Multi-physics phase-field modeling of magnetic materials

With the fast growth of economies around the globe, especially in warmer climate regions, the demand of cooling devices is expected to increase drastically within the next decades and with it the emission of greenhouse gases. In an attempt to develop a more energy efficient and environment friendly cooling device, a multi-stimuli concept utilizing the magneto- and elastocaloric effect was proposed. The goal of this work is to build a multi-physics phase-field model for the simulation of this multi-stimuli concept. Micromagnetic simulations are firstly introduced as a tool to simulate the relation between magnetic properties and microstructure. Micromagnetic simulations are performed on Y-Co and Sm-Co structures, showing that the magnetic properties, especially the coercivity of permanent magnets, strongly depend on microstructural features. In a second step, a new methodology for the extrapolation of micromagnetic simulations to temperatures around and above TC is introduced. A combination of micromagnetic simulations and the Arrott-Noakes equation allows for the calculation of the magnetocaloric effect, taking into account the influence of microstructure and magnetocrystalline anisotropy. Applying the methodology on Co2B nanograins shows good agreement with experimental results. In order to not only consider second-order materials, a multi-physics phase-field model is presented which combines a tetragonal martensite and cubic austenite phase-field model with micromagnetism. With a finite element implementation of this three-dimensional real-space model, the structural and magnetic features observed in MSMA are simulated. In addition, it is shown that the temperature-dependent energy formulation allows for the simulation of the martensite-austenite transition, including the thermal hysteresis. As final step, the micromagnetic energy terms are modified to also take into account magnetic transitions that occur along the martensite-austenite transition. Depending on the modification of the magnetic energy terms with the phase order parameter, the model can take into account the transition between a ferromagnetic martensite and paramagnetic austenite, as well as the transition between a paramagnetic martensite and ferromagnetic austenite. While the application of uniaxial pressure shifts Tt to higher temperature, the direction of the shift with applied magnetic fields depends on the magnetic transition considered. Summarizing, after presenting the individual physics to be considered, this work presents a new multi-physics phase-field model, which is capable of capturing the martensite-austenite transition under the consideration of different magnetic transitions. With the ability to simulate the thermal hysteresis and shift of Tt with external stimuli, the presented model is capable of simulating the multi-stimuli concept