粗糙面在梯度表面层上滑动接触的应力分布

对粗糙面在梯度表面层上的滑动过程进行应力分布研究,以模拟实际摩擦过程中,考虑塑性变形情况下,梯度覆层体中的应力分布规律,同时与均质体及单覆层体进行比较研究,分析了在表面载荷相同时滑动接触的应力分布。结果表明覆层体出现塑性变形后,在接触表面上的压力分布与弹性变形时有很大变化,在界面处梯度层的应力分布比单层膜更为理想,其应变梯度也较小;受相同表面载荷作用下产生塑性变形时,梯度层膜在基体产生塑性变形较小     

Non-axisymmetric thermal stress of a functionally graded coated circular inclusion in an infinite matrix

This paper is to study the non-axisymmetric two-dimensional problem of thermal stresses in an infinite matrix with a functionally graded coated circular inclusion based on complex variable method. With using the method of piece-wise homogeneous layers, the general solution for the functionally graded coating having radial arbitrary elastic properties is derived when the matrix is subjected to uniform heat flux at infinity, and then numerical results are presented for several special examples. It is found that the existence of the functionally graded coating can change interfacial thermal stresses, and choosing proper change ways of the radial elastic properties in the coating can obviously reduce the thermal stresses.     

An Improved Weighting Method for Inversely Determining Elastic Constants of Coating Layers from Dispersion Curves of Surface Acoustic Waves

This paper investigates the inversion of elastic constants of a coating layer from measured dispersion curves of a layered half-space sample. A systematic analysis on the sensitivity of dispersion curves is performed and the results provide important information in constructing a better inversion process. Numerical simulation has been given to demonstrate several possibilities for obtaining accurate elastic constants from the measured dispersion data over different frequency domains. Experiments have also been carried out using broadband Poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] focusing transducers and their surface wave measurement system over a wide frequency range of 4?~?120 MHz. Nickel coating layers electroplated on thick glass substrates are tested for the inversion. It is observed that the proposed inversion method, which carefully chooses the dispersion data at specific frequency ranges as well as adding some weightings to them, is indeed significantly improve the accuracy and convergence of the obtained elastic constants of the coated nickel layers. Young’s modulus of the coated nickel layers is also measured by a nano-indentation system and the results show good agreement with the data determined by the proposed inversion method.     

Effect of friction on subsurface stresses in sliding line contact of multilayered elastic solids

A numerical integral scheme based on Fourier transformation approach is employed to investigate the effect of friction on subsurface stresses arising from the two-dimensional sliding contact of two multilayered elastic solids. The analysis incorporates bonded and unbonded interface boundary conditions between the coating layers. Two line contact problems are presented. The first one is the contact problem between a rigid cylinder and a two-layer half space and the second one is the indentation of a multilayered elastic half-space by a flat rigid punch. The effects of the surface coating on the contact pressure distribution and subsurface stress field are presented and discussed.     

平头压痕试验确定热障涂层弹性模量的方法研究

本文模拟了典型热障涂层(TBC)结构在平头压痕作用下的力学响应,重点研究利用平头压痕法确定TBC涂层弹性模量的方法。研究发现k(单位压入应力下压头的压入位移)不仅与材料的性质有关,还与压头的半径有关。本文提出:通过两个不同尺寸的平压头可以同时确定陶瓷层和粘结层的弹性模量。     

一维六方准晶弹性层合悬臂梁的解析解

本文利用一维六方准晶的平面本构关系,以及简化为平面问题的物理方程,在悬臂梁的弹性应力解的基础上,假设准晶层和弹性层的应力分布,求出了各自的位移表达式,再利用层间连续条件和放松的边界条件,推导出一维六方准晶层合悬臂梁仅在自由端受集中力作用下声子场和相位子场的位移解析解,为研究准晶涂层材料的力学性质提供参考。     

Free-edge stresses and progressive cracking in surface coatings of circular torsion bars

