Plastic deformation under cyclic loading using two-back stress hardening models

In the present work, the constitutive relations based on the combination of two-back stresses are developed using the Armstrong–Frederick and Phillips type hardening rules in order to describe the plastic strain accumulation under a cyclic loading. Using the combined kinematic hardening rules, the ratcheting behavior under uniaxial cyclic loading is investigated and compared with numerical results. Various evolutions of the kinematic hardening parameter can be obtained by means of a simple combination of the hardening rules using a conventional rule of mixtures. The plastic deformation under cyclic loading turns out to be strongly dependent on the description of back stress evolution and its hardening parameters. It is shown that the ratcheting behaviors for a given material can be depicted by adjusting the control material parameters such as the fractional factor which determines the dominant evolution of the back stress. The present result is verified by comparing the existing experimental data available in the literature (Hassan and Kyriakides) [Hassan T, Kyriakides S. Ratcheting of cyclically hardening and softening materials: I. uniaxial behavior. Int J Plasticity 1994;10(2):149–84; Hassan T, Kyriakides S. Ratcheting in cyclic plasticity, part I: uniaxial behavior. Int J Plasticity 1992;8(1):91–116] and it shows good agreement with the published data in some cases.