The dynamic form of dislocations and the topological quantization of Burgers vector projection were obtained in 3-dimensional Riemann-Cartan space by extending the dislocation-density projection and the Burgers-vector projection to a topological current. A study was made of the origin and bifurcation of dislocations when the tangent stress inside the body and the order parameters of the dislocations were changed. The branch solutions at the limit point, and the various directions of all branch curves at the bifurcation point, were calculated. Because the dislocation current was identically conserved, the total topological quantum numbers of the branched dislocations remained constant; which was just the conservation law for the Burgers vector in a dislocated and disclinated continuum. It was pointed out that a dislocation with a higher value of the Burgers vector was unstable, and would evolve into a lower-valued Burgers vector via a bifurcation process. It was concluded that the generation and bifurcation of dislocations were not gradual changes during variations in the tangent stress, but were instead sudden changes.

The Origin and Bifurcation of Dislocations in the Gauge Field Theory of Dislocation and Disclination Continuum. G.H.Yang, Y.S.Duan: International Journal of Engineering Science, 1999, 37[8], 1037-50