The Study Of Constitutive Theory For Giant Magnetostrictive Materials

Giant magnetostrictive material (GMM)is a kind of new type of functional material, which exhibits many outstanding advantages and has been used to design and fabricate many intelligent devices such as active vibration absorbers, linear motors, micro-pumps, micro-valves, and micro-positioners etc. However, many experiments show that there is nonlinear property of magnetic-elastic-thermal coupling and hysteresis inherent to giant magnetostrictive materials and it is difficult to design and control the corresponding giant magnetostrictive actuators in application. In the paper, a general theoretical study incorporating magnetic-elastic-thermal coupling and hysteresis is developed by thermodynamic relations or magnetic domain theory or combining both of them. The constitutive study can clarify the micromechanism of the complicated properties of giant magnetostrictive materials. Furthermore, it can describe macroscopic constitutive behavior of the materials under dc and ac magnetic field.Firstly, a nonlinear unhysteresis constitutive model to describe magnetic-elastic-thermal coupling property is suggested in this paper. The model considered here is built on the Gibbs free energy function G(σ,M,T) and thermodynamic relations are used to obtain the constitutive expressions. Based on the previous magnetic-elastic model , both thermal strain and strain due to thermal-magnetic coupled are considered. Secondly, a hysteresis model for giant magnetostrictive materials is deduced by considering the hysteresis loss, the classical loss and the excess loss. Here the energy contribution from magnetic interaction among domains is incorporated to the Gibbs free energy function, thus the effect field of the hysteresis model involves the contribution of magnetic-elastic-thermal coupling and the Weiss molecular field. Thus the model can describe coupled hysteresis behavior of the materials under dc and ac field. In order to ensure closure of minor loop, the "volume fraction" for magnetization is considered in the model. Finally, a Meso- physical model for giant magnetostrictive materials is derived from magnetic domain theory and it involves the contribution of the domain rotation and the domain wall motion to magnetization under the pre-pressure and magnetic field. In the model, the micromechanism mechanics of the complicated properties of giant magnetostrictive materials are clarified. Results based on above theoretical studies show that the nonlinear properties of giant magnetostrictive materials, such as the magnetic-elastic-thermal coupling and hysteresis effect, are in excellent agreement with experimental data in quality or in quantify. Furthermore the theoretical results can describe the effect of micro-parameter, such as inclusion, internal stress and domain size etc., on the magnetic properties well.Sumary, a general theoretical study about constitutive behavior of the giant magnetostrictive materials is developed, and the further study on the design, application and control of the corresponding actuators problems can be carried out based on the work.