Phenomenological Simulation of the Phase and Structural Deformation in Shape Memory Alloys. One-Dimensional Case

Abstract

Structural elements made of shape memory alloys (SMAs) undergo cooling/heating and stresses changing in value and direction during operation. As a result, phase and structural transformations, which are accompanied by the shape memory effect, cross hardening and martensitic inelasticity, occur in a material. Moreover, a change in the stresses causes a shift in the phase-transition temperatures, and forward and reverse phase transitions are possible during an isothermal increase or decrease in the load (superelasticity phenomenon). The purpose of this work is to develop a phenomenological model in terms of a general approach to take into account these phenomena, since they substantially affect the state of stress in a construction. This model is based on the relation between forward transformation and martensitic inelasticity diagrams, which implies a general description of the strains of phase and structural transformations. This approach seems to be useful, since both strain components are caused by the formation of oriented martensite. A set of series-connected martensitic structural elements, each of which has a specific structural transformation limit (initial stress), is introduced into consideration. This limit depends on the conditions of appearance of an element during a phase transition and the subsequent deformation history. This approach can take into account the influence of, first, phase deformation and structural deformation on each other and, second, the deformation history on the subsequent transformation. To demonstrate the possibilities of the model, we solve the problem of joint deformation of a stack of SMA rods, which illustrates the evolution of the state of stress in the system during the simultaneous phase and structural transformations induced by an external thermomechanical action.