Study On Micromechanics Constitutive Models For Martensitic Transformation Materials

The study on the constitutive relation of solid materials with special microstructures and behavior, one of which is martensitic transformation (MT) material, has long been a focus in solid mechanics and material science. The constitutive models of monocrystal and polycrystal MT materials are presented in this dissertation.The transformation processes for thermoelastic MT materials are controlled by nucleation. Based on martensitic forward and reverse transformation conditions (nucleating criterion) of unconstrained single crystal, those conditions of bulk materials are obtained by means of Mori-Tanaka' s mean-field theory which is used to calculate internal stresses and interaction of microstructures. Two interal variables of different levels are introduced to describe transformation process. Microstrain,as order parameter,shows the microscopic phase structure of materials, whose variance leads to transformation condition. Martensitic phase volume fraction indicates MT' s macroprocess,whose evolution controls macrobe-havior. The transformation plastic strain is obtained directly from the crystallographic theory for MT. The constitutive equations for three kinds of MT materials are given here.The constitutive equations of monocrystal SMA (shape memory alloys) are presented first. The forward and reverse transformation plastic yield surfaces are polyhedral,whose evolution exhibits mixed hardening or softening.In the derivation of the constitutive equations for polycrystal SMA, two kinds of hardening mechanisms are considered. First, the change of martensitic variant orientations from the most favorable to the most unfavorable results in the form of the corners in subsequent yield surfaces, al-though initial yield surface is smooth. Second, the morphology of martensitic variant of each orientation turns from thin to thick oblate spheroid?which corresponds to the parallel motion of the yield surfaces for different orientations in subsequent yielding. But when grains of each orientation have turned into martensitic phase,the corresponding forward transformation plastic yield surfaces vanish and vice versa. The evolution of martensitic volume fraction can be expressed by an integral equation, whose variable is the rate at which the volume fraction—the ratio of the volume of each variant to that of corresponding grain—varies. Numerical calculation shows that the constitutive model given here can well simulate the behavior of polycrystal MT.Finally,the research on ceramic materials with MT is given. Because of the significant change of volume caused by MT of the ZrO2 particles in ceramic, microstrains consist of two components, including volumetric strain and shear strain on the habit plane. The research methods and final results are similar to those for polycrystal SMA, but the macrobehavior exhibits pressure-sensitivity and has softening characterstics at lower temperature, which correspond to the autocatalysis for ceramic MT.Candidate for Ph. D. SONG Gu-Quan(Solid Mechanics)Directed by Prof. HWANG Keh-Chih Prof. SUN Qing-Ping...