Interaction between a screw dislocation and an elastic elliptical inhomogeneity with interfacial cracks

The elastic interaction between a screw dislocation and an elliptical inhomogeneity with interfacial cracks is studied. The screw dislocation may be located outside or inside the inhomogeneity. An efficient complex variable method for the complex multiply connected region is developed, and the general solutions to the problem are derived. As illustrative examples, solutions in explicit series form for complex potentials are presented in the case of one or two interfacial cracks. Image forces on the dislocation are calculated by using the Peach-Koehler formula. The influence of crack geometries and material properties on the image forces is evaluated and discussed. It is shown that the interfacial crack has a significant effect on the equilibrium position of the dislocation near an elliptical-arc interface. The main results indicate, when the length of the crack goes up to a critical value, the presence of the interfacial crack can change the interaction mechanism between a screw dislocation and an elliptical inclusion. The present solutions can include a number of previously known results as special cases.

Interaction between many parallel screw dislocations and a semi-infinite crack in a magnetoelectroelastic solid

Based on the fundamental equations of magnetoelectroelastic material and the analytic theory, and using the Muskhelishvili-introduced well-known elastic techniques combined with the superposition principle, the closed form solution of the generalized stress field of the interaction between many parallel screw dislocations and a semi-infinite crack in an infinite magnetoelectroelastic solid is obtained, on the assumption that the surface of the crack is impermeable electrically and magnetically. Besides, the Peach-Koehler formula of n parallel screw dislocations is given. Numerical examples show that the generalized stress varies with the position of point z and is related to the material constants. The results indicate that the stress concentration occurs at the dislocation core and the tip of the crack. The result of interaction makes the system stay in a lower energy state.

Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack

Shielding effect and emission criterion of a screw dislocation near an interracial blunt crack are dealt with in this paper. Utilizing the conformal mapping technique, the closed-form solutions are derived for complex potentials and stress fields due to a screw dislocation located near the interracial blunt crack. The stress intensity factor on the crack tips and the critical stress intensity factor for dislocation emission are also calculated. The influence of the orientation of the dislocation and the morphology of the blunt crack as well as the material elastic dissimilarity on the shielding effect and the emission criterion is discussed in detail. The results show that positive screw dislocations can reduce the stress intensity factor of the interfacial blunt crack tip （shielding effect）. The shielding effect increases with the increase of the shear modulus of the lower half-plane, but it decreases with the increase of the dislocation azimuth angle. The critical loads at infinity for dislocation emission increases with the increase of emission angle and curvature radius of blunt crack tip, and the most probable angle for screw dislocation emission is zero. The present solutions contain previous results as special cases.

Interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional hexagonal quasicrystal with piezoelectric effect

The interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional(1 D) hexagonal quasicrystal with piezoelectric effect is considered. A general formula of the generalized stress field, the field intensity factor, and the image force is derived, and the special cases are discussed. Several numerical examples are given to show the effects of the material properties and the dislocation position on the field intensity factors and the image forces.

A SCREW DISLOCATION IN A THREE-PHASE COMPOSITE CYLINDER MODEL WITH INTERFACIAL RIGID LINES

The problem of the elastic interaction between a screw dislocation and a three-phase circular inclusion with interracial rigid lines （anti-cracks） is investigated. An efficient and concise method for the complex multiply connected region is developed, with which explicit series form solutions of the complex potentials in the matrix, and the interphase layer and inclusion regions are derived. Based on the complex potentials, the image force on the screw dislocation is then calculated by using the Peach-Koehler formula. The equilibrium position of the dislocation is discussed in detail for various rigid line geometries, interphase layer thicknesses and material property combinations. The main results show that the interracial rigid lines exert a significant perturbation effect on the motion of the screw dislocation near the circular inclusion surrounded by an interphase layer.

INTERACTION OF A SCREW DISLOCATION WITH AN INTERFACIAL EDGE CRACK IN A TWO-PHASE PIEZOELECTRIC MATERIAL

The interaction of a screw dislocation with an interracial edge crack in a two-phase piezoelectric medium is investigated.Closed-form solutions of the elastic and electrical fields induced by the screw dislocation are derived using the conformal mapping method in conjunction with the image principle.Based on the electroelastic fields derived,the stress and electric displacement intensity factors,the image force acting on the dislocation are given explicitly.We find that the stress and electric displacement intensity factors depend on the effective electroelastic material constants.In the case where one of two phases is purely elastic,the stress intensity factor and image force are plotted to illustrate the influences of electromechanical coupling effect,the position of the dislocation and the material properties on the interaction mechanism.

