Constitutive modeling of cyclic deformation of metals under strain controlled axial extension and cyclic torsion

The present work provides a formulation of a constitutive model for metals with the aim to simulate cyclic deformation under axial extension or compression assisted by cyclic torsional (or shearing) straining of specified amplitude and frequency. Such a mode of deformation was recently implemented in technological processes such as extrusion, forging and rolling, cf. Bochniak and Korbel (Eng Trans 47:351–367, 1999, J Mater Process Technol 134:120–134, 2003, Philos Mag 93:1883–1913, 2013, Mater Sci Technol 16:664–674, 2000). The constitutive model accounting for combined hardening (isotropic–kinematic) with both hardening and recovery effects is presented and calibrated for several materials: pure copper, aluminum alloy (2024), and austenitic steel. The experimental data are used to specify model parameters of materials tested, and next the cyclic response for different shear strain amplitudes is predicted and confronted with empirical data. The constitutive model is developed in order to simulate technological processes assisted by cyclic deformation.