功能梯度材料共线裂纹、任意角度裂纹断裂以及热应力问题研究
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摘要
功能梯度材料是一种热力性质连续变化的多相复合材料,主要充当涂层和界面带,可以在恶劣的热力载荷环境下缓解热应力,提供热保护。新型发展起来的功能梯度材料已经在航空、汽车以及制造业有了广泛的应用,并引起了人们极大的研究兴趣。最近,功能梯度材料的范围已经从最初的耐热功能梯度材料发展到压电功能梯度材料。尽管功能梯度材料具有许多优良的综合特性,但在高温和机械载荷下,尤其是在动态载荷下,材料的非均匀性也容易导致材料的破坏。为了指导功能梯度材料的设计、优化以及性能的评估,必须对裂纹的增长和扩展,尤其是断裂行为加以研究。
本文以功能梯度材料作为研究对象,分析了它们在各种结构及载荷形式下的断裂行为。首先研究了功能梯度涂层-均匀基底间界面单裂纹和周期裂纹在反平面载荷作用下的问题。运用标准的积分变换和有限傅立叶变换,将单裂纹和周期裂纹问题转化为分别求解带Cauchy型和Hilbert型奇异核的积分方程。
其次,运用Lapace和Fourier变换以及得力的奇异积分方程方法,分别研究了功能梯度涂层-功能梯度基底模型共线裂纹的静态和动态冲击问题,文中考虑了功能梯度涂层-功能梯度基底的内部裂纹、表面裂纹以及裂纹通过界面问题。对于裂纹通过界面问题,本文利用复势理论估计和证明了裂纹尖端的奇异性,并得到了应力强度因子的表达式。
在过去十几年里,有一些学者对功能梯度材料含任意斜裂纹的问题进行了研究,但基于问题的复杂性大都局限于静态分析。在本文的研究中,分析了功能梯度材料含任意斜裂纹在动态机械载荷作用下的断裂问题,结果显示,材料非均匀常数以及裂纹方向角都对动态应力强度因子产生影响。
最后,考虑新的边界条件,假设裂纹区域存在导热热阻,裂纹面部分绝热,推导了功能梯度涂层-功能梯度基底结构的温度场和位移场的奇异积分方程组。分析了材料特性(弹性模量,热膨胀系数以及热传导系数)的梯度参数和无量纲热阻对温度分布及热应力强度因子的影响。
随着复合材料技术的出现,更多复杂材料的微结构性、非均匀性和非线性力学性质逐步呈现了出来。本文基于力学和应用数学模型,对材料结构的研究进行了一个尝试,本文的研究结果在涡轮组成和燃烧室的热障碍涂层以及许多材料在宏观上呈现非均匀性质的材料上有广泛的应用。
Functionally graded materials (FGMs) are generally multi-phasecomposites with continuously varying theromechanical properties. Theyare primarily used as coatings and interfacial zones and they tend toreduce residual stresses and provide protection against severe thermaland mechanical environments. The newly developed FGMs have at-tracted considerable research interests as candidate materials for struc-tural applications ranging from aerospace to automobile to manufac-turing. Recently, the concept of FGMs has been extended from theinitial high-temperature components to the piezoelectric components.Although FGMs have many good comprehensive properties, the inho-mogeneity of FGMs can sometimes lead to the failure of materials underthe high temperature and mechanical loads, especially dynamic loading.In order to guide the microstructure selection and the design and per-formance assessment of components made of FGMs, it is necessary toanalyze the knowledge of crack growth and propagation, especially theirfracture behaviors.
The fracture behaviors of various functionally graded structuresare investigated under diferent loads in this thesis. Firstly, the inter- face crack problems in functionally graded media are analyzed underantiplane shear loads. A standard integral-transform techniques andfinite Fourier transform techniques are employed to reduce the singlecrack problem and periodic cracks problem to the solution of an integralequation with Cauchy-type or Hilbert-type singular kernel, respectively.
Then, using Laplace and Fourier transform and a very powerful sin-gular integral equation (SIE) method, the collinear cracks in a bi-FGMscoating-substrate structure is studied under static fractue problem or dy-namic fracture problem. The bi-FGMs coating-substrate structure withinternal and surface crack and crack crossing the interface configurationsare considered. For the case of crack crossing the interface, we evaluatedand proved the singularites of the crack tips by using complex potentialtheory, and obtained the expression of stress intensity factor(SIF).
Some crack problems of an arbitrarily oriented crack in FGMs havebeen solved during the past ten years, but most of these studies limitedto static analyses. In this paper, the problem of an arbitrarily orientedcrack in a FGMs is investigated under dynamic loading. The resultsdemonstrated that the dynamic stress intensity factor (DSIF) is sensitiveto the nonhomogeneity constant and crack orientation angle.
Finally, considering a new boundary condition, it is assumed thatinterface crack is partially insulated the temperature drop across thecrack surfaces is the result of the thermal resistant due to the heat con-duction through the crack region. The governing equations of the tem-perature fields and displacement fields for bi-FGMs coating-substrate structure are converted into a system of singular integral equations. Theinfluences of material properties (i.e. the elastic module, the thermal ex-pansion coefcient and the thermal conductivities) gradient parametersand dimensionless thermal resistant on the temperature distribution andthe thermal stress intensity factors (TSIF) are figured.
