非完美界面复合材料有效传热性和弹性性能理论研究

发布时间：2018-01-09 03:25

本文关键词：非完美界面复合材料有效传热性和弹性性能理论研究　出处：《西南交通大学》2015年硕士论文　论文类型：学位论文

【摘要】：本论文旨在研究含不完美界面的两相复合材料的有效力学性能：有效热传导和弹性性能,和描述不完美界面对有效力学性能的影响。本文首先对复合材料过渡层的物理场不连续的现象进行研究,给出物理量在粘合过渡层的跳跃关系,并对其进行数学表示,随后用没有厚度的具有相同不连续性质的不完美界面来取代存在的过渡层。然后在不同的物理背景下：热学和线弹性,分别得到相应的通用不完美界面的理论模型。最后以界面跳跃条件和边界条件来约束引入的合适的物理场函数,通过细观力学模型求得有效模量。论文的第一个研究目标是得到含椭球夹杂和通用不完美界面的复合材料的有效热传导率。组成此复合材料的夹杂和基体相的材料为各向同性导热材料。关于热传导的通用不完美界面描述为在此界面处温度场和法向热流不连续,温度场的跳跃与法向热流的界面处平均值成正比,而界面处的法向热流跳跃与温度场的界面处平均值的平面拉普拉斯算子成正比。当通用不完美界面模型只包括温度场跳跃,且温度场的跳跃与法向热流的界面处平均值成正比时,通用不完美界面模型变成Kapitza热阻界面模型；反之,只存在界面处的法向热流跳跃,并与温度场的界面处平均值的平面拉普拉斯算子成正比的这种情况下的界面模型被称为高导热界面模型(HC)。由于目标复合材料中包含的夹杂为椭球形状,论文采用了Lame函数来描述复合材料中的温度场,通过傅立叶定律求得热流密度。随后根据施加的边界条件和不完美界面处温度场和法向热流密度的跳跃关系确定温度场。最后采用Dilute模型和Mori-Tanaka模型求得夹杂稀疏分布和非稀疏分布下的复合材料有效热导率。求得的通用不完美界面复合材料的有效热导率经过简化与前人得到的Kapitza热阻界面模型和高导热界面模型情况下有效热导率进行比较,并研究夹杂的尺寸和形状对有效热导率的影响。第二个研究目的是通过广义自洽模型(GSCM)得到圆柱型纤维增强复合材料的5个横观各向同性的有效线弹性模量的解析解。此纤维增强复合材料的组成相：纤维夹杂和基体,都是各向同性线弹性材料。目标复合材料中存在于基体和纤维的界面被认为是不完美的。可以用通用各向同性弹性模型来对这个不完美界面进行数学描述,这个各向同性不完美界面模型包含了两个被广泛应用的特殊界面：弹簧界面模型(Spring-layer interface model)和薄膜界面模型(Membrane-type interface model)。通过对目标复合材料的边界上施加5种基础的均匀荷载,分别求出在这5种情况下的位移,应变和应力场函数,然后利用GSCM来求得有效弹性模量的解析解。由于弹簧界面模型和薄膜界面模型是通用各向同性弹性模型的两种特殊情况,所以所得到的结果在一定程度上扩展了以往含有弹簧界面或薄膜界面纤维复合材料的结果。数值算例来说明有效弹性模量随纤维横截面半径变化而变化的趋势。最后,本篇论文对所做工作进行了总结。
[Abstract]:This paper aims to study the effective mechanical properties of containing imperfect two-phase composite material interface: effective heat conduction and elastic properties, and describe the effects of imperfect interface on the effective mechanical properties. The thesis studied the physical field of the composite transition layer discontinuous phenomenon, given physical quantities in the relationship between the jump adhesion transition layer. And carries on the mathematical representation, followed by not having the same thickness of the discontinuous nature of imperfect interface to replace the transition layer exists. Then in different physical backgrounds: thermal and elastic, respectively corresponding to the general theoretical model of imperfect interface. The physical field function suitable to the interface jump conditions and finally the boundary condition constraints, the micromechanics model to obtain the effective modulus. The first goal of this thesis is to get the inclusion and general imperfect interface with complex ellipsoid The effective thermal conductivity of the composite material. The rate of composite inclusions and matrix phase composed of isotropic conductive materials. The general of the heat conduction and imperfect interface description for this interface at the temperature field and heat flux method to discontinuous, temperature jump and method to the surface heat flux is proportional to the average value of, and the interface method to the heat flux at the interface with the operator Laplasse jump plane temperature field is proportional to the average value. When general imperfect interface model only includes temperature field and temperature field of the jump, jump and method to interface heat flux is proportional to the average value, general imperfect interface model into Kapitza model and interface thermal resistance; that exists only at the interface of the normal flux jumps, the interface model and temperature field at the interface of the average value of the plane is proportional to the Laplasse operator is called high thermal interface model (HC). Because the target composite contains inclusions as ellipsoid shape, this paper uses the Lame function to describe the temperature field of composite material, the heat flux obtained by the Fu Liye's law. Then according to the boundary conditions and imperfect interface temperature field and heat flux jump method to determine the temperature field is obtained. Finally the relationship between mixed composite materials the effective thermal conductivity of the sparse distribution and non sparse distribution rate by using Dilute model and Mori-Tanaka model. The general is not perfect after the effective thermal conductivity and thermal resistance of Kapitza interface model is simplified by predecessors and high thermal interface model are compared with the case of effective thermal conductivity of composite interface rate, and inclusion in the size and shape effects on effective thermal conductivity the rate of second. The purpose of this study is through the generalized self consistent model (GSCM) to get cylindrical fiber reinforced composite material 5 transversely with The effective elastic modulus of analytic solution. The composition of this phase: fiber reinforced fiber inclusions and matrix are isotropic linear elastic material. The composite target exists in the matrix and fiber interface is not perfect. You can use generic isotropic elastic model of the imperfect interface the mathematical description, the isotropic imperfect interface model consists of two special interface is widely used: spring interface model (Spring-layer interface model) and film interface (Membrane-type interface model) model. The uniform load applied on the 5 basic goals according to the composite boundary, calculates the displacement in the 5 under the condition of strain and stress field analysis function, then to calculate the effective elastic modulus of the GSCM solution. The interface interface spring model and the thin film model is general isotropic Two special elastic model, so the results obtained in a certain extent, extends the previous spring containing film interface interface or fiber composite results. Numerical examples show that the effective elastic modulus varies with the radius of the fiber cross-section change trend. Finally, this thesis summarizes the work.

【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB33

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