Fields of stress and electric displacement produced by dislocations and disclinations in three-dimensional, anisotropic, elastic, and piezoelectric media. II. Infinite straight dislocation and Frank disclination

Abstract

The fields of stress and electric displacement caused by infinitely extended straight dislocations and Frank disclinations are deduced from the author's statements for the fields caused by a continuous distribution of dislocations and disclinations (S. Minagawa, Phil. Mag. 84 2229 (2004)). The multiple integrals in the original statements are converted into functions of space coordinates. Cauchy's theorem plays an important part. The improper integral that appears in computations of the fields around a Frank disclination is interpreted as its finite part by Hadamard. Examples are the fields around an infinite straight defect in caesium copper chloride, as well as those in gallium arsenide. The contours and zero lines are plotted to illustrate the fields caused by a dislocation and a disclination dipole.

Notes

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In terms of

, e _pj and ϵ _ij ,

So that, d ₁₁, d ₁₂ are independent of e ₁₄, ϵ₁₁ and ϵ₃₃, and therefore ζ₁ and ζ₂ are independent of the electrical properties of the crystal.

For example,