A Constitutive Model for Commercially Pure Titanium

Abstract

Flow stress data for CP titanium were obtained using the torsion test in the temperature range from ambient to 750°C and at shear strain-rates in the range from 0.192 to 122.0 s−1. The temperature rise because of deformation heating was calculated numerically. It was found that the temperature rise is insignificant for strain rates below 0.192 s−1 where the deformation conditions are essentially isothermal while for strain rates above 27.0 s−1 deformation conditions are adiabatic. Large temperature gradients exist in the longitudinal direction of the specimen with the maximum temperature occurring at the middle of the gage length. The temperature gradients in the radial direction are much smaller and can be neglected for most practical applications. Isothermal shear stress-shear strain curves for CP titanium were obtained from the experimental torsion test data by accounting for the temperature rise produced by deformation. It was found that the data exhibits a good fit to a Johnson-Cook relationship with exponential thermal softening. The work emphasizes the importance of the need to consider the role of deformation heating when interpreting data on the effect of strain rate and temperature on the mechanical properties of materials.