Probabilistic evaluation of the one-dimensional Brinson model’s sensitivity to uncertainty in input parameters

Abstract

Brinson model is one of the most widely used shape memory alloy models due to its prediction power over a wide range of operating temperatures and inclusion of measurable engineering variables. The model involves parameters that are determined based on experimental data specific to a particular alloy. Therefore, it is subject to both experimental uncertainty and natural random variability in its parameters that propagate throughout the loading/unloading of the material. In this article, we analyse the sensitivity of the Brinson model to its parameters using a probabilistic approach, and present how the uncertainties in these parameters at different operating temperatures propagate as evidenced by the resulting stress–strain curves. The analyses were performed for isothermal loading/unloading and at various operating temperatures representing possible phase changes between martensite–austenite and martensite–martensite variants. The results show that the sensitivity of the model varies considerably based on the operating temperature and loading conditions. In addition, the variability in the model’s output is amplified after phase transitions during loading, and loading the material above the critical stress for martensite transition reduces variability during unloading. Based on the results of the sensitivity analysis, recommendations as to which parameters affect the variability of the model-predicted stress–strain curves are presented.