With the advent of composite materials technology, more complexmaterial microstructures are being introduced, and more mechanics is-sues such as inhomogeneity and nonlinearity come into play. This paperwork is an attempt to meet these challenges by making contributionsto both mechanics modeling and applied mathematics. Results in thisstudy have wide-ranging applications, such as thermal barrier coatingson turbine components, combustion chambers, and many more applica-tions where the material is macroscopically nonhomogeneous.
本文以功能梯度材料作为研究对象,分析了它们在各种结构及载荷形式下的断裂行为。首先研究了功能梯度涂层-均匀基底间界面单裂纹和周期裂纹在反平面载荷作用下的问题。运用标准的积分变换和有限傅立叶变换,将单裂纹和周期裂纹问题转化为分别求解带Cauchy型和Hilbert型奇异核的积分方程。
其次,运用Lapace和Fourier变换以及得力的奇异积分方程方法,分别研究了功能梯度涂层-功能梯度基底模型共线裂纹的静态和动态冲击问题,文中考虑了功能梯度涂层-功能梯度基底的内部裂纹、表面裂纹以及裂纹通过界面问题。对于裂纹通过界面问题,本文利用复势理论估计和证明了裂纹尖端的奇异性,并得到了应力强度因子的表达式。
在过去十几年里,有一些学者对功能梯度材料含任意斜裂纹的问题进行了研究,但基于问题的复杂性大都局限于静态分析。在本文的研究中,分析了功能梯度材料含任意斜裂纹在动态机械载荷作用下的断裂问题,结果显示,材料非均匀常数以及裂纹方向角都对动态应力强度因子产生影响。
最后,考虑新的边界条件,假设裂纹区域存在导热热阻,裂纹面部分绝热,推导了功能梯度涂层-功能梯度基底结构的温度场和位移场的奇异积分方程组。分析了材料特性(弹性模量,热膨胀系数以及热传导系数)的梯度参数和无量纲热阻对温度分布及热应力强度因子的影响。
随着复合材料技术的出现,更多复杂材料的微结构性、非均匀性和非线性力学性质逐步呈现了出来。本文基于力学和应用数学模型,对材料结构的研究进行了一个尝试,本文的研究结果在涡轮组成和燃烧室的热障碍涂层以及许多材料在宏观上呈现非均匀性质的材料上有广泛的应用。
Functionally graded materials (FGMs) are generally multi-phasecomposites with continuously varying theromechanical properties. Theyare primarily used as coatings and interfacial zones and they tend toreduce residual stresses and provide protection against severe thermaland mechanical environments. The newly developed FGMs have at-tracted considerable research interests as candidate materials for struc-tural applications ranging from aerospace to automobile to manufac-turing. Recently, the concept of FGMs has been extended from theinitial high-temperature components to the piezoelectric components.Although FGMs have many good comprehensive properties, the inho-mogeneity of FGMs can sometimes lead to the failure of materials underthe high temperature and mechanical loads, especially dynamic loading.In order to guide the microstructure selection and the design and per-formance assessment of components made of FGMs, it is necessary toanalyze the knowledge of crack growth and propagation, especially theirfracture behaviors.
The fracture behaviors of various functionally graded structuresare investigated under diferent loads in this thesis. Firstly, the inter- face crack problems in functionally graded media are analyzed underantiplane shear loads. A standard integral-transform techniques andfinite Fourier transform techniques are employed to reduce the singlecrack problem and periodic cracks problem to the solution of an integralequation with Cauchy-type or Hilbert-type singular kernel, respectively.
Then, using Laplace and Fourier transform and a very powerful sin-gular integral equation (SIE) method, the collinear cracks in a bi-FGMscoating-substrate structure is studied under static fractue problem or dy-namic fracture problem. The bi-FGMs coating-substrate structure withinternal and surface crack and crack crossing the interface configurationsare considered. For the case of crack crossing the interface, we evaluatedand proved the singularites of the crack tips by using complex potentialtheory, and obtained the expression of stress intensity factor(SIF).
Some crack problems of an arbitrarily oriented crack in FGMs havebeen solved during the past ten years, but most of these studies limitedto static analyses. In this paper, the problem of an arbitrarily orientedcrack in a FGMs is investigated under dynamic loading. The resultsdemonstrated that the dynamic stress intensity factor (DSIF) is sensitiveto the nonhomogeneity constant and crack orientation angle.
Finally, considering a new boundary condition, it is assumed thatinterface crack is partially insulated the temperature drop across thecrack surfaces is the result of the thermal resistant due to the heat con-duction through the crack region. The governing equations of the tem-perature fields and displacement fields for bi-FGMs coating-substrate structure are converted into a system of singular integral equations. Theinfluences of material properties (i.e. the elastic module, the thermal ex-pansion coefcient and the thermal conductivities) gradient parametersand dimensionless thermal resistant on the temperature distribution andthe thermal stress intensity factors (TSIF) are figured.
With the advent of composite materials technology, more complexmaterial microstructures are being introduced, and more mechanics is-sues such as inhomogeneity and nonlinearity come into play. This paperwork is an attempt to meet these challenges by making contributionsto both mechanics modeling and applied mathematics. Results in thisstudy have wide-ranging applications, such as thermal barrier coatingson turbine components, combustion chambers, and many more applica-tions where the material is macroscopically nonhomogeneous.
引文
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