【摘要】：涂層結構(由涂層和被涂層所覆蓋的基體共同組成的結構)使得各種工程裝備具有了耐磨、耐腐蝕、耐高溫等各種優(yōu)異性能,廣泛應用于機械、電子、航空航天和生物醫(yī)學等各高科技領域。涂層結構普遍具有五個特點：(1)涂層越來越薄,很多涂層的厚度在微米級；(2)服役狀態(tài)下,大量的機械能和熱能會貯存在涂層中,而且機械場和溫度場在薄薄的涂層中以極高的梯度變化；(3)涂層結構是多相結構,涂層和基體的界面會產生復雜的界面效應；(4)隨著新材料不斷投入使用,各向異性涂層結構越來越多；(5)涂層結構常處于熱、力、化學等多場耦合工作狀態(tài)。這些特點使得對于涂層結構的準確分析,無論是基于解析求解還是數(shù)值求解都面臨著困難,普遍存在著算不準的問題。而對于先進涂層結構的分析和設計又迫切需要一種高效穩(wěn)定的精細計算方法和專用仿真平臺。本學位論文即是在這一背景下,開展了以下三方面的工作：首先,針對工程中常見的正交各向異性和橫觀各向同性涂層結構,分別利用由調和函數(shù)表示的二維和三維通解,系統(tǒng)地給出了在法向和切向點力作用下涂層和基體內彈性場的二維和三維格林函數(shù),并基于所得格林函數(shù)揭示了材料的各向異性屬性與涂層結構彈性場的關系。首先綜合考慮通解的形式、載荷的類型、涂層和基體內場的分布特點、涂層和基體在界面的相互影響和制約關系、以及便于進一步的應用和計算機程序實現(xiàn)等多個因素,利用試錯的方法,以初等函數(shù)的形式,系統(tǒng)地構造了含有待定常數(shù)的調和函數(shù)。然后將該調和函數(shù)代入通解,并通過表面邊界條件和界面連續(xù)條件確定待定常數(shù),得到了涂層和基體內彈性場的格林函數(shù)。最后基于所得格林函數(shù),分析了材料的各向異性參數(shù)與涂層結構彈性場之間的變化規(guī)律。其次,基于各向同性熱彈性材料的三維控制方程,利用微分算子理論、Almansi定理以及各種變換方法,推導得到了用四個調和函數(shù)表示的各向同性熱彈性材料的三維完備通解。利用該通解,針對工程中常見的熱阻涂層結構,給出了在點熱源作用下涂層和基體內熱彈性場的三維格林函數(shù),并基于所得格林函數(shù)揭示了材料的力熱屬性與涂層結構熱彈性場的關系以及該型涂層結構的失效機理。通解是求解偏微分耦合方程組的重要一環(huán),通解的形式是否簡潔直接影響到后面的求解方法和難度。本論文獲得的各向同性熱彈性材料的三維通解均由調和函數(shù)來表達,便于進一步用來求解各種工程問題。由于熱阻涂層的研究涉及到熱力耦合效應,在基于所得通解構造調和函數(shù)時所需要考慮的因素更為豐富,也同時涉及到機械場和溫度場的邊界條件和界面連續(xù)條件,這增加了問題的復雜性。本論文充分考慮這些綜合因素,構造了點熱源作用下的調和函數(shù),獲得了相應的格林函數(shù)。并基于所得格林函數(shù)揭示了熱阻涂層結構熱彈性場的耦合機理以及該型涂層結構的失效機理。最后,基于本論文所得涂層結構的一系列格林函數(shù),并利用疊加原理,給出了能對任意分布載荷作用下的涂層結構進行全場精細求解的計算方法—BGM算法(Based on Green's Function Method),并以BGM算法為內核,依托MATLAB GUI編程平臺,設計開發(fā)了涂層結構的專用數(shù)值仿真平臺,為工程界對各種先進涂層結構進行精細分析和設計提供了有力的工具。BGM算法充分發(fā)揮了格林函數(shù)精細求解的優(yōu)勢,使得涂層內部劇烈變化的機械場和溫度場以及界面上的復雜的應力分布都得以準確的計算和描述。本文通過Scarborough準則對BGM算法的計算精度進行了控制,通過消除冗余計算和只考慮格林函數(shù)對計算目標貢獻的方法對BGM算法進行了優(yōu)化。給出了典型的接觸問題(包括橢圓接觸、錐形接觸和圓柱接觸)以及分布熱載荷作用下涂層結構全場各分量的精細計算結果,顯示了BGM算法在工程應用中具有高精度、高效率和高穩(wěn)定性。依托BGM算法開發(fā)的涂層結構的專用數(shù)值仿真平臺界面簡潔友好,易于學習和操作,非常方便于工程界的應用。
[Abstract]:Coating structure (composed of coating and substrate covered by coating) makes all kinds of engineering equipment have excellent properties such as wear resistance, corrosion resistance, high temperature resistance and so on. It is widely used in mechanical, electronic, aerospace and biomedical fields. The thickness of multi-coatings is in the micron level; (2) In service, a large amount of mechanical and thermal energy will be stored in the coatings, and the mechanical and temperature fields in the thin coatings with a very high gradient; (3) coating structure is multiphase structure, coating and matrix interface will produce complex interface effects; (4) with the continuous input of new materials. More and more anisotropic coatings have been used. (5) Coating structures are often in thermal, mechanical, chemical and other coupled working conditions. These characteristics make the accurate analysis of coatings structure, whether based on analytical or numerical solutions are faced with difficulties, there is a general problem of inaccuracy. This dissertation is devoted to the following three aspects: Firstly, two-dimensional and three-dimensional general solutions expressed by harmonic functions are used for orthotropic and transversely isotropic coatings, which are commonly used in engineering. The two-dimensional and three-dimensional Green's functions of elastic field in coating and substrate under normal and tangential point forces are given systematically, and the relationship between anisotropic properties of materials and elastic field of coating structure is revealed based on the obtained Green's functions. By means of trial and error, the harmonic function with undetermined constants is constructed systematically in the form of elementary functions. Then the harmonic function is substituted into the general solution, and the surface