On the evolution of β1/β′ coupled-structures in Mg–Y–Nd alloys: A simulation study

In magnesium alloys based on the Mg–Y–Nd system, the key strengthening precipitate phases, β ₁ and β′, often form coupled-structures, with β′ precipitates invariably attached to both ends of the β ₁. A question here is how the attached β′ precipitates evolve as the β ₁ lengthens within the solid magnesium matrix. To investigate this, this study uses a multi-scale model based on a three-dimensional phase field approach to simulate the evolution of β ₁ and β′ precipitates in a β ₁/β′ coupled-structure. The simulation results reveal that, during the evolution process, the β ₁ precipitate lengthens, while the attached β′ precipitates grow only at the side located along the direction of β ₁ extension and dissolves at the opposite side. This results in a visual effect where the β′ precipitates appear to “move” within the solid matrix. This phenomenon is governed by the interplay between chemical free energy and elastic strain energy. Chemical free energy promotes uniform growth of the β′ precipitates. However, the elastic strain energy, generated by the β′ precipitates and the stress field concentrated at the end of the β ₁ plate to which they are attached, favours growth of only one side of the β′ precipitates while causing dissolution at the other side. When the evolution of a coupled-structure is influenced by neighbouring coupled-structures, the evolution of β′ precipitates is strongly driven by the minimization of elastic strain energy. In general, the β′ precipitates tend to grow under tensile stress fields and dissolve under compressive stress fields.