This paper considers the explicit solutions of free-edge stresses near circumferential cracks in surface coatings of circular torsion bars and their application in determining the progressive cracking density in the coating layers. The problem was formulated within the framework of linear elastic fracture mechanics (LEFM). The free-edge stresses near crack tip and the shear stresses in the cross-section of the torsion bar were approached in explicit forms based on the variational principle of complementary strain energy. Criterion for progressive cracking in the coating layer was established in sense of strain energy conservation, and the crack density is thereby estimated. Effects of external torque, aspect ratio, and elastic properties on the density of progressive cracking were examined numerically. The present study shows that, in the sense of inducing a given crack density, compliant coating layer with lower modulus has much higher critical torque than that of a stiffer one with the same geometries and substrate material, i.e., compliant coating layer has greater cracking tolerance. Meanwhile, the study also indicates that thicker surface coating layer is more pliant to cracking than the thinner ones. The present model can be used for analyzing the damage mechanism and cracking tolerance of surface coatings of torsion shafts and for data reduction of torsional fracture test of brittle surface coatings, etc.     

Frictionless contact of two parallel congruent rigid cylindrical surfaces coated with thin elastic transversely isotropic incompressible layers: an analytic solution

The paper deals with a frictionless contact problem of two parallel rigid cylindrical surfaces, one encased in the other, coated with thin elastic transversely isotropic and incompressible layers. The coatings of the two circular cylinders may differ. A simplifying approximation for the displacement in the coating enables the problem to be formulated using stress and strain averaged through the coating thickness (for the method, see [Matthewson, M.J., 1981. Axi-symmetric contact on thin compliant coatings. J. Mech. Phys. Solids 29, 89–113]). Analytical results are obtained for the contact width and contact stress distribution. Given this contact stress distribution, an asymptotic analytical solution for the displacement in the coating is then obtained. The results are applied to the human ankle joint and generalized for articular cartilage with depth-dependent properties.     

Approximate dynamic boundary conditions for a thin piezoelectric layer

Approximate dynamic boundary conditions of different orders are derived for the case of a thin piezoelectric coating layer bonded to an elastic material. The approximate boundary conditions are derived using series expansions of the elastic displacements and the electric potential in the thickness coordinate of the layer. All the expansion functions are then eliminated with the aid of the equations of motion and boundary/interface conditions of the layer. This results in boundary conditions on the elastic material that may be truncated to different orders in the thickness of the layer to obtain approximate boundary conditions. The approximate boundary conditions may be used as a replacement for the piezoelectric layer and thus simplify the analysis significantly. Numerical examples show that the approximate boundary conditions give good results for low frequencies and/or thin piezoelectric layers.     

The Effect of Elastic Surface Coating on the Finite Deformation and Bifurcation of a Pressurized Circular Annulus

A plane-strain theory of an elastic solid coated with a thin elastic film on part or all of its boundary was developed recently by Steigmann and Ogden (1997a). In this paper the theory is applied to the (plane-strain) problem of a thick-walled circular cylindrical tube which is subject to both internal and external pressure and which has an elastic coating on one or both of its circular cylindrical boundaries. The effect of the coating on the symmetrical response of the annular cross-section of the tube is determined first. It is noted, in particular, that while the pressure may exhibit a maximum followed by a minimum during inflation for an uncoated tube it may be a monotonic increasing function of the radius for a coated tube with coating elastic modulus sufficiently large. Next, the possibility of bifurcation from a symmetrical configuration is examined and again the influence of the coating is analysed. The effect of a coating on the outer boundary is compared with that on the inner boundary. Specifically, during compression, coating on the outer boundary delays bifurcation compared with the uncoated case. On the other hand, when the coating is on the inner boundary, bifurcation is either delayed or advanced relative to the uncoated situation depending on the values of the bending stiffness and tube thickness parameters. Generally, bifurcation is delayed by an increase in the magnitude of the bending stiffness of the coating at fixed values of the other parameters. This revised version was published online in August 2006 with corrections to the Cover Date.     

