New approach in constitutive modelling of commercially pure titanium thermo-mechanical processing

Abstract The pure titanium, as a biomaterial destined for production of load-demanding prostheses, requires thermo-mechanical processing to increase its strength. The most common way to achieve this is the method of grain fragmentation. Thermo-mechanical deformation of titanium is a complex process, which makes it very difficult to describe it by means of constitutive equations. Such constitutive relations are very useful as they can be implemented in the finite element method tools in order to simulate and optimize the whole process. Cylindrical specimens were compressed at elevated temperatures on a thermo-mechanical simulator. The tests were performed at four different strain rates (from 10 $$^{\mathrm {-2}}$$ - 2 s $$^{\mathrm {-1}}$$ - 1 to 10 s $$^{\mathrm {-1}})$$ - 1 ) and at 775 K and 875 K temperatures. The collected data allowed us to create strain–stress graphs characterizing the process. Observations on the scanning electron microscope and scanning transmission electron microscope were done as well as the electron backscatter diffraction analysis, revealing significant grain fragmentation. The aim of the studies described in the paper was to verify and select a proper mathematical model for the process of titanium grain fragmentation obtained in a thermoplastic process. Four different constitutive models were considered. The calculation of theoretical stress values based on the Arrhenius-type equation, Anand viscoplastic model, Johnson–Cook model and Khan Huang-Liang model was done and compared to experimental results. The theoretical curves were generated and fitted to experimental, which made it possible to calibrate the constants in the mathematical models. The curve-fitting analyses showed that the Anand constitutive model described the titanium behaviour best.