The origin and bifurcation of dislocations in the gauge field theory of dislocation and disclination continuum

Abstract

In 3-dimensional Riemann–Cartan space, the dynamic form of dislocation and the topological quantization of Burgers vector projection are obtained by extending the dislocation density projection and Burgers vector projection to a topological current. When the tangent stress inside the material body and order parameters of dislocation change, the origin and bifurcation of dislocations are studied. The branch solutions at the limit point and the different directions of all branch curves at the bifurcation point are calculated. Since the dislocation current is identically conserved, the total topological quantum numbers of the branched dislocations will remain constant, which is just the conservation law of Burgers vector in dislocation and disclination continuum. It is pointed out that a dislocation with a higher value of the Burgers vector is unstable, and it will evolve to the lower value of Burgers vector through a bifurcation process. Furthermore, one can see that the origin and bifurcation of dislocations are not gradual changes but sudden changes with the varying of tangent stress.