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.

Interaction between a screw dislocation and a bridged crack with surface elasticity

2016 ◽  
Vol 22 (12) ◽  
pp. 2217-2239 ◽  
Author(s):  
Moxuan Yang ◽  
Xu Wang
Keyword(s):  
Screw Dislocation ◽  
Crack Opening Displacement ◽  
Crack Opening ◽  
Surface Elasticity ◽  
Image Force ◽  
Opening Displacement ◽  
Crack Bridging ◽  
Line Force ◽  
Crack Tips ◽  
Crack Faces

We examine the contribution of crack bridging and surface elasticity to the elastic interaction between a mode III finite crack and a screw dislocation. The surface effect on the crack faces is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. The crack faces are subjected to a bridging force which is assumed to be proportional to the crack opening displacement, whereas the bridging stiffness is allowed to vary arbitrarily along the crack. By considering a continuous distribution of both screw dislocations and line forces on the crack, the boundary value problem is reduced to two decoupled first-order Cauchy singular integro-differential equations. After the expansion of the unknown line dislocation and line force densities and the known variable bridging stiffness into Chebyshev polynomials, these singular integro-differential equations are solved numerically using the collocation method. Owing to the incorporation of surface elasticity, the stresses at the crack tips only exhibit the weak logarithmic singularity when the dislocation is located on the real axis where the crack is located, whereas in the case when the dislocation is not on the real axis, the stresses at the crack tips exhibit both the weak logarithmic and the strong square-root singularities. The two densities, the crack opening displacement across the crack faces and the image force acting on the screw dislocation are specifically calculated. We note that crack bridging only exerts an effect on the line dislocation density but has no influence on the line force density. In addition, we demonstrate that both surface elasticity and crack bridging can reduce the strengths of the logarithmic stress singularity at the crack tips and the magnitude of the crack opening displacement across the crack faces. Our results also clearly show that both crack bridging and surface elasticity exert a significant influence on the magnitude and direction of the image force acting on the screw dislocation.

scholarly journals Effect of surface elasticity on an interface crack in plane deformations

2011 ◽  
Vol 467 (2136) ◽  
pp. 3530-3549 ◽  
Author(s):  
C. I. Kim ◽  
P. Schiavone ◽  
C.-Q. Ru
Keyword(s):  
Interface Crack ◽  
Surface Elasticity ◽  
Shear Mode ◽  
Plane Shear ◽  
Linear Elastic ◽  
Interface Theory ◽  
Chebychev Polynomials ◽  
Crack Tips ◽  
Plane Deformations ◽  
Effect Of Surface

We consider the effect of surface elasticity on an interface crack between two dissimilar linearly elastic isotropic homogeneous materials undergoing plane deformations. The bi-material is subjected to either remote tension (mode-I) or in-plane shear (mode-II) with the faces of the (interface) crack assumed to be traction-free. We incorporate surface mechanics into the model of deformation by employing a version of the continuum-based surface/interface theory of Gurtin & Murdoch. Using complex variable methods, we obtain a semi-analytical solution valid throughout the entire domain of interest (including at the crack tips) by reducing the problem to a system of coupled Cauchy singular integro-differential equations, which is solved numerically using Chebychev polynomials and a collocation method. It is shown that, among other interesting phenomena, our model predicts finite stress at the (sharp) crack tips and the corresponding stress field to be size-dependent. In particular, we note that, in contrast to the results from linear elastic fracture mechanics, when the bi-material is subjected to uniform far-field stresses (either tension or in-plane shear), the incorporation of surface effects effectively eliminates the oscillatory behaviour of the solution so that the resulting stress fields no longer suffer from oscillatory singularities at the crack tips.

A crack with surface effects in a piezoelectric material

2016 ◽  
Vol 22 (1) ◽  
pp. 3-19 ◽  
Author(s):  
Xu Wang ◽  
Kun Zhou
Keyword(s):  
Differential Equations ◽  
Piezoelectric Material ◽  
Logarithmic Singularity ◽  
Coupled System ◽  
First Order ◽  
Size Dependent ◽  
Crack Tips ◽  
Piezoelectric Solid ◽  
Interaction Approximation ◽  
The Continuum

We study the contribution of surface piezoelectricity to the anti-plane deformations of a hexagonal piezoelectric material weakened by a crack. The surface piezoelectricity is incorporated by using an extended version of the continuum-based surface/interface model of Gurtin and Murdoch. The original boundary value problem is finally reduced to a system of two coupled first-order Cauchy singular integro-differential equations by considering a distribution of line dislocations and electric-potential-dislocations on the crack. Through a diagonalization strategy, the coupled system can be transformed into two independent singular integro-differential equations, each of which contains only one single unknown function and can be numerically solved by the collocation method. Our solution demonstrates that the stresses, strains, electric displacements and electric displacements exhibit the logarithmic singularity at the crack tips. The obtained solution is further used to predict the size-dependent effective electroelastic properties of a piezoelectric solid containing multiple nanocracks with surface piezoelectricity within the framework of non-interaction approximation.

