Modeling of an actuator body consisting of a shape memory alloy rod and an elastic displacement body taking into account translational hardening

One of the applications of shape memory alloys is automotive industry, where they can be used as a material for working bodies of actuators. The movement of the working body is provided by the accumulation of direct transformation deformation during cooling and the shape memory effect during heating. In this paper, the behavior of the actuator, which consists of the rod made from shape memory alloy and the series-connected elastic displacement body, is studied in the framework of the combined model of nonlinear deformation taking into account isotropic and translational hardening. Inelastic deformation produced by the structural transformation in the martensitic state and during thermoelastic phase transitions is described with the use of a loading surface in the stress deviator space. The maximum value of the intensity of phase-structural deformation averaged over the martensitic part of the representative volume is assumed as a non-integral isotropic hardening parameter in the loading surface equation. The formation of martensitic elements during direct thermoelastic transition as well as their evolution are considered. The results of numerical modeling of the working stroke are compared with the data obtained without translational hardening, and the conditions, at which translational hardening can be ignored, are determine. Analysis shows that deformation by a structural mechanism and translational shift of the loading surface are possible under the action of the applied payload and during the working stroke. It has been found that during the working stroke the translational shift of the center of the loading surface significantly affects the stress level in the shape memory rod and the displacement of the point of connection of the working body and translational body. The maximum values of these parameters are reached at the end of the working stroke and are independent of the hardening modulus. The effect of the translational hardening on the results of simulation significantly reduces with an increase in the initial deformation of the working body and an increase of the ratio of the working body flexibility to the elastic body flexibility. It is shown, that during the idle stroke the center of the loading surface is not displaced. The consideration for translational hardening does not affect the selection of parameters providing closeness of the cycle, i.e. the return of the system to its initial state after idling.