Anisotropic effect of regular particle distribution in elastic–plastic composites: The modified tangent cluster model and numerical homogenization

IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
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引用次数: 0

Abstract

Estimation of macroscopic properties of heterogeneous materials has always posed significant problems. Procedures based on numerical homogenization, although very flexible, consume a lot of time and computing power. Thus, many attempts have been made to develop analytical models that could provide robust and computationally efficient tools for this purpose. The goal of this paper is to develop a reliable analytical approach to finding the effective elastic–plastic response of metal matrix composites (MMC) and porous metals (PM) with a predefined particle or void distribution, as well as to examine the anisotropy induced by regular inhomogeneity arrangements. The proposed framework is based on the idea of Molinari & El Mouden (1996) to improve classical mean-field models of thermoelastic media by taking into account the interactions between each pair of inhomogeneities within the material volume, known as a cluster model. Both elastic and elasto-plastic regimes are examined. A new extension of the original formulation, aimed to account for the non-linear plastic regime, is performed with the use of the modified tangent linearization of the metal matrix constitutive law. The model uses the second stress moment to track the accumulated plastic strain in the matrix. In the examples, arrangements of spherical inhomogeneities in three Bravais lattices of cubic symmetry (Regular Cubic, Body-Centered Cubic and Face-Centered Cubic) are considered for two basic material scenarios: “hard-in-soft” (MMC) and “soft-in-hard” (PM). As a means of verification, the results of micromechanical mean-field modeling are compared with those of numerical homogenization performed using the Finite Element Method (FEM). In the elastic regime, a comparison is also made with several other micromechanical models dedicated to periodic composites. Within both regimes, the results obtained by the cluster model are qualitatively and quantitatively consistent with FEM calculations, especially for volume fractions of inclusions up to 40%.

弹性塑料复合材料中规则颗粒分布的各向异性效应:修正的正切簇模型和数值均质化
异质材料宏观特性的估算一直是个大问题。基于数值均质化的程序虽然非常灵活,但却耗费大量时间和计算能力。因此,人们多次尝试开发分析模型,以便为此提供稳健且计算效率高的工具。本文的目标是开发一种可靠的分析方法,以找到具有预定颗粒或空隙分布的金属基复合材料(MMC)和多孔金属(PM)的有效弹塑性响应,并研究规则不均匀排列引起的各向异性。所提出的框架基于 Molinari & El Mouden(1996 年)的想法,即通过考虑材料体积内每对非均质物之间的相互作用(即群集模型)来改进热弹性介质的经典均场模型。对弹性和弹塑性状态都进行了研究。为了考虑非线性塑性状态,对原始公式进行了新的扩展,使用了金属基体构成定律的修正切线线性化。该模型使用第二应力矩来跟踪基体中的累积塑性应变。在示例中,考虑了三种立方对称布拉维晶格(常规立方、体心立方和面心立方)中球形非均质体的排列,以及两种基本材料情况:"软中硬"(MMC)和 "硬中软"(PM)。作为验证手段,将微机械平均场建模结果与使用有限元法(FEM)进行数值均质化的结果进行了比较。在弹性状态下,还与其他几种专门用于周期性复合材料的微机械模型进行了比较。在这两种情况下,群集模型得到的结果在质量和数量上都与有限元法的计算结果一致,尤其是当夹杂物的体积分数达到 40% 时。
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来源期刊
International Journal of Engineering Science
International Journal of Engineering Science 工程技术-工程:综合
CiteScore
11.80
自引率
16.70%
发文量
86
审稿时长
45 days
期刊介绍: The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome. The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process. Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.
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