Journal ArticleDOI
Stress fields produced by dislocations in anisotropic media
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In this paper, the displacements and distortions produced by dislocation loops are represented as Fourier integrals, which are then reduced to obtain solutions for the fields produced by infinite straight dislocations, a finite straight segment of a dislocation line and an elliptical dislocation loop.Abstract:
Representations of the displacements and distortions produced by dislocation loops are given as Fourier integrals. These integrals are then reduced, to obtain solutions which are more explicit than any obtained previously, for the fields produced by infinite straight dislocations, a finite straight segment of a dislocation line and an elliptical dislocation loop, all in generally anisotropic media. The results should reduce the solution of many dislocation problems in which anisotropy cannot reasonably be ignored to fairly simple problems of routine computation.read more
Citations
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Journal ArticleDOI
Anisotropic continuum theory of lattice defects
Journal ArticleDOI
Dislocations and stacking faults
J W Christian,V Vítek +1 more
TL;DR: A comprehensive introduction to dislocation theory for the physicist who is not a specialist in crystal plasticity is given in this article, with a survey of the established theory relating to the geometrical and topological properties of dislocations.
Journal ArticleDOI
The precise evaluation of derivatives of the anisotropic elastic Green's functions
TL;DR: Using Fourier transforms, a simple scheme for numerically obtaining derivatives of the tensor Green's functions of elasticity with great precision is derived as mentioned in this paper, which circumvents the need for solving an auxiliary eigenvalue problem and a related sextic algebraic equation.
Journal ArticleDOI
The fracture mechanics of slit-like cracks in anisotropic elastic media
David M. Barnett,R J Asaro +1 more
TL;DR: In this paper, the authors considered the problem of a slit-like crack in an arbitrarily-anisotropic linear elastic medium stressed uniformly at infinity, where the crack faces may be either freely sliding or loaded by arbitrary equal and opposite tractions.
Journal ArticleDOI
Model validation of a 3d simulation of dislocation dynamics: discretization and line tension effects
Benoit Devincre,M. Condat +1 more
TL;DR: In this article, a detailed study of related approximations, such as the discretization of space and of dislocation line curvature, is presented together with the results of a detailed analysis of related 3D computer modelling of plastic flow.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Journal ArticleDOI
Dislocations and Cracks in Anisotropic Elasticity
TL;DR: In this paper, the authors considered the elastic equations for the case in which the state of the solid is independent of one of the three Cartesian coordinates, and the stresses due to a dislocation, a wall of parallel dislocations, and a crack in an arbitrary non-uniform stress field were obtained.
Journal ArticleDOI
Anisotropic elasticity with applications to dislocation theory
TL;DR: In this article, a general solution of the elastic equations for an arbitrary homogeneous anisotropic solid is found for the case where the elastic state is independent of one (say x3) of the three Cartesian coordinates x1, x2, x3.