Inner loops of pseudoelastic hysteresis of shape memory alloys: Preisach approach
Inner loops of pseudoelastic hysteresis of shape memory alloys: Preisach approach
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DOI：
10.1117/12.474993
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发表时间：
2002-07
期刊：
影响因子：
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通讯作者：
Y. Matsuzaki;Ken Funami;H. Naito
中科院分区：
文献类型：
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作者：
Y. Matsuzaki;Ken Funami;H. Naito
形状记忆合金（SMA）由于相变和重排而表现出非常复杂的热机械行为，包括大的边界滞后应力-应变环以及它们的内环。在我们以前的分析中，将相相互作用能函数（PIEF）作为耗散势与合金的自由能，我们提出了一个宏观模型的SMA的伪弹性和形状记忆效应。分析边界回路推导出的可以准确地模拟实验结果的电线进行循环负载高达1Hz，包括温度变化。在本文中，进一步扩展的PIEF的概念，我们提出了一个微观的方法，考虑到在单晶晶粒的多晶SMA的伪弹性滞后。在每个晶粒中，我们假设滞后行为由Preisach模型表示。再次，结合PIEF与晶粒的自由能，并总结了整个材料，我们推导出的应力-应变关系，其中柯西分布函数用于马氏体和逆相变的概率。我们将表明，已确定的解析应力-应变模型使用的实验数据的边界环可以很好地描述其内部循环。
Shape memory alloys (SMA) show very complicated thermomechanical behavior due to phase transformations and rearrangements, including large bounding hysteretic stress-strain loops as well as their inner loops. In our previous analyses, incorporating the phase interaction energy function (PIEF) as a dissipation potential with the free energy of the alloy, we proposed a macroscopic model of SMA for the pseudoelasticity and shape memory effect. Analytical bounding loops derived could accurately model experimental results of a wire subjected to cyclic loads up to 1Hz, including the temperature change. In the present paper, to further extend the concept of the PIEF, we propose a microscopic approach by taking into account the pseudoelastic hysteresis in single crystal grains of polycrystalline SMA. In each grain, we assume that the hysteretic behavior is represented by the Preisach model. Again, incorporating the PIEF with the free energy of the grain, and summing up over the whole material, we have derived the stress-strain relationship in which the Cauchy distribution function is used for the probability of the martensitic and the reverse transformation. We will show that the analytical stress-strain model which has been determined using experimental data of a bounding loop can well describe its inner loops.