Dislocation Force Research Articles

Energy analysis of dislocation arrays near bimaterial interfaces

Expressions for the elastic strain energies due to dislocation arrays near bimaterial interface or near the free surface of a semi-infinite body are derived. Arrays with periodic straight dislocations of edge, screw and combined type are considered. Expressions for the complete stress distribution and dislocation forces are also presented.

Screw dislocations near a crack penetrating through an interface

Screw dislocations near a crack penetrating through an interface were investigated. Based on the solution of homogeneous solid, we derived the stress field, stress intensity factors and crack extension forces at both crack tips, and the image force and strain energy of screw dislocations. The mechanical behavior arising from a crack penetrating through an interface is different from that arising from an interfacial crack. The effect of the ratio of shear modulus and crack length on the mechanical variables was examined. The mechanical behavior of a dislocation emitted from a crack tip is different from that of a dislocation originating elsewhere. Special cases are discussed.

Analytical Solutions for Anisotropic Out-of-Plane Problems Containing Elliptical Cavity or Inclusion and Their Numerical Examples.

This paper presents the analytical solutions for an anisotropic medium containing an elliptical cavity or inclusion subjected to uniform out-of-plane loads at infinity, concentrated force, screw dislocation or dipole force at an arbitrary point. An elliptical inclusion can be assumed to be rigid or elastic. For the case of elastic inclusion, some sliding between the matrix and the inclusion at the elliptical boundary is assumed.

Screw dislocations near an interfacial cross crack

The screw dislocations near an interfacial cross crack are investigated. The stress field, stress intensity factor, image force, and strain energy of screw dislocations are derived based on the solution of a single medium. The effects of vertical and horizontal crack lengths on the stress intensity factor at the upper crack tip and image force components Fx and Fy are examined. The dislocation source is also studied.

Interactions Among General Systems of Cracks and Anticracks: An Integral Equation Approach

Cracks and rigid line inclusions, or anticracks, are commonly observed in many engineering materials, such as ceramics, intermetallics, etc. Interactions among these cracks and anticracks can significantly affect the load-carrying capacities and other mechanical properties of these materials. Accordingly, modeling of the interactions among general systems of cracks and anticracks subject to general loading conditions is the main thrust of this paper. An integral equation approach based on the fundamental solutions due to point loads and point dislocations in an elastic body is utilized for this purpose. A Gauss-Chebychev quadrature is used to reduce the integral equations to a system of linear equations consisting of the distributions of Burger’s dislocation vectors and forces on the cracks and the anticracks, respectively. The proposed solution procedure also allows direct determination of the rigid-body rotations for the anticracks. For a collinear crack-anticrack system, the results obtained from the present analysis are verified against those obtained from a Green’s function approach. Numerical results are also presented for sample systems of cracks and anticracks, and salient features of amplification and shielding of stress singularities are investigated.

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

The image force and shielding effects of a moving edge dislocation near a semi-infinite crack were investigated. The crack surface was simulated by continuous dislocations. After the dislocation distribution in the crack was obtained, the stress field in the entire space was calculated. Based on the stress field, the stress intensity factor and crack extension force on the crack tip, and the image force on the edge dislocation were computed. The crack shielding or antishielding arising from the edge dislocation slip or climb was studied in detail. The transition velocity of changing behavior of edge dislocation and Lorentz force were discussed. Newton’s third law was invalid in the system of moving edge dislocation and crack.

