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It is shown that vortices and dislocations can be treated as virtually identical from both a physical and mathematical perspective. This allows the lowest-energy configurations of such defects to be predicted. In particular, it is suggested that, similar to the way in which a dislocation cell structure forms at high deformations, an analogous vortex cell structure is generated at high fluid velocities. In addition, both arrangements are believed to underlie the concept of turbulence.

A discrete dislocation analysis of the continuous plastic crack is carried out for ordered alloys. The crack is assumed to nucleate and reach a size where it will emit a set of lattice dislocations in order to decrease its energy. Further growth of the crack takes place elastically until it can emit the next set of lattice dislocations. Repeated emission of lattice dislocations, with elastic crack growth in between, leads to the Griffith configuration where the energy variation with size of the crack is zero. It is shown that a crack, either tensile or shear, can be stabilized by the presence of antiphase boundary energy alone. In the absence of frictional stress or with the very low frictional stresses encountered in real materials, the lattice dislocations are generated in pairs on each slip plane. However, when the frictional stress is high, the lattice dislocations are generated as single ones, giving rise to an antiphase boundary between the crack and the lattice dislocation.

The method of continuously distributed dislocations and the method of discrete distribution of dislocations have been used to determine the effect of surface energy on the surface boundary conditions of a semi-infinite solid containing an edge dislocation. The surface dislocation model which incorporates two surface dislocation arrays, the primary and the secondary, in order of importance, is used to study the effect of surface energy. The surface dislocation model in conjunction with the method of continuously distributed dislocations enables the exact determination of the dislocation distribution function of the primary and secondary dislocation arrays and the effect of surface energy tends to lower both the total Burgers vector associated with the surface arrays and dislocations in evaluating the effect of surface energy is illustrated and is compared with the method of continuously distributed dislocations. It has been found that the surface energy tends to lower both the total Burgers vector associated with the surface arrays and the length of the region within which they are spread on the surface. Although the effect on the primary surface arrays is not very large, the secondary surface arrays are completely eliminated with normal values of surface energy encountered in real solids. Thus, the effect of surface energy is to bring non-vanishing stress components to the surface. The surface is also non-uniformly stressed. The superiority of the surface dislocation model over the other methods hitherto used in the literature is illustrated.

The fracture surfaces of slowly cooled Fe-Al alloys containing up to 28 at. % Al were examined using scanning electron microscopy techniques. It was found that the fracture modes changed from void coalescence to transgranular and finally, to intergranular as the Al concentration increased. The latter two modes of fracture were of the brittle type and were associated with the onset of long range order in these alloys. In particular, it has been postulated that atomic ordering leads to markedly reduced cross-slip, in turn reducing the degree to which void coalescence, with accompanying ductility, can occur.

An extensive scanning electron microscopy study was carried out with respect to the fracture surfaces of Portland cement hydrated for various times. It is shown that the two major products of hydration are calcium silicate hydrate spherulites, which consist of radiating fibres and calcium hydroxide platelets. These fibres bond with one another to hold the spherulites together. The volume between the spherulites consists of calcium hydroxide platelets. The fracture is frequently found to be across the weakly bonded basal planes of the calcium hydroxide, and is believed to limit the strength of the Portland cement.

An extensive transmission electron microscopy study has been made of the structure of high and low angle grain boundaries in both ordered and disordered FeCo alloys which were electrochemically thinned from the bulk material. The grain boundaries observed were determined to be of the primary coincidence type and were found to contain numerous secondary grain-boundary dislocations. These secondary dislocations were either of the true grain-boundary types or else crystal lattice dislocations. The secondary grain-boundary dislocations were presumed to arise from the migration of the grain boundaries during grain growth and were frequently found to dissociate into crystal lattice dislocations arranged in the form of low angle boundaries within one of the adjacent grains.

A model of sliding wear, based upon the concept of surface dislocations, has been proposed. In particular, a dislocation cell structure is created in the plastically deformed surface layer, which in turn gives rise to shear crack initiation at the interface between this surface layer and the undeformed interior of the body. These shear cracks then grow with subsequent delamination of the surface layers. It is shown that the most important parameter in this theory is the rate of work hardening of the materials in question.

Any surface, in order to decrease its surface energy, contracts. It is shown for the first time that this contraction is formally equivalent to the introduction of a continuous distribution of surface dislocations. Equilibrium is attained when the increase in strain energy associated with these surface dislocations just balances the corresponding decrease due to the reduction in free surface area. Numerical calculations have been carried out for finite solid and liquid bodies as well as for liquid droplets in contact with solids. These findings suggest that it is possible to reformulate the behaviour of liquids in terms of dislocation theory in a much more general way than has hitherto been done.

