Stress state dependence of cyclic ratchetting behavior of two rail steels

Abstract

Abstract Cumulative inelastic deformation or ratchetting occurs during cyclic loading in the presence of a mean stress. This problem has received considerable recent attention. The nonlinear kinematic hardening rule originally proposed by Armstrong and Frederick (AF rule) [1966] has been widely used for description of the overall character of hysteresis response during cyclic plasticity. However, this model generally overpredicts cyclic strain accumulation (ratchetting) under asymmetric loading with mean stress ( Bower [1987]; Bower & Johnson [1989]; Clement & Guionnet [1985]; Chaboche [1989,1991]; Chaboche & Nouailhas [1989]; McDowell & Lamar [1989]; McDowell [1992]). Moreover, unloading-reloading behavior associated with subcycle events under even uniaxial conditions ( Chaboche [1989]) are not adequately represented by the AF rule. The same comments apply to other nonlinear kinematic hardening rules of equivalent or similar nature such as bounding surface plasticity theory (cf. McDowell & Moyar [1991]). In this work, a modification of the dynamic recovery term of the AF rule is considered as recently proposed by Ohno and Wang [1991a,1991b]. The approach is established based on certain assumed crystalline slip system behavior and interaction between dislocation interactions at different size scales. Several important criteria are discussed for models capable of representing stress state and amplitude dependence of ratchetting behavior. Experimental results obtained on both a carbon rail steel and a heat-treated rail steel subjected to various uniaxial and nonproportional loading conditions are presented and correlated with an extension of the Ohno and Wang model, which accounts for a broader range of stress state and amplitude effects. An algorithm is developed to extrapolate the ratchetting rates obtained at relatively early cycles to very large numbers of cycles for test specimens. The method provides for dependence on the mean stress as well as amplitude of loading. The algorithm is applied to both carbon and heat-treated rail steels.