Multiplicative AF kinematic hardening in plasticity

The basic innovation proposed in this work is to consider one of the two coefficients of the Armstrong and Frederick (AF) evolution equation for the back stress, function of another dimensionless second order internal variable evolving also according to an AF equation in what can be called a multiplicative AF kinematic hardening rule. Introducing the foregoing modification into some of the components of the back stress additive decomposition model proposed by Chaboche et al. [Chaboche, J.L., Dang-Van, K., Cordier, G., 1979. Modelization of strain memory effect on the cyclic hardening of 316 stainless steel. In: Transactions of the 5th International Conference on Structural Mechanics in Reactor Technology, Berlin, no. Div L in 11/3], one obtains a refined model with improved performance in partial unloading/reloading and ratcheting. In many respects the multiplicative AF kinematic hardening scheme plays a role equivalent to that of the back stress with a threshold scheme introduced by Chaboche [Chaboche, J.L., 1991. On some modifications of kinematic hardening to improve the description of ratcheting effects. Int. J. Plasticity 7, 661–678] to improve ratcheting simulations. The basis equations are presented for both uniaxial and multiaxial stress spaces and the calibration of the model constants is addressed in detail. Numerical applications are executed for uniaxial cyclic loading only, and indicate that the proposed refinement can perform quite well in simulating uniaxial experimental data, including ratcheting, while the potential to simulate successfully multiaxial loading data is an issue to be addressed in the future.