A multiscale approach based on the phase-field model is developed to simulate homogeneous and heterogeneous formation of θ' 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 θ' 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 θ' precipitates with orientation relationship (001)θ'//(001)α and [100]θ'//[100]α 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 θ' 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. (J. LLorca) 2 IntroductionPrecipitation hardening is well-established as one of the most efficient strategies to increase the yield strength of metallic alloys [1][2][3]. Precipitates are normally intermetallic particles with sizes in the range from a few to a few hundred nm which appear during ageing. They hinder the glide of dislocations that have to by-pass or shear the precipitates, increasing the critical resolved shear stress to move the dislocation in the slip plane. The strengthening effect of the precipitates depends on a number of factors, which include their size, shape [4][5][6][7] and spatial distribution [8][9][10][11]. Precipitation hardened alloys are usually subjected after casting to a homogenization treatment above the solvus temperature followed by quenching, which leads to a supersatured solid solution of the solute atoms. Afterwards, precipitation is promoted by ageing the alloy at intermediate temperatures (sometimes in combination with mechanical deformation) and the final precipitate structure can be controlled up to some extent from the ageing temperature and time [2][3]12]. In general, it is accepted that the highest hardening is provided by uniform distributions of precipitates with large aspect ratio but the optimum combination of precipitate size, shape and spatial distribution depends on many factors, including the actual number of slip systems, the critical resolved shear stress of each system, the presence of other deformation mechanisms (such as twinning), etc. Thus, the design of novel precipitation hardened alloys and the optimization of the current ones is based on the ability to determine the precip...
A multidisciplinary approach is presented to analyse the precipitation process in a model Al-Cu alloy.Although this topic has been extensively studied in the past, most of the investigations are focussed either on transmission electron microscopy or on thermal analysis of the processes. The information obtained from these techniques cannot, however, provide a coherent picture of all the complex transformations that take place during decomposition of supersaturated solid solution. Thermal analysis, high resolution dilatometry, (high resolution) transmission electron microscopy and density functional calculations are combined to study precipitation kinetics, interfacial energies, and the effect of second phase precipitates on the mechanical strength of the alloy. Data on both the coherent and semicoherent orientations of the ′′ / interface are reported for the first time. The combination of the different characterization and modelling techniques provides a detailed picture of the precipitation phenomena that take place during aging and of the different contributions to the strength of the alloy. This strategy can be used to analyse and design more complex alloys.
The mechanisms of dislocation/precipitate interactions were analyzed in an Al-Cu alloy containing a homogeneous dispersion of θ precipitates by means of discrete dislocation dynamics simulations. The simulations were carried out within the framework of the discrete-continuous method and the precipitates were assumed to be impenetrable by dislocations. The main parameters that determine the dislocation/precipitate interactions (elastic mismatch, stress-free transformation strains, dislocation mobility and cross-slip rate) were obtained from atomistic simulations, while the size, shape, spatial distribution and volume fraction of the precipitates were obtained from transmission electron microscopy. The predictions of the critical resolved shear stress (including the contribution of solid solution) were in agreement with the experimental results obtained by means of compression tests in micropillars of the Al-Cu alloy oriented for single slip. The simulations revealed that the most important contribution to the precipitation hardening of the alloy was provided by the stress-free transformation strains followed by the solution hardening and the Orowan mechanism due to the bow-out of the dislocations around the precipitates.
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