scholarly journals Singularities interacting with interfaces incorporating surface elasticity under plane strain deformations

2014 ◽  
Vol 41 (4) ◽  
pp. 267-282 ◽  
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Plane Strain ◽  
Edge Dislocation ◽  
Surface Elasticity ◽  
Point Force ◽  
Interface Model ◽  
Interface Elasticity ◽  
Interface Parameters ◽  
Surface Mechanics ◽  
The Continuum

We consider problems involving singularities such as point force, point moment, edge dislocation and a circular Eshelby?s inclusion in isotropic bimaterials in the presence of an interface incorporating surface/interface elasticity under plane strain deformations and derive elementary solutions in terms of exponential integrals. The surface mechanics is incorporated using a version of the continuum-based surface/interface model of Gurtin and Murdoch. The results indicate that the stresses in the two half-planes are dependent on two interface parameters.

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.

Interaction between a nanocrack with surface elasticity and a screw dislocation

2016 ◽  
Vol 22 (2) ◽  
pp. 131-143 ◽  
Author(s):  
Xu Wang ◽  
Hui Fan
Keyword(s):  
Screw Dislocation ◽  
Real Axis ◽  
Analytical Study ◽  
Logarithmic Singularity ◽  
Surface Elasticity ◽  
Spontaneous Generation ◽  
The Real ◽  
Crack Tips ◽  
Interaction Problem ◽  
The Continuum

In the present analytical study, we consider the problem of a nanocrack with surface elasticity interacting with a screw dislocation. The surface elasticity is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. By considering both distributed screw dislocations and line forces on the crack, we reduce the interaction problem to two decoupled first-order Cauchy singular integro-differential equations which can be numerically solved by the collocation method. The analysis indicates that if the dislocation is on the real axis where the crack is located, the stresses at the crack tips only exhibit the weak logarithmic singularity; if the dislocation is not on the real axis, however, the stresses exhibit both the weak logarithmic and the strong square-root singularities. Our result suggests that the surface effects of the crack will make the fracture more ductile. The criterion for the spontaneous generation of dislocations at the crack tip is proposed.

Plane Deformations of an Inhomogeneity–Matrix System Incorporating a Compressible Liquid Inhomogeneity and Complete Gurtin–Murdoch Interface Model

2018 ◽  
Vol 85 (12) ◽  
Author(s):  
Ming Dai ◽  
Min Li ◽  
Peter Schiavone
Keyword(s):  
Analytic Solution ◽  
Elastic Solid ◽  
Compressible Liquid ◽  
External Loading ◽  
Interface Model ◽  
Interface Tension ◽  
Soft Solids ◽  
Remote Loading ◽  
Interface Elasticity ◽  
Plane Deformations

We consider the plane deformations of an infinite elastic solid containing an arbitrarily shaped compressible liquid inhomogeneity in the presence of uniform remote in-plane loading. The effects of residual interface tension and interface elasticity are incorporated into the model of deformation via the complete Gurtin–Murdoch (G–M) interface model. The corresponding boundary value problem is reformulated and analyzed in the complex plane. A concise analytical solution describing the entire stress field in the surrounding solid is found in the particular case involving a circular inhomogeneity. Numerical examples are presented to illustrate the analytic solution when the uniform remote loading takes the form of a uniaxial compression. It is shown that using the simplified G–M interface model instead of the complete version may lead to significant errors in predicting the external loading-induced stress concentration in gel-like soft solids containing submicro- (or smaller) liquid inhomogeneities.

Combination of Continuum and Atomistic Approaches for the Study of Dislocation Nucleation from Atomic Size Surface Defects

2001 ◽  
Vol 677 ◽  
Author(s):  
Sandrine Brochard ◽  
Pierre Beauchamp ◽  
Jean Grilhé
Keyword(s):  
Stress Concentration ◽  
Surface Defects ◽  
Dislocation Nucleation ◽  
Point Force ◽  
Atomistic Simulations ◽  
Elastic Precursor ◽  
Atomic Size ◽  
Strong Localization ◽  
Elastic Shear ◽  
The Continuum

ABSTRACTAtomistic simulations realized on an f.c.c. crystal containing atomic size surface defects (step and groove) show that the defects are privileged sites for dislocation nucleation. Before nucleation, an elastic shear, precursor of the dislocation, appears in the plane in zone with the step where the dislocation will be nucleated. In order to explain the strong localization of the localized elastic precursor shear, we have analyzed the stress concentration near the surface defects using the continuum point force approach. For the step case, the origin of the localized shear is related to an increase in the interplanar separation due to the stress concentration.

