Mode-I penny-shaped crack problem in an infinite space of one-dimensional hexagonal piezoelectric quasicrystal: exact solutions

IF 2.2 3区工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY

International Journal of Fracture Pub Date : 2023-09-07 DOI:10.1007/s10704-023-00742-7

Jiaqi Zhang, Xiangyu Li, Guozheng Kang

{"title":"Mode-I penny-shaped crack problem in an infinite space of one-dimensional hexagonal piezoelectric quasicrystal: exact solutions","authors":"Jiaqi Zhang, Xiangyu Li, Guozheng Kang","doi":"10.1007/s10704-023-00742-7","DOIUrl":null,"url":null,"abstract":"<div><p>This paper aims to study the Mode-I penny-shaped crack problem of an infinite body of one-dimensional hexagonal piezoelectric quasicrystal. The problem is transformed into a mixed-boundary value problem in the context of electro-elasticity of quasicrystals, and the corresponding integro-differential equations are analytically solved. Two extreme cases of electrically impermeable and permeable crack surface are considered. By virtue of the generalized potential theory method, the three-dimensional complete analytical solutions of three-dimensional crack problems under symmetric concentrated and uniform loads are expressed in terms of elementary functions. Important parameters in fracture mechanics are explicitly derived, such as crack surface displacements, the distributions of generalized stresses at the crack tip and the corresponding generalized stress intensity factors. The validity of the proposed solutions and the coupling effect of phonon-phason-electric fields are investigagted through numerical examples.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"246 2-3","pages":"203 - 223"},"PeriodicalIF":2.2000,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Fracture","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10704-023-00742-7","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

This paper aims to study the Mode-I penny-shaped crack problem of an infinite body of one-dimensional hexagonal piezoelectric quasicrystal. The problem is transformed into a mixed-boundary value problem in the context of electro-elasticity of quasicrystals, and the corresponding integro-differential equations are analytically solved. Two extreme cases of electrically impermeable and permeable crack surface are considered. By virtue of the generalized potential theory method, the three-dimensional complete analytical solutions of three-dimensional crack problems under symmetric concentrated and uniform loads are expressed in terms of elementary functions. Important parameters in fracture mechanics are explicitly derived, such as crack surface displacements, the distributions of generalized stresses at the crack tip and the corresponding generalized stress intensity factors. The validity of the proposed solutions and the coupling effect of phonon-phason-electric fields are investigagted through numerical examples.

Abstract Image

查看原文本刊更多论文

一维六边形压电准晶体无限空间中的i型便士型裂纹问题:精确解

本文旨在研究一维六方压电准晶体无限体的 Mode-I 笔形裂纹问题。将该问题转化为准晶体电弹性背景下的混合边界值问题，并分析求解了相应的积分微分方程。考虑了裂缝表面不透电和透电的两种极端情况。利用广义势理论方法，用初等函数表达了对称集中载荷和均匀载荷下三维裂纹问题的三维完整解析解。明确推导出了断裂力学中的重要参数，如裂纹表面位移、裂纹尖端的广义应力分布以及相应的广义应力强度因子。通过数值示例研究了所提解决方案的有效性以及声-声-电场的耦合效应。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

International Journal of Fracture 物理-材料科学：综合

CiteScore

4.80

自引率

8.00%

发文量

审稿时长

13.5 months

期刊介绍： The International Journal of Fracture is an outlet for original analytical, numerical and experimental contributions which provide improved understanding of the mechanisms of micro and macro fracture in all materials, and their engineering implications. The Journal is pleased to receive papers from engineers and scientists working in various aspects of fracture. Contributions emphasizing empirical correlations, unanalyzed experimental results or routine numerical computations, while representing important necessary aspects of certain fatigue, strength, and fracture analyses, will normally be discouraged; occasional review papers in these as well as other areas are welcomed. Innovative and in-depth engineering applications of fracture theory are also encouraged. In addition, the Journal welcomes, for rapid publication, Brief Notes in Fracture and Micromechanics which serve the Journal''s Objective. Brief Notes include: Brief presentation of a new idea, concept or method; new experimental observations or methods of significance; short notes of quality that do not amount to full length papers; discussion of previously published work in the Journal, and Brief Notes Errata.