2, University of Michigan, Ann Arbor, Michigan, United States
The morphologies of precipitates in metal alloys can often be complex due to competing mechanisms such as anisotropic interfacial energy and misfit strain energy. For these systems, multiphysics computer simulations can be powerful tools since researchers can artificially “turn off” individual mechanisms while holding all other variables constant. For instance, this approach has been used by investigators to elucidate the effects of misfit strain, interfacial energy, and anisotropic growth rates on experimentally observed precipitate morphologies in magnesium-rare earth alloys. Unfortunately, the inherent complexity of these computer simulations often makes them inaccessible for novice learners.
For educational uses, we have published a tool on nanoHUB that simulates two-dimensional equilibrium morphologies of an isolated precipitate within a matrix. The simulation tool, available at https://nanohub.org/tools/prismspfmisfit, is implemented using a black-box approach with a graphic user interface (GUI). To run a simulation, a user only needs to provide material parameters such as anisotropic interfacial energies, anisotropic misfit strains, elastic moduli, and Poisson’s ratios for the system. Underlying the simple GUI is an application built using PRISMS-PF, an open-source phase field framework that uses the finite element method to solve phase field equations to predict microstructural evolution. The nanoHUB tool launches a finite element simulation for a precipitate in a matrix, which is then evolved until it reaches equilibrium. The equilibrium precipitate morphology is output to the user, along with the dimensions of the precipitate and the volume fraction, for further analysis.
We use this online tool to help materials science and engineering students develop expert knowledge on the fundamentals of precipitate morphology. One trait of a subject-matter expert is the many deep connections between the facts they have learned, such as the interplay between interfacial energy and misfit strain energy. To develop these connections in novice students, we have developed an inquiry-based teaching module. Students are presented with a micrograph of metallic precipitates and are prompted to explain the shape and the aspect ratio based on misfit strain energy and anisotropic interfacial energy. Using the PRISMS-PF tool, students run simulations that vary the misfit strain and anisotropy to build mental models of these effects and ultimately identify the dominant mechanism(s) in the precipitate morphology. Finally, we present an evaluation of metacognitive questions that are used for formative assessment of this activity.