Studies On The Constitutive Theory And Experiment Of Ferromagnetic Materials

Ferromagnetic materials have been widely used in modern science and technology. With the development of material science, ferromagnetic materials have become the important functional materials. The magneto-mechanical coupling behaviour is studied systematically in this dissertation. The experiments of ferromagnetic materials were conducted, and mesoscopic and macroscopic constitutive models are developed, respectively. The work involved in the following aspects:1. Based on the mesoscopic mechanics, two different analytical methods, the Green's function method and the equivalent inclusion method, were employed to investigate the ferromagnetic inclusion and inhomogeniety problem. The results show that these two solutions are completely equivalent to each other. Based on the generalized Budiansky's energy-equivalent framework, the general expressions of effective magneto-elastic moduli were obtained. Furthermore, by using the well-known double inclusion method, the magneto-mechanical fields in magnetostrictive composites were decoupled and the strain induced by magnetostriction in magnetostrictive particles was regarded as eigen-strain, then, the effective modulus and effective magnetostriction of the composites were obtained successfully. The theoretical results were compared with both experimental results and those calculated from other models, which shows that the proposed model is coincident well with the experimental results.2. A magnetomechanical-coupling testing setup was established by ourselves, which was controlled by an industrial PC. The software was programmed to monitor the testing process and deal with the acquired data. There are three kinds of ferromagnetic materials used to investigate the magneto-mechanical coupling behavior, such as the soft-ferromagnetic metal of Ni6 and electrolytic nickel, the giant-magnetostrictive material (Terfenol-D), and the ferromagnetic shape memory material (NiMnGa). The characteristic curves of ferromagnetic materials were measured, including the hysteresis loops and the magnetostriction curves under different compressive stress and stress-strain curves under different external magneticfields. 3. Based on the domain theory, a domain-switching model was developed from the experimental results of Terfenol-D and domain rotation model. In the proposed model, only 90° switching occurs. Based on the Gibbs free energy, the criteria of domain switching are established to judge the state of ferromagnetic domains. Then the macroscopic constitutive relations could be obtained by introducing the orientation distribution function.4. The response of ferromagnetic materials is dependent on the loading history because of energy dissipation, which was similar to the classical plastic theory. Based on the thermodynamic framework, two kinds of phenomenological models were developed: (1) According to J2 flow theory, the remanent strain and the remanent magnetization are introduced as internal variables, then the magneto-mechanical yield surface is introduced to govern the evolution of the remanent strain and the remanent magnetization. Then the model based on the flow theory was constructed. (2) According to Karafillis-Boyce model of anisotropic plastic theory, the general constitutive model based on the internal variable theory has been developed for ferromagnetic and magnetostrictive materials. A non-quadratic magneto-mechanical yield surface is introduced for both isotropic and anisotropic materials. The anisotropy includes both magnetic anisotropy and elastic anisotropy, which can be described by introducing a set of irreducible tensorial state variables. The linear transformation from anisotropy to isotropy is presented. Then, the proposed model is generalized for both isotropic materials and anisotropic materials. Furthermore, the magneto-mechanical yield surface of magnetostrictive material Terfenol-D was measured and the magneto-mechanical hardening moduli can be determined by Helmholtz free energy. The calculated results are consistent with the experimental data well.