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Abstract

The mechanical properties of ultra-fine grained and nanocrystalline metals depend to a large extend on the tensile strength and sliding resistance of the interfaces in the microstructure. Based on ab initio density functional theory (DFT) calculations we derive an analytical expression for the interplanar potential of both, grain boundaries and single crystals, as a function of coupled tensile and shear displacements. This energy function does not contain any fit parameters, but all four coefficients and exponents represent material properties. In spite of its simplicity it captures important details of the grain boundary behaviour, such as the tension-softening of the shear instability of aluminium grain boundaries, with good accuracy. The good agreement between the analytical model and the DFT calculations is mainly achieved by introducing two new characteristic parameters, namely the position of the generalised unstable stacking fault with respect to the stable stacking fault, and the ratio of stable and unstable generalised stacking fault energies. The interface specific parameters of the potential can also be used to judge if a crack at the grain boundary would advance in a brittle manner or rater blunt by dislocation emission. Furthermore, the fact that the potential only relies on material properties makes it valuable for developing guidelines for alloy design, as it can be applied to derive constitutive relationships for application in continuum models, or by carrying out sensitivity studies.