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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:0376-9429
1573-2673
DOI:10.1007/s10704-022-00657-9