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首页> 外文期刊>International Journal of Plasticity >On the coupling of plastic slip and deformation-induced twinning in magnesium: A variationally consistent approach based on energy minimization
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On the coupling of plastic slip and deformation-induced twinning in magnesium: A variationally consistent approach based on energy minimization

机译：镁中塑性滑移和形变孪生的耦合：基于能量最小化的变分一致方法

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The present paper is concerned with the analysis of the deformation systems in single crystal magnesium at the micro-scale and with the resulting texture evolution in a polycrystal representing the macroscopic mechanical response. For that purpose, a variationally consistent approach based on energy minimization is proposed. It is suitable for the modeling of crystal plasticity at finite strains including the phase transition associated with deformation-induced twinning. The method relies strongly on the variational structure of crystal plasticity theory, i.e.; an incremental minimization principle can be derived which allows to determine the unknown slip rates by computing the stationarity conditions of a (pseudo) potential. Phase transition associated with twinning is modeled in a similar fashion. More precisely, a solid-solid phase transition corresponding to twinning is assumed, if this is energetically favorable. Mathematically speaking, the aforementioned transition can be interpreted as a certain rank-one convexification. Since such a scheme is computationally very expensive and thus, it cannot be applied to the analysis of a polycrystal, a computationally more efficient approximation is elaborated. Within this approximation, the deformation induced by twinning is decomposed into the reorientation of the crystal lattice and simple shear. The latter is assumed to be governed by means of a standard Schmid-type plasticity law (pseudo-dislocation), while the reorientation of the crystal lattice is considered, when the respective plastic shear strain reaches a certain threshold value. The underlying idea is in line with experimental observations, where dislocation slip within the twinned domain is most frequently seen, if the twin laminate reaches a critical volume. The resulting model predicts a stress-strain response in good agreement with that of a rank-one convexification method, while showing the same numerical efficiency as a classical Taylor-type approximation. Consequently, it combines the advantages of both limiting cases. The model is calibrated for single crystal magnesium by means of the channel die test and finally applied to the analysis of texture evolution in a polycrystal. Comparisons of the predicted numerical results to their experimental counterparts show that the novel model is able to capture the characteristic mechanical response of magnesium very well.
机译：本文涉及在微观尺度上分析单晶镁中的变形系统，并涉及代表宏观机械响应的多晶中的织构演变。为此，提出了一种基于能量最小化的变化一致的方法。它适用于对有限应变下的晶体可塑性进行建模，包括与形变孪生相关的相变。该方法强烈依赖于晶体可塑性理论的变化结构，即：可以导出增量最小化原理，该原理允许通过计算（伪）势的平稳性条件来确定未知的滑移率。与孪生相关的相变以相似的方式建模。更精确地，假设在能量上有利的是对应于孪晶的固-固相变。从数学上讲，上述过渡可以解释为一定的一阶凸化。由于这种方案在计算上非常昂贵，因此不能应用于多晶的分析，因此阐述了一种在计算上更有效的近似方法。在该近似值内，由孪晶引起的变形分解为晶格的重新取向和简单的剪切。假定后者是通过标准的Schmid型可塑性定律（伪位错）控制的，而当各个塑性剪切应变达到某个阈值时，则考虑晶格的重新定向。基本思想与实验观察一致，如果孪晶层压板达到临界体积，则在孪晶畴内最常出现位错滑移。所得模型预测的应力-应变响应与第一级凸化方法的应力应变响应非常一致，同时显示出与经典泰勒型近似法相同的数值效率。因此，它结合了两种极限情况的优点。通过通道模测试对单晶镁进行了模型校准，最后将其应用于多晶体的织构演变分析。预测数值结果与实验结果的比较表明，该新型模型能够很好地捕捉镁的特征机械响应。

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