Interaction Between an Edge Dislocation and a Lamellar Inhomogeneity With a Slipping Interface

1992 ◽  
Vol 59 (1) ◽  
pp. 215-217 ◽  
Author(s):  
L. Stagni ◽  
R. Lizzio
Keyword(s):  
Elastic Constants ◽  
Edge Dislocation ◽  
Stable Equilibrium ◽  
Finite Thickness ◽  
Elastic Field ◽  
Image Force ◽  
Plane Elasticity ◽  
Matrix Interface ◽  
Stable Equilibrium Position ◽  
Plane Elasticity Problem

The plane elasticity problem of an internal stress source located near a lamellar inhomogeneity is considered. It is assumed that the lamella-matrix interface does not transmit tangential displacements or shear tractions (slipping interface). The elastic field is given in terms of the source bulk field and one parameter formed from the elastic constants. The image force on an edge dislocation near the lamella is calculated and discussed. A dislocation stable-equilibrium position exists in a domain of elastic constants and Burgers vector directions. This result is characteristic of the interaction with a slipping lamellar inhomogeneity having finite thickness.

An Edge Dislocation in a Three-Phase Composite Cylinder Model

1991 ◽  
Vol 58 (1) ◽  
pp. 75-86 ◽  
Author(s):  
H. A. Luo ◽  
Y. Chen
Keyword(s):  
Edge Dislocation ◽  
Stable Equilibrium ◽  
Phase Model ◽  
Composite Cylinder ◽  
Two Phase ◽  
Trapping Mechanism ◽  
Three Phase ◽  
Cylinder Model ◽  
Stable Equilibrium Position ◽  
The Stability

An exact solution is given for the stress field due to an edge dislocation embedded in a three-phase composite cylinder. The force on the dislocation is then derived, from which a set of simple approximate formulae is also suggested. It is shown that, in comparison with the two-phase model adopted by Dundurs and Mura (1964), the three-phase model allows the dislocation to have a stable equilibrium position under much less stringent combinations of the material constants. As a result, the so-called trapping mechanism of dislocations is more likely to take place in the three-phase model. Also, the analysis and calculation show that in the three-phase model the orientation of Burgers vector has only limited influence on the stability of dislocation. This behavior is pronouncedly different from that predicted by the two-phase model.

Elastic Force on a Point Defect in or Near a Surface Layer

1996 ◽  
Vol 63 (4) ◽  
pp. 1042-1045 ◽  
Author(s):  
H. Yua ◽  
S. C. Sanday ◽  
D. J. Bacon
Keyword(s):  
Surface Layer ◽  
Free Surface ◽  
Point Defect ◽  
Layer Thickness ◽  
Elastic Constants ◽  
Equilibrium Position ◽  
Stable Equilibrium ◽  
Elastic Force ◽  
Image Method ◽  
Stable Equilibrium Position

The elastic force on a point defect within or near a surface layer is determined by the image method. There is no stable equilibrium position for the point defect in the surface layer, it is attracted either to the free surface or to the interface. When the point defect is in the substrate it is attracted to the interface when the surface layer is softer than the substrate and to an equilibrium position in the substrate when the surface layer is stiffer than the substrate, the equilibrium position being a function of the elastic constants and the layer thickness.

The elastic field outside an ellipsoidal inclusion

1959 ◽  
Vol 252 (1271) ◽  
pp. 561-569 ◽  
Keyword(s):  
Velocity Field ◽  
Viscous Fluid ◽  
Elastic Constants ◽  
Strain Energy ◽  
Elastic Field ◽  
Ellipsoidal Inclusion ◽  
Harmonic Potential ◽  
Surface Distribution ◽  
Shear Transformation ◽  
General Method

The results of an earlier paper are extended. The elastic field outside an inclusion or inhomogeneity is treated in greater detail. For a general inclusion the harmonic potential of a certain surface distribution may be used in place of the biharmonic potential used previously. The elastic field outside an ellipsoidal inclusion or inhomogeneity may be expressed entirely in terms of the harmonic potential of a solid ellipsoid. The solution gives incidentally the velocity field about an ellipsoid which is deforming homogeneously in a viscous fluid. An expression given previously for the strain energy of an ellipsoidal region which has undergone a shear transformation is generalized to the case where the region has elastic constants different from those of its surroundings. The Appendix outlines a general method of calculating biharmonic potentials.

The Stress Field Due to an Edge Dislocation Interacting With Two Circular Inclusions

2016 ◽  
Vol 33 (2) ◽  
pp. 161-172 ◽  
Author(s):  
C.-K. Chao ◽  
F.-M. Chen ◽  
T.-H. Lin
Keyword(s):  
Stable Equilibrium ◽  
Complex Stress ◽  
Explicit Dependence ◽  
Closed Form Solutions ◽  
General Series ◽  
Stable Equilibrium Position ◽  
Arbitrary Plane ◽  
Plane Elastostatics ◽  
Combination Of Material ◽  
Extended Matrix

AbstractA general series solution to the problem of interacting circular inclusions in plane elastostatics is presented in this paper. The analysis is based on the use of the complex stress potentials of Muskhelishvili and the theorem of analytical continuation. The general forms of the complex potentials are derived explicitly for the circular inhomogeneities under arbitrary plane loading. Using the alternation technique, these general expressions were subsequently employed to treat the problem of an infinitely extended matrix containing two arbitrarily located inhomogeneities. The major contribution of the present proposed method is shown to be capable of yielding approximate closed-form solutions for multiple inclusions, thus providing the explicit dependence of the solution on the pertinent parameters. The result shows that the dislocation has a stable equilibrium position at a certain combination of material constants. The case of an inhomogeneity interacting with a circular hole under a remote uniform load is also investigated.

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