Earlier surface dislocation analysis of a grain boundary recognized the tendency of the grain-boundary surfaces to coalesce in order to reduce surface energy. The coalescence process is described by a distribution of surface dislocations on the grain-boundary surfaces. In the present paper, previous analysis is further refined. In particular, the sum of the Burgers vectors of the surface array of grain-boundary dislocations is not equal to the Burgers vector of the grain-boundary lattice dislocation. Instead, the Burgers vector of the surface array is determined as a function of the coalescence of the grain-boundary surfaces. The conservation of Burgers vectors of dislocations is used to predict the presence of a screening array of dislocations. The screening array of dislocations is determined by minimization of the total energy of the configuration. The distortion around the boundary is relaxed by the screening array. In general, the distribution of the screening array is two dimensional. This result has been proved by the presence of a minimum energy configuration for two sets of screening arrays of dislocations situated at different distances from the boundary.

The surface dislocation method developed earlier for solving the free surface boundary problem is now extended to the two-phase interface boundary problem wherein a lattice dislocation is situated in one of the phases. The interface is planar where two semi-infinite half spaces of different elastic properties are joined. The interface consists of four surface arrays of dislocations, two in each phase, so that the continuity of two stress components and two displacement components is maintained. The continuous distribution of dislocations is employed to arrive at the distribution function representing the surface arrays. The Airy stress functions for the two phases are derived and shown to give the same result as that obtained earlier by other methods. The distortions involved across the interface are represented in terms of simple surface arrays to show the advantage of the surface dislocation model. The stress field around the dislocation in the two-phase medium is plotted and the effect of the shear modulus of the second phase and of Poisson's ratio discussed. The advantages of applying the surface dislocation model either by the continuous distribution method or the discrete dislocation method are indicated.

A geometrical analysis of the deformation of internal boundaries is presented using the slip systems as reference co-ordinate axes to describe the orientation of the two phases adjacent to the boundary. The present analysis can be applied to any type of boundary such as a grain boundary, a twin boundary or a two-phase interface. The nature of the disturbance left by a dislocation cutting through the boundary is characterized by a boundary dislocation, the Burgers vector of which can be determined from the orientation relationship between the adjacent slip systems. Whenever the crystal dislocation, cutting through the boundary, has a Burgers vector component normal to the boundary, the disturbance also possesses a ledge character, the motion of which may cause both grain boundary sliding as well as migration. The formulae derived are applied to simple cases to determine the nature of the boundary dislocations.

The foundations have been laid with respect to a generalized theory of phase transformations in solids. In particular, the methods of differential geometry have been employed and such important tensor quantities as distortion, metric, torsion, and anholonomic object have been developed with respect to such transformations. It is further shown that both Riemannian as well as non-Riemannian (dislocation) geometries are needed to describe these transformations properly.

The tensor properties of simple internal surfaces, such as two-phase interfaces and grain boundaries, have been studied in detail. In particular, these tensor quantities have been defined with respect to the original crystal lattice as well as to a common coincidence site lattice that is a characteristic of the boundary. Such lattices allow a given type of distortion to be represented in either a Riemannian or a non-Riemannian (dislocated) space. This particular generality provides a powerful method of anlysing problems in continuum mechanics.

It is shown that the classical picture of a grain boundary in terms of a single array of lattice dislocations is incomplete. In addition, it is also necessary to incorporate into the boundary a second array of continuously distributed surface dislocations of infinitesimal strength and of opposite sign to those of the lattice dislocations, but with the same total magnitude. Furthermore, the lattice dislocations can also dissociate into a continuous distribution by the formation of cores. As the angular misorientation of the grain boundary increases, more and more of the surface dislocations combine with the lattice dislocations, in turn resulting in the formation of a larger and larger stress-free ledge, with a consequent overall reduction in the strength of the remaining lattice dislocation.

A detailed scanning electron microscopy study has been made of spherulites in meltcrystallized polyethylene. In particular, unetched, ion etched, nitric acid etched and plastically deformed polyethylene samples have been examined. It appears that the spherulites visible on the surface of these samples consist of lamellae which possess alternate right- and left-handed partial twists. It is quite possible that enough material was removed from the surfaces of the samples by ion etching that the spherulites visible on etched samples could be representative of bulk samples. While questions remain both about the half twist model and about the current full twist model, the half twist model deserves consideration as an alternate model for spherulite structure.

A detailed numerical analysis has been made of the passing of superlattice dislocations in the presence of frictional forces and the results compared with those for ordinary dislocations. In particular, it was shown that the behaviour of superlattice dislocations is similar to that of ordinary dislocations, only at very high frictional stresses or at very low vertical separations. It was also shown that dipole strength can be increased significantly by decreasingy, the vertical separation, untily reaches a critical value,y c, when the cross-slip forces due to the internal stresses are sufficient to induce non-thermal cross-slip thus annihilating the passing dislocations. Edge dislocations, on the other hand, cannot annihilate themselves by climb, and hence, smaller vertical separation can be obtained increasing the dipole strength significantly. The effect of thermal and nonthermal cross-slip on the work-hardening of ordered alloys is discussed in detail. For the purpose of illustration, the calculations were made for FeCo. The results, however, are quite general and are applicable to all B2-structure alloys.