A theoretical study on asymmetric bending for functionally graded shape memory alloy beam

Abstract

Bending is an attractive mode of operation and application of functionally graded shape memory alloy (FG-SMA). For decades, numerical methods, such as the finite element method, have been used to model the mechanical behavior of these alloys. In this paper, combining with the critical stress–temperature relationship and stress–strain relationship of shape memory alloy, it researched the mechanical behavior of FG-SMA beam under thermal and mechanical loads with the macroscopic constitutive model. The split-step method was adopted to analyze the process of FG-SMA phase transformation in the loading process. The relationship between stress distribution and three factors that included tension–compression asymmetry coefficient, temperature and power exponent were obtained, and the nonlinear controlling equations of FG-SMA beam were acquired. The influence of tension–compression asymmetry coefficient, temperature and power exponent on deflection, curvature and cross section stress, neutral axis and phase boundary were obtained by solving the equations. It was found that the phase transformation of FG-SMA beam became more and more difficult as the increase in temperature and power exponent. Furthermore, the tension–compression asymmetry coefficient had a great influence on the compression side phase boundary, but it had a little influence on the tension side phase boundary.