Dynamics of grain boundary motion coupled to shear deformation: An analytical model and its verification by molecular dynamics

Many atomically ordered grain boundaries (GBs) couple to applied mechanical stresses and are moved by them, producing shear deformation of the lattice they traverse. This process does not require atomic diffusion and can be implemented at low temperatures by deformation and rotation of structural units. This so-called coupled GB motion occurs by increments and can exhibit dynamics similar to the stick-slip behavior known in atomic friction. We explore possible dynamic regimes of coupled GB motion by two methods. First, we analyze a simple one-dimensional model in which the GB is mimicked by a particle attached to an elastic rod and dragged through a periodic potential. Second, we apply molecular dynamics (MD) with an embedded-atom potential for Al to simulate coupled motion of a particular tilt GB at different temperatures and velocities. The stress-velocity-temperature relationships established by both methods are qualitatively similar and indicate highly nonlinear dynamics at low temperatures and/or large velocities. At high temperatures and/or slow velocities, the character of the GB motion changes from stick slip to driven random walk and the stress-velocity relation becomes approximately linear. The MD simulations also reveal multiple GB jumps due to dynamic correlations at high velocities, and a transition from coupling to sliding at high temperatures.