Rate-dependent hardening model for pure titanium considering the effect of deformation twinning

Abstract

This paper is concerned with the strain hardening behavior of commercially pure titanium for a wide range of strain rates. Pure titanium has been described as having three stages of strain hardening behavior during compressive deformation. The stress-strain curve of pure titanium can be divided into three stages according to the strain hardening rate, and the strain hardening rate can be determined by the slope of the stress-strain curve. In the first stage, the strain hardening rate decreases as deformation continues due to dynamic recovery. The strain hardening rate shows a trend similar to general industrial metals. In the second stage, however, the strain hardening rate begins to increase as deformation continues. Following the second stage, the strain hardening rate decreases again in the third stage. Many researchers have determined that a sudden increase in the strain hardening rate in the second stage is caused by the generation of deformation twins, and the strain hardening behavior of pure titanium is influenced by the tendency of twin generation and evolution. In this paper, the effect of deformation twinning on the strain hardening behavior of pure titanium is investigated using OIM (Orientation Imaging Microscopy) analyses. EBSD (Electron Backscatter Diffraction) analyses are conducted to quantitatively observe the generation and evolution of deformation twins. The strain rate effect on the strain hardening is also investigated. Both tensile and compressive tests are conducted at strain rates ranging from 0.001/s to 10/s, and the effect of the strain rate on the three stages of the strain hardening behavior is quantified by observing the micro-structures of deformed specimens at the various strain rates. A novel rate-dependent hardening model is proposed by keeping trace of deformation twins with increase in the compressive strain, which induces the variation of the strain hardening rate. The proposed model is defined with a function of the plastic strain and the strain rate based on OIM results in terms of twin volume fraction and grain size distribution. The three stages of strain hardening behavior of titanium for a wide range of strain rates can be represented by one equation, and this equation can provide useful and simple way that can be applied to the numerical analysis.