Yielding and shear induced melting of 2D mixed crystals of spheres and dimers

Abstract

We performed constant stress and constant shear rate non-equilibrium molecular dynamics simulations to study the effects on mechanical properties of introducing varying amounts of dimers (dumbbells) in two-dimensional mixed crystals of monomers (spheres) and dimers. We observe that dislocation cages formed by blocking orientations of dimer particles introduce two opposing effects on the mechanical strength and rheological properties of such systems. Upon increasing the dimer concentration, the number of dislocations and vacancies increases, ‘weakening’ the crystal, but also the size of dislocation cages reduces, reinforcing the crystal by an effect similar to ‘grain-boundary strengthening’. In our constant stress simulations, these competing effects lead to a non-monotonic dependence of yield stress on the dimer fraction wherein it first drops and then increases. In our constant shear simulations, the crystals exhibit a plateau region in the stress vs. strain rate curves right around the yield stress values, confirming a change in dynamical and structural behavior at these points. Further, we find evidence of an unusual transitional phase before the crystal melts as shear increases: for any composition of the crystal an intermediate state is reached where a dynamic balance occurs between the rate of crystal growth (driven by thermodynamics) and the rate of melting (driven by shear). Such an intermediate state (whose onset agrees with the plateau region in the stress vs. strain curves) exhibits a heterogeneous structure and shear banding at a local level, while exhibiting a hexatic-like behavior at the macroscopic level. We also find differences in the solid and hexatic-like phases with respect to their stress relaxation mechanism, with the latter exhibiting a phase lag between the instantaneous stress and the ‘micro-structural yielding’ event.