Edge dislocations near phase boundaries in the gradient theory of elasticity

Mikaelyan, K. N.; Gutkin, M. Yu.; Aifantis, Elias C.

doi:10.1134/1.1309447

Cited by 10 publications

(8 citation statements)

References 10 publications

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“…It is, thus, desirable for the interface stress jump to be eliminated from the solution of this problem as was the case with gradient solutions for dislocations near planar Gutkin et al, 2000a,b;Mikaelyan et al, 2000) and circular (Davoudi et al, 2009) interfaces.…”

Section: Classical Solutionmentioning

confidence: 96%

“…For the stress field, which is governed by Eq. (2) 2 , we impose the following boundary conditions as proposed in (Gutkin et al, 2000a,b;Mikaelyan et al, 2000) r…”

Section: Gradient Solutionmentioning

confidence: 99%

“…Moreover, the examination of dislocation behavior in a two-phase solid with a planar interface within the gradient elasticity demonstrates some additional profits, the principal of which are continuous stresses at the interface and elimination of singularity from the image force acting on a dislocation near the interface Gutkin et al, 2000a,b;Mikaelyan et al, 2000). Recently Lazar (2007) has extended Eq.…”

Section: Introductionmentioning

confidence: 96%

“…(1) and (2) have been used to eliminate classical singularities in elastic fields at the crack tips (Ru and Aifantis, 1993b), dislocation Gutkin and Aifantis, 1999a;Gutkin et al, 2000a,b;Mikaelyan et al, 2000) and disclination Gutkin and Aifantis, 1999b) lines, and edges of a rectangular inclusion (Gutkin, 2006) as well. Moreover, the examination of dislocation behavior in a two-phase solid with a planar interface within the gradient elasticity demonstrates some additional profits, the principal of which are continuous stresses at the interface and elimination of singularity from the image force acting on a dislocation near the interface Gutkin et al, 2000a,b;Mikaelyan et al, 2000).…”

Section: Introductionmentioning

confidence: 99%

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A screw dislocation near a circular nano-inhomogeneity in gradient elasticity

Davoudi

Gutkin

Shodja

2010

International Journal of Solids and Structures

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a b s t r a c tA screw dislocation outside an infinite cylindrical nano-inhomogeneity of circular cross section is considered within the isotropic theory of gradient elasticity. Fields of total displacements, elastic and plastic distortions, elastic strains and stresses are derived and analyzed in detail. In contrast with the case of classical elasticity, the gradient solutions are shown to possess no singularities at the dislocation line. Moreover, all stress components are continuous and smooth at the interface unlike the classical solution. As a result, the image force exerted on the dislocation due to the differences in elastic and gradient constants of the matrix and inhomogeneity, remains finite when the dislocation approaches the interface. The gradient solution demonstrates a non-classical size-effect in such a way that the stress level inside the inhomogeneity decreases with its size. The gradient and classical solutions coincide when the distances from the dislocation line and the interface exceed several atomic spacings.

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Section: Classical Solutionmentioning

confidence: 96%

“…For the stress field, which is governed by Eq. (2) 2 , we impose the following boundary conditions as proposed in (Gutkin et al, 2000a,b;Mikaelyan et al, 2000) r…”

Section: Gradient Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A screw dislocation near a circular nano-inhomogeneity in gradient elasticity

Davoudi

Gutkin

Shodja

2010

International Journal of Solids and Structures

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“…The second method requires information about the potential of non-local interaction. For describing the surface phenomena it is possible to use gradient theories (for example [5,6]). They use a higher order differential equation of motions.…”

Section: Introductionmentioning

confidence: 99%

Theory of the elasticity of the materials of the second order

Shorkin¹,

Gordon²

2006

WIT Transactions on the Built Environment, Vol 85

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It is admitted that a solid body is obtained by means of extraction from an infinite medium, and at the same time its state changes. To describe this phenomenon there a linear theory of elasticity of isotropic materials of the second order was used, generalized for the case of availability of the initial stressed state described by tensors of various ranks. They depend upon the physical nature of the body, the form of its boundary and position of points for their determination. The boundary effect -existence of surface tension and surface energy is described. The analysis of known test data regarding values of these quantities, wave dispersion in resilient media, calculus results on the basis of the model offered and one-dimensional theory of the crystalline lattice of elastic energy density for a number materials allowed values of elastic modulus and initial stresses to be determined. The created model of medium is used for the description of the stressed state of bodies adhered together, when their adhesion is considered to be one of the kinds of contact interaction. The calculus results of adhesion energy are confronted with the known data. Keywords: theory of the elasticity, materials of the second order, the initial stressed state, and surface energy, adhesion energy.

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