Evaluation of biaxial flow stress based on elasto-viscoplastic self-consistent analysis of X-ray diffraction measurements

Biaxial flow behavior of an interstitial free steel sample was investigated with two experimental methods: (1) Marciniak punch test with in situ X-ray diffraction for stress analysis; (2) hydraulic bulge test. The stress analysis based on X-ray diffraction using {2 1 1} lattice planes was accompanied by the use of stress factors and intergranular (IG) strains. Stress factors and IG strains were experimentally obtained ex situ on samples after prescribed equi-biaxial deformations. An elasto-viscoplastic self-consistent (EVPSC) crystal plasticity model was used to predict the stress factors and the IG strains. The model predictions of the stress factors were in good agreement with the experiments. However, the predictions of IG strains were in poor agreement with their experimental counterparts. As a result, the flow stress solely based on the computationally predicted stress factors and IG strains was unrealistic. The input of the experimental stress factors and IG strains for stress analysis improved the agreement with a reference flow curve obtained by a hydraulic bulge tester. The resulting flow curves based on X-ray diffraction were in good agreement with that of the bulge test up to an effective strain of 0.3. However, an unrealistic softening was observed in larger deformations regardless of whether the stress factor used were experimentally measured or determined from EVPSC calculations.