用均质化技术估计多晶的力学场波动

R. Brenner, O. Castelnau, L. Badea
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引用次数: 41

摘要

研究了多晶中产生的力学场波动。这些材料被视为具有大量各向异性相和“颗粒”拓扑结构的Hashin-Shtrikman型复合材料。我们证明了相内应力和应变(速率)秒矩的估计归结为线性方程组的分辨率。应用于线性粘性面心立方(FCC)多晶,观察到即使当相应的施密德因子由于晶间相互作用而消失时,也可以估计出显著的局部滑移率。对于粘塑性多晶体的应用,比较了自洽格式的割线和仿射非线性扩展。在大应力敏感性(n = 30)下,观察到割线线性化导致每个阶段所有滑移系统的滑移率几乎均匀,而仿射方法预测的滑移率要大得多。此外,相平均应力(或应变率)与相应的第二弯矩之间没有一对一的关系。强调在处理微观组织演化时应考虑相内应变速率非均质性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mechanical field fluctuations in polycrystals estimated by homogenization techniques
The fluctuation of mechanical fields arising in polycrystals is investigated. These materials are viewed as composites of the Hashin–Shtrikman type with a large number of anisotropic phases and a ‘granular’ topology. We show that the estimation of the intra–phase stress and strain (rate) second moments comes down to the resolution of a linear system of equations. Applied to a linear viscous face–centred cubic (FCC) polycrystal, it is observed that significant local slip rates are estimated even when the corresponding Schmid factor vanishes, due to the intergranular interactions. For the application to viscoplastic polycrystals, the secant and affine nonlinear extensions of the self–consistent scheme are compared. At large stress sensitivity (n = 30), it is observed that the secant linearization leads to almost uniform slip rates for all slip systems in every phase, whereas the affine approach predicts a much larger spread. Furthermore, there is no one–to–one relation between the phase–average stress (or strain rate) and the corresponding second moment. It is emphasized that intra–phase strain–rate heterogeneities should be accounted for when dealing with microstructure evolution.
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