Investigation on ultrasonic vibration effects on plastic flow behavior of pure titanium: Constitutive modeling

Ultrasonic vibration (UV) assisted plastic forming technology is an ideal way to improve the formability of titanium and its alloys at room temperature, due to the softening effect which is more effective than thermal input. Thus, UV assisted compression test of commercially pure titanium is carried out and the deformation behavior is focused in this study. For an accurate prediction of the flow behavior and further application in UV forming process, the original Johnson–Cook (JC) model and its modified formulae have been adopted to construct the constitutive relation of pure titanium deformed with high-frequency oscillation. The yield stress reduction is related to both the amplitude and its square. The other material constants in JC model are established as the function of the amplitude. The comparative analysis of the predicted stress through the built JC model with the measured one is performed, showing the improved JC model can precisely describe the stress-strain relation in a large deformation range at different vibration amplitudes and strain rates.