boundary conditions and the interface continuity are obtained. The Green's function of the elastic field in the coating and substrate is obtained. Finally, based on the Green's function, the variation law between the anisotropic parameters of the material and the elastic field of the coating structure is analyzed. Secondly, based on the three-dimensional governing equation of the isotropic thermoelastic materials, the differential operator theory, Almansi theorem and various properties are used. A three-dimensional complete general solution of isotropic thermoelastic materials expressed by four harmonic functions is derived by means of the transformation method. Based on the general solution, the three-dimensional Green's function of the thermoelastic field in the coating and substrate under the action of point heat source is given for the common thermal resistive coating structures in engineering, and the force of the materials is revealed based on the obtained Green's function. The relationship between thermal properties and thermoelastic field of coatings and the failure mechanism of the coatings are discussed. The general solution is an important step in solving the coupled partial differential equations. As the study of thermal resistive coatings involves the thermo-mechanical coupling effect, the factors needed to be considered in constructing the harmonic function based on the obtained general solution are more abundant, and the boundary conditions and interface continuity conditions of mechanical and temperature fields are also involved, which adds to the complexity of the basic theory. Considering these comprehensive factors, the harmonic function under the action of point heat source is constructed, and the corresponding Green's function is obtained. Based on the Green's function, the coupling mechanism of thermoelastic field and the failure mechanism of the coating structure are revealed. Finally, a series of Green's functions of the coating structure obtained in this paper are used and the corresponding Green's function is obtained. Based on the superposition principle, the BGM (Based on Green's Function Method) algorithm, which can be used to solve the coating structure under arbitrarily distributed loads, is presented. With the BGM algorithm as the kernel and the MATLAB GUI programming platform as the support, a special numerical simulation platform for the coating structure is designed and developed, which can provide advanced information for the engineering community. The BGM algorithm gives full play to the advantages of the fine solution of Green's function, so that the drastically changed mechanical field and temperature field inside the coating and the complex stress distribution on the interface can be accurately calculated and described. The accuracy is controlled, and the BGM algorithm is optimized by eliminating redundant calculation and considering only the contribution of Green's function to the calculation objective. Typical contact problems (including elliptical contact, conical contact and cylindrical contact) and precise calculation results of the whole field components of the coating structure under distributed thermal load are given, which show the BGM. The algorithm has high precision, high efficiency and high stability in engineering application. The special numerical simulation platform for coated structure based on BGM algorithm has simple and friendly interface, is easy to learn and operate, and is very convenient for engineering application.
【學位授予單位】：湖南大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O302;O174

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本文編號：2242118