Phase-Field Simulation of Orowan Strengthening by Coherent Precipitate Plates in an Aluminum Alloy

The density-functional theory and phase-field dislocation model have been used to compute and simulate the strength of θ′ plates and precipitate-dislocation interactions in an Al-4Cu-0.05Sn (wt pct) alloy that is strengthened exclusively by coherent θ′ precipitate plates. The density-functional theory computation indicates that a 1.06 GPa applied stress is required for a dislocation to shear through a θ′ plate, which is far larger than the critical resolved shear stress increment (ΔCRSS) of the peak-aged sample of the alloy. The ΔCRSS values of the alloy aged for 0.5, 3, 48, and 168 hours at 473 K (200 °C) are computed by the phase-field dislocation model, and they agree well with experimental data. The phase-field simulations suggest that the ΔCRSS value increases with an increase in plate aspect ratio and number density, and that the change of ΔCRSS is not sensitive to the variation of the distribution of θ′ plate diameters when the average diameter of θ′ plates is fixed, and that the coherency strain of θ′ plates does not contribute much to ΔCRSS of the alloy when the θ′ number density and aspect ratio are below certain values. The simulations further suggest that, when the volume fraction of θ′ is constant, the ΔCRSS value for a random spatial distribution of the θ′ plates is 0.78 times of that for a regular spatial distribution.