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Constitutive Relations Of Polycrystals With Effects Of The ODF And Their Measurements

Posted on:2007-10-06Degree:MasterType:Thesis
Country:ChinaCandidate:W F HuangFull Text:PDF
GTID:2121360185960942Subject:Chemical Process Equipment
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Most of mechanical equipments in chemical engineering are made by metals, such as pressure vessels, pipelines, pumps, and so on. The properties of the metals affect the making and running on these equipments. A metal polycrystal can be taken as aggregate of tiny crystallites. The macroscopic constitutive relation of the polycrystal depends on chemical composition of its crystallites and the microstructures of the polycrystal, which include crystalline orientations, crystalline sizes, crystallites' orientation correlation, and crystalline boundary structures. During the casting, plastic forming, and hot processing, the sizes, orientation distributions, and boundary structures of the crystallites change and produce various microstructures. Herein we study the constitutive relation of the polycrystal with effects of microstructures and discuss the experimental methods of measuring the constitutive relation of the polycrystal with the texture coefficients. Our creative work mainly includes:(1) Assume a polycrystal to be an anisotropic aggregate of many tiny quasi- D5 crystallites. Using microstructure theory and group theory and considering the symmetry of the quasi- D5 crystals, we deduce the constitutive form of single quasi- D5 crystal which contains five elastic constants of single crystals. In this paper, we use the orientation distribution function (ODF) w(R)to describe the probability density of finding a crystallite with orientation R . Under Voigt model and Reuss model, we obtain the average elastic stiffness tensor C and the average elastic softness tensor S of an anisotropic aggregate of quasi- D5 crystallites with effect of the texture coefficients, respectively. An example is given to show C|-≥ (S|-)-1 which is consistent with Hill's theorem.(2) The r-value or named Lankford coefficient is an important parameter of plastic materials. By the relations between yield function and the ODF, Man obtained a r-value formula of the orthorhombic sheets of cubic metals. Herein we give a r-value expression of an anisotropic aggregate of cubic crystallites with effect of the texture coefficients.(3) There are many methods to measure the ODF. Huang (2004a) deduced an effective elastic stiffness tensor for an orthorhombic aggregate of cubic crystallites by the self-consistent method. By the effective elastic stiffness tensor, we find the relation between the texture coefficients and...
Keywords/Search Tags:cubic crystallites, quasi- D5 crystallite, constitutive relation of anisotropic polycrystal, orientation distribution function (ODF), texture coefficients, r-value, ultrasonic wave measuremeent
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