Tilting analysis of circular elastic layers interleaving with flexible reinforcements

Bonding with reinforcements can increase the stiffness of elastic layers in the normal direction. The flexibility effect of the reinforcement on the bonded elastic layers of a circular cross-section subjected to pure bending moment is analyzed through a theoretical approach. Based on two kinematics assumptions in the elastic layers, the closed-form solutions of the horizontal displacements in the elastic layers and the reinforcements are solved using the governing equations established by stress equilibrium in the elastic layers and the reinforcements. Through these solved displacements, the tilting stiffness of the bonded elastic layer, the shear stress on the bonding surfaces, and the internal forces of the reinforcements are derived in closed forms.     

热障涂层弹性模量和残余应力测试研究

采用数字图像相关法实验研究了热喷涂制作的热障涂层的弹性模量和残余应力。首先,采用三点弯测试方法对热障涂层试件进行加载,并利用二维数字图像相关方法对热障涂层试件加装过程中的弯曲变形进行了精确的测量,进而获得了热障涂层在受拉和受压两种状态下的弹性模量,结果表明,受拉时热障涂层试件陶瓷层的弹性模量为31GPa,而受压时其弹性模量为34GPa。其次,基于内力平衡,推导了考虑曲率变化的涂层残余应力计算公式;利用三维数字图像相关法测量了喷涂前后基体曲率的变化,进而获得了涂层残余应力的大小,结果表明,热喷涂后的热障涂层残余应力为压应力,大小为-86^-70MPa。     

Surface Forces Driven Wrinkling of an Elastic Half-Space Coated with a Thin Stiff Surface Layer

This paper studies surface instability of a coated semi-infinite linear elastic body interacting with another flat rigid body through surface van der Waals (vdW) forces under plane strain conditions. The emphasis is on the effect of the surface coating layer on the wavelength of surface wrinkling. It is shown that the surface of the coated elastic half-plane is always unstable even in the presence of a very stiff coating layer. However, the numerical results show that the stiff coating layer has a significant effect on the wavelength of the surface instability mode and can effectively prevent the surface from short-wavelength wrinkling. In particular, the surface tangential displacement associated with the surface instability vanishes when the elastic half-plane is incompressible. In this case, the in-plane rigidity of the coating layer has no effect on surface instability while the bending stiffness of the coating layer has an effect on the wave-length of the surface instability mode. Furthermore, the Poisson’s ratio of elastic half-plane has a significant role in the surface instability and the associated wave-length. C. Q. Ru is on leave from the University of Alberta, Edmonton, T6G. 2G8, Canada.     

Modeling the contact wear fracture of a two-layer basement

We develop a method for calculating the kinetics of fatigue fracture of a two-layer elastic basement by a periodic system of indenters sliding on the surface and modeling the surface microroughness. The method is based on solving the contact problem for a periodic system of indenters and a two-layer elastic basement, determining the internal stresses with friction forces taken into account, and constructing the damage function in the two-layer basement. We calculate the kinetics of the fatigue fracture of the surface layer (the coating) and find the characteristics of the process depending on the strength and mechanical properties of the coating and basement materials, the loading and geometric characteristics of the system, and the friction coefficient.     

CRACK PROPAGATING IN FUNCTIONALLY GRADED COATING WITH ARBITRARILY DISTRIBUTED MATERIAL PROPERTIES BONDED TO HOMOGENEOUS SUBSTRATE

In this paper, a finite crack with constant length （Yoffe type crack） propagating in a functionally graded coating with spatially varying elastic properties bonded to a homogeneous substrate of finite thickness under anti-plane loading was studied. A multi-layered model is employed to model arbitrary variations of material properties based on two linearly-distributed material compliance parameters. The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. Some numerical examples are given to demonstrate the accuracy, efficiency and versatility of the model. The numerical results show that the graded parameters, the thicknesses of the interfacial layer and the two homogeneous layers, the crack size and speed have significant effects on the dynamic fracture behavior.     

