sheet rolling direction. A 3-parameter Voce hardening function was then fitted to each flow curve in order to determine true stress and true strain based on constant amount of plastic work per unit volume to calculate the normalized yield stress as well as the r-value for each material orientation. Yoshida’s 6th-order polynomial anisotropic yield function, expressed as a function of the second and third invariants of the deviatoric stress tensor (J2 and J3, respectively), was used to predict the mechanical response of these two sheet materials. A new optimization method based on the Markov chain Monte Carlo (MCMC) MetropolisHastings (MH) algorithm was employed to calibrate the anisotropic yield function and determine the anisotropic coefficients. The yield loci for both materials were then derived as a function of only, and also as a function of both J2 and . The performance of each function is evaluated and validated by comparing the numerical predictions of r-value and flow stress directionality with the experimental results. And the effects of J2 and J3 in predicting the shape of the yield locus of DP600 and TRIP780 are also discussed.