Subhrangsu Saha , John E. Dolbow , Oscar Lopez-Pamies
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Centered around experimental observations, the idea consists in: (<span><math><mi>i</mi></math></span>) viewing the critical energy release rate <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> <em>not</em> as a material constant but rather as a material function of both space <span><math><mi>X</mi></math></span> and time <span><math><mi>t</mi></math></span>, (<span><math><mrow><mi>i</mi><mi>i</mi></mrow></math></span>) one that decreases in value as the loading progresses, this solely within a small region <span><math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>ℓ</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> around crack fronts, with the characteristic size <span><math><mi>ℓ</mi></math></span> of such a region being material specific, and (<span><math><mrow><mi>i</mi><mi>i</mi><mi>i</mi></mrow></math></span>) with the decrease in value of <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> being dependent on the history of the elastic fields in <span><math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>ℓ</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>. By construction, the proposed Griffith formulation is able to describe any Paris-law behavior of the growth of large cracks in nominally elastic brittle materials for the limiting case when the loading is cyclic. For the opposite limiting case when the loading is monotonic, the formulation reduces to the classical Griffith formulation. Additional properties of the proposed formulation are illustrated via a parametric analysis and direct comparisons with representative fatigue fracture experiments on a ceramic, mortar, and PMMA.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0000,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022509624002205/pdfft?md5=d2f7aaa8c90f1b113e4afa2571d129bc&pid=1-s2.0-S0022509624002205-main.pdf","citationCount":"0","resultStr":"{\"title\":\"A Griffith description of fracture for non-monotonic loading with application to fatigue\",\"authors\":\"Subhrangsu Saha , John E. Dolbow , Oscar Lopez-Pamies\",\"doi\":\"10.1016/j.jmps.2024.105754\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>With the fundamental objective of establishing the universality of the Griffith energy competition to describe the growth of large cracks in solids <em>not</em> just under monotonic but under general loading conditions, this paper puts forth a generalization of the classical Griffith energy competition in nominally elastic brittle materials to arbitrary <em>non-monotonic</em> quasistatic loading conditions, which include monotonic and cyclic loadings as special cases. Centered around experimental observations, the idea consists in: (<span><math><mi>i</mi></math></span>) viewing the critical energy release rate <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> <em>not</em> as a material constant but rather as a material function of both space <span><math><mi>X</mi></math></span> and time <span><math><mi>t</mi></math></span>, (<span><math><mrow><mi>i</mi><mi>i</mi></mrow></math></span>) one that decreases in value as the loading progresses, this solely within a small region <span><math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>ℓ</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> around crack fronts, with the characteristic size <span><math><mi>ℓ</mi></math></span> of such a region being material specific, and (<span><math><mrow><mi>i</mi><mi>i</mi><mi>i</mi></mrow></math></span>) with the decrease in value of <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> being dependent on the history of the elastic fields in <span><math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>ℓ</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>. By construction, the proposed Griffith formulation is able to describe any Paris-law behavior of the growth of large cracks in nominally elastic brittle materials for the limiting case when the loading is cyclic. For the opposite limiting case when the loading is monotonic, the formulation reduces to the classical Griffith formulation. Additional properties of the proposed formulation are illustrated via a parametric analysis and direct comparisons with representative fatigue fracture experiments on a ceramic, mortar, and PMMA.</p></div>\",\"PeriodicalId\":17331,\"journal\":{\"name\":\"Journal of The Mechanics and Physics of Solids\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":5.0000,\"publicationDate\":\"2024-06-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0022509624002205/pdfft?md5=d2f7aaa8c90f1b113e4afa2571d129bc&pid=1-s2.0-S0022509624002205-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of The Mechanics and Physics of Solids\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022509624002205\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Mechanics and Physics of Solids","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022509624002205","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
本文的基本目标是建立格里菲斯能量竞争的普遍性,以描述固体中大裂缝的生长,不仅在单调加载条件下,而且在一般加载条件下,提出了名义弹性脆性材料中经典格里菲斯能量竞争的一般化,以适应任意非单调准静态加载条件,包括作为特例的单调和循环加载。以实验观察为中心,该想法包括:(i) 将临界能量释放率 Gc 视为空间 X 和时间 t 的材料函数,而不是材料常数;(ii) 随着加载的进行,Gc 的值会减小,这仅仅是在裂纹前沿周围的一个小区域 Ωℓ(t)内,该区域的特征尺寸 ℓ 取决于具体材料;(iii) Gc 值的减小取决于 Ωℓ(t)中弹性场的历史。根据构造,在循环加载的极限情况下,所提出的格里菲斯公式能够描述名义弹性脆性材料中大裂缝生长的任何巴黎定律行为。对于单调加载时的相反极限情况,该公式可还原为经典的格里菲斯公式。通过参数分析以及与陶瓷、砂浆和聚甲基丙烯酸甲酯的代表性疲劳断裂实验的直接比较,说明了所提公式的其他特性。
A Griffith description of fracture for non-monotonic loading with application to fatigue
With the fundamental objective of establishing the universality of the Griffith energy competition to describe the growth of large cracks in solids not just under monotonic but under general loading conditions, this paper puts forth a generalization of the classical Griffith energy competition in nominally elastic brittle materials to arbitrary non-monotonic quasistatic loading conditions, which include monotonic and cyclic loadings as special cases. Centered around experimental observations, the idea consists in: () viewing the critical energy release rate not as a material constant but rather as a material function of both space and time , () one that decreases in value as the loading progresses, this solely within a small region around crack fronts, with the characteristic size of such a region being material specific, and () with the decrease in value of being dependent on the history of the elastic fields in . By construction, the proposed Griffith formulation is able to describe any Paris-law behavior of the growth of large cracks in nominally elastic brittle materials for the limiting case when the loading is cyclic. For the opposite limiting case when the loading is monotonic, the formulation reduces to the classical Griffith formulation. Additional properties of the proposed formulation are illustrated via a parametric analysis and direct comparisons with representative fatigue fracture experiments on a ceramic, mortar, and PMMA.
期刊介绍:
The aim of Journal of The Mechanics and Physics of Solids is to publish research of the highest quality and of lasting significance on the mechanics of solids. The scope is broad, from fundamental concepts in mechanics to the analysis of novel phenomena and applications. Solids are interpreted broadly to include both hard and soft materials as well as natural and synthetic structures. The approach can be theoretical, experimental or computational.This research activity sits within engineering science and the allied areas of applied mathematics, materials science, bio-mechanics, applied physics, and geophysics.
The Journal was founded in 1952 by Rodney Hill, who was its Editor-in-Chief until 1968. The topics of interest to the Journal evolve with developments in the subject but its basic ethos remains the same: to publish research of the highest quality relating to the mechanics of solids. Thus, emphasis is placed on the development of fundamental concepts of mechanics and novel applications of these concepts based on theoretical, experimental or computational approaches, drawing upon the various branches of engineering science and the allied areas within applied mathematics, materials science, structural engineering, applied physics, and geophysics.
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