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Dislocations Jam At Any Density

Crystalline materials deform in an intermittent way via dislocation-slip avalanches. Below a critical stress, the dislocations are jammed within their glide plane due to long-range elastic interactions and the material exhibits plastic response, while above this critical stress the dislocations are mobile (the unjammed phase) and the material fails. We use dislocation dynamics and scaling arguments in two dimensions to show that the critical stress grows with the square root of the dislocation density. Consequently, dislocations jam at any density, in contrast to granular materials, which only jam below a critical density.