Development of a distributed dislocation dipole technique for the analysis of multiple straight, kinked and branched cracks in an elastic half-plane

The effective role of a distributed dislocation technique accompanied by a nonlocal elasticity model has been demonstrated for the crack problem in a half-plane. The dislocation solution is employed to model and analyze the anti-plane crack problem for nonlocal elasticity using the distributed dislocation technique. The solution of dislocation in the half-plane has been extracted through the solution of dislocation in an infinite plane by the image method. The dislocation solution has been utilized to formulate integral equations for dislocation density functions on the surface of a smooth crack embedded in the half-plane under anti-plane loads. The integral equations are of the Cauchy singular type, and have been solved numerically. Multiple cracks with different configurations have been solved; results demonstrate that the nonlocal theory predicts a certain stress value in the crack tip.

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A New Defect in Polyethylene Single Crystals

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100070795 ◽

1973 ◽

Vol 31 ◽

pp. 70-71

Author(s):

E. L. Thomas ◽

S. L. Sass

Keyword(s):

Single Crystals ◽

Screw Dislocation ◽

Small Distance ◽

Dipole Model ◽

Dislocation Dipole ◽

Chain Folding ◽

Black And White ◽

Polymer Crystal ◽

Different Types

In polyethylene single crystals pairs of black and white lines spaced 700-3,000Å apart, parallel to the [100] and [010] directions, have been identified as microsector boundaries. A microsector is formed when the plane of chain folding changes over a small distance within a polymer crystal. In order for the different types of folds to accommodate at the boundary between the 2 fold domains, a staggering along the chain direction and a rotation of the chains in the plane of the boundary occurs. The black-white contrast from a microsector boundary can be explained in terms of these chain rotations. We demonstrate that microsectors can terminate within the crystal and interpret the observed terminal strain contrast in terms of a screw dislocation dipole model.

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Formation of Persistent Slip Band in Fatigued Copper Single Crystals

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100054807 ◽

1982 ◽

Vol 40 ◽

pp. 470-471

Author(s):

N. Y. Jin

Keyword(s):

Volume Fraction ◽

Fatigue Cracks ◽

Wall Structure ◽

Matrix Structure ◽

Dislocation Dipole ◽

Slip Bands ◽

Persistent Slip Bands ◽

The Matrix ◽

Hard Shell ◽

Copper Single Crystals

Localised plastic deformation in Persistent Slip Bands(PSBs) is a characteristic feature of fatigue in many materials. The dislocation structure in the PSBs contains regularly spaced dislocation dipole walls occupying a volume fraction of around 10%. The remainder of the specimen, the inactive "matrix", contains dislocation veins at a volume fraction of 50% or more. Walls and veins are both separated by regions in which the dislocation density is lower by some orders of magnitude. Since the PSBs offer favorable sites for the initiation of fatigue cracks, the formation of the PSB wall structure is of great interest. Winter has proposed that PSBs form as the result of a transformation of the matrix structure to a regular wall structure, and that the instability occurs among the broad dipoles near the center of a vein rather than in the hard shell surounding the vein as argued by Kulmann-Wilsdorf.

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New possibilities for phaseless microwave diagnostics. Part2: The uniqueness problem and half plane imaging

IEE Proceedings H Microwaves Antennas and Propagation ◽

10.1049/ip-h-2.1985.0054 ◽

1985 ◽

Vol 132 (5) ◽

pp. 299 ◽

Cited By ~ 1

Author(s):

S. Sali

Keyword(s):

Half Plane ◽

Uniqueness Problem ◽

Microwave Diagnostics

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ErdoÌ‹s distance problem in the hyperbolic half-plane

10.32469/10355/5341 ◽

2009 ◽

Author(s):

Steven Senger

Keyword(s):

Half Plane ◽

Distance Problem

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Approximate Solution Of A Singular Integral Equation With A Multiplicative Cauchy Kernel In The Half-Plane

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2008-0010 ◽

2008 ◽

Vol 8 (2) ◽

pp. 143-154 ◽

Cited By ~ 1

Author(s):

P. KARCZMAREK

Keyword(s):

Integral Equation ◽

Approximate Solution ◽

Singular Integral Equation ◽

Half Plane ◽

Singular Integral ◽

Trigonometric Polynomials ◽

Cauchy Kernel

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

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