Effect of tension-compression asymmetry and partial transformation on the response of shape memory alloy beam structures

Abstract

Shape Memory Alloys (SMAs) constitute a class of materials that are distinguished by their highly non-linear, thermo-mechanically coupled behaviour which is related with the phenomena accompanying the diffusion-less, solid-state phase transformation. This transition from the parent phase of Austenite to the product phase of Martensite and vice versa is also bound with the uncommon characteristic of “memory” exhibited when the material undergoes variable thermo-mechanical loadings. When a transformation reversal takes place, the material seems to inherently remember its state and adapts its future response in order to form closed paths, strongly dependent on the induced transformation history. Furthermore, another characteristic trait of SMAs is the asymmetry of their response when under tension or compression. During mixed loading states, such as bending of a beam, the evolution of transformation is observed to be different based on the sign of the load. The aforementioned peculiarities significantly affect the implementation SMAs in the design and realization of smart engineering structures intended for use in a wide range of fields that include but are not limited to aerospace, biomedical, wind energy, civil and automotive. To this end, efficient constitutive modeling of the phenomena related to the phase transformation is essential and of high importance in order to predict the complex performance of these materials. In this paper, emphasis is placed upon the investigation of the combined effect of tension-compression asymmetry and partial transformation on the response of SMA beams subjected to threepoint bending loading conditions. In this context, modeling of tension-compression asymmetry is investigated by using a set of different phase transformation functions based on the principles of computational plasticity, while a modified hardening function is considered to account for partial transformation behaviour. The produced numerical results are compared with respective cases that omit these phenomena in order to quantify their effect in terms of the developed stresses, material state and production/recovery of transformation strain.