A thin-film-covered mode III crack with dislocation-free zones

We use complex variable methods and the theory of singular integral equations to study a thin-film-covered mode III crack with dislocation-free zones (DFZs) under uniform remote anti-plane shear stress. The equilibrium condition is formulated in terms of a single singular integral equation construct...

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Published in:	International journal of fracture Vol. 239; no. 1; pp. 1 - 12
Main Authors:	Wang, Xu, Schiavone, Peter
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01.01.2023 Springer Nature B.V
Subjects:	Automotive Engineering Characterization and Evaluation of Materials Chebyshev approximation Civil Engineering Classical Mechanics Complex variables Corrosion Crack tips Distribution functions Engineering Equilibrium Equilibrium conditions Integral equations Mechanical Engineering Original Paper Plastic zones Screw dislocations Shear stress Singular integral equations Stress intensity factors Thin films Thin-film-covered crack Singular integral equation Dislocation-free zone Dislocation shielding effect Plastic zone Complex variable method
ISSN:	0376-9429, 1573-2673
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Abstract	We use complex variable methods and the theory of singular integral equations to study a thin-film-covered mode III crack with dislocation-free zones (DFZs) under uniform remote anti-plane shear stress. The equilibrium condition is formulated in terms of a single singular integral equation constructed in the image plane via the solution of the problem of a single screw dislocation interacting with a completely coated crack and the method of continuously distributed dislocations. The singular integral equation is solved numerically using the Gauss–Chebyshev integration formula to arrive at the dislocation distribution function, the DFZ condition, the total number of dislocations in the plastic zone and the local mode III stress intensity factor at the crack tip.
AbstractList	We use complex variable methods and the theory of singular integral equations to study a thin-film-covered mode III crack with dislocation-free zones (DFZs) under uniform remote anti-plane shear stress. The equilibrium condition is formulated in terms of a single singular integral equation constructed in the image plane via the solution of the problem of a single screw dislocation interacting with a completely coated crack and the method of continuously distributed dislocations. The singular integral equation is solved numerically using the Gauss–Chebyshev integration formula to arrive at the dislocation distribution function, the DFZ condition, the total number of dislocations in the plastic zone and the local mode III stress intensity factor at the crack tip.
Author	Schiavone, Peter Wang, Xu
Author_xml	– sequence: 1 givenname: Xu orcidid: 0000-0001-7509-8012 surname: Wang fullname: Wang, Xu email: xuwang@ecust.edu.cn organization: School of Mechanical and Power Engineering, East China University of Science and Technology – sequence: 2 givenname: Peter orcidid: 0000-0003-4741-0165 surname: Schiavone fullname: Schiavone, Peter email: p.schiavone@ualberta.ca organization: Department of Mechanical Engineering, University of Alberta
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Cites_doi	10.1007/BF00183821 10.1063/1.351613 10.1115/1.2888330 10.1023/A:1022240026345 10.1016/0013-7944(94)00207-X 10.1016/0036-9748(82)90382-9 10.1063/1.349319 10.1063/1.328692 10.1080/01418619008235559 10.1016/0001-6160(83)90035-4 10.1007/BF00032475 10.1090/qam/408277 10.1016/0020-7225(87)90107-8 10.1023/A:1007422431415 10.1016/S0020-7683(99)00238-3 10.1007/s10704-008-9185-7 10.1016/0956-7151(93)90249-R 10.1063/1.331448 10.1016/1359-6454(96)00066-3 10.1016/j.engfracmech.2015.10.001 10.1063/1.344111 10.1023/A:1007467331180 10.1007/BF00963390 10.1093/oso/9780195074475.001.0001
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SubjectTerms	Automotive Engineering Characterization and Evaluation of Materials Chebyshev approximation Civil Engineering Classical Mechanics Complex variables Corrosion Crack tips Distribution functions Engineering Equilibrium Equilibrium conditions Integral equations Mechanical Engineering Original Paper Plastic zones Screw dislocations Shear stress Singular integral equations Stress intensity factors Thin films
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Title	A thin-film-covered mode III crack with dislocation-free zones
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