{"title":"Mode III crack approaching the wedge-shaped elastic inclusion","authors":"Victor V. Tikhomirov","doi":"10.1016/j.spjpm.2017.06.001","DOIUrl":null,"url":null,"abstract":"<div><p>The problem on an antiplane semi-infinite crack approaching an elastic wedge-shaped inclusion is considered. The problem has been solved exactly using the Mellin integral transformation and the Wiener–Hopf method. The asymptotic behavior of the stress intensity factor <em>K</em><sub>III</sub> in the crack tip was studied for short distances from the crack to the inclusion vicinity. Depending on the composition parameters, the crack was shown to be stable (<em>K</em><sub>III</sub> <!-->→<!--> <!-->0) or unstable (<em>K</em><sub>III</sub> <!-->→<!--> <!-->∞). Provided that the interface has a corner point, the crack growth can be unstable (unlike the smooth interface) for some parameter values even though the crack approaches, from a soft material, a relatively harder inclusion. Alternatively, the possibility of <em>K</em><sub>III</sub> <!-->→<!--> <!-->0 exists provided the crack approaching a soft inclusion from a hard material.</p></div>","PeriodicalId":41808,"journal":{"name":"St Petersburg Polytechnic University Journal-Physics and Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2000,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.spjpm.2017.06.001","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Polytechnic University Journal-Physics and Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2405722317300579","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
The problem on an antiplane semi-infinite crack approaching an elastic wedge-shaped inclusion is considered. The problem has been solved exactly using the Mellin integral transformation and the Wiener–Hopf method. The asymptotic behavior of the stress intensity factor KIII in the crack tip was studied for short distances from the crack to the inclusion vicinity. Depending on the composition parameters, the crack was shown to be stable (KIII → 0) or unstable (KIII → ∞). Provided that the interface has a corner point, the crack growth can be unstable (unlike the smooth interface) for some parameter values even though the crack approaches, from a soft material, a relatively harder inclusion. Alternatively, the possibility of KIII → 0 exists provided the crack approaching a soft inclusion from a hard material.
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