On superelastic bending of shape memory alloy beams

Abstract

In this paper, a closed-form solution is presented for bending analysis of shape memory alloy (SMA) beams. Two different transformation functions are considered: a J2-based model with symmetric tension–compression response, and a J2–I1-based model for considering the tension–compression asymmetry that is observed in experiments. The constitutive equations are reduced to an appropriate form for studying the pseudoelastic bending response of SMAs. Closed-form expressions are given for the stress and martensitic volume fraction distributions in the cross section and the bending moment–curvature relation is obtained analytically. Both circular and rectangular cross sections are considered and several case studies are presented for testing the accuracy of the method and also the effect of taking into account the tension–compression asymmetry on the bending response of SMAs. The results of a three-point bending test on an SMA beam are presented and compared with the theoretical predictions. Using some experimental data on bending of a nickel–titanium micropillar the applicability of the present method in the micro scale is studied. It is shown that this method can be used for assessing the tensile properties of materials in this special case, where the compressive and bending responses are known from experiments while the tensile properties are very difficult to be measured experimentally.