Multiple cracking of elastic coatings under transient thermal load

A periodic array of cracks in an elastic coating bonded to a homogeneous substrate is considered. The medium is subjected to mechanical loads and/or thermal loads. The problem is formulated in terms of a singular integral equation with the crack face displacement as the unknown variable. In addition to the time-varying stress intensity factors and stresses for various parameters of the problem, the effect of periodic cracking on the relaxation of the transient stress on the coating surface is discussed. Solution techniques for a single elastic layer and an elastic coating bonded to an infinite substrate are given. It is found that, if the crack density attains a saturation value, the transient thermal stress in the medium could be released significantly, suggesting that further cracking is difficult.     

Contact problems on soft and rigid coatings of an elastic half-plane

The solutions of contact problems on a soft or rigid coating of an elastic half-plane are of great practical interest. Accordingly, the present paper is divided into two parts: in the first part, we consider the problem of interaction between a rigid biquadratic die and an elastic half-plane through a thin soft coating; in the second part, we consider the problem of interaction between a rigid plane die and an elastic half-plane through a thin rigid coating. We derive integral equations for the problems under study and construct their approximate solutions by a regular asymptotic method. Earlier, the question of studying such problems was posed, for example, in [1–3]. Here we use these results to a large extent.     

圆柱基体热障涂层制备工艺中的残余应力分析

由于基体和热障涂层各层材料的热膨胀系数不同,在温度变化时各部分变形大小也不同,从而导致涂层内部产生残余应力。本文利用过盈配合模型求解圆柱形基体上热障涂层的残余应力,计算了涂层的厚度、弹性模量和热膨胀系数对残余应力的影响,并从应力角度探讨热障涂层的剥落失效。     

Cracking in thin multi-layers with finite-width and periodic architectures

Many applications involve thin multi-layers comprised of repeating patterns of different material sections, notably interconnect–dielectric structures in microelectronics. This paper considers a variety of failure scenarios in systems with periodically arranged features within a single layer. Crack driving forces are presented for (i) debonding between alternating material sections in a thin film (i.e. channel and tunnel cracking at material junctions), and (ii) channel cracking in a thin uniform coating above a layer comprised of alternating sections of different materials. The effects of elastic mismatch, feature spacing, crack spacing and residual stress are illustrated for a wide range of parameters. The results presented here illustrate that residual stresses in intact sections can strongly promote cracking in adjacent layers, which is in contrast to analyses of blanket film multi-layers which predict that residual stress in adjacent layers has no effect. An important finding is that decreasing the relative size of low-modulus sections significantly increases the crack driving force in adjacent layers. The implications of these results are discussed in the contexts of critical feature spacing and the impact of incorporating low elastic-modulus sections (such as polymer dielectrics) on thermo-mechanical reliability.     

The torsion problem of a multilayered finite cylinder with the multiple interface cylindrical cracks

The torsion axisymmetric problem for a finite cylinder consisting of an arbitrary quantity of cylindrical coaxial layers is solved. Multiple cylindrical cracks with free of loading branches are situated on adjoining surfaces of the layers. The boundary problem is reduced to the system of integro-differential equations, its solution is found with the help of the orthogonal polynomials method. The novelty of the paper is in the construction of a solution for an arbitrary number of cylinder layers which allows the approximation of the initial problem for functionally graded materials by the problem for coaxial cylinders with jumplike changing elastic constants of the materials. Since the solution is built regardless of the number of layers (the elastic parameters of all layers are included in the constructed solution), one can refine an initial problem’s statement by increasing the number of layers. The stress intensity factors are found for an arbitrary number of cylindrical interface cracks in the multilayered cylinder of a finite length.