  Although magnesium alloys deform extensively through shear strains and
crystallographic re-orientations associated with the growth of twins, little is
known about the strengthening mechanisms associated with this deformation mode.
A crystal plasticity based phase field model for twinning is employed in this
work to study the strengthening mechanisms resulting from the interaction
between twin growth and precipitates. The full-field simulations reveal in
great detail the pinning and de-pinning of a twin boundary at individual
precipitates, resulting in a maximum resistance to twin growth when the
precipitate is partially embedded in the twin. Furthermore, statistically
representative precipitate distributions are used to systematically investigate
the influence of key microstructural parameters such as precipitate
orientation, volume fraction, size, and aspect ratio on the resistance to twin
growth. The results indicate that the effective critical resolved shear stress
(CRSS) for twin growth increases linearly with precipitate volume fraction and
aspect ratio. For a constant volume fraction of precipitates, reduction of the
precipitate size below a critical level produces a strong increase in the CRSS
due to the Orowan-like strengthening mechanism between the twin interface and
precipitates. Above this level the CRSS is size independent. The results are
quantitatively and qualitatively comparable with experimental measurements and
predictions of mean-field strengthening models. Based on the results,
guidelines for the design of high strength magnesium alloys are discussed.
