On the dynamical origin of dislocation patterns

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The formation and stability of dislocation patterns are interpreted on the basis of instabilities occurring in partial differential equations modelling the dynamics of dislocation species. Under certain circumstances, these equations are shown to be a coupled system of the diffusion reaction type for the densities of the immobile and mobile dislocation populations. The applied mechanical stress plays the role of a bifurcation parameter for that system. In particular, we confine attention to monocrystals and cyclic loading conditions and examine the nucleation and stability of the layer structure of persistent slip bands from initially homogeneous states. This can essentially be considered within a one-dimensional picture and the associated periodic pattern with its intrinsic wavelength arises as a dynamical instability due to the competition of gradient and non-linear terms modelling respectively the motion and the production or annihilation of dislocation species. The competition between the ladder-like structure of persistent slip bands and the rod-like structure of surrounding veins can be more elaborately considered within a three-dimensional picture and the corresponding situation is also discussed here qualitatively. © 1986.

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Materials Science and Engineering