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首页> 外文期刊>International Journal of Solids and Structures >An embedded crack in a functionally graded orthotropic coating bonded to a homogeneous substrate under a frictional Hertzian contact
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An embedded crack in a functionally graded orthotropic coating bonded to a homogeneous substrate under a frictional Hertzian contact

机译：功能梯度正交各向异性涂层中的嵌入裂纹，在摩擦赫兹接触下粘结到均质基材上

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摘要

In this paper, we consider the elasto-static problem of an embedded crack in a graded orthotropic coating bonded to a homogeneous substrate subject to statically applied normal and tangential surface loading. The crack direction is parallel to the free surface. The coating is graded in the thickness direction and is orthogonal to the crack direction. This coating is modelled as a non-homogeneous medium with an orthotropic stress-strain law. The equivalent crack surface stresses are first obtained and substituted in the plane elasticity equations. Using integral transforms, the governing equations are converted into singular integral equations which are solved numerically to yield the displacement field as well as the crack-tip stress intensity factors. This study presents a complete theoretical formulation for the problem in the static case. A numerical predictive capability for solving the singular integral equations and computing the crack-tip stress intensity factors is proposed. Since the loading is compressive, a previously developed crack-closure algorithm is applied to avoid interpenetration of the crack faces. The main objective of the paper is to investigate the effects of the material orthotropy and non-homogeneity of the graded coating on the crack-tip stress intensity factors, with and without using the crack-closure algorithm, for the purpose of gaining better understanding on the behavior and design of graded coatings.
机译：在本文中，我们考虑了在静态施加法向和切向表面载荷的情况下，粘结在均质基材上的正交各向异性梯度涂层中的嵌入式裂纹的弹静问题。裂纹方向平行于自由表面。涂层在厚度方向上分级，并且与裂纹方向正交。该涂层被建模为具有正交各向异性应力-应变定律的非均匀介质。首先获得等效的裂纹表面应力，并将其代入平面弹性方程。使用积分变换，将控制方程式转换为奇异积分方程式，对其进行数值求解，以得出位移场以及裂纹尖端应力强度因子。这项研究为静态情况下的问题提供了完整的理论表述。提出了求解奇异积分方程和计算裂纹尖端应力强度因子的数值预测能力。由于载荷是压缩的，因此采用了先前开发的裂纹闭合算法，以避免裂纹面相互渗透。本文的主要目的是研究在不使用裂纹闭合算法的情况下，梯度涂层的材料正交性和非均匀性对裂纹尖端应力强度因子的影响，以便更好地理解裂纹闭合算法。渐变涂料的性能和设计。

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