热障涂层界面热力耦合破坏边界元法研究

Thermal barrier coatings (TBCs) are one of the key materials for high temperature components of aircraft engines and gas turbines. Due to the large difference between the force and thermal properties for coating material and these for substrate material, and the large difference between the characteristic thickness of coating and substrate, thermal mismatch residual stress is caused between the coating and substrate. And the stress singularity near interfaces is also caused. Cracks are formed and then propagate, which tends to the interface failure. Evaluation and prediction of the interface failure of TBCs need accurate analysis of thermal stress field, the initiation and propagation of cracks. Accurate analysis of the propagation of cracks which is a stress singularity problem in the interface thermo-mechanical failure of TBCs using the finite element method. Thus in this project, the boundary element method (BEM) is applied for analysis and prediction of the interface thermo -mechanical failure of TBCs. The contents of this project are as follows. Computation of nearly singular, singular and hypersingular integrals with high accuracy and efficiency is proposed for the cross-scale analysis of BEM and accurate simulation of thermal barrier coating thermal stress distribution is performed. Then the region of stress concentration and crack initiation can be predicted. The thermo-mechanical BEM for thermoelastic crack is proposed for accurate calculation of stress intensity factor. The new extensions of crack surface and crack front are represented by NURBS. The local coordinate system of the crack front can be naturally established and the problem which the deflection angle is discontinuous can be overcome. Then the process of the interface crack propagation in TBCs can be analyzed and the life prediction is performed. The goal of this project is to present accurate, effective, general method and theoretical guidance for thermo-mechanical interface damage of TBCs.

热障涂层是航空发动机和燃气轮机高温部件的关键材料。涂层与基体材料热力性能参数及特征厚度相差很大，涂层与基体间会产生热不匹配残余应力和界面附近的奇异性应力，萌生裂纹，裂纹扩展导致界面破坏。热障涂层界面破坏评价和预测需要准确分析其热应力场、裂纹萌生与扩展。有限元法难以准确分析热障涂层界面热力耦合破坏过程中出现的裂纹扩展这类应力奇异性问题。本项目拟采用边界元法，分析并预测热障涂层界面热力耦合破坏过程。研究内容包括：精确高效的近奇异积分、奇异积分和超奇异积分算法，能准确模拟热障涂层热应力场，预测应力集中和裂纹萌生区域；热障涂层热力耦合热裂纹边界元算法，精确计算裂纹的应力强度因子；NURBS曲面来表征新扩展裂纹面和裂纹前沿，可自然建立裂纹前沿的局部坐标系，解决裂纹扩展角不连续问题，分析热障涂层界面裂纹扩展过程，进行寿命预测。目标为热障涂层热力耦合界面破坏过程分析供一种精确高效且通用的计算理论和方法。

热障涂层是航空发动机和燃气轮机高温部件的关键材料。涂层与基体材料热力性能参数及特征厚度相差很大，涂层与基体间会产生热不匹配残余应力和界面附近的奇异性应力，萌生裂纹，裂纹扩展导致界面破坏。热障涂层界面破坏评价和预测需要准确分析其热应力场、裂纹萌生与扩展。本项目开发了可用于模拟该结构裂纹扩展过程的边界元算法。主要研究内容包括：热力耦合边界积分方程公式推导，热力耦合边界元程序的设计和编制、并通过经典算例进行验证；研究了奇异积分的单元形状效应包括顶端大张角（大于120度）和大边长比（大于5）对奇异积分计算精度的影响，以及近奇异积分点落在积分单元不同位置对近奇异积分计算精度的影响。针对奇异积分的单元形状效应，构造了三角形单元奇异积分的子单元细分技术，可以有效减少源点偏移量对计算结果的影响，尽可能保持计算结果的稳定性。针对近奇异积分点落在单元边界附近，则考虑近奇异积分径向和环向的近奇异性，分别引入角度变换距离变换和距离sinh变换，有效提高了计算精度，减少了环向近奇异性的影响。引入Duffy变换，成功实现了近奇异性的双向分离，并构造了双向sinh（迭代sinh）变换，有效提高了计算结果的精度和稳定性；根据裂纹尖端位移展开的渐近性质，构造了二维断裂问题的裂尖单元，以及三维断裂问题的三角形单元和四边形单元裂尖单元，与双边界积分方程结合建立双边界元法新求解格式，提高了裂纹尖端附近位移、应力强度因子的计算精度；开发了双边界积分方程裂纹面上奇异积分和超奇异积分的算法，克服了奇异积分和超奇异积分单元形状效应，提高了计算精度和计算效率；针对裂纹扩展的动态过程，建立了裂纹扩展准则判别，能判定裂纹是否扩展、扩展的方向。对裂纹扩展每一个扩展过程、进行了迭代求解，准确获得了扩展过程中应力强度因子以及裂纹下一步扩展准则判断。可以为热障涂层热力耦合裂纹扩展提供一种精确高效且通用的计算理论和方法。

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