  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.
