{"title":"Interaction among interfacial offset cracks in composite materials under the anti‐plane shear loading","authors":"A. Tanwar, Subir Das, E. Crăciun, H. Altenbach","doi":"10.1002/zamm.202300081","DOIUrl":null,"url":null,"abstract":"The present article considers an anti‐plane stress problem of three cracks at different orthotropic materials' interfaces. According to the geometry of the problem, the governing equations and mixed boundary conditions have been formulated. Fourier integral transformation is used to convert the mixed boundary value problem into dual integral equations, which gives two equations containing infinite series. The investigation of the problem concerning anti‐plane cracks subjected to static loadings is done with the help of the Schmidt method to satisfy the given boundary conditions. The difference in displacements is expanded to proceed further in the problem, which becomes zero outside the cracks. Numerical computations are carried out for the graphical representation of stress intensity factors (SIFs) at all cracks' tips. The Interaction among the cracks as those are in close proximity to each other or move away are represented pictorially. Detailed numerical results and discussion are done for the considered materials, which include aluminium, epoxy and graphite epoxy. The novelty of the present article is the numerical analysis and pictorial presentation of SIFs at the tips of interfacial offset parallel cracks for various crack lengths and normalised heights for different combinations of materials. The authors have obtained variations in SIFs for the cracks at the interfaces of dissimilar composite materials.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1002/zamm.202300081","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The present article considers an anti‐plane stress problem of three cracks at different orthotropic materials' interfaces. According to the geometry of the problem, the governing equations and mixed boundary conditions have been formulated. Fourier integral transformation is used to convert the mixed boundary value problem into dual integral equations, which gives two equations containing infinite series. The investigation of the problem concerning anti‐plane cracks subjected to static loadings is done with the help of the Schmidt method to satisfy the given boundary conditions. The difference in displacements is expanded to proceed further in the problem, which becomes zero outside the cracks. Numerical computations are carried out for the graphical representation of stress intensity factors (SIFs) at all cracks' tips. The Interaction among the cracks as those are in close proximity to each other or move away are represented pictorially. Detailed numerical results and discussion are done for the considered materials, which include aluminium, epoxy and graphite epoxy. The novelty of the present article is the numerical analysis and pictorial presentation of SIFs at the tips of interfacial offset parallel cracks for various crack lengths and normalised heights for different combinations of materials. The authors have obtained variations in SIFs for the cracks at the interfaces of dissimilar composite materials.
期刊介绍:
ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.