Journal Article10.1007/PL00020063
Surface dislocation model of a dislocation in a two-phase medium
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TL;DR: The surface dislocation method developed earlier for solving the free surface boundary problem is now extended to the two-phase interface boundary problem wherein a lattice dislocation is situated in one of the phases as mentioned in this paper.
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Abstract: The surface dislocation method developed earlier for solving the free surface boundary problem is now extended to the two-phase interface boundary problem wherein a lattice dislocation is situated in one of the phases. The interface is planar where two semi-infinite half spaces of different elastic properties are joined. The interface consists of four surface arrays of dislocations, two in each phase, so that the continuity of two stress components and two displacement components is maintained. The continuous distribution of dislocations is employed to arrive at the distribution function representing the surface arrays. The Airy stress functions for the two phases are derived and shown to give the same result as that obtained earlier by other methods. The distortions involved across the interface are represented in terms of simple surface arrays to show the advantage of the surface dislocation model. The stress field around the dislocation in the two-phase medium is plotted and the effect of the shear modulus of the second phase and of Poisson's ratio discussed. The advantages of applying the surface dislocation model either by the continuous distribution method or the discrete dislocation method are indicated.
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Citations
Straight Edge Dislocation in a Thin Two‐Phase Plate I. Elastic Stress Fields
M. Yu. Gutkin,Alexey E. Romanov +1 more
TL;DR: In this article, the boundary value problem in the theory of elasticity for straight edge dislocations placed parallel to interfaces in thin two-phase different-modulus plates is received for the first time with the aid of the modernized method of the surface virtual dislocation.
66
Modeling crosshatch surface morphology in growing mismatched layers. Part II: Periodic boundary conditions and dislocation groups
Aaron Maxwell Andrews,Richard LeSar,M. A. Kerner,James S. Speck,A. E. Romanov,Anna L. Kolesnikova,Manfred Bobeth,Wolfgang Pompe +7 more
TL;DR: In this paper, the authors used solutions for the stress fields and displacement fields for periodic misfit dislocation (MD) arrays in strain-relaxed heteroepitaxial films to avoid truncation errors associated with finite dislocation arrays.
Virtual Circular Dislocation-Disclination Loop Technique in Boundary Value Problems in the Theory of Defects
TL;DR: In this paper, a technique for elastic boundary value problem solutions for defects in solids is developed based on the introduction of virtual circular dislocation-disclination loops distributed continuously for satisfying the prescribed boundary conditions at free surface and interfaces.
30
Dislocation and disclination loops in the virtual-defect method
TL;DR: In this article, a method of virtual circular defect loops is developed for determining the elastic fields produced by defects in a bounded medium in the case of an axially symmetric geometry.
25
The stress fields of edge dislocations near wedge-shaped boundaries and bonded wedges
M Hecker,A.E Romanov +1 more
TL;DR: In this paper, the stress fields in a composite elastic space consiting of two bonded wedges with differnt elastic moduli and containing a straigth edge dislocation parallel to the boudaries are calculated using a refined method of virtual surface dislocations.
18
References
•Book
Elementary Dislocation Theory
Johannes Weertman,Julia R. Weertman +1 more
- 01 Dec 1966
TL;DR: In this article, the authors describe the stress field around a Dislocation and the forces on the Dislocations, as well as the effects of point defect on point defects.
X. The Interaction of Dislocations and Boundaries
TL;DR: In this paper, the image forces on a screw dislocation due to a grain boundary, or a free surface on which is a surface film, are evaluated and it is shown that there is an equilibrium position for the dislocation, at a depth in the metal approximately equal to the thickness of the oxide film.
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