Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.

A Cyclic Constitutive Model Based on Crystal Plasticity for Body-Centered Cubic Cyclic Softening Metals

Under the framework of the small deformation crystal plasticity theory,a crystal plastic cyclic constitutive model for body-centered cubic(BCC)cyclic softening polycrystalline metals is established.The constitutive model introduces the isotropic softening rule that includes two different mechanisms:namely softening under monotonic deformation and softening under cyclic deformation on each slip system.Meanwhile,a modified Armstrong-Frederick nonlinear kinematic hardening rule is adopted.The appropriate explicit scale transition rule is selected to extend the single crystal constitutive model to the polycrystalline constitutive model.Then the model is used to predict the uniaxial and multiaxial ratcheting deformation of BCC axle steel EA4T to verify the rationality of the proposed model.The simulation results indicate that the newly established crystal plasticity model can not only describe the cyclic softening characteristics of BCC axle steel EA4T well,but also reasonably describe the evolution laws of uniaxial ratcheting and nonproportional multiaxial ratcheting deformation.Moreover,the established crystal plastic cyclic constitutive model can reasonably predict the ratcheting behavior of BCC single crystal as well.