考虑温度记忆效应的形状记忆合金本构模型

近年来在形状记忆合金（Shape Memory Alloy，SMA）中发现的由于不完全马氏体逆相变引起的温度记忆效应，在智能材料与结构等领域具有潜在的应用价值，建立克服现存SMA本构模型不能考虑SMA温度记忆效应这一局限性的SMA本构模型具有理论和工程实际意义．本文在前期研究的基础上，基于作者提出的形状记忆因子的概念，综合运用热力学、连续介质力学和马氏体相变学的相关理论，建立了描述SMA的形状记忆因子、应力、温度间关系的形状记忆方程和描述SMA的应变、应力、温度间关系的力学本构方程．由形状记忆方程和力学本构方程构成的SMA本构模型，克服了现存SMA本构模型不能考虑SMA温度记忆效应的局限性．数值结果表明，该SMA本构模型能有效描述经历不完全马氏体逆相变的SMA的热力学行为，可为SMA温度记忆效应的应用研究提供理论基础．

A constitutive model of shape memory alloy with temperature memory effect

Temperature memory effect occurring in some shape memory alloys has potential values in various fields such as smart materials and structures, and so on. It is of theoretical and practical interests to develop a new constitutive model of shape memory alloy to overcome the limitation that the previous constitutive models of shape memory alloy failed to express the temperature memory effect of shape memory alloy. This paper focuses on the foregoing issue based on the previous work of the authors. A new shape memory equation is developed to describe the relationship of shape memory factor, stress and temperature in shape memory alloy using the differential relationship of phase transformation free energy and martensitic volume fraction and the concept of shape memory factor defined by the author of this paper. A new mechanical constitutive equation is developed to predict the relationship of strain, stress and temperature in shape memory alloy based on the thermodynamics and continuum medium mechanics. The supposed constitutive model of shape memory alloy, which includes the new shape memory equation and new mechanical constitutive equation, is able to overcome the limitation that previous constitutive models of shape memory alloy failed to express the temperature memory effect of shape memory alloy. This work can provide a theoretical basis for the practical applications of temperature memory effect of shape memory alloy in various fields.