Macroscopic And Microscopic Constitutive Studies On Ferroelectrics And Shape Memory Alloys

Ferroelectric materials and shape memory alloys are widely used functional materials in modern science and technology, and have very good prospects of development. Investigating their constitutive behaviors is very important to both theory and application. The following researches on ferroelectric materials and shape memory alloys are presented in this dissertation.From the view of whole domain pattern, we proposed the macroscopic-microscopic constitutive theory -I based on the domain distribution within the ferroelectric material. Orientation distribution function (ODF) is used to depict the domain distribution and its evolution reflects the changes of domain patterns. The main achievements that have been obtained in this part are as follows.1. The concise expressions for the four forms of piezoelectric equations with eigenvalues are introduced. The accurate definition of the four forms of eigenvalues and their relations are given. It can help to avid misleading due to the unclear conception of the relation among the four forms of eigenvalues.2. Considering the interaction of different inclusions and the finite piezoelectric media, the coupling mechanical-electrical field in an inclusion is given by applying the theoretical result of an ellipsoidal inclusion embedded in an infinite piezoelectric media, equivalent inclusion method, and by expanding the Mori-Tanaka mean field theory into piezoelectric media.3. The Gibbs free energy in the constituent element is obtained by micromechanics approaches and ODF is introduced into the energy functional. The Fourier coefficients of the orientation distribution functionare considered as internal variables describing the patterns of internal rearrangement resulting from the domain switching. The evolution equations for ODF and the coupling mechanical-electrical incremental constitutive relations are formulated. This constitutive model can account for the macroscopic constitutive behavior caused by domain switching under complex thermodynamic loading conditions. The theoretical predictions are in good agreement with experimental results.From the view of switching type of each domain, we proposed the constitutive theory -II based on the change of domain types. The main achievements that have been obtained in this part are as follows.1. Six domain types defined in the fixed local coordinate of each domain are introduced based on the analysis of ferroelectric transformation of perovskite type ferroelectric ceramics. It is convenient to express the 90° and 180° domain switching by the changes of domain types.2. A general form of energy criteria for 90° and 180° domain switching is proposed based on the analysis of the difference of energy dissipation during 90° and 180° domain switching.3. The coupling mechanical-electrical constitutive relations considering the history of loading are formulated. The theoretical predictions are in good agreement with experimental results.4. The relations between microscopic quantities, such as spontaneous polarization and spontaneous strain, and macroscopic quantities, such as remnant polarization and remnant strain, are obtained. It provides a way to calculate the microscopic quantities that are difficult to measure from the values of the macroscopic quantities that are easy to measure.The microscopic changes of CuAlNi single crystal during its pseudoelaslicdeformation are investigated systematically. It is the first time to observe and record the changes of matensite stripes on the surface of the specimen by long-focus microscope during loading and unloading. The result is important to reveal the mechanism and process of stress-induced matensitic transformation.It is the first time to obtain the experimental results on pseudoelastic behavior of CuAINi single crystal under biaxial loading. The tester we designed can solve some of the problems that are encountered during biaxial loading. The results are very important to the research of stress-induced martensitic transformation, and to the study and test of constitutive theories for shape memory alloys.