Interactions among cracks and rigid lines near a free surface

Cracks and rigid-line inclusions, or anticracks, are commonly observed in many engineering materials, such as intermetallics and ceramic composites. Interactions among these cracks and rigid lines can significantly affect the strength of these materials. Strength degradation due to finishing operations, such as grinding, also depend to a large extent on these interactions near a free surface and their associated surface and subsurface damage evolutions. Accordingly, modeling of interactions among general systems of cracks and rigid lines in the vicinity of a free surface, subject to general loading conditions, is the main thrust of this paper. An integral equation approach based on the fundamental solutions due to point loads and point dislocations in an elastic half plane is utilized for this purpose. The integral equations are reduced to a system of linear equations consisting of the distributions of Burger's dislocation vectors and forces on the cracks and the anticracks, respectively. The proposed solution procedure also allows direct determination of the rigid-body rotations for the rigid lines. The results obtained from the present analysis are first verified against existing results for a single crack or rigid line near a free surface. The amplification and shielding effects on stress intensity factors due to interactions among various distributions of cracks and rigid lines are then investigated. Such interactions near a free surface play crucial roles in surface and subsurface damage evolutions during high-speed machining of ceramic materials.

Effects of an inhomogeneous elliptic insert on the elastic field of an edge dislocation

The problem of an edge dislocation in the vicinity of an elliptical inhomogeneity is solved analytically in the form of infinite series. The inhomogeneous inclusion is assumed to be either perfectly bonded or sliding along the interface with the surrounding matrix. The problem is formulated in terms of Papkovich-Neuber displacement potentials and the results for the perfectly bonded and sliding interface are compared. The effects of the inclusion/matrix shear moduli ratio, inclusion/dislocation relative distance and inclusion aspects ratio on the interface stresses and the dislocation force are evaluated.

Antiplane Shear Interface Cracks in Anisotropic Bimaterials

An analysis of antiplane shear interface cracks in a finite anisotropic composite body is presented. The analysis is done by a new complex-variable integral equation formulation based on the solutions of a dislocation and body force in an infinite composite body. Numerical results of the stress intensity factors are presented for the composite bodies with finite rectangular cross-sections under uniform shear. The composite bodies are formed by bonding an orthotropic material to an isotropic material. The numerical results show that there exists a lower bound for the stress intensity factor for a fixed crack-length-to-height ratio and that the lower bound is attained in the case of isotropic bimaterial.

Incident Wave and Dislocation Acceleration Effects in Dislocation Emission From Cracks

Some previous transient analyses of dislocation emission from dynamically loaded cracks have treated glide at constant speeds, and have invoked an emissions criterion that allows the dislocation force to exceed the yield stress level during glide. In the context of nonstrain-hardening plasticity, this analysis requires that the force remain at the yield stress level. For an exact solution to the problem of screw dislocation emission from a crack subjected to plane SH-wave diffraction, the result is an equation of motion for the dislocation, which can be integrated exactly. The dislocation is found to accelerate during glide to a high but subcritical speed, before decelerating to its arrest position. A general incident SH-wave is considered, but is then specialized to the cases of a step-stress and a sinusoidal wave. Calculations on the basis of material and wave parameters show that purely brittle fracture can be difficult to achieve, and that wavelength/frequency cutoffs exist, beyond which emission cannot occur.

Transient studies of screw and edge dislocation generation at crack edges

Exact transient analyses of the generation of screw and edge dislocations at the edges of stationary cracks subjected to the diffraction of, respectively, plane SH- and SV-waves, and their subsequent arrest are performed. The solutions are examined in light of a dislocation emission criterion which is based, simultaneously, on standard dislocation force concepts and quasi-static emission studies. This examination allows expressions for the times of emission and arrest, the distances traveled by the dislocations, and the dynamic stress intensity factors to be derived in terms of parameters such as dislocation speed and yield stress. These expressions exhibit distinctive dynamic effects and reveal several features of the generation process: In particular, the times and distances are, while on a micromechanical scale, not necessarily insignificant, and imply that purely brittle fracture may not easily occur. Then, edge dislocation emission would appear to occur at a preferred speed, while screw dislocation emission apparently prefers to take place quasi-statically. Examination of a general incident waveform class shows that a continuous wave could cause dislocation generation to occur before a step-stress wave can. Moreover, the emission process depends upon a weighted time history of the incident wave stress, not its instantaneous value. This, in turn, implies that dislocation emission does not necessarily shield the crack edge by lowering the dynamic stress intensity factor. Finally, unless the dislocations are allowed to decelerate to zero speed upon arrest, a repetitious process of start-stop motion can in principle take place.

