J. Dundurs

Interaction between an edge dislocation and a circular inclusion

Abstract Exact elasticity solutions are used to discuss the interaction between a circular inclusion and an edge dislocation in the matrix. The force on the dislocation is given, and it is shown that for certain combinations of material constants, the dislocation has a stable equilibrium position in the matrix near the interface. Moreover, the interaction is very much affected by the orientation of the Burgers vector with respect to the inclusion. The results also exhibit a strong dependency on the difference between the Poissons ratios of the matrix and the inclusion.

Effect of Elastic Constants on Stress In A Composite Under Plane Deformation

When a composite body consisting of two isotropic and elastic phases is subjected to prescribed surface tractions, generally the stress field depends on three parameters involving the elastic con stants. If the composite is in a state of plane deformation, and there are no net forces on internal boundaries, however, the stress depends on only two combinations of elastic constants. Convenient constants for the composite material are proposed.

Edge dislocation inside a circular inclusion

Abstract Equilibrium positions of an edge dislocation inside a circular inclusion are investigated using elasticity solutions. The conditions under which the centre of the inclusion is stable equilibrium position are given, and it is shown that the equilibrium positions away from the centre are unstable. The results indicate that the Poissons ratios play an important role in characterizing the different types of behaviour.

A Green’s Function Formulation of Anticracks and Their Interaction With Load-Induced Singularities

This paper provides a Greens function formulation of anticracks (rigid lamellar inclusions of negligible thickness that are bonded to the surrounding elastic material). Apart from systematizing several previously known solutions, the article gives the pertinent fields for concentrated forces, dislocations, and a concentrated couple applied on the line of the anticrack

Contact between elastic bodies with wavy surfaces

The contact between two elastic semi-infinite bodies with wavy surfaces is considered. For mathematical tractability, the surface profiles are taken as purely sinusoidal. The formulation leads to a pair of dual series equations, which can be reduced to an integral equation of the Abel type. The integral equation can be solved and the quantities of most interest physically extracted in closed elementary forms.ZusammenfassungEs wird das Kontaktproblem zweier elastischer halb-unendlicher Körper mit wellenförmigen Oberflächen untersucht. Zur vereinfachten mathematischen Behandlung werden die Oberflächenprofile rein sinusförmig angenommen. Man erhält zwei duale Summengleichungen, die auf eine Integralgleichung vom Abelschen Typ zurückgeführt werden können. Die Integralgleichung kann gelöst werden und die interessierenden Größen lassen sich in elementarer geschlossener Form angeben.

Stability Considerations in Thermoelastic Contact

A simple one-dimensional model is described in which thermoelastic contact conditions gioe rise to nonuniqueness of solution. The stability of the various steady-state solutions discovered is investigated using a perturbation method. The results can be expressed in terms of the minimization of a certain energy function, but the authors have so far been unable to justify the use of such a function from first principles in view of the nonconservative nature of the system.

Elastic fields of a dislocation loop in a two-phase material

The purpose of this study is to set forth the mathematical framework for an efficient treatment of a plane dislocation loop in a two-phase material, and to carry the elastostatic part of the analysis far enough, so that the results are immediately tractable for applications to solid state. The two-phase material is idealized as two isotropic elastic half-spaces with perfect adhesion, while the loop is placed in a plane parallel to the interface. It is shown that the elastic fields can be obtained by differentiating two types of integrals and, thus, are readily evaluated for any shape of the loop for which the integrals are available from potential theory. Explicit results are given for circular prismatic and glide loops.ZusammenfassungMit der vorliegenden Arbeit wird die Absicht verfolgt, den mathematischen Rahmen zu einer leistungsfähigen Behandlung von ebenen Versetzungsschleifen in einem Zweiphasenmaterial zu erweitern und den elastostatischen Teil der Berechnung so weit fortzuführen, daß die Resultate für die Anwendung in der Festkörperphysik unmittelbar zur Verfügung stehen. Das Zweiphasen-Material wird idealisiert durch zwei isotrope elastische Halbräume mit perfekter Adhäsion, während die Versetzungsschleife in einer Ebene parallel zur Trennfläche angenommen wird. Es wird gezeigt, daß die elastischen Felder durch Differentiation zweier Integraltypen und damit für jede beliebige Form der Versetzungsschleife erhalten werden können, für die die Integrale sich aus der Potentialtheorie ergeben. Explizite Resultate werden für kreisförmige prismatische und gleitende Schleifen angegeben.

Exact analysis of an edge dislocation near a surface layer

Abstract Some explanations of how very thin coatings affect mechanical properties of crystals are based on the interaction of the surface layer with dislocations. Although analysis of this interaction has been accomplished for a screw dislocation, the equally interesting case of an edge dislocation has not been solved up to this time. The present paper provides an exact analysis of an edge dislocation near a surface layer with no restrictions other than isotropy. The results show that the edge dislocation has stable equilibrium positions whenever it is repelled by the layer nearby. Especially for layers with higher shear moduli, the equilibrium positions are much closer to the layer than for screws dislocations.

Heat conduction between bodies with wavy surfaces

Abstract Theoretical treatment is provided for the conductive heat transfer between two solids with wavy surfaces. The problem is set in two dimensions, and it is assumed that the surface profiles are purely sinusoidal and deformations elastic. It is also assumed that heat is transmitted only where there is solid to solid contact, and there is no resistance due to contamination of the surfaces. The temperature problem is solved exactly, but deformations are treated by relying on the results due to Hertz. The expression derived for the constriction resistance exhibits a directional effect. It is also shown that perfectly flat surfaces may become wavy, as heat is transmitted from one body to another.

Structural fluctuations in small particles

Abstract We present a theoretical analysis of a phenomenon recently observed by high-resolution electron microscopy that involves rapid structural fluctuations in small f.c.c. particles below 10 nm in size. The different energy contributions to the total energy of the particle and the magnitude of the potential energy barrier between different shapes is evaluated and compared with the available energy during particle-beam interactions. The results indicate that the activation energy barrier existing between different shapes is only a few electron volts, whilst a rough estimate indicates that during electron-beam irradiation the available energy may be as much as 100–1000eV.