Multiscale modelling of the morphology and spatial distribution of {\theta}' precipitates in Al-Cu alloys

A multiscale approach based on the phase-field model is developed to simulate homogeneous and heterogeneous formation of {\theta}' precipitates during high temperature ageing in Al-Cu alloys. The model parameters that determine the different energy contributions (chemical free energy, interfacial energy, lattice parameters, elastic constants) were obtained from either computational thermodynamics databases or from first-principles density functional theory and molecular statics simulations. From the information, the evolution and equilibrium morphology of the {\theta}' precipitates is simulated in 3D using the phase-field model. The model was able to reproduce the evolution of the different orientation variants of plate-like shaped {\theta}' precipitates with orientation relationship (001){\theta}'//(001){\alpha} and [100]{\theta}'//[100]{\alpha} during homogeneous nucleation as well as the heterogeneous nucleation on dislocations, leading to the formation of precipitate arrays. Heterogeneous nucleation on pre-existing dislocation(s) was triggered by the interaction energy between the dislocation stress field and the stress-free transformation strain associated to the nucleation of the {\theta}' precipitates. Moreover, the mechanisms controlling the evolution of the morphology and the equilibrium aspect ratio of the precipitates were ascertained. All the predictions of the multiscale model were in good agreement with experimental data.