Multivariant Formulation of the Thermomechanically Coupled Mu¨ller-Achenbach-Seelecke-Model for Shape Memory Alloys

Abstract

Temperature changes caused by latent transformation heats are an integral part of the behavior of shape memory alloys and inevitably couple the thermal and the mechanical fields. This general behavior is covered by the Mu¨ller-Achenbach-Seelecke (MAS) model. Its versatility has been documented extensively in the literature. In the original formulation the MAS model is restricted to uniaxial states of stress in a SMA, which limits its application to cases where such stress states prevail, such as axial loading in wires and trusses, as well as pure beam bending, pure torsion and shrink-fit problems. Unreliable results, however are expected under arbitrary multiaxial loading conditions. To overcome this limitation we present an extension of the model capable of arbitrary stress/strain/temperature states in 3D. Our model adopts ideas presented by Xie but employs a different non-convex free energy function. Rate equations are employed to model temperature or stress/strain induced transformations between austenite and eight variants of martensite present in the model. As the MAS model, the multi-variant model is capable of fully-coupled thermo-mechanical processes which is shown by simulations of temperature-induced processes, quasiplasticity and pseudoelasticity under variable load directions. At the present level of sophistication, the model is restricted to single crystalline SMA. All examples are explained by the use of a standalone model implementation. The model is intended for future implementation into the finite-element-method environment ABAQUS™ to provide a powerful tool useful in the framework of engineering design studies, especially in situations which require non-isothermal conditions and phase transitions.