A criterion for arrest of a threading dislocation in a strained epitaxial layer due to an interface misfit dislocation in its path

In a strained layer grown epitaxially on a substrate, the motion of a dislocation on any particular glide plane in the layer can be influenced by the presence of dislocations on other glide planes. The focus here is on the glide of a dislocation extending from the free surface of the layer to the layer-substrate interface, the so-called threading dislocation. A general definition of driving force for glide of a threading dislocation in a nonuniform stress field is adopted to calculate the driving force on a threading dislocation due to an encounter with an interface misfit dislocation on an intersecting glide plane. The result is examined in detail for the case of cubic materials, taking into account different combinations of Burgers vectors. The analysis makes it clear that the misfit dislocation forces the threading dislocation to glide through a channel of width less than the full layer thickness. A blocking criterion is proposed, based on the presumption that blocking will occur if the channel width is less than the critical thickness for the local reduced strain. The results indicate that this effect can be significant in blocking the glide of a threading dislocation, depending on the mismatch strain magnitude and the layer thickness.

An Exact Transient Study of Dislocation Emission and its Effects on Dynamic Fracture Initiation

Closed-form transient solutions for the micromechanical process of screw dislocation emission from a stationary crack which is subjected to SH-wave diffraction are presented. The dislocations are allowed to leave the crack edge in arbitrary directions, either singly or in pairs. Imposition of an emission criterion that is both based on the dislocation force concept and is similar to criteria applied to quasi-static emission studies allows expressions for the instants of dislocation emission and arrest and the distance traveled by the dislocation to be obtained. These expressions are studied for their dependence on parameters such as emission direction and speed, and several distinctive dynamic effects are observed. A standard fracture criterion is then imposed, and conditions for determining whether fracture will precede or follow emission are established in terms of real time. Finally, some estimates for the orders of magnitudes of the parameters involved in this micromechanical process are given.

Analysis of strained-layer superlattice effects on dislocation density reduction in GaAs on Si substrates

High quality GaAs films with dislocation densities of 1–2×106 cm−2 on (100)Si substrates have been obtained for combination of strained-layer superlattice insertion and thermal cycle growth using the metalorganic chemical vapor deposition method. In this letter, remarkable reduction effects of dislocation density in the GaAs layers due to InGaAs/GaAs and InGaAs/GaAsP strained-layer superlattice insertion on Si have been analyzed by calculating the dislocation force exerted by the misfit due to the strained-layer superlattice insertions. Threshold layer thickness needed for dislocation reduction and critical thickness for dislocation generation have been clarified for several strained-layer superlattice systems.

Transient analysis of dislocation emission from a growing crack

A n exact transient solution for screw dislocation emission in arbitrary directions from a Mode III crack growing due to SH-wave diffraction is performed. An emission criterion based on the dislocation force is then imposed to obtain the instant of emission, the distance traveled by the emitted dislocation prior to its arrest, and the instant of arrest. The formulae for these quantities are examined for dependence on parameters such as emission angle, material yield stress and crack and dislocation speeds. Dynamic effects are clear, and order-of-magnitude evaluations suggest that the quantities are on a micromechanical scale, but not insignificant. In particular, the emission instant behavior indicates that purely brittle fracture is difficult and, moreover, that the instant itself might be incorporated in the emission criterion. Indeed, general suggestions for rendering the criterion more precise are noted. The solution and formulae are then modified to study multiple emission, post-arrest behavior, emission in the crack plane and the response of the dynamic stress intensity factor. These studies indicate that dislocation shielding is enhanced in a transient analysis but decreases after dislocation arrest occurs, and that dislocation arrest can be momentary.

