Multiscale modelling of the morphology and spatial distribution of θ′ precipitates in Al-Cu alloys

Abstract

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...

Multiscale modelling of precipitation hardening in Al–Cu alloys: Dislocation dynamics simulations and experimental validation

“…The θ precipitate has a body-centered tetragonal (BCT) structure (space group I4/mmm) with lattice parameters a θ = 0.404 nm and c θ = 0.580 nm) [9]. The orientation relationship between θ and α-Al is (001) θ (001) α and [100] θ [100] α , leading to three orientation variants for the θ precipitates [29]. The θ precipitates have a disk-shape and the broad faces of the disk are nearly fully coherent with the α-Al matrix while the edges of the plates are semi-coherent.…”

“…3). The transformation matrix, T, that links the lattice parameters of α-Al (e α ) and θ (e θ ) through Te α = e θ is given by [32,29]:…”

“…3. The transformation matrix includes both strains and rigid body rotations and the corresponding Lagrangian stress-free transformation strain (SFTS), 0 , can be expressed in the axis defined by the FCC Al as [29]…”

Alloy design for mechanical properties: Conquering the length scales

“…Article Template Beyerlein/April 2019 8 calculated ratios of the tensile yield stress to the compressive yield stress. Overall the values are consistent with experimental measurements.…”

“…Once the initial dimensions and sh the precipitate nucleus have been determined, growth precipitate to its stable shape is calculated using the fi eld method. 8 Multiscale simulations from this strategy can reve stability and growth sequences of precipitation, as w the expected fi nal precipitate microstructure. Figure 2 onstrates the profound effect dislocatio have on the fi nal equilibrium shape o cipitates, being fl at disks when nuclea homogeneous versus cones and platelet morphologically rough edges when nuc is heterogeneous.…”