Analytical elasto-creep model of interfacial thermal stresses and strains in trilayer assemblies

A two-dimensional model has been developed for thermal stresses, elastic strains, creep strains, and creep energy density at the interfaces of short and long trilayer assemblies under both plane stress and plane strain conditions. Both linear (viscous) and non-linear creep constitutive behavior under static and cyclic thermal loading can be modeled for all layers. Interfacial stresses and strains are approximated using a combination of exact elasticity solutions and elementary strength of materials theories. Partial differential equations are linearized through a simple finite difference discretization procedure. The approach is mathematically straightforward and can be extended to include plastic behavior and problems involving external loads and a variety of geometries. The model can provide input data for thermal fatigue life prediction in solder or adhesive joints. For a typical solder joint, it is demonstrated that the predicted cyclic stress–strain hysteresis shows shakedown and a rapid stabilization of the creep energy dissipation per cycle in agreement with the predictions of finite element analysis.     

Elastic compensation simulation of elastic/plastic axisymmetric circular plate bending using a deformation model

A deformation plasticity model is used to implement the elastic compensation (iterative use of linearly elastic models to approximate elastic/plastic response) simulation of small axisymmetric circular plate deformations by the finite element method. Representative numerical results are presented graphically and used to demonstrate the utility of the approach.     

Analytical modelling of thermal stresses in anisotropic composites

This paper represents a continuation of the author's previous work which deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid elastic continuum. This continuum consists of anisotropic spherical particles which are periodically distributed in an anisotropic infinite matrix. The infinite matrix is imaginarily divided into identical cubic cells with central particles. This multi-particle–matrix system represents a model system which is applicable to two-component materials of the precipitate–matrix type. The thermal stresses, which originate due to different thermal expansion coefficients of components of the model system, are determined within the cubic cell. The analytical modelling results from fundamental equations of continuum mechanics for solid elastic continuum (Cauchy's, compatibility and equilibrium equations, Hooke's law). This paper presents suitable mathematical procedures which are applied to the fundamental equations. These mathematical procedures lead to such final formulae for the thermal stresses which are relatively simple in comparison with the final formulae presented in the author's previous work which are extremely extensive. Using these new final formulae, the numerical determination of the thermal stresses in real two-component materials with anisotropic components is not time-consuming.     

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.     

A new analytical model for thermal stresses in multi-phase materials and lifetime prediction methods

Based on the fundamental equations of the mechanics of solid continuum, the paper employs an analytical model for determination of elastic thermal stresses in isotropic continuum represented by periodically distributed spherical particles with different distributions in an infinite matrix, imaginarily divided into identical cells with dimensions equal to inter-particle distances, containing a central spherical particle with or without a spherical envelope on the particle surface. Consequently, the multi-particle-（envelope）- matrix system, as a model system regarding the analytical modelling, is applicable to four types of multi-phase materials. As functions of the particle volume fraction v, the inter-particle distances dl, d2, d3 along three mutually per- pendicular axes, and the particle and envelope radii, R1 and R2, respectively, the thermal stresses within the cell, are originated during a cooling process as a consequence of the difference in thermal expansion coefficients of phases rep- resented by the matrix, envelope and particle. Analytical-（experimental）-computational lifetime prediction methods for multi-phase materials are proposed, which can be used in engineering with appropriate values of parameters of real multi-phase materials.     

Elastic stresses in a half-plane with a periodic system of exogeneous circular inclusions located along the boundary of the half-plane

Podol'sk Engineering Institute. Translated from Prikladnaya Mekhanika, Vol. 27, No. 6, pp. 59–64, June, 1991.     

Thermal stresses and shakedown in wheel/rail contact

Summary  Sliding friction between railway wheels and rails results in considerable contact temperatures and gives rise to severe thermal stresses at the surfaces of the wheels and rails. An approximate analytical solution is presented for a line contact model. The increased bulk temperature of the wheel after a long period of constant operating conditions is also taken into account. The thermal stresses have to be superimposed on the mechanical contact stresses. They reduce the elastic limit of the wheel and rail, and yielding begins at lower mechanical loads. When residual stresses build up during the initial cycles of plastic deformation, the structure can carry higher loads with a purely elastic response in subsequent load cycles. This phenomenon is referred to as shakedown. Due to the distribution of temperature, the rail surface is generally subjected to higher stresses than the wheel surface. This can cause structural changes in the rail material and hence rail damage. Received 7 May 2002; accepted for publication 3 September 2002     

Acoustic emission assessment of interface cracking in thermal barrier coatings

In this paper, acoustic emission (AE) and digital image correlation methods were applied to monitor interface cracking in thermal barrier coatings under compression. The interface failure process can be identified via its AE features, including buckling, delamination incubation and spallation. According to the Fourier transformation of AE signals, there are four different failure modes: surface vertical cracks, opening and sliding interface cracks, and substrate deformation. The characteristic frequency of AE signals from surface vertical cracks is 0.21 MHz, whilst that of the two types of interface cracks are 0.43 and 0.29 MHz, respectively. The energy released of the two types of interface cracks are 0.43 and 0.29 MHz, respectively. Based on the energy released from cracking and the AE signals, a relationship is established between the interface crack length and AE parameters, which is in good agreement with experimental results.     