An exact transient analysis of dislocation emission and fracture

D islocation-crack interaction studies have led to the development of criteria for fracture in terms of dislocation emission from crack edges, and to consideration of crack edge shielding effects due to dislocations. These studies have generally been quasi-static. To illustrate, therefore, the extension of the basic concepts involved to dynamic situations, three exact analytical results are presented. These involve screw dislocation motion near a crack which may be growing, and which may be subjected to dynamic loading due to SH-wave diffraction. Study of these results allows some useful insights. In particular, fracture initiation and dislocation emission times and, thus, their order of occurrence, can be determined. Moreover, it is shown that crack edge shielding can be temporary, and that parameters such as the dislocation force and the distance traveled by an emitted dislocation prior to arrest can have pronounced dynamic overshoot effects. Finally, it is found that this arrest distance depends only implicitly upon the applied loading.

Transient generalized forces due to dislocation array-growing crack interaction

For insight into the dynamic interaction between growing cracks and dislocations during fracture, the dislocation forces and the crack driving force due to the dislocations themselves are calculated for a Mode III crack initially in equilibrium with a stationary array of screw dislocations. The calculations are based on the exact closed-form solution for a single, arbitrarily-placed, screw dislocation and a crack growing at a largely arbitrary speed. They show that, in the absence of an applied stress in the material, the dislocation has no tendency to follow the crack edge as it moves but is, instead, attracted to the crack surface. If the dislocation is a member of an array, however, it can either be attracted to or repulsed by the crack surface, and could very well follow the crack edge by jogging. More generally, both the dislocation and crack driving forces exhibit dynamic effects embodied in the crack edge speed, and undergo rapid changes at fracture initiation, especially if the crack instantaneously attains a finite speed.

Transient analyses of dislocation emission in the three modes of fracture

Exact transient solutions for a micromechanical process of dislocation emission from stationary cracks in each of the three Modes of fracture are assembled. Each process involves a possible slip mechanism for the Mode, and the loading in each case is due to plane wave diffraction. The solutions are examined in view of an emissions criterion similar to one developed for quasi-static studies on the basis of standard dislocation force concepts. Among the results are formulas for three parameters: emission time, distance traveled by an emitted dislocation prior to arrest, and the time of arrest. The formulas involve material properties such as yield stress and surface energy, as well as a dimensionless variable parameter governing the size of a zone of dislocation attraction at the crack edge. The parameters themselves exhibit dislocation speed-dependent dynamic effects, but, on the other hand, the Mode I and Mode III cases achieve minimum emission times for the zero-speed limit. The effect of crack blunting serves to raise the emission time required. Order-of-magnitude estimates of the parameters indicate that they are definitely on a micromechanical scale, suggesting that emission may depend only on the region very near the crack edge.

Forces on Dislocations in Multilayer Structures

ABSTRACTIn multilayer structures, dislocation forces that arise from coherency strains are well understood in both the isotropic and anisotropic elastic cases. Image forces produced by elastic inhomogeneity have also been developed for single layers surrounded by extended phases. Image forces for the multilayers are shown to reduce to the simpler single embedded layer case to a good approximation. Image forces are shown to lead to a “stand-off” position of interface dislocations from the interface, with several implications for the properties of multilayer structures.

Dislocation-crack edge interaction in dynamic brittle fracture and crack propagation

Due to the formation of small inelastic zones near crack edges, brittle fracture and crack propagation involve dislocation-crack edge interaction. An approximate transient solution for a single screw dislocation moving near a propagating Mode III crack is obtained here, and used to study dislocation arrays which exist prior to fracture in circular zones around the crack edge. Using dislocation force concepts, it is found that these dislocations coalesce into bands near the crack surface when fracture is triggered by SH-wave diffraction and, if their speeds exceed that of the crack edge, collapse onto the crack surface itself. Moreover, this dislocation motion has a noticeable if brief effect on the dynamic stress intensity factor.