The aim of this paper was to provide new results and insights for a straight screw dislocation in functionally graded media within the gauge theory of dislocations. The equations of motion for dislocations in inhomogeneous media were presented. The equations of motion for a screw dislocation in a functionally graded material were specified. The material properties were assumed to vary exponentially along the x and y directions. The analytical gauge field theoretical solution to the problem of a screw dislocation in inhomogeneous media was given here. Using the dislocation gauge approach, rigorous analytical expressions for the elastic distortions, the force stresses, the dislocation density and the pseudomoment stresses were obtained depending upon the moduli of gradation and an effective intrinsic length scale characteristic for the functionally graded material under consideration. Because of the gradation, the field equations contained gradients of the constitutive moduli. A new effective inverse length scale, j, was found which was characteristic of the gauge-theoretical anti-plane problem of functionally graded media. All of the analytical solutions were given in terms of the effective length-scale, 1/j, as well as the gradation length scale, 1/a. So-called perturbed Helmholtz equations were found to be the governing partial differential equations, and these were solved. Exact analytical gauge-theoretical solutions were found which could be used by materials scientists.

A Screw Dislocation in a Functionally Graded Material Using the Translation Gauge Theory of Dislocations. M.Lazar: International Journal of Solids and Structures, 2011, 48[11-12], 1630-6