Poroelastic Solution of a Plane Strain Point Displacement Discontinuity

1987 ◽  
Vol 54 (4) ◽  
pp. 783-787 ◽  
Author(s):  
E. Detournay ◽  
A. H-D. Cheng
Keyword(s):  
Plane Strain ◽  
Edge Dislocation ◽  
Crack Surface ◽  
Displacement Discontinuity ◽  
Decomposition Technique ◽  
Poroelastic Medium ◽  
Elasticity Equation ◽  
Continuous Point ◽  
The One ◽  
Flux Jumps

The plane strain fundamental solution of an instantaneous and a continuous point displacement discontinuity is presented in this paper. These solutions, together with the one of a fluid source, are obtained on the basis of a decomposition technique proposed by Biot, which separates the displacement field into a time independent part satisfying an elasticity equation, and an irrotational part governed by a diffusion equation. We begin the derivation by presenting a continuous edge dislocation. The continuous point displacement discontinuity is obtained by differentiating, along the direction of the cut, the corresponding edge dislocation solution. The instantaneous influence functions are determined by further differentiating with respect to time. The displacement discontinuity and source singularities can be distributed on a crack surface to create displacement and flux jumps required for the numerical modeling of a fracture in a poroelastic medium.

Analysis for Stress Singular Fields Near a Wedge Corner in 2D Joints Considering Interface Stress and Interface Elasticity

2012 ◽  
Author(s):  
Hideo Koguchi ◽  
Osamu Kato
Keyword(s):  
Boundary Condition ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Stress Singularity ◽  
Anisotropic Elasticity ◽  
Interface Stress ◽  
Surface Strain ◽  
Surface Pattern ◽  
Singular Stress ◽  
Interface Elasticity

Surface stress and surface elasticity are related to an organization of surface morphology, surface pattern and surface atomic structures. As a size of structure reduces to a nanometer level, a ratio of its surface to volume increases. Generally, surface energy in deformable solids depends on surface strain. Surface stress and elasticity influence on the distribution of bulk stress near the surface. Interface stress and elasticity also exist in an interface of materials and characterize interface properties. In this study, singular stress at a wedge corner in an anisotropic 2D joint under a tensile loading is analyzed using molecular dynamic (MD) method and the anisotropic elasticity theory using the boundary condition with interface stress and interface elasticity. Interface stress and interface elasticity are obtained through the MD analysis. In the case of 2D joint. the obtained interface stress and elasticity depend on the distance from the wedge corner. The stress field around the wedge corner obtained by the MD analysis had a larger value of order of singularity than a value predicted from the ordinary boundary condition at the interface. In the analysis of anisotropic elasticity, eigenequation for determining the order of stress singularity is newly derived using the boundary condition with interface stress and interface elasticity. The order of stress singularity varies with the distance from the wedge corner. The stress distribution near the wedge corner can be approximated using the relation between the order of stress singularity and the distance from the wedge corner.

Energy Changes and the Lattice Resistance

2006 ◽  
Vol 317-318 ◽  
pp. 271-276 ◽  
Author(s):  
W.J. Clegg ◽  
L. Vandeperre ◽  
J.E. Pitchford
Keyword(s):  
Edge Dislocation ◽  
Reasonable Agreement ◽  
Low Energy ◽  
Peierls Stress ◽  
Continuum Approach ◽  
Linear Elastic ◽  
Lattice Resistance ◽  
Continuum Description ◽  
The Continuum

The aim of this paper is to study the effect of relaxing the assumption in the Peierls analysis that the dislocation must be wide compared to the atom spacing. To do this the use of the continuum description of the in-plane strains caused by the presence of an edge dislocation is replaced by an atomistic interaction taken to be linear elastic. It is found that in this case the inplane interactions give a contribution to the overall misfit energy changes that are not present in the Peierls analysis because of the use of a continuum approach. This contribution modifies these energy changes so that the total misfit energy is a minimum at the conventional low energy positions (whereas in the Peierls analysis it is a maximum) and gives values of the Peierls stress in reasonable agreement with those measured.

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