Atomistic Simulations of the Effect of Helium on the Dissociation of Screw Dislocations in Nickel

The interactions of He with dissociated screw dislocations in face-centered-cubic （fcc） Ni are investigated by using molecular dynamics simulations based on an embedded-atom method model. The binding and formation energies of interstitial He in and near Shockley partial cores are calculated. The results show that interstitial He atoms at tetrahedral sites in the perfect fee lattice and atoms occupying sites one plane above or below one of the two Shockley partial cores exhibit the strongest binding energy. The attractive or repulsive nature of the interaction between interstitial He and the screw dislocation depends on the relative position of He to these strong binding sites. In addition, the effect of He on the dissociation of screw dislocations are investigated. It is found that Fie atoms homogeneously distributed in the glide plane can reduce the stacking fault width.

INTERACTION OF A SCREW DISLOCATION IN THE INTERPHASE LAYER WITH THE INCLUSION AND MATRIX

The interaction of a screw dislocation in the interphase layer with the circular inhomogeneity and matrix was dealt with . An efficient method for multiply connected regions was developed by combining the sectionally subholomorphic function theory, Schwatz symmetric principle and Cauchy integral technique. The Hilbert problem of the complex potentials for three material regions was reduced to a functional equation in the complex potential of the interphase layer, resulting in an explicit series solution . By using the present solution the interaction energy and force acting dislocation were evaluated and discussed.

A screw dislocation near one open inhomogeneity and another closed inhomogeneity both permitting constant interior stresses

We prove that the interior stresses within both a non-parabolic open inhomogeneity and another interacting non-elliptical closed inhomogeneity can still remain constant when the matrix is simultaneously under the action of a screw dislocation and uniform remote anti-plane stresses.The constancy of interior stresses is realized through the construction of a conformal mapping function for the doubly connected domain occupied by the surrounding matrix.The mapping function is endowed with the information describing the screw dislocation via the incorporation of two specifically defined logarithmic terms.The constant interior stress fields are observed to be independent of the specific open and closed shapes of the two inhomogeneities and the existence of the screw dislocation.In contrast,the existence of the neighboring screw dislocation significantly affects the open and closed shapes of the two inhomogeneities.

ANALYSIS OF A SCREW DISLOCATION INSIDE A CIRCULAR INCLUSION WITH INTERFACIAL CRACKS IN PIEZOELECTRIC COMPOSITES

The electroelastic interaction of a screw dislocation inside a circular inclusion with inteffacial cracks in piezoelectric composite materials under anti-plane shear and in-plane electric loads at infinity is investigated. The general solution to this problem was obtained by means of Riemann-Schwarz＇ s symmetry principle integrated with analysis of singularities of corresponding complex potentials. As a typical example, closed form expressions of the complex potentials and electroelastic field components in the matrix and inhomogeneity regions were derived explicitly when the interface contains a single crack. The image force acting on the screw dislocation was calculated by using the generalized Peach-Koehler formula. The influence of interfacial crack geometry and piezoelectric material property combinations upon the image force was discussed in detail. The results show that interfacial crack has a significant perturbation effect on the image force and the equilibrium position of the screw dislocation. The presence of the interfacial crack can change the direction of the image force when the length of the crack goes up to a critical value. The obtained explicit solutions can be used as Green＇s functions to study the problem on the interaction between interfacial cracks and arbitrary shape crack inside the inclusion. The present solutions can lead to previously known results as the special case.

MOVING SCREW DISLOCATION IN CUBIC QUASICRYSTAL

The elasticity theory of the dislocation of cubic quasicrystals is developed. The governing equations of anti-plane elasticity dynamics problem of the quasicrystals were reduced to a solution of wave equations by introducing displacement functions, and the analytical expressions of displacements, stresses and energies induced by a moving screw dislocation in the cubic quasicrystalline and the velocity limit of the dislocation were obtained. These provide important information for studying the plastic deformation of the new solid material.

ELECTROELASTIC INTERACTION BETWEEN A PIEZOELECTRIC SCREW DISLOCATION AND A CIRCULAR INHOMOGENEITY WITH INTERFACIAL CRACKS

A piezoelectric screw dislocation in the matrix interacting with a circular inhomogeneity with interfacial cracks under antiplane shear and in-plane electric loading at infinity was dealt with. Using complex variable method, a general solution to the problem was presented. For a typical case, the closed form expressions of complex potentials in the inhomogeneity and the matrix regions and the electroelastic field intensity factors were derived explicitly when the interface contains single crack. The image force acting on the piezoelectric screw dislocation was calculated by using the perturbation technique and the generalized Peach-Koehler formula. As a result, numerical analysis and discussion show that the perturbation influence of the interfacial crack on the interaction effects of the dislocation and the inhomogeneity is significant which indicates the presence of the interfacial crack will change the interaction mechanism when the length of the crack goes up to a critical value. It is also shown that soft inhomogeneity can repel the dislocation due to their intrinsic electromechanical coupling behavior.

