{"title":"Solution of a Dugdale–Barenblatt crack in an infinite strip by a hyper-singular integral equation","authors":"","doi":"10.1016/j.tafmec.2024.104625","DOIUrl":null,"url":null,"abstract":"<div><p>This work treats the case of a Dugdale–Barenblatt crack within an infinite strip through the resolution of a hyper singular integral equation. The crack is perpendicular to the strip boundaries and located at its center. The solution approach is based on second order Chebyshev polynomials and requires meticulous treatment of the jump discontinuities within the loading distribution along the crack faces. The relationship between the width of the strip and the length of the cohesive zone has been established. The variation in applied load with the increase in crack length, considering different ratios of the initial crack length to the strip width is illustrated. Furthermore, the crack propagation is simulated. Validation of our approach is achieved through comparison with both the infinite medium case and the work of H. Tada et al. <em>“The Stress Analysis of Cracks Handbook, Del Research Corporation, Hellertown, Pennsylvania. 1973”</em>.</p></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":null,"pages":null},"PeriodicalIF":5.0000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Applied Fracture Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167844224003756","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
This work treats the case of a Dugdale–Barenblatt crack within an infinite strip through the resolution of a hyper singular integral equation. The crack is perpendicular to the strip boundaries and located at its center. The solution approach is based on second order Chebyshev polynomials and requires meticulous treatment of the jump discontinuities within the loading distribution along the crack faces. The relationship between the width of the strip and the length of the cohesive zone has been established. The variation in applied load with the increase in crack length, considering different ratios of the initial crack length to the strip width is illustrated. Furthermore, the crack propagation is simulated. Validation of our approach is achieved through comparison with both the infinite medium case and the work of H. Tada et al. “The Stress Analysis of Cracks Handbook, Del Research Corporation, Hellertown, Pennsylvania. 1973”.
本研究通过超奇异积分方程的解析，处理了无限带钢中的 Dugdale-Barenblatt 裂纹问题。裂缝垂直于带钢边界，位于带钢中心。求解方法以二阶切比雪夫多项式为基础，需要对沿裂纹面的载荷分布中的跳跃不连续性进行细致处理。条带宽度与内聚区长度之间的关系已经确定。考虑到初始裂缝长度与带宽的不同比例，图解了施加载荷随裂缝长度增加而产生的变化。此外，还模拟了裂纹的扩展。通过与无限介质情况和 H. Tada 等人的著作 "The Stress Analysis of Cracks Handbook, Del Research Corporation, Hellertown, Pennsylvania.1973".
期刊介绍：
Theoretical and Applied Fracture Mechanics'' aims & scopes have been re-designed to cover both the theoretical, applied, and numerical aspects associated with those cracking related phenomena taking place, at a micro-, meso-, and macroscopic level, in materials/components/structures of any kind.
The journal aims to cover the cracking/mechanical behaviour of materials/components/structures in those situations involving both time-independent and time-dependent system of external forces/moments (such as, for instance, quasi-static, impulsive, impact, blasting, creep, contact, and fatigue loading). Since, under the above circumstances, the mechanical behaviour of cracked materials/components/structures is also affected by the environmental conditions, the journal would consider also those theoretical/experimental research works investigating the effect of external variables such as, for instance, the effect of corrosive environments as well as of high/low-temperature.
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