T. Mura

Elastic Fields and Energies of a Circular Edge Disclination and a Straight Screw Disclination

The displacement and stress fields for a circular edge disclination are derived from Greens tensor function. The elastic strain energy of this circular edge disclination is calculated and compared with the energy of two different kinds of circular dislocation loops. Finally, the stress field and elastic strain energy of a straight screw disclination is computed and is compared to the case of a straight screw dislocation.

Dislocation Pile‐up in Two‐Phase Materials

Based on the theory of continuously distributed dislocations, the equilibrium equations for both edge‐and screw‐dislocation pile‐ups in materials composed of soft and hard phases are formulated in terms of a singular integral equation. The integral equation is solved exactly by using the Wiener‐Hopf technique with Mellin transforms.The dislocation distribution function is found in explicit form. It is shown that the number of dislocations in the piled‐up array can be determined directly from the Mellin transform of the distribution function without its inverse transform.

Elastic Field and Strain Energy of a Circular Wedge Disclination

The displacement and stress fields for a circular wedge disclination loop are derived by the Fourier integral method, and expressed in terms of tabulated functions. The associated elastic‐strain energy is also derived.

On the Internal Friction of Cold‐Worked and Quenched Martensitic Iron and Steel

A theoretical explanation is given for the internal friction peaks which are observed at 200°∼250°C for cold‐worked iron and steels and for steels in the martensitic condition. The theory for the peaks is based upon the addition of a term to the free energy in order to account for the strain energy due to the interaction of an atmosphere and the line imperfections. The standard linear solid was obtained from the model in which dislocations are vibrating with an atmosphere of carbide precipitates.

Circular disclinations and interface effects

The elastic fields of a circular wedge disclination and a twist disclination in the two‐phase materials and a twist disclination in a plate are given. The elastic strain energies and forces on the loops are then obtained to arrive at the studies of the interface effects on the loops.

Dislocation Stresses in a Thin Film Due to the Periodic Distributions of Dislocations

The state of stresses and displacements in thin films due to the presence of a periodic distribution of screw dislocations and edge dislocations is investigated by the method of continuously distributed dislocations and the three‐dimensional theory of elasticity. The dislocations are straight and pierce obliquely the surfaces of the thin films in both cases. As a special case the exact solution is presented for a straight‐edge dislocation piercing normally the surfaces of the films. Emphasis is placed upon the stress relaxation caused by the presence of free surfaces. The result will be useful for the contrast study of dislocation images in electron microscopy.

Dislocation Configurations in Cylindrical Coordinates

General expressions are derived for the stress components due to an arbitrary continuous distribution of dislocations prescribed in a cylindrical coordinate system. Results are obtained for the stress field of a helical dislocation of uniform shape with the Burgers vector along its axis. The additional energy arising from the interaction of a point defect with the helix is obtained and the behavior of the defect examined.It is also shown how results for circular dislocation loops are readily obtained from the general expressions and in particular the problem of a rotational loop, which is formed by twisting the two faces of the slip surface relative to each other, is solved.

Dislocation Pile‐Up in Half‐Space

If an obstacle exists in the vicinity of the free surface of a half‐space and a stress field is applied in such a manner that dislocations are pushed towards the obstacle, an array of dislocations then piles up into an equilibrium distribution against the obstacle. The distributions of dislocations are obtained by the Wiener‐Hopf technique for the edge and screw dislocations. The total strength of dislocations (Burgers vector multiplied by the number of dislocations) distributed in the distance L is calculated as 0.92π(1−v)σAL/G for edge dislocations and 2σAL/G for screw dislocations, where G, v are the shear modulus and Poisson ratio respectively and σA is the applied stress. The result can be applied to crack problems. The above two numbers for the total strength of dislocations give the crack openings at the free surface for the extensional mode and the antiplane shear mode of fracture, respectively.

Circular twist disclination in viscoelastic materials

A general formulation of the displacements induced by plastic distortion, β*ji, with small intertia forces in viscoelastic materials is derived. The elastic fields of a twist disclination in viscoelastic materials are then obtained from this formulation. Finally, the fading property of the strength of the disclination is determined for the disclination in the standard linear viscoelastic materials, and the variations of the elastic fields of the disclination are discussed.

Periodic Dislocation Distributions in a Half‐Space

A solution is given to the stress field produced by an arbitrary periodic distribution of dislocations (or plastic distortion) in a half‐space. It is shown how the known results for discrete dislocations are obtained quite simply from this. The solution to the problem of a Frank dislocation network near a free surface is given and its stability examined. The whole‐space stress field decreases exponentially with the distance from the plane of the network, as do the stress terms due to the free surface which decrease exponentially with the distance from this surface. It is shown that the network always experiences a force attracting it to the free surface.