Crack problems in FGM layers under thermal stresses
Crack problems in FGM layers under thermal stresses
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DOI：
10.1080/01495739608946172
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发表时间：
1996-04-01
影响因子：
2.8
通讯作者：
Wu, BH
中科院分区：
文献类型：
--
作者：
Erdogan, F;Wu, BH
在这项研究中，一个无约束的弹性层下静态自平衡热应力或残余应力被认为是。该层被假定为功能梯度材料（FGM），这意味着其热机械性能被假定为厚度坐标的连续函数。该层包含垂直于其边界的嵌入裂纹或表面裂纹。使用叠加的问题是减少到一个摄动问题，其中裂纹表面的牵引力是唯一的外力。原始问题的尺寸、几何形状和载荷条件使得摄动问题可以近似为无限层的平面应变I型裂纹问题。在对热应力问题进行一般性讨论后，建立了非均匀介质中的裂纹问题。考虑到梯度涂层和界面区的应用，假定热机械性能的厚度变化是单调的。因此，诸如杨氏模量、热膨胀系数和热导率的函数可以通过两参数曲线拟合由适当的指数函数表示。将裂纹问题转化为一个具有广义柯西核的积分方程，并进行数值求解。在给出一些关于热应力分布的样本结果后，给出了嵌入和表面裂纹的应力强度因子。还包括在FGM层，是在压缩附近和在表面和张力在内部区域的裂纹/接触问题的结果。
In this study an unconstrained elastic layer under statically self-equilibrating thermal or residual stresses is considered. The layer is assumed to be a functionally graded material (FGM), meaning that its thermo-mechanical properties are assumed to be continuous functions of the thickness coordinate. The layer contains an embedded or a surface crack perpendicular to its boundaries. Using superposition the problem is reduced to a perturbation problem in which the crack surface tractions are the only external forces. The dimensions, geometry, and loading conditions of the original problem are such that the perturbation problem may be approximated by a plane strain mode I crack problem for an infinite layer. After a general discussion of the thermal stress problem, the crack problem in the nonhomogeneous medium is formulated. With the application to graded coatings and interfacial zones in mind, the thickness variation of the thermo-mechanical properties is assumed to be monotonous. Thus, the functions such as Young's modulus, the thermal expansion coefficient, and thermal conductivity may be expressed by appropriate exponential functions through a two-parameter curve fit. The crack problem is reduced to art integral equation with a generalized Cauchy kernel and solved numerically. After giving some sample results regarding the distribution of thermal stresses, stress intensity factors for embedded and surface cracks are presented. Also included are the results for a crack/contact problem in a FGM layer that is under compression near and at the surface and tension in the interior region.