Relaxation oscillations and negative strain rate sensitivity in the portevin-Le chatelier effect
Relaxation oscillations and negative strain rate sensitivity in the portevin-Le chatelier effect
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DOI：
10.1103/physreve.61.3664
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发表时间：
2000-01
期刊：
影响因子：
--
通讯作者：
Rajesh;Ananthakrishna
中科院分区：
文献类型：
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作者：
Rajesh;Ananthakrishna
Portevin-Le Chatelier效应或急流的一个特征是应力-应变曲线的粘滑性质，这被认为是由于流动应力的负应变率相关性造成的。后者被认为是控制急流动力学的几个相关时间尺度竞争的结果。我们在一个急流模型的框架内讨论了时间尺度的问题及其与流动应力的负应变率敏感性的联系，该模型已知再现了几个实验观察到的特征，包括流动应力的负应变率敏感性。我们试图通过分析模型中弛豫振荡背后的慢流形的几何结构来理解上述问题。我们证明了弛豫振荡的本质是慢流形的非典型弯曲几何的结果。对慢流形结构的分析有助于我们理解慢流形不同区域的时间尺度。利用这一信息，我们能够建立与流动应力的应变率敏感性之间的联系。这一分析还有助于我们对应变速率灵敏度的负分支提供适当的动力学解释。
A characteristic feature of the Portevin-Le Chatelier effect, or the jerky flow, is the stick-slip nature of stress-strain curves which is believed to result from the negative strain rate dependence of the flow stress. The latter is assumed to result from the competition of a few relevant time scales controlling the dynamics of jerky flow. We address the issue of time scales and its connection to the negative strain rate sensitivity of the flow stress within the framework of a model for the jerky flow, which is known to reproduce several experimentally observed features, including the negative strain rate sensitivity of the flow stress. We attempt to understand the above issues by analyzing the geometry of the slow manifold underlying the relaxational oscillations in the model. We show that the nature of the relaxational oscillations is a result of the atypical bent geometry of the slow manifold. The analysis of the slow manifold structure helps us to understand the time scales operating in different regions of the slow manifold. Using this information we are able to establish connection with the strain rate sensitivity of the flow stress. The analysis also helps us to provide a proper dynamical interpretation for the negative branch of the strain rate sensitivity.