Theory of Disclinations: IV. Straight Disclinations

The general theory of disclinations developed earlier is applied to the special case of a straight disclination line. First the geometrical fields are found, such as the defect loop densities which correspond to Mura's new concepts of "plastic distortion" and "plastic rotation," the basic plastic fields (strain and bend-twist), the defect densities (dislocation and disclination), the characteristic vectors (Burgers and Frank), and the incompatibility. Then the static fields are found for the isotropic case, such as the displacement, total distortion, basic elastic fields, and the stress. It is shown that the disclination axis is moved by adding a dislocation to the disclination line. All these special results for the straight disclination line are shown to satisfy the general equations of the theory. As corollaries the following topics are also treated: 1. The finite and infinitesimal straight disclination dipole, which can be biaxial or uniaxial. It resembles the straight dislocation line. 2. The dislocation models of the straight disclination line and of the finite disclination dipole. They are terminating dislocation walls (tilt and twist). 3. The compensated disclination line and the bent dislocation wall. 4. Finally we show analytically a special case of a dislocation ending on a disclination.