Micromechanics Constitutive Researches For Transformable Materials And Transformation Localization Analysis

Advanced materials are the cornerstones of modern science and technology. The constitutive behavior of materials has long been one of the most active subjects in solid mechanics. Three parts of contents on the constitutive behaviors of three kinds of transformable materials are presented in this dissertation.In the first part, a generalized micromechanics constitutive theory is established to describe the thermoelastic martensitic forward transformation, reverse transformation and reorientation of single crystal induced by applied stress and/or temperature. In the derivation, the transformation plastic strain is obtained from the crystallographic theory for martensitic transformation directly. Then the free energy of the constitutive element is derived by using micromechanics approaches and the vohune fractions of various kinds of martensite variants are considered as internal variables describing the pattern of internal rearrangement resulting from the phase transformation and reorientation in the loading history. In the framework of the Hill-Rice's internal variable thermodynamics constitutive theory, the forward transformation, reverse transformation and reorientation yield functions and incremental stress-strain relations are formulated. This constitutive model can describe monocrystalline macroscopic constitutive behavior caused by the microstrutures forward transformation, reverse transformation and reorientation under complex thermodynamic loading conditions. It can explain some experimental observations such as thin inartensite blades, softening and plateau in stress — strain curvcs under uniaxial tension. Quantitatively applied to uniaxial tension, the forward and reverse transformation yield stresses, number of the kinds of appearing variants and their orientations given by the theoretical predictions consist well with experiment results.In the second part, the macroscopic constitutive behavior of ferroelectric ceramics induced by domain switching is investigated. Orientation distribution function (ODF) isadopted to represent the situation of the domain switching. By using the solution of an ellipsoidal inclusion embedded in an infinite homogeneous piezoelectric medium, the equivalent inclusion method and Mori-Tanaka average field theory, the electroelastic field of the constitutive element is analysed. According to thermodynamic requirement, the condition to determine the ODF is derived and a total model relation between stress, electric displacement and strain, electric field intensity is established.In the third part, the transformation plastic localization in ZrO2 -containing ceramics is analysed by using the Sun, Hwang and Yu (SHY) micromechanics model in the continuum mechanics framework. The condition for the onset of localization is derived and the orientation of localization is predicted. These analytic results are consistent with available experiments of uniaxial tension and uniaxial compression.