Dislocation mediated shear instability of a 2D solid in a constant stress field

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Abstract
It is shown that the low-temperature behaviour of a pure 2D solid approaching plastic instability under a constant shear field can be modelled as a sort of continuous phase transition from a metastable equilibrium state to a time-dependent state of a flowing solid with vanishing shear modulus. With the difference that here the control parameter is the external shear strength and not the temperature, the mechanisms of the instability, in the high dislocation core energy regime are the same invoked in the KTHNY theory of 2D melting: the dissociation and proliferation of dislocation dipoles with vanishing net Burgers vector. In this way, in two dimensions, some hidden similar statistical and structural properties of a melting solid and a plastically flowing one are put forward apart from the obvious analogies based on the common fluid behaviour. With the caution that the theory does not treat critical fluctuations properly, all the relevant thermodynamic functions exhibit essential singularities approaching the critical point. However, the excess specific heat is foreseen to be experimentally measurable within a stress range where fluctuations are negligible.