Line Tension Model Research Articles

Capillary equilibria of surfaces intersected by dislocations

Abstract The equilibrium shape of the pit where a dislocation intersects a free surface is calculated in a variational formalism. The constant dislocation line tension approximation, made by previous workers, is shown to be clearly inadequate for all realistic cases. Employment of a variable dislocation line tension model for the case of finite dislocation density shows the existence of two regimes of behaviour. In the first, pits formed at dislocation-surface intersections have a well defined shape and are of finite depth. However, a second regime exists, in which the pit depth is infinite and the dislocation core size exceeds the bulk value. This may result in the formation of open-core dislocations, as discussed by Frank.

The radius of curvature of dislocation segments in MgO crystals stressed in the high-voltage electron microscope

Abstract MgO single crystals have been deformed inside the high-voltage electron microscope. The local radius of curvature of dislocation segments bowing out between strong obstacles was determined by photometric measurement of the dislocation coordinates and by piecewise fitting of third-order polynomials to these coordinates. While individual segments show very different dependences of the local radius of curvature on the dislocation orientation, averages over greater numbers of segments agree fairly well with theoretical results obtained using the line tension model with isotropic elasticity. During unloading, the segments have the form of almost straight sections connected by strongly curved regions, probably as a result of obstacles to their back-motion. The bowing out of the segments is influenced by interactions with neighbouring segments. The radii of curvature depend on the length of the segments. The dependence found experimentally is much stronger than is predicted theoretically; this would con...

The study of glide dislocation loops on {001} planes in a f.c.c. alloy

Abstract Single crystals of disordered Ni3Fe oriented for single slip were deformed in tension at room temperature. Ni3Fe represents a f.c.c. alloy in the solid solution range having both a high value of stacking fault energy γ and friction stress τf. Electron microscopy methods are used to study undissociated glide dislocations (b = a/2[110]) bowing out on (001) planes. The local radius of curvature of these half loops is rather low for dislocation characters near 35° and 90° and therefore their shape deviates from the elliptical one normally observed for glide dislocations on {111} planes in f.c.c. metals. The experimentally observed loop shapes agree very well with shapes calculated using a line tension model. From this agreement it can be concluded that τf balancing the stress of the loop does not depend on the character of the dislocation. This result is confirmed by computations showing that τf mainly arises from modulus and short-range-order (SRO) effects. Finally the values of the locally effectiv...

Method of Evaluating Geometrical‐Statistical Parameters of the Interaction between Dislocations and Point Obstacles from Electron Micrographs

AbstractElectron micrographs of MgO crystals deformed in the HVEM show screw dislocations of curly shape. The dislocations are pinned at localized obstacles and bow out between them. The paper describes a measuring procedure for the geometrical interaction parameters between the dislocations and the obstacles. Such are the effective stress, the obstacle distance and the force acting on the obstacles. The procedure consists in a graphical fit of loops calculated by the DE WITT‐KOEHLER line tension model to the observed dislocation segments.

Strength of γ′ hardened nickel-base alloy

Results from isothermal ageing of a commercial nickel-base alloy are presented. Particle sizes are determined by electron microscopy. The particle coarsening is found to obey the Lifschitz-Wagner theory. The volume fraction of γ′ particles is 0.15. The proof stress is determined for a series of ageing times. The Taylor factor is calculated taking the texture of the material into account.A theory is presented for the critical resolved shear stress due to γ′ particles. The motion of a pair of dislocations is considered. The dislocations interact with the particles through the generation of antiphase boundary and through the misfit strain field. The dissociation of the dislocations into partials is taken nto account. A line tension model is used which depends on the dislocation configuration. A statistical theory is used to calculate the critical resolved shear stress from a three-dimensional distribution of particles. A good agreement between theory and experiment is obtained by using an antiphase boundary energy of 0.19 J m−2 and a constrained misfit ratio of 0.35% for the particles. Antiphase boundary hardening accounts for approximately half of the particle-induced strength of the alloy.

The strength of a precipitation hardened AlZnMg alloy

An Al, 2.0 at.% Zn, 1.4 at.% Mg alloy is aged at 120°C for 3 h up to 32 days. The proof stress is determined for polycrystals. A texture analysis is preformed to obtain a reliable Taylor factor. Particle size distributions are obtained for spherical GP zones for ageing times up to 12 h and also η-particles for longer ageing times. The yield is controlled by screw dislocations in the under and overaged conditions. The experimental results are intrepreted in terms of a model for shear modulus hardening of GP zones. The incoherent η particles are overcome by the dislocations with an Orowan mechanism. A dislocation line tension model is used which depends on the dislocation configuration. The critical resolved shear stress is calculated with a statistical theory. The distribution of particle sizes and different particle positions relative to the dislocation glide plane are considered. Several properties of the dislocation at the yield stress are calculated as for example the average distance between particles. Good agreement between theory and experiment is obtained with a shear modulus of 4.3 × 10 10Pa of the GP zones.

Microstress distributions in single crystals of silicon

AbstractA combined theoretical and experimental method for determining elastic microstress distributions in externally loaded single metallic crystals, in particular of silicon, is described in this paper. Utilizing a line tension model of a dislocation segment, an expression is obtained which describes the stresses acting on a dislocation in terms of its geometric parameters. An existing X-ray Lang scanning technique is then used to obtain the dislocation pattern in an elastically stressed silicon single crystal. From the geometric characteristics of dislocations measured from such a pattern, the stress field acting on each individual dislocation is calculated from the analytical expression deduced in this present study. Stresses, so deduced, are taken to be representative of the actual microstress situation and hence lead to the determination of microstress distributions in single crystals of silicon. Resume Les auteurs decrivent ici une methode tant theorique qu'experimentale qui perlnet de determiner ...

The bowing of a dislocation segment

Abstract The bowing under stress of a segment of an otherwise straight dislocation line has been determined for an isotropic solid. A digital computer is used to relax the dislocation to its equilibrium shape, using a variant of the Brown self-stress method. The critical stress required to make the dislocation become unstable has been determined for a wide range of segment lengths, and is in fair agreement with the predictions of the line tension model. The results are relevant to a Frank-Read source, since the elevation of the side-arms is shown to have a relatively minor effect on the critical bowing. The bowing of a screw dislocation between several attractive forest screw dislocations has also been considered.

A Method for Describing a Flexible Dislocation

AbstractA procedure for determining the equilibrium shape of a dislocation under the influence of both internal and external stress fields is described. The method, which is an extension of that used by Brown to determine the shape of extended nodes, does not require the explicit numerical integration of line integrals to obtain the self‐stress, and line shapes are therefore computed with comparative simplicity. The procedure has been used to study the bowing characteristics and the critical shapes and stresses of Frank‐Read sources of various lengths and orientations, and the results are compared with those of the line tension model. The effects on the critical features of an orientation‐dependent friction stress have also been studied. Similar results on the bowing characteristics of a dissociated dislocation in the f.c.c. structure and their dependence on stacking fault energy are also presented.