Metadynamic Simulations to determine the free energy profile of shear in Aluminium single crystals and at grain boundaries
Final Report Abstract
We have carried out molecular statics as well as molecular dynamics simulations to determine the shear strength of grain boundaries as a function of temperature, identify the shear mechanisms on the atomistic scale, and to relate them to basic physical and structural properties of the interfaces. Our model systems were a twist and several symmetrical tilt grain boundaries in Aluminium, as well as three rotational boundaries in γ-TiAl. Shear strains at a constant strain rate of 10^9 s−1 and at different temperatures were applied to all interfaces parallel to the interface plane, along different in-plane directions. Both, shear strength as well as shear mechanism, display a strong anisotropy with respect to the loading direction. In the case of symmetrical tilt grain boundaries, the direction of the tilt axis is always an easy-shearing direction, along which the interface deforms at a comparatively low stress by rigid grain sliding. Apart from rigid grain sliding, which is realised by atomic shuffling at the interface and/or temporary creation and re-absorption of stacking faults, three more distinct mechanisms could be identified: grain boundary migration, coupled sliding and migration, and dislocation nucleation. In all cases the shear strength decreases linearly with increasing temperature, as long as the mechanism does not change. Among the Al grain boundaries which have been investigated, the shear mechanism changes only for the Σ11 grain boundary, perpendicular to the easy-sliding direction, from dislocation nucleation to grain boundary migration. The linear behaviour was attributed to the thermal expansion of the lattice, which lowers the stacking fault energy, respectively its equivalent in the grain boundary plane. This could be verified by calculating the generalised stacking fault energy surface (GSFE) for all Al grain boundaries at different temperatures. The slope of the energy barriers along the relevant shear directions, its maximum being the theoretical shear strength, also decreases linearly with increasing temperature. The influence of lattice strain on the shear strength was investigated further by calculating the energy profiles for grain boundary shear at different superimposed tensile strains, at a constant temperature of 0 K. A systematic dependency was observed, which can be parameterised in terms of physical quantities, and is true for all interface geometries. This potential can be used as constitutive relationship, e.g. in meso-scale modeling of fracture. The interpretation of the shear behaviour in terms of stacking fault energies could be verified by introducing a multilayer-GSFE concept, which was established for the rotational boundaries in TiAl, but is transferrable to other grain boundaries under shear load parallel to the interface. Using this, the shear mechanism of a given grain boundary can be predicted.
Publications
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“Temperature-dependent shear behaviour of different grain boundaries in aluminium: An MD and metadynamics study”, Spring Meeting of the German Physical Society (DPG), Dresden, 4th - 8th of March 2014
X. Pang, R. Janisch
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“Can we model the mechanical properties of grain boundaries based on a few material properties?” Grain Boundary Migration 2015 Workshop, Günzburg, 21st - 24th of June 2015
R. Janisch
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“Interplanar potential for tension-shear coupling at grain boundaries derived from ab initio calculations”. Modelling Simul. Mater. Sci. Eng. 2016 Modelling Simul. Mater. Sci. Eng. 24 015007
X. Pang, R. Janisch, A. Hartmaier
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“Stacking fault based analysis of shear mechanisms at interfaces in lamellar TiAl alloys”. Acta Mater. Vol 106, March 2016, Pages 208-218
M. Kanani, A. Hartmaier, R. Janisch
