DISLOCATIONS AD DISCLINATIONS IN TRANSVERSELY ISOTROPIC ELASTIC SOLIDS

A recently developed method to obtain the elastic fields due to defects in isotropic solids has been extended to include the case of fields due to dislocations and disclinations with arbitrary orientations in transversely isotropic infinite solids. The extension hinges on the introduction of a newly defined stress vector function, the hexagonal stress vector, which, together with the Green functions for double force and for double force with moment, yields closed-form solutions. The solution is first obtained for infinitesimal Volterra dislocation loops. The elastic fields due to dislocations and disclinations are then obtained by integrating the solution for the infinitesimal loop over the surface of the cut that generates the line defects. Along with the Newtonian and biharmonic potential functions that are used for isotropic solids, two more harmonic potential functions are introduced to express the solution in transversely isotropic solids. Closed-form solutions for straight dislocation and disclination lines, and circular dislocation loops are presented as examples to illustrate the application of the method.