A Probabilistic-Phase Field Model for the Fracture of Brittle Materials

IF 1.9 4区材料科学 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY

Modelling and Simulation in Materials Science and Engineering Pub Date : 2023-11-06 DOI:10.1088/1361-651x/ad09ea

MOHAMMAD A ALABDULLAH, Nasr M Ghoniem

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Abstract

Abstract We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase ﬁeld theory, where the complete fracture process is viewed as ”damage percolation” along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to ﬁnite domains, where it is implemented within the Finite Element (FE) framework. The results of phase-ﬁeld simulations at the ”percolation threshold” are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers [1] in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.

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脆性材料断裂的概率相场模型

提出了一种确定脆性材料在一般力学载荷条件下破坏概率的计算方法。该方法由两部分组成:(1)使用相场理论对具有多个裂纹的材料进行数值模拟，其中完整的断裂过程被视为沿关键路径或裂纹簇的“损伤渗透”，而不是传统的Weibull弱链接破坏机制;(2)将Batdorf断裂统计理论扩展到有限域，在有限元(FE)框架内实现。在“渗流阈值”处的相场模拟结果被用作Batdorf理论中的失效数据，以确定总体失效概率。这种方法的输入是原始材料中裂纹的尺寸分布。本文给出了一个例子，其中Abe和同事[1]先前在四点加载中测试的氧化铝样品与我们的数值模拟结果进行了比较。这里开发的方法具有可扩展到更复杂的热机械载荷的优点。

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

Modelling and Simulation in Materials Science and Engineering 工程技术-材料科学：综合

CiteScore

3.30

自引率

5.60%

发文量

审稿时长

1.7 months

期刊介绍： Serving the multidisciplinary materials community, the journal aims to publish new research work that advances the understanding and prediction of material behaviour at scales from atomistic to macroscopic through modelling and simulation. Subject coverage: Modelling and/or simulation across materials science that emphasizes fundamental materials issues advancing the understanding and prediction of material behaviour. Interdisciplinary research that tackles challenging and complex materials problems where the governing phenomena may span different scales of materials behaviour, with an emphasis on the development of quantitative approaches to explain and predict experimental observations. Material processing that advances the fundamental materials science and engineering underpinning the connection between processing and properties. Covering all classes of materials, and mechanical, microstructural, electronic, chemical, biological, and optical properties.