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.

On wave dispersion characteristics of fluid-conveying smart nanotubes considering surface elasticity and flexoelectricity approach

2020 ◽  
pp. 095440622096561
Author(s):  
Amir-Reza Asghari Ardalani ◽  
Ahad Amiri ◽  
Roohollah Talebitooti ◽  
Mir Saeed Safizadeh
Keyword(s):  
Wave Propagation ◽  
Strain Gradient ◽  
Surface Elasticity ◽  
Shear Deformation Theory ◽  
Wave Dispersion ◽  
Strain Gradient Theory ◽  
Wave Number ◽  
Gradient Theory ◽  
Specific Domain ◽  
Size Dependent

Wave dispersion response of a fluid-carrying piezoelectric nanotube is studied in this paper utilizing an improved model for piezoelectric materials which capture a new effect known as flexoelectricity in conjunction with the surface elasticity. For this aim, a higher order shear deformation theory is employed to model the problem. Furthermore, strain gradient effect as well as nonlocal effect is taken into consideration throughout using the nonlocal strain gradient theory (NSGT). Surface elasticity is also considered to make an accurate size-dependent formulation. Additionally, a non-compressible and non-viscous fluid is taken into consideration to model the flow effect. The wave propagation solution is then implemented to the governing equations obtained by Hamiltonian’s approach. The phase velocity and group velocity of the nanotube is determined for three wave modes (i.e. shear, longitudinal and bending waves) to study the influence of various involved factors including strain gradient, nonlocality, flexoelectricity and surface elasticity and flow velocity on the wave dispersion curves. Results reveal a considerable effect of the flexoelectric phenomenon on the wave propagation properties especially at a specific domain of the wave number. The size-dependency of this effect is disclosed. Overall, it is found that the flexoelectricity exhibits a substantial influence on wave dispersion properties of the smart fluid-conveying systems. Hence, such size-dependent effect should be considered to achieve exact and accurate knowledge on wave propagation characteristics of the system.

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

Nanoindentation hardness of a Steigmann–Ogden surface bounding an elastic half-space

2018 ◽  
Vol 24 (9) ◽  
pp. 2754-2766 ◽  
Author(s):  
Xiaobao Li ◽  
Changwen Mi
Keyword(s):  
Surface Tension ◽  
Half Space ◽  
Surface Elasticity ◽  
Elastic Half Space ◽  
Indentation Hardness ◽  
Bending Rigidity ◽  
Size Dependent ◽  
Significant Difference ◽  
Nanoindentation Hardness ◽  
Membrane Stiffness

Previous studies demonstrate that, for nanostructures under transverse bending, the effective Young modulus is appreciably greater (in magnitude) than that of the same elements under axial loads. Therefore, in addition to the conventional residual surface tension and membrane stiffness, the curvature dependence of surface energy is desired for inhomogeneously strained nanostructures. In this paper, we aim to reevaluate the size-dependent nanoindentation hardness of an elastic half-space subjected to nanosized frictionless traction, through the use of both the curvature-independent Gurtin–Murdoch and the curvature-dependent Steigmann–Ogden models of surface elasticity. The nanoindentation problem is solved by the integration of Boussinesq’s method of displacement potentials and Hankel integral transforms. As examples, the effects of residual surface tension, membrane stiffness, and bending rigidity of the half-space boundary are parametrically analyzed in detail for a uniform circular pressure and a concentrated normal force. The observations in semianalytical calculations suggest a significant difference in the nanoindentation hardnesses predicted from the two popular models of surface mechanics. In most cases, the inclusion of bending rigidity results in smaller displacements and stresses, and therefore higher indentation hardness. Based on physically interpretable numerical values of surface material properties, we show that a curvature-dependent model of surface elasticity is required in order to characterize the size-dependent feature of nanoindentation problems correctly.

Sign in / Sign up

Export Citation Format

Share Document