Spring-back behaviors of Ti-6Al-4V sheet under effect of strain rate

Abstract

By using Impact Hydro-bending (IHB), the room-temperature spring-back of Ti-6Al-4V sheet can be reduced significantly. However, the existing analytical models for spring-back prediction do not take into account complex space-time deformation history, and thus cannot predict the spring-back behavior under IHB accurately. Although numerical simulation can achieve high accuracy of spring-back prediction, it cannot obtain the values and distributions of tangential strain/stress efficiently, and it is also unable to quantitatively distinguish the influence of space-time deformation history on the level of spring-back. In this paper, a theoretical model considering both the effects of the space-time deformation history and the strain rate is creatively established to predict the spring-back behaviors. In the proposed model, a novel shape equation is established to describe the space-time deformation history of sheet. When using the shape equation, only two parameters (kv and pv) need to be adjusted to accurately obtain the desired shape history of sheet. Specifically, both the effects of strain rate and cyclic loading can be considered in the proposed constitutive equation used for the analytical analysis. By utilizing the analytical model, the effect of space-time deformation history and strain rate on the spring-back reduction can be quantitatively characterized, and the result shows that the space-time deformation history is the primary factor affecting the spring-back reduction under high-strain-rate bending. The analytical model is further utilized to reveal the mechanism of spring-back reduction. According to the analytical results, cyclic loading occurred at the sidewall of sheet under IHB. Additionally, the plastic zone widens and the plastic level improves significantly under IHB compared to conventional punch bending (CPB). By observing the distributions of tangential stress at the end of deformation, it is found that in certain regions under IHB, the compressive stress in the outer layer is greater than that in the inner layer, which makes the sheet to bend towards its inner side after unloading, and thus promotes the reduction of spring-back.