参数任意变化的功能梯度材料的2维摩擦滑动接触力学

本文建立了一种多层介质模型用于分析参数任意变化的功能梯度材料的2维摩擦滑动接触力学问题。将功能梯度材料分为非均匀多层介质,其中剪切模量线性变化,泊松比为常数。接触摩擦遵循库仑定律。首先求得了功能梯度材料覆层半空间作用垂直和水平集中力时的解,然后以此为基本解

Two-dimensional sliding frictional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties

Liao-Liang Ke, Yue-Sheng Wang *

Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, People’s Republic of China.

Abstract

A multi-layered model for sliding frictional contact analysis of functionally graded materials (FGMs) with arbitrarily varying elastic modulus under plane strain-state deformation has been developed. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is pided into several sub-layers and in each sub-layers the shear modulus is assumed to be a linear function while the Possion’s ratio is assumed to be a constant. On the contact area, it is assumed that the friction is one of Coulomb type. With this model the fundamental solutions for concentrated forces acting perpendicular and parallel to the FGMs layer surface are obtained. Then the sliding frictional contact problem of a functionally graded coated half-space is investigated. The transfer matrix method and Fourier integral transform technique are employed to cast the problem to a Cauchy singular integral equation. The contact stresses and contact area are calculated for various moving stamps by solving the equations numerically.

Keywords : Contact mechanics; Functionally graded materials; Friction; Plane strain-state; Coating

Nomenclature

(,)b a ? contact area

0h coating thickness

m slope of the triangular or wedge-shaped stamp

N total number of sub-layers

P applied normal load

Q applied

tangential load c P

dimensionless normal load for a cylindrical stamp, 00/P h μ w P

dimensionless normal load for a wedge-shaped stamp, 00/P mh μ ()p x

normal contact pressure ()q x tangential contact traction R radius of a cylindrical stamp

i μ shear modulus at the sub-interfaces, 1,2i N ="

0μ

shear modulus at the surface of the coating * Correspondence: E-mail: yswang@http://www.77cn.com.cn , Fax: ++86-10-51682094, Tel: ++86-10-51688417.

http://www.77cn.com.cn

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本文建立了一种多层介质模型用于分析参数任意变化的功能梯度材料的2维摩擦滑动接触力学问题。将功能梯度材料分为非均匀多层介质,其中剪切模量线性变化,泊松比为常数。接触摩擦遵循库仑定律。首先求得了功能梯度材料覆层半空间作用垂直和水平集中力时的解,然后以此为基本解

http://www.77cn.com.cn *

μshear modulus of the homogeneous half-space

νPoisson’s ratio

δmaximum indentation depth

1. Introduction

Functionally graded materials (FGMS) consist of a gradual change in the volume fraction of constituents from one location to the other in a component. Used as coatings and interfacial zones they tend to reduce stresses resulting from material property mismatch, increase the bonding strength, improve the surface properties and provide protection against adverse thermal and chemical environment. Thus the concept provides the materials scientists and engineers with an important tool to design new materials for some special applications, for example, in aerospace, automobile, biomedicine, nuclear energy, gas turbine engine and many other fields. Extensive technical literatures [1] can be found concerning the thermal stress analysis and fracture mechanics of FGMs.

It is well-known that sliding frictional contact on homogeneous brittle substrates may give rise to special cracking patterns. Such cracks result from highly concentrated tensile stresses and are responsible for initiating failures related to sliding contact, as well as contact fatigue. In order to avoid such type of damage, FGMs have been proposed as protective coatings between contacting surfaces. In the past few years, many studies [2-5] indicate that controlled gradients in mechanical properties of compositions and structures offer unprecedented opportunities for the design of surfaces with resistance to contact deformation and damage that cannot be realized in conventional homogeneous materials. These results can be explained by the research of Giannakopoulos and Suresh [6,7]. In their papers,the axisymmetric problems of graded half-spaces subjected to a concentrated load or to flat, spherical and conical indenters were considered. The elastic modulus is assumed to vary in depth direction in the manner of a power function or an exponential function. It was demonstrated that appropriate gradual variation of the elastic modulus could significantly alter the stresses around the indenter and lead to suppression of Hertzian cracking at the edge of the contact region. Suresh et al. [8], Jorgensen et al. [9] and Krumova et al. [10] also presented the theoretical and experimental investigations of indentation testing methods to characterize the local properties of FGMs such as the elastic modulus, yield strength, strain hardening exponent, hardness and fracture toughness. Giannakopoulos and Pallot [11] presented the closed form analytical solutions for two-dimension sliding contact of rigid cylinders on elastic substrates which have elastic modulus varying with a power function. Edrogan and his coworkers [12,13] have developed a model where the material properties vary as exponential functions and solve the sliding contact and coupled crack/contact problems of functionally graded coatings.

It should be noted that all those models of FGMs mentioned above assume the power function [14] or exponential function …… 此处隐藏：26155字，全部文档内容请下载后查看。喜欢就下载吧 ……