It was recalled that crystalline materials deform in an intermittent way via dislocation-slip avalanches. Below a critical stress, the dislocations were jammed within their glide plane due to long-range elastic interactions and the material exhibited a plastic response while, above this critical stress, the dislocations were mobile (the unjammed phase) and the material flowed. Dislocation dynamics and scaling arguments in two dimensions were used to show that the critical stress increased as the square root of the dislocation density for straight parallel edge dislocations. Dislocations could therefore jam at any density, in contrast to granular materials, which only jammed below a critical density. It was noted that there were analogies between the present phenomena, the Taylor hardening relationship and the effective velocity of a point vortex in two-dimensional hydrodynamics. It was possible to perform analytical calculations for any power-law interaction and for arbitrary dimensions. The theoretical result agreed with the present simulation to within logarithmic corrections which were difficult to measure at system sizes which were amenable to simulation. The results, both numerical and theoretical, showed that - for dislocations or particles having long-range interactions - there could be no jamming-point at a finite density; provided that there was no screening.

Dislocations Jam at Any Density. G.Tsekenis, N.Goldenfeld, K.A.Dahmen: Physical Review Letters, 2011, 106[10], 105501