The effect of internal stresses due to precipitates on twin growth in magnesium

Twinning is an important deformation mode in hexagonal close packed (HCP) metals, including magnesium alloys. Precipitates are used to provide strengthening in many of these alloys. The effect of precipitates in strengthening against deformation by slip is well understood, but this is not the case for twinning. Recent studies have indicated that precipitates are usually not sheared by twins, but the Orowan law for strengthening against slip by dislocation bowing does not give a good prediction when applied to twinning. It has therefore been proposed that the dominant strengthening effect inhibiting thickening of a twin arises from an additional back-stress that results from embedding a unsheared precipitate in twinned matrix. The present paper uses an Eshelby model to assess the influence of precipitate shape and habit on the internal stresses that arise from embedding a non-shearing precipitate in a {101¯2} twin (the dominant twin type). It is demonstrated that the elastic stresses generated easily exceed the critical resolved shear stress for activation of slip and therefore plastic relaxation is to be expected. In all cases, the predicted plastic zone is confined to a region local to the particle. The implications of these predictions for design of precipitation strengthened HCP alloys are discussed.