形状记忆合金单晶细观本构关系的一种相变动力学模型及算法

形状记忆合金是由马氏体相和奥氏体相组成的非均质材料,热力载荷及相变不可避免地在材料中引起残余微应力场,它与外界驱动力的叠加可能导致低应力水平下发生马氏体相变或逆相变.论文假设马氏体相变及逆相变的驱动力是马氏体体积分数的连续函数,发展了形状记忆合金伪弹性的本构描述及相应的数值分析方法.分析表明,所发展的方法与理想相变模型间的误差远小于已有工作中引入的容许误差.对形状记忆合金单晶伪弹性响应的计算结果与试验结果或已有模型计算结果的比较表明所发展的方法具有较高的精度.此外,所发展的方法具有明晰的物理背景,且无需对每个变体的相变发生与否及其方向进行判断,简化了计算过程,提高了计算效率和收敛性.

A KINEMATIC MODEL AND NUMERICAL ALGORITHM FOR CONSTITUTIVE BEHAVIOR OF SINGLE CRYSTAL SHAPE MEMORY ALLOY

Based on the concept that NiTi shape memory alloys(SMAs) are substantially heterogeneous and there inevitably exist residual micro residual stress fields,and the superposition of the residual stress and the stress induced by applied thermal-mechanical loads may cause martensitic transformation at low level of applied thermal-mechanical loads,a new transformation driving force model is proposed for an existing description for martensite variants in NiTi SMAs.The corresponding numerical algorithm is developed and the pseudoelasticity of NiTi SMAs is analyzed,and compared with experimental results and the results by Gall et al.In the proposed model the transformation driving force is considered as a continuous function of martensite volume fraction,however,the transformation as well as its rate is insignificantly small as the transformation driving force is far from its saturated magnitude.Analysis shows that the range of the transformation driving force with respect to prescribed tolerance of transformation volume fraction is much smaller that that adopted in the existing work,and vice versa,indicating higher computation accuracy of the proposed approach.On the other hand,no assessment is needed for the occurrence of the transformation and its direction in each variant a priori,which is significant in computation,especially in the case of multiaxial thermal-mechanical loading.Since the proposed approach avoids the discontinuity in the evolution of the transformation driving force at the instant when transformation starts,and the additional numerical process for the identification of the variants where transformation proceeds or not,it can not only simplify the numerical process,but also enable the computation process be more stable and efficient.