超弹性镍钛形状记忆合金单轴相变棘轮行为的宏观唯象本构模型

A MACROSCOPIC PHENOMENOLOGICAL CONSTITUTIVE MODEL FOR THE UNIAXIAL TRANSFORMATION RATCHETING OF SUPER-ELASTIC NiTi SHAPE MEMORY ALLOY

超弹性镍钛形状记忆合金因其良好的力学性能以及独特的超弹性和形状记忆效应已广泛应用于土木工程、航空航天和生物医疗等多个领域,在实际服役环境中超弹性镍钛合金元件不可避免地会承受不同应力水平的循环载荷作用,亟待建立描述相变棘轮行为(即峰值应变和谷值应变随着正相变和逆相变循环的进行不断累积)的循环本构模型.为此,基于已有的超弹性镍钛形状记忆合金在不同峰值应力下的单轴相变棘轮行为实验研究结果,在广义黏塑性框架下,对Graesser等提出的通过背应力非线性演化方程反映超弹性镍钛形状记忆合金超弹性行为的一维宏观唯像本构模型进行了拓展,考虑了正相变和逆相变过程中特征变量的差异及其随循环的演化,以非弹性应变的累积量为内变量引入了正相变开始应力、逆相变开始应力、相变应变和残余应变的演化方程,同时通过峰值应力与正相变完成应力的比值来确定演化方程中的相关系数,建立了描述超弹性镍钛合金单轴相变棘轮行为的本构模型.将模拟结果与对应的实验结果进行对比发现,建立的宏观唯像本构模型能够合理地描述超弹性镍钛形状记忆合金的单轴相变棘轮行为及其峰值应力依赖性,模型的预测结果和实验结果吻合得很好.

Super-elastic NiTi shape memory alloy(SMA)has been extensively used in many fields such as civil engineering,aerospace and bio-medical fields due to its good mechanical properties,including unique super-elasticity and shape memory e_ect.In practical applications,the SMA-based devices are unavoidable subjected to cyclic loadings at di_erent stress levels.However,it is necessary to establish a cyclic constitutive model to describe the transformation ratcheting behavior,i.e.,the peak strain and valley strain accumulate cyclically during forward transformation and reverse transformation.Based on the existing experimental results of the transformation ratchetting of the super-elastic NiTi shape memory alloy obtained under the stress-controlled cyclic tension-unloading tests with di_erent peak stresses,the one-dimensional macroscopic phenomenological constitutive model of super-elastic NiTi shape memory alloy proposed by Graesser,where super-elastic behavior is reflected by the nonlinear evolution equation of back stress,was extended to describe the uniaxial transformation ratchetting within the framework of generalized visco-plasticity.In the extended model,the di_erences of characteristic variables and their evolutions between the forward transformation and reverse transformation were considered,the evolution equations of the start stress of forward transformation,the start stress of reverse transformation,maximum transformation strain and residual strain were introduced by the internal variable of relative accumulated inelastic strain.In the meantime,the correlation coe_cients in these evolution equations were determined by the ratio of the peak stress and the finish stress of forward transformation.The comparison of the experiments and simulations shows that the extended model can reasonably describe the dependence of uniaxial transformation ratcheting of super-elastic NiTi shape memory alloy on the peak stress,and the simulated results are in good agreement with the experimental ones.