【作者】 黄为福；

【导师】 黄模佳；

【作者基本信息】 南昌大学 ， 化工过程机械， 2006， 硕士

【摘要】 化工机械设备，如压力容器、管道、泵等大多为金属材料所制造，金属材料的力学性能对这些设备的生产制造及安全运行有重要的影响。金属材料是多晶体材料，由微小晶粒集合而成，晶粒的化学成分、尺寸大小、取向分布等决定了多晶体材料的宏观力学性能。金属的铸造、塑性成形、热处理等过程会使晶粒的尺寸大小、取向分布、形状等发生一定的变化，产生不同的微结构。本文主要研究金属微结构对金属材料力学性能的影响及其材料微结构的测量方法，并取得了以下具有创新意义的成果： （1） 针对准D₅晶粒任意集合的多晶体材料，考虑晶粒的对称性，通过微结构理论和群论，推导出了准D₅晶粒的本构形式，该本构由5个单晶常数组成；本文用晶粒取向分布函数（ODF）w（R）描述多晶体中的晶粒取向为R的可能性密度，并基于Voigt模型和Reuss模型，推导出了考虑织构系数影响的准D₅晶粒任意集合的多晶体材料的平均弹性刚度张量（?）和平均弹性柔度张量（?）；算例表明（?）≥（?）^-1，与Hill理论相吻合： （2） 金属材料塑性性能的一个重要指标是r-值或称Lankford系数；通过多晶体材料的屈服函数与取向分布函数（ODF）的关系，Man推导出了立方晶粒正交集合板材的r-值；本文在Man研究的基础上，推导出了考虑织构系数影响的立方晶粒任意集合板材的r-值表达式； （3） ODF的测量方法有很多；Huang（2004）由自洽法推导出了立方晶粒正交集合的有效弹性刚度张量，本文基于他的结果，研究了立方晶粒正交集合板材的弹性模量与织构系数c_m0⁴（m=0，2，4）的关系，通过测量板材的弹性模量确定板材的织构系数； （4） 本文根据Christoffel方程，采用Huang和Man（2002，2003）推导出的立方晶粒各向异性集合金属材料的有效弹性刚度张量，通过客观性原理，建立了超声波波速与九个织构系数c_m0⁴（m=0，1，2，3，4）之间的近似关系式，其结果可以用于超声波测量立方晶粒各向异性金属的织构系数；数值计算表明：如果超声波仪器能够准确地测量纵波速度，本文的近似关系式能够给出很好的结果。更多还原

【Abstract】 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更多还原