A moving screw dislocation near interfacial rigid lines in two dissimilar anisotropic media

This paper attempts to investigate the problem for the interaction between a uniformly moving screw dislocation and interface rigid lines in two dissimilar.anisotropic. materials. Integrating Riemann-Schwarz＇s symmetry principle with the analysis singularity of complex functions, we present the general elastic solutions of this problem and the closed form solutions for interfaces containing one and two rigid lines. The expressions of stress intensity factors, at the rigid line tips and image force acting on moving dislocation are derived explicitly. The results show that dislocation velocity has an antishielding effect on the rigid line tip and a larger dislocation velocity leads to the equilibrium position of dislocation closing with the rigid line. The presented solutions contain previously known results as the special cases.

Analysis of a piezoelectric screw dislocation inside an elliptical inhomogeneity with confocal rigid line in piezoelectric material

This paper deals with the electro-elastic coupling interaction between a piezoelectric screw dislocation which is located inside the elliptical inhomogeneity and an electrically conductive confocal rigid line under remote anti-plane shear stresses and in-plane electrical loads in piezoelectric composite material. The analytical-functions of the complex potentials, stress fields and the image force acting on the piezoelectric screw dislocation are obtained based on the principle of conformal mapping, the method of series expansion, the technical of analytic continuation and the analysis of singularity of complex potentials. The rigid line and the piezoelectric material property combinations upon the image force and the equilibrium position of the dislocation are discussed in detail by the numerical computation.

INTERACTION BETWEEN A SCREW DISLOCATION AND A PLASTIC ZONE OF AN ARBITRARY SHAPE

A plastic deformation zone near a screw dislocation is treated as an equivalent transformation inclusion by means of the Eshelby inclusion theory. A closed form solution for determining the interaction between a screw dislocation and a plastically deformed zone of an arbitrary shape is obtained by using the solution between a dislocation and an equivalent transformation inclusion.

Interaction between a screw dislocation and a circular nano-inhomogeneity with a bimaterial interface

The problem of a screw dislocation interacting with a circular nano-inhomogeneity near a bimaterial interface is investigated. The stress boundary condition at the interface between the inhomogeneity and the matrix is modified by incorporating surface/interface stress. The analytical solutions to the problem in explicit series are obtained by an efficient complex variable method associated with the conformal mapping function. The image force exerted on the screw dislocation is also derived using the generalized Peach–Koehler formula. The results indicate that the elastic interference of the screw dislocation and the nano-inhomogeneity is strongly affected by a combination of material elastic dissimilarity, the radius of the inclusion, the distance from the center of inclusion to the bimaterial interface, and the surface/interface stress between the inclusion and the matrix. Additionally, it is found that when the inclusion and Material 3 are both harder than the matrix（ μ1 〉 μ2 and μ3 〉 μ2）, a new stable equilibrium position for the screw dislocation in the matrix appears near the bimaterial interface; when the inclusion and Material 3 are both softer than the matrix（ μ1 〈 μ2 and μ3 〈 μ2）, a new unstable equilibrium position exists close to the bimaterial interface.

Atlantoaxial pedicle screw system for treatment of unstable atlantoaxial dislocation post traction

Objective To explore the technique and clinical outcome of the atlantoaxial pedicle screw system in the treatment of the unstable altantoaxial dislocation post traction.

A model of crack based on dislocations in smectic A liquid crystals

A plastic crack model for smectic A liquid crystals under longitudinal shear is suggested. The solution of the screw dislocation in smectic A is the key to the correct result that we obtained by overcoming a longstanding puzzle. We further use the dislocation pile-up principle and the singular integral equation method to construct the solution of the crack in the phase. From the solution, we can determine the size of the plastic zone at the crack tip and the crack tip opening （tearing） displacement, which are the parameters relevant to the local stability/instability of materials. Our results may be useful for developing soft-matter mechanics.

Investigation of dislocations in 8° off-axis 4H-SiC epilayer

This paper reports that the etching morphology of dislocations in 8° off-axis 4H-SiC epilayer is observed by using a scanning electronic microscope. It is found that different types of dislocations correspond with different densities and basal plane dislcation （BPD） array and threading edge dislocation （TED） pileup group lie along some certain crystal directions in the epilayer. It is concluded that the elastic energy of threading screw dislocations （TSDs） is highest and TEDs is lowest among these dislocations, so the density of TSDs is lower than TEDs. The BPDs can convert to TEDs but TSDs can only propagate into the epilyer in spite of the higher elastic energy than TEDs. The reason of the form of BPDs array in epilayer is that the big step along the basal plane caused by face defects blocked the upstream atoms, and TEDs pileup group is that the dislocations slide is blocked by dislocation groups in epilayer.

晶体生长的缺陷机制

Crystal growth is a complicated phase transition process.A perfect mechanism for practical crystal growth process has not been proposed and well recognized up till now.A model,i.e.screw dislocation model presented by F.C.Frank for imperfect crystal growth was adopted during early 1950’s.No systemic research on defects other than screw dislocation has been conducted during a quite long time. Since 1980’s,we have engaged systematically in the investigation of the defect mechanism of crystal growth,and our conclusion is that any defect providing step sources in the growing surface can make contribution to continuous crystal growth.These steps contain both complete(whole)steps and sub steps(incomplete steps).