Self-consistent homogenization approach for polycrystals within second gradient elasticity

IF 1.9 4区 工程技术 Q3 MECHANICS
Yury Solyaev
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引用次数: 0

Abstract

In this paper, we propose a generalized variant of Kröner’s self-consistent scheme for evaluation of the effective standard and gradient elastic moduli of polycrystalline materials within Mindlin-Toupin second-gradient elasticity theory. Assuming random orientation of crystallites (grains) we use an extended Eshelby’s equivalent inclusion method and mapping conditions between the prescribed linear distribution of macro-strain and corresponding micro-scale field variables averaged over the volume and all possible orientations of single grain. It is found that the developed self-consistent scheme predicts an absence of gradient effects at the macro-scale level for the model of ellipsoidal grains made of the first gradient (Cauchy-type) material. However, for the case of the second gradient crystallites, established approach allows to obtain a set of non-linear relations for determination of all effective standard and gradient elastic moduli of polycrystals. Example of calculations under simplified constitutive assumptions is presented for the model of anisotropic cubic Fe crystallites with spherical shape. It is shown that the presented approach predicts an increase of the effective length scale parameter of polycrystalline aggregates due to misorientation of grains axes and takes into account the size effects related to the mean diameter of grains.

二阶梯度弹性下多晶体的自洽均匀化方法
本文在Mindlin-Toupin二阶梯度弹性理论中,提出了Kröner自一致方案的广义变体,用于评估多晶材料的有效标准弹性模量和梯度弹性模量。假设晶体(晶粒)的取向是随机的,我们采用扩展的Eshelby等效包合方法,并在规定的宏观应变线性分布与相应的微尺度场变量在体积上的平均和单个晶粒的所有可能取向之间建立映射条件。研究发现,所建立的自洽格式预测了由第一梯度(柯西型)材料构成的椭球颗粒模型在宏观尺度上不存在梯度效应。然而,对于第二梯度晶体,所建立的方法允许获得一组非线性关系,用于确定多晶体的所有有效标准和梯度弹性模量。给出了球面各向异性立方铁晶体模型在简化本构假设下的计算实例。结果表明,该方法预测了由于晶粒轴向错误导致的多晶聚集体有效长度尺度参数的增加,并考虑了与晶粒平均直径相关的尺寸效应。
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来源期刊
CiteScore
4.10
自引率
4.20%
发文量
114
审稿时长
9 months
期刊介绍: Mechanics Research Communications publishes, as rapidly as possible, peer-reviewed manuscripts of high standards but restricted length. It aims to provide: • a fast means of communication • an exchange of ideas among workers in mechanics • an effective method of bringing new results quickly to the public • an informal vehicle for the discussion • of ideas that may still be in the formative stages The field of Mechanics will be understood to encompass the behavior of continua, fluids, solids, particles and their mixtures. Submissions must contain a strong, novel contribution to the field of mechanics, and ideally should be focused on current issues in the field involving theoretical, experimental and/or applied research, preferably within the broad expertise encompassed by the Board of Associate Editors. Deviations from these areas should be discussed in advance with the Editor-in-Chief.
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