Image force and shielding effects of a moving edge dislocation near a semi‐infinite crack

1993 ◽  
Vol 73 (10) ◽  
pp. 4869-4877 ◽  
Author(s):  
Yu‐Zen Tsai ◽  
Sanboh Lee
Keyword(s):  
Edge Dislocation ◽  
Image Force ◽  
Shielding Effects

Surface stress mediated image force and torque on an edge dislocation

2018 ◽  
Vol 98 (19) ◽  
pp. 1731-1743 ◽  
Author(s):  
R. M. Raghavendra ◽  
Divya ◽  
Ganesh Iyer ◽  
Arun Kumar ◽  
Anandh Subramaniam
Keyword(s):  
Edge Dislocation ◽  
Surface Stress ◽  
Image Force

Interaction between an edge dislocation near a circular void within the framework of the theory of strain gradient elasticity

2018 ◽  
Vol 27 (3-4) ◽  
Author(s):  
Kamyar Davoudi
Keyword(s):  
Edge Dislocation ◽  
Function Method ◽  
Dislocation Line ◽  
Gradient Elasticity ◽  
Image Force ◽  
Strain Gradient Elasticity ◽  
Gradient Solution ◽  
Stress Function Method ◽  
Classical Size ◽  
Isotropic Theory

AbstractThe purpose of this paper was to consider an edge dislocation near a circular hole within the isotropic theory of gradient elasticity. The stress field is derived with the help of a stress function method. The gradient stresses possess no singularity at the dislocation line. As a result, the image force exerted on the dislocation due to the presence of the hole remains finite when the dislocation approaches the interface. The gradient solution demonstrates a non-classical size effect.

scholarly journals Elastodynamic image forces on dislocations

2015 ◽  
Vol 471 (2181) ◽  
pp. 20150433 ◽  
Author(s):  
Beñat Gurrutxaga-Lerma ◽  
Daniel S. Balint ◽  
Daniele Dini ◽  
Adrian P. Sutton
Keyword(s):  
Free Surface ◽  
Rayleigh Wave ◽  
Edge Dislocation ◽  
Wave Speed ◽  
Image Force ◽  
Inertial Effects ◽  
Screw Dislocations ◽  
The Core ◽  
Slow Moving ◽  
Rayleigh Wave Speed

The elastodynamic image forces on edge and screw dislocations in the presence of a planar-free surface are derived. The explicit form of the elastodynamic fields of an injected, quiescent screw dislocation are also derived. The resulting image forces are affected by retardation effects: the dislocations experience no image force for a period of time defined by the arrival and reflection at the free surface of the dislocation fields. For the case of injected, stationary dislocations, it is shown that the elastodynamic image force tends asymptotically to the elastotatic prediction. For the case of injected, moving dislocations, it is shown that the elastodynamic image force on both the edge and the screw dislocations is magnified by inertial effects, and becomes increasingly divergent with time; this additional effect, missing in the elastostatic description, is shown to be substantial even for slow moving dislocations. Finally, it is shown that the elastodynamic image force of an edge dislocation moving towards the surface at the Rayleigh wave speed becomes repulsive, rather than attractive; this is suggestive of instabilities at the core of the dislocation, and likely resonances with the free surface.

Interaction of a screw dislocation with a crack in an anisotropic body

1991 ◽  
Vol 6 (12) ◽  
pp. 2578-2584 ◽  
Author(s):  
Tong-Yi Zhang ◽  
J.E. Hack
Keyword(s):  
Screw Dislocation ◽  
Stress Component ◽  
Anisotropic Body ◽  
Image Force ◽  
Shielding Effect ◽  
Crack Plane ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Isotropic Media ◽  
Shielding Effects

The stress field, image force, and shielding effect of a screw dislocation in the vicinity of a Mode III crack were formulated for both semi-infinite and finite length cracks. The results show that there is an abnormal stress component, ŝ31, on the crack plane. This leads to a nonzero image force along the axis perpendicular to the crack plane when the dislocation is located on the crack plane. However, the abnormal stress component and image force disappear for orthotropic and isotropic media. The image force along a slip plane has the same expression as in isotropic media with an effective shear modulus. Generally the shielding effects are the same as in isotropic media. The anisotropy changes only the magnitude of the shielding effects. The case of multiple dislocations is also discussed.

Interaction Between an Edge Dislocation and a Crack With Surface Elasticity

2015 ◽  
Vol 82 (2) ◽  
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Edge Dislocation ◽  
Analytical Study ◽  
Surface Elasticity ◽  
Image Force ◽  
Size Dependent ◽  
Interface Theory ◽  
Singular Integrodifferential Equations ◽  
Finite Crack ◽  
Crack Tips ◽  
The Continuum

We undertake an analytical study of the interaction of an edge dislocation with a finite crack whose faces are assumed to have separate surface elasticity. The surface elasticity on the faces of the crack is described by a version of the continuum-based surface/interface theory of Gurtin and Murdoch. By using the Green's function method, we obtain a complete exact solution by reducing the problem to three Cauchy singular integrodifferential equations of the first-order, which are solved by means of Chebyshev polynomials and a collocation method. The correctness of the solution is rigorously verified by comparison with existing analytical solutions. Our analysis shows that the stresses and the image force acting on the edge dislocation are size-dependent and that the stresses exhibit both the logarithmic and square root singularities at the crack tips when the surface tension is neglected.

Critical Size for Edge Dislocation Free Free-Standing Nanocrystals by Finite Element Method

2010 ◽  
Vol 10 ◽  
pp. 93-103 ◽  
Author(s):  
Prasenjit Khanikar ◽  
Anandh Subramaniam
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Edge Dislocation ◽  
Critical Size ◽  
Image Force ◽  
Domain Size ◽  
Peierls Stress ◽  
Free Standing ◽  
Free Strain ◽  
Element Method

As the size of a free-standing crystal approaches a few tens of nanometers, the image force experienced by a dislocation can exceed the Peierls force. This will lead to dislocations leaving the nanocrystal without the application of an external stress and thus making it dislocation free. In this investigation a finite element methodology is developed for the calculation of the critical size at which a free-standing crystal becomes edge dislocation free. A simple edge dislocation is simulated using Finite Element Method (FEM) by feeding-in the appropriate stress-free strain in an idealized domains corresponding to the introduction of an extra half-plane of atoms. The image force experienced by the edge dislocation is calculated as the gradient of the plot of the energy of the system as a function of the position of the simulated dislocation. In nanocrystals, due to the proximity of multiple surfaces, the net image force due to multiple images has to be calculated. Additionally, surface or/and domain deformations have to be taken into account in nanocrystals; which can drastically alter the image force. For the crystal to become dislocation free, the minimum image force experienced by the dislocation, has to exceed the Peierls force. Minimum image force values calculated from the FEM models are compared with the Peierls stress values obtained from literature to determine the critical domain size at which crystal becomes edge dislocation free.

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.

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