Analytical Equation for the Stress-Strain Curve of Iron-Based Shape Memory Alloys Under Semi-cyclic Loading

There is a wide variety of shape memory alloys, being iron-based shape memory alloys (Fe-SMA) a particular case that is emerging for structural engineering applications due to the relatively low cost compared to other shape memory alloys. One of its promising capabilities in structural design and retrofitting is its unique self-prestressing ability after being heated up to about 160 ºC if it has been previously prestrained up to 2–4% of its original shape. The feasibility of using Fe-SMA rebars or strips for improving the structural behavior of reinforced concrete beams has been successfully demonstrated in several experimental researches. However, most existing experimental studies have commonly focused on applications where the structural elements are subjected to an increasing monotonic loading. Nevertheless, in most cases, loading and unloading are mostly experienced by the reinforcement under live loads, fatigue, vibrations, and seismic actions. Those aspects make it necessary to characterize the behavior of the Fe-SMA during loading and unloading actions. Furthermore, an important gap in the numerical simulation of structures using Fe-SMA is the lack of mathematical models; cyclic constitutive law models are still needed for numerical models, structural design, and assessment. In this paper, a monotonic and semi-cyclic stress-strain model for Fe-SMA are proposed based on the Giuffre-Menegotto-Pinto model. The monotonic equation presented aims to be an envelope equation for the proposed semi-cyclic analytical equation. Those equations are fitted with the mechanical characterization results of a 0.5 mm-thick Fe-SMA strip. The outcome of this study will facilitate developing accurate analytical and numerical models for estimating the cyclic response of Fe-SMA and will also assist in developing design guidelines for the use of Fe-SMA subjected to cycling actions.