Indentation of solids with gradients in elastic properties .1. Point force
Indentation of solids with gradients in elastic properties .1. Point force
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DOI：
10.1016/s0020-7683(96)00171-0
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发表时间：
1997-07-01
影响因子：
3.6
通讯作者：
Suresh, S
中科院分区：
文献类型：
--
作者：
Giannakopoulos, AE;Suresh, S
分析和计算结果上的应力和位移的演变，由于压痕从一个正常的点力的弹性基板上的杨氏模量E的变化作为深度的函数，z，下面的压痕表面。除了性质随深度的变化，材料被假定为线性弹性和局部各向同性。本文导出了泊松比、上挠率和E的变化量的几个固定值的封闭解，这些值满足z的两个预定函数：（1）简单幂律E = E（0）z（k），其中0 ≤ k < 1是无量纲指数;（2）指数定律，E = E（0）e（α z），其中E-0是表面处的杨氏模量，α < 0表示硬化表面（例如，金属基底上的梯度陶瓷涂层）和α> 0表示软表面（例如，对于固体和岩石，测量的模量变化是地表下深度的函数）。通过详细的有限元模拟来检查解析解。结果表明，对于幂律的情况下，存在一个临界泊松比，uppermance（cr），在点荷载下的应力分布发生剧烈变化。有限元结果表明，然而，响应是相对不太敏感的变化的上升（在任何一侧的上升（cr））比E随深度的变化。本研究结果的应用进行了讨论，在适当的情况下，工程结构，厚涂层，薄膜多层微电子器件的表面处理，并在土壤力学和岩石力学的背景下解决的基础。(C)1997 Elsevier Science Ltd.
Analytical and computational results are presented on the evolution of stresses and displacements due to indentation from a normal point force on an elastic substrate whose Young's modulus E varies as a function of depth, z, beneath the indented surface. With the exception of variation of properties with depth, the material is assumed to be linearly elastic and locally isotropic. Closed-form solutions are derived for several fixed values of the Poisson ratio, upsilon, and variations in E which follow two prescribed functions of z: (1) a simple power law, E = E(0)z(k), where 0 less than or equal to k < 1 is a non-dimensional exponent; (2) an exponential law, E = E(0)e(alpha z), where E-0 is Young's modulus at the surface, alpha < 0 denotes a hardened surface (e.g., graded ceramic coatings on metallic substrates) and alpha > 0 denotes a soft surface (e.g., modulus variations measured as a function of depth beneath the earth's surface for solids and rocks). The analytical solutions are checked with detailed finite element simulations. It is shown that, for the power law case, there exists a critical Poisson ratio, upsilon(cr), above which drastic changes occur in the stress distribution under the point load. Finite element results reveal, however, that the response is relatively less sensitive to the variation of upsilon (on either side of upsilon(cr)) than to the variation of E with depth. Applications of the present results are discussed, wherever appropriate, to surface treatments of engineering structures,thick coatings, thin-film multilayers for microelectronic devices, and settling of foundations in the context of soil mechanics and rock mechanics. (C) 1997 Elsevier Science Ltd.