Evolving asymmetric and anisotropic hardening of CP-Ti sheets under monotonic and reverse loading: Characterization and modeling

Commercially pure titanium (CP-Ti) sheets are promising to manufacture high-performance and lightweight components in many fields such as aerospace, marine, energy, electrics and healthcare. However, due to its low symmetric hexagonal close-packed (HCP) structure and complex thermal-mechanical processing history, CP-Ti sheets may exhibit significant asymmetry and anisotropy under monotonic and reverse loading. Therefore, the coupling effect of loading-path dependent asymmetric and anisotropic hardening behaviors of CP-Ti sheets need to be systemically characterized and accurately described under monotonic and reverse loading paths. In this study, firstly, the rheological tests were performed to systemically explore the evolving asymmetric and anisotropic hardening behavior of CP-Ti sheet under monotonic and reverse loading modes. With the help of anti-buckling support fixture and DIC system in tension and compression tests, the coupling effect of asymmetric and anisotropic hardening under monotonic and reverse loading of CP-Ti sheet was identified. Secondly, a loading-path dependent constitutive modeling framework was constructed in which the stress invariants-based model (SIM) integrated with distorted hardening (DH) under reverse loading (RL) conditions (SIM+DH+RL) were considered. Within the proposed modeling framework, a judging criterion of stress reversal for explicit solution method and an activation criterion of different reverse loading modes were introduced. Finally, the proposed SIM+DH+RL model was implemented, calibrated and further applied to simulate typical V-/U-bending of CP-Ti sheets. The results show that the proposed SIM+DH+RL model can significantly improve the prediction accuracy of V-/U-bending springback with the relative errors less than 7.8% and 2.1%, compared with 15.2% and 12% relative errors of Mises+IH, 19.5% and 7.3% relative errors of SIM+DH, 15.1% and 8.4% relative errors of Yoon2014+IH, 14.5% and 5.2% relative errors of CPB06+IH, and 17.3% and 11.5% relative errors of Hill48+IH. It is noted that for the thickness distributions after V-/U-bending springback, the above used models have similar prediction accuracies with the relative errors less than 1.8%.