中文摘要：

超弹性是形状记忆合金最主要的特性之一,本文假设其在相变过程中具有层状微结构,利用理想界面条件推导出相变发展过程的单晶本构关系,同时引入临界应力,累积残余应变和累积马氏体体积分数3个变量,利用临界应力,循环次数N构造相变驱动力随循环次数N变化的表达式。在每一次加载中相变驱动力作为一个材料参数控制正相变和逆相变的发生过程,联合累积马氏体体积分数和累积残余应变就得到考虑循环效应的单晶本构模型。利用Taylor假设推广到多晶模型。最后为证实本模型的可行性,进行了数值模拟,结果与实验结果吻合较好。

英文摘要：

Super elasticity is one of the main characteristics of shape memory alloys（ SMAs）. Assuming that the shape memory alloys have laminated microstructure during phase transformation process,perfect interfacial condition is used to deduce the single crystal constitutive model. At the same time,critical stress,cumulated residual strain,cumulated martensite volume fraction are introduced. Critical stress and cyclic number（ N） is used to construct the expression of phase transformation driving force changing with cyclic number（ N）. In each loading process,phase transformation driving force is used as a material parameter that controls the generating process of forward phase transformation and reverses phase transformation in one load cycle. With combining cumulated martensite volume fraction and cumulated residual strain,single crystal constitutive model considering cyclic effect can be obtained. Taylor assumption is used to deduce polycrystalline model. The feasibility of this model is verified and numerical simulation is done. The results of simulation match the experimental results very well.