Simulation of precipitation and strengthening in MG-RE alloys

Magnesium - rare earth (Mg-RE) alloys have received considerable attention in the past decades for wider applications in the aerospace industry due to their relatively high strength and excellent creep resistance. Most rare-earth containing magnesium alloys, such as Mg-Y, Mg-Gd, and Mg-Y-Nd, are precipitation hardenable. A technical barrier to the wider applications of such alloys is the lack of a sufficiently large age hardening response. To further improve this response, an improved understanding is required of the nucleation and growth behaviours of the key strengthening phases, metastable β' and β1. These behaviours are examined in this research. Previous studies have found that the β' phase has a base centred orthorhombic structure (a = 0.321 nm, b = 22.240 nm and c = 0.521 nm) and a Mg₇RE composition in some Mg-RE alloys, such as Mg-Y, Mg-Gd, Mg-Dy and Mg-Gd-Y. However, the morphologies of β' particles in Mg-Y and in Mg-Gd alloys are different, as they have a faceted and nearly equiaxed shape in the Mg-Y alloys, but a truncated lenticular shape in the Mg-Gd alloys. The first stage of this research was focused on an investigation of the nucleation and growth behaviour of β' particles, and the factors that cause the difference in the equilibrium shapes of β'-Mg₇Y and β'-Mg₇Gd. It was found that during the nucleation and growth of β' particles, the habit plane of β' particles gradually changes from {11 ̅00}ₐ to {112 ̅0}ₐ. The equilibrium shape of β' precipitates in both Mg-Y and Mg-Gd alloys is determined by the competition between interfacial energy and elastic strain energy anisotropy. The research also indicates that the difference between the shapes of β'-Mg₇Y and β'-Mg₇Gd precipitates is due to the difference in lattice parameters between β'-Mg₇Y and β'-Mg₇Gd particles, i.e., compared with interfacial energy anisotropy, the anisotropy of elastic strain energy plays a dominant role in the shape difference. Two ways of increasing the aspect ratio are increasing the elastic strain energy anisotropy and decreasing the interfacial energy anisotropy. When the elastic strain energy anisotropy is increased, rather than when the interfacial energy anisotropy is decreased, the aspect ratio increases is larger. It was also found that one possible way to increase elastic strain energy anisotropy of β' precipitates is by selecting the appropriate alloying elements which have a larger atomic radius and occupy the Y atom lattice sites in the β'-Mg₇Y phase. The second stage of this research was to investigate the nucleation, growth and equilibrium morphology of β₁ particles. Previous research indicated that the β₁ phase has a cubic structure (a = 0.74 nm) and a Mg₃RE composition. In addition, the β₁ particles have a plate-like shape, and, in some Mg-RE alloys, such as WE54, individual β₁ plates always form with β' particles attached each end. However, the reason behind the latter phenomenon is not clear. The simulation results in this research suggest that the coherency elastic strain energy at the two edge facets of a β₁ particle can be significantly reduced by the attachment of β' particles. In addition, β₁ particles may form first then act as heterogeneous nucleation sites for β' particles. Previous experimental results indicated that the β₁ precipitates form preferentially on dislocations, i.e., the distribution of β₁ precipitates could be controlled by pre-existing dislocations. However, it was not clear how a pre-existing dislocation can assist the nucleation of β₁ precipitates. To investigate this problem, the interaction energy between the stress fields of pre-existing dislocations and β₁ precipitates was calculated, and the heterogeneous nucleation and growth of β₁ precipitates on the pre-existing dislocations was simulated. It was found that the elastic strain energy can be decreased if β₁ precipitates nucleate on pre-existing dislocations. If β₁ precipitates nucleate heterogeneously near a screw dislocation, they will form as ultra-thin laths with abnormally large aspect ratios under the influence of the stress field of the screw dislocation. Under the influence of the stress field of an edge dislocation, a zigzag pattern consisting of two β₁ orientation variants of much smaller aspect ratios will form. If β₁ particles nucleated heterogeneously near a pre-existing mixed dislocation, then a variety of discrete particle arrays of β₁ particles, which often belong to a single variant, will form. The variation in the morphology and distribution of β₁ precipitates is due to the change in the interaction energy between the elastic strain fields of the precipitates and dislocations. When predicting the distribution of β₁ precipitates nucleated on a complex dislocation structure, such as a dislocation loop or a hexagonal network, the complex dislocation structure can be treated as a combination of smaller dislocation segments, with each segment being a straight dislocation. In the final stage of this project, the effects of number density, aspect ratio, and spatial distribution of plate-shaped particles on changes to ΔCRSS were quantitatively examined. A Mg-3wt.% Nd alloy aged for 3 hours at 200°C was selected as the model alloy with β₁ as the main strengthening phase. Under the condition that plastic deformation occurs by basal slip, an increase in the average aspect ratio of β₁ plates from 13:1 to 60:1, increases the ΔCRSS by a factor of 2.00, and, when the precipitate number density per unit volume increases by a factor of 2, the ΔCRSS will increased by 1.313 times. For a given volume fraction of β₁ plates with the same average diameter, a random spatial distribution of the β₁ plates can result in a ΔCRSS value that is 0.78 times that resulting from a regular spatial distribution. The new insights into the formation mechanism of β₁ and β' precipitates, and the influence of the stress field of pre-existing dislocations on the spatial distribution of β₁ particles are provided by this project. The major findings of this project will enable the better selection of the alloy compositions, thermo-mechanical processing conditions and micro-alloying elements to further improve the nucleation rate (i.e., the number density) and the aspect ratio of precipitates, and to generate a uniform distribution of these precipitates, thus obtaining Mg-RE alloy with higher strength.