Abstract This paper is concerned with modelling of propagating instabilities and transformation patterns in NiTi tubes subjected to combined tension–torsion loading. A recently developed gradient-enhanced finite-strain model of pseudoelasticity is employed for this purpose, and respective finite-element computations are carried out. It is shown that the model is capable of representing a number of experimentally observed effects. The major effect, which has not been successfully modelled to date, is that the transformation is inhomogeneous under tension-dominated loading and alters towards a homogeneous transformation as the level of torsion is increased. To capture this effect, the model must deliver a non-monotonic (up-down-up) stress–strain response in tension and a monotonic one in torsion, and this can be achieved if the model includes three features: tension–compression asymmetry, transverse isotropy of the transformation strain, and deformation-dependent hardening/softening response. A detailed study is also carried out regarding the transformation yield locus. The results reveal an ambiguity in determination of the yield locus for tension-dominated loading and hence an ambiguity in determination of the tension–compression asymmetry. This aspect seems to have been overlooked in the literature despite its impact on correct interpretation of experimental results.

中文翻译：

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组合拉扭作用下假弹性镍钛管中的传播不稳定性建模：螺旋带和表观屈服轨迹

摘要 本文涉及对承受拉扭联合载荷的 NiTi 管中的传播不稳定性和转变模式进行建模。为此，采用了最近开发的伪弹性梯度增强有限应变模型，并进行了相应的有限元计算。结果表明，该模型能够代表许多实验观察到的效果。迄今为止尚未成功建模的主要影响是，在以张力为主的载荷下，转变是不均匀的，随着扭转水平的增加，转变为均匀转变。为了捕捉这种效果，模型必须在张力中提供非单调（上下）应力应变响应，在扭转中提供单调响应，如果模型包括三个特征，则可以实现这一点：拉压不对称性、转变应变的横向各向同性和变形相关的硬化/软化响应。还对转化产量基因座进行了详细研究。结果表明，在确定张力主导载荷的屈服轨迹时存在歧义，因此在确定拉压不对称性时也存在歧义。这方面似乎在文献中被忽视了，尽管它对正确解释实验结果有影响。结果表明，在确定张力主导载荷的屈服轨迹时存在歧义，因此在确定拉压不对称性时也存在歧义。这方面似乎在文献中被忽视了，尽管它对正确解释实验结果有影响。结果表明，在确定张力主导载荷的屈服轨迹时存在歧义，因此在确定拉压不对称性时也存在歧义。这方面似乎在文献中被忽视了，尽管它对正确解释实验结果有影响。