A general class of non-linear kinematic models to predict mean stress relaxation and multiaxial ratcheting in fatigue problems – Part I: Ilyushin spaces

Ratcheting is an accumulation of plastic strain that can influence fatigue lives of structural components due to the premature exhaustion of the material ductility, much earlier than predicted by traditional fatigue crack initiation models. Ratcheting is usually associated with a significant mean stress component in either uniaxial or multiaxial stress-controlled histories. The very same process can induce mean stress relaxation in strain-controlled histories, affecting fatigue lives due to consequent mean or maximum stress effects. Such processes are mainly caused by a local distortion of the yield surface, which would require the use of complex yield functions other than von Mises’ to be properly described. The addition of non-linear terms to the kinematic hardening rules compensates for this requirement, rendering it possible to model ratcheting effects using the von Mises yield function without dealing with distortion. In this two-part work, the formulation of the main non-linear kinematic (NLK) models is unified into a generalized equation, represented using engineering notation in a reduced-order five-dimensional (5D) space that may lower in half the associated computational cost. Part I introduces the proposed 5D stress and strain spaces, which are a scaled version of Ilyushin’s 5D spaces. These 5D spaces are then applied to the qualitative study of uniaxial ratcheting, multiaxial ratcheting, and mean stress relaxation. Part II of this work derives all incremental plasticity equations from the NLK approach in the spaces proposed in Part I, and discusses its advantages over the classical 6D formulation. These NLK models are then used in Part II to quantitatively predict uniaxial ratcheting, multiaxial ratcheting, and mean stress relaxation, validated from experiments with 316L steel cylindrical and tubular specimens.