Two types of response of a planar GB to an applied shear stress t. (a) Initial bicrystal; (b) GB motion due to coupling; (c) GB sliding. The dotted line crossing the GB represents a set of inert markers embedded in the lattice or any other fiduciary line. vn and v? are the velocities of normal GB motion and grain translation, respectively.
Two types of response of a planar GB to an applied shear stress t. (a) Initial bicrystal; (b) GB motion due to coupling; (c) GB sliding. The dotted line crossing the GB represents a set of inert markers embedded in the lattice or any other fiduciary line. vn and v? are the velocities of normal GB motion and grain translation, respectively.

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Molecular dynamics (MD) simulations confirm that normal grain boundary (GB) motion must often be coupled to tangential translation of grains and will then produce shear deformation of the lattice traversed by the GB. Conversely, shear stresses applied to a GB can induce its normal motion. Using [0 0 1] symmetrical tilt GBs in copper as a model, the coupling factor β between the GB motion and grain translations has been calculated by MD simulations over the entire misorientation range and a wide range of temperatures. The coupling factor is multivalued, can be positive or negative, and shows an abrupt switch from one branch to another at a tilt angle of about 35°. At high temperatures the response of high-angle GBs to shear changes from coupling to sliding until coupling disappears. No sliding is observed for low-angle GBs up to near the melting point. A geometric model of coupling proposed in this work predicts the misorientation dependence of β in excellent agreement with MD results and relates the multivalued character of β to the point symmetry of the crystal. Two kinds of low-angle GBs with different dislocations occur when the tilt angle is small and again when it approaches 90°. In these limits, the multiplicity of β is explained by different Burgers vectors of the dislocations. The results of this work are summarized as a temperature–misorientation diagram of mechanical responses of GBs. Unsolved problems and future work in this area are discussed.

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