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The critical resolved shear stress of an Al 4 wt. \% Cu alloy containing a homogeneous distribution of $\theta''$ precipitates was determined by means of dislocation dynamics simulations. The size distribution, shape, orientation and volume fraction of the precipitates in the alloy were obtained from transmission electron microscopy observations while the parameters controlling the dislocation/precipitate interactions (elastic mismatch, transformation strains, dislocation mobility and cross-slip probability, etc.) were calculated from atomistic simulations. The precipitates were assumed to be either impenetrable or shearable by the dislocations, the latter characterized by a threshold shear stress that has to be overcome to shear the precipitate. The predictions of the simulations in terms of the critical resolved shear stress and of the dislocation/precipitate interaction mechanisms were in good agreement with the experimental results. It was concluded that the optimum strength of this alloy is attained with a homogeneous distribution of $\theta''$ precipitates whose average size ($\approx$ 40 nm) is at the transition between precipitate shearing and looping. Overall, the dislocation dynamics strategy presented in this paper is able to provide quantitative predictions of precipitate strengthening in metallic alloys.

The mechanisms of dislocation/precipitate interactions were analyzed in an Al-Cu alloy containing a homogeneous dispersion of $\theta'$ 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.

The interaction between edge dislocations and Guinier-Preston zones in an Al-Cu alloy was analyzed by means of atomistic simulations. The different thermodynamic functions that determine the features of these obstacles for the dislocation glide were computed using molecular statics, molecular dynamics and the nudged elastic band method. It was found that Guinier-Preston zones are sheared by dislocations and the rate at which dislocations overcome the precipitate is controlled by the activation energy, $\Delta U$, in agreement with the postulates of the harmonic transition state theory. Moreover, the entropic contribution to the Helmholtz activation free energy was in the range 1.3-1.8$k_b$, which can be associated with the typical vibrational entropy of solids. Finally, an estimation of the initial shear flow stress as a function of temperature was carried out from the thermodynamic data provided by the atomistic simulations. Comparison with experimental results showed that the effect of the random precipitate distribution and of the dislocation character and dislocation/precipitation orientation has to be taken into account in the simulations to better reproduce experiments.

The mechanisms of dislocation/precipitate interaction were studied by means of discrete dislocation dynamics within a multiscale approach. Simulations were carried out using the discrete continuous method in combination with a fast Fourier transform solver to compute the mechanical fields. The original simulation strategy was modified to include straight dislocation segments by means of the field dislocation mechanics method and was applied to simulate the interaction of an edge dislocation with a $\theta'$ precipitate in an Al-Cu alloy. It was found that the elastic mismatch has a negligible influence on the dislocation/precipitate interaction in the Al-Cu system. Moreover, the influence of the precipitate aspect ratio and orientation was reasonably well captured by the simple Orowan model in the absence of the stress-free transformation strain. Nevertheless, the introduction of the stress-free transformation strain led to dramatic changes in the dislocation/precipitate interaction and in the critical resolved shear stress to overcome the precipitate, particularly in the case of precipitates with small aspect ratio. The new multiscale approach to study the dislocation/precipitate interactions opens the possibility to obtain quantitative estimations of the strengthening provided by precipitates in metallic alloys taking into account the microstructural details.