A Cyclic Constitutive Model Based on Fractional Derivative for Rate-Dependent Ratcheting of EA4T Axle Steel

Within the framework of elastoplastic theory, this study develops and improves a fractional cyclic constitutive model capable of describing rate-dependent ratcheting behavior by defining the ratcheting parameter as a function of the cumulative plastic strain rate and describing the plastic strain rate and back stress in fractional-order forms. Additionally, a brief introduction is provided on the numerical implementation process and parameter determination method of this model. The newly improved fractional-order model was subsequently employed to simulate and predict the cyclic deformation of the cyclically softening material, EA4T axle steel. The following conclusions can be drawn: owing to the incorporation of fractional calculus, the newly improved model can predict both the monotonic tensile curves and the cyclic softening behavior of materials under different strain rates—capabilities that are not achievable with conventional elastic–plastic cyclic constitutive models. By defining the ratcheting parameter as a function of the cumulative plastic strain rate, the improved fractional model can reasonably predict the evolution laws of both uniaxial and non-proportional multiaxial ratcheting. By describing the evolution of plastic strain rate and back stress in fractional-order forms, the newly improved fractional model can provide a relatively accurate prediction of the rate-dependent uniaxial and multiaxial ratcheting behaviors.