Abstract In this paper, the interaction between an isotropic thin film and an orthotropic substrate is considered under the plane strain state. The perfectly bonded thin film is exposed to a predefined temperature gradient. The strain compatibility condition and the plane elasticity formulation are utilized to extract the governing integral equations. Employing the Gauss- Chebyshev discretization method, the interfacial shear as well as the flexural surface in-plane stresses are determined. The influences of the material stiffness and the orthotropy parameters on both surface and subsurface stresses are investigated. The numerical results confirm that the proper adjustment of the orthotropic substrate properties can alleviated the severe stress gradients. The results indicate that the surface in-plane stress tensile peak significantly decreases if the stiffness of the orthotropic half-plane along the film interface is lower than its corresponding value through the depth. Also, the maximum von Mises stress in the substrate decreases about 50% for an orthotropic material possessing a large shear parameter.

中文翻译：

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热载荷下粘合到正交各向异性衬底的薄膜的应力分析

摘要 本文考虑了平面应变状态下各向同性薄膜与正交各向异性衬底之间的相互作用。完美结合的薄膜暴露于预定的温度梯度。利用应变相容性条件和平面弹性公式来提取控制积分方程。采用高斯-切比雪夫离散化方法，确定界面剪切以及弯曲表面平面内应力。研究了材料刚度和正交各向异性参数对表面和次表面应力的影响。数值结果证实，适当调整正交各向异性衬底特性可以缓解严重的应力梯度。结果表明，如果沿薄膜界面的正交各向异性半平面的刚度低于其通过深度的相应值，则表面面内应力拉伸峰值显着降低。此外，对于具有大剪切参数的正交各向异性材料，衬底中的最大 von Mises 应力降低了约 50%。