Statistical properties of effective elastic moduli of random cubic polycrystals

IF 1.2 4区工程技术 Q3 ENGINEERING, MECHANICAL

Mechanics & Industry Pub Date : 2023-01-01 DOI:10.1051/meca/2023030

Ningyue Sheng, Shahram Khazaie, Mathilde Chevreuil, Sylvain Fréour

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引用次数: 1

Abstract

The homogenized elastic properties of polycrystals depend on the grain morphology and crystallographic orientations. For simplification purposes, the orientations of the grains are usually considered three independent Euler angles. However, experimental investigations reveal spatial correlations in these angles. The Karhunen–Loève expansion is used to generate random fields of Euler angles having exponential kernel functions with varying correlation lengths. The effective elastic moduli for numerically generated statistically equiaxed cubic polycrystals are estimated via the classical Eshelby–Kröner Self-Consistent homogenization model. The influence of the correlation lengths of the orientations’ random fields on the statistical properties of the effective elastic moduli has been investigated. Our results show that spatially correlated Euler angles could increase the variability of the homogenized elastic properties compared to the ones having uncorrelated Euler angles. Nevertheless, using independent random variables for Euler angles remains valid when correlation lengths are close to the average grain size.

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随机立方多晶有效弹性模量的统计性质

多晶的均匀弹性性能取决于晶粒形态和晶体取向。为简化起见，晶粒的取向通常被认为是三个独立的欧拉角。然而，实验研究揭示了这些角度的空间相关性。利用karhunen - lo展开生成具有不同相关长度的指数核函数的欧拉角随机场。通过经典的Eshelby-Kröner自洽均匀化模型，估计了数值生成的统计等轴立方多晶的有效弹性模量。研究了方向随机场的相关长度对有效弹性模量统计性质的影响。我们的研究结果表明，与不相关欧拉角相比，空间相关欧拉角可以增加均匀化弹性特性的可变性。然而，当相关长度接近平均晶粒尺寸时，使用独立随机变量表示欧拉角仍然有效。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mechanics & Industry ENGINEERING, MECHANICAL-MECHANICS

CiteScore

2.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： An International Journal on Mechanical Sciences and Engineering Applications With papers from industry, Research and Development departments and academic institutions, this journal acts as an interface between research and industry, coordinating and disseminating scientific and technical mechanical research in relation to industrial activities. Targeted readers are technicians, engineers, executives, researchers, and teachers who are working in industrial companies as managers or in Research and Development departments, technical centres, laboratories, universities, technical and engineering schools. The journal is an AFM (Association Française de Mécanique) publication.