Investigation of precipitate refinement in Mg alloys by an analytical composite failure model

• The stress fields inside a particle embedded in an inelastic matrix are determined.
• A failure criterion relates the loading parameters to failure of the particle.
• Loads leading to failure of secondary phase particles in an Mg alloy are studied.

An analytical model is developed to simulate precipitate refinement in second phase strengthened magnesium alloys. The model is developed based on determination of the stress fields inside elliptical precipitates embedded in a rate dependent inelastic matrix. The stress fields are utilized to determine the failure mode that governs the refinement behavior. Using an AZ31 Mg alloy as an example, the effects the applied load, aspect ratio and orientation of the particle is studied on the macroscopic failure of a single α-Mg17Al12 precipitate. Additionally, a temperature dependent version of the corresponding constitutive law is used to incorporate the effects of temperature. In plane strain compression, an extensional failure mode always fragments the precipitates. The critical strain rate at which the precipitates start to fail strongly depends on the orientation of the precipitate with respect to loading direction. The results show that the higher the aspect ratio is, the easier the precipitate fractures. Precipitate shape is another factor influencing the failure response. In contrast to elliptical precipitates with high aspect ratio, spherical precipitates are strongly resistant to sectioning. In pure shear loading, in addition to the extensional mode of precipitate failure, a shearing mode may get activated depending on orientation and aspect ratio of the precipitate. The effect of temperature in relation to strain rate was also verified for plane strain compression and pure shear loading cases.