Dislocation pattern formation and strain hardening in solids

Abstract

At the microscale plastically deformed solid behaves as a strongly nonlinear system governed by instability transitions. According to the model proposed for cell forming materials the stored dislocations, mostly in the form of dipolar loops, are arranged into a characteristic pattern of tangles, veins or walls giving rise to strain hardening. Annihilation of stored dislocations in the high density regions changes the wavelength and profile of the pattern. The process tends to reach a steady state, in which the generation and annihilations of stored dislocations are balanced. The geometry of stabilized cell walls derived for single, double and multi slip corresponds well to observed deformation microstructures. However, the dislocation cell formation may be seriously interfered by geometrical instability. The internal bending type instability causes transformation of cell walls into subgrain boundaries or formation of dislocation grids. The second type of geometrical instability triggers strain localization into shear bands or persistent slip bands destroying the original dislocation structure and forming the new one.