Stress distribution around a circular cylindrical cavity in a prestressed plate

A system of equilibrium equations for nonthin transversely isotropic plates with a uniform prestress field is derived by expanding the unknown functions into Fourier-Legendre series. A method of finding the general solution of this system is expounded and used to determine the stress state of a plate with a circular cylindrical cavity __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 28–39, January 2008.     

Residual stresses in thin film systems: Effects of lattice mismatch,thermal mismatch and interface dislocations

This paper explores the mechanisms of the residual stress generation in thin film systems with large lattice mismatch strain, aiming to underpin the key mechanism for the observed variation of residual stress with the film thickness. Thermal mismatch, lattice mismatch and interface misfit dislocations caused by the disparity of the material layers were investigated in detail. The study revealed that the thickness-dependence of the residual stresses found in experiments cannot be elucidated by thermal mismatch, lattice mismatch, or their coupled effect. Instead, the interface misfit dislocations play the key role, leading to the variation of residual stresses in the films of thickness ranging from 100 nm to 500 nm. The agreement between the theoretical analysis and experimental results indicates that the effect of misfit dislocation is far-reaching and that the elastic analysis of dislocation, resolved by the finite element method, is sensible in predicting the residual stress distribution. It was quantitatively confirmed that dislocation density has a significant effect on the overall film stresses, but dislocation distribution has a negligible influence. Since the lattice mismatch strain varies with temperature, it was finally confirmed that the critical dislocation density that leads to the measured residual stress variation with film thickness should be determined from the lattice mismatch strain at the deposition temperature.     

Elastic wave scattering and dynamic stress concentrations in exponential graded materials with two elliptic holes

Based on the elastodynamics, employing complex functions and conformal mapping methods, and local coordinates, the scattering of elastic waves and dynamic stress concentrations in infinite exponential graded materials with two holes are investigated. A general solution of the problem and expression satisfying the given boundary conditions are derived. The problem can be reduced to the solution of an infinite system of algebraic equations. As an example, numerical results of dynamic stress concentration factors for two elliptic holes in exponential graded materials are presented, and the influence of incident wave number and holes spacing on dynamic stress distributions is analyzed.     

含圆形嵌体弹性平面中径向裂纹问题的超奇异积分方程方法

根据含圆形嵌体平面问题在极坐标下的弹性力学基本解,使用Betti互换定理,在有限部积分意义下将问题归结为两个以裂纹岸位移间断为基本未知量、对于Ⅰ型和Ⅱ型问题相互独立的超奇异积分方程,对含圆形嵌体弹性平面中的径向裂纹问题进行了研究.根据有限部积分原理,建立了问题的数值算法.计算结果表明,嵌体半径、裂纹位置及材料剪切弹性模量等都对裂纹应力强度因子具有较为明显的影响.     

含两个圆孔的正交异性板孔口补强应力分析

应用数学弹性力学和Ｆａｂｅｒ级数展开的方法，对于含有两个圆孔，且孔周各补强一弹性加强环的正交异性板，给出了其在无限远处均布的外力作用下，环及板内的应力场解；其特例与前人结果一致。     

复合材料层合板在加工固化后期降温速率对残余热应力的影响

本文采用非线性有限元方法，对材料性质与温度有关的复合材料层合板在加工固化后期降温过程中的温度速场和热应力场进行了分析，对降温度速率对板中固化残余热应力的影响进行了研究，获得一些对层合板固化成型工艺和固化残余热应力分析模型的选取均有意义的结果。     

两个相等圆孔板弯曲时的三维应力集中

根据Hellinger-Reissner原理建立了具有一个无外力圆柱表面的三维八节点杂交应力元,其假设应力场严格满足柱坐标下三维平衡方程及圆柱面上无外力边界条件;当元退化为二维时也满足协调方程。数值算例表明,这种特殊杂交应力元可高效地分析具有两个圆孔薄板和厚板的应力集中,特别是三维应力集中。     

Recursive geometric integrators for wave propagation in a functionally graded multilayered elastic medium

The differential equations governing transfer and stiffness matrices and acoustic impedance for a functionally graded generally anisotropic magneto-electro-elastic medium have been obtained. It is shown that the transfer matrix satisfies a linear 1st order matrix differential equation, while the stiffness matrix satisfies a nonlinear Riccati equation. For a thin nonhomogeneous layer, approximate solutions with different levels of accuracy have been formulated in the form of a transfer matrix using a geometrical integration in the form of a Magnus expansion. This integration method preserves qualitative features of the exact solution of the differential equation, in particular energy conservation. The wave propagation solution for a thick layer or a multilayered structure of inhomogeneous layers is obtained recursively from the thin layer solutions. Since the transfer matrix solution becomes computationally unstable with increase of frequency or layer thickness, we reformulate the solution in the form of a stable stiffness-matrix solution which is obtained from the relation of the stiffness matrices to the transfer matrices. Using an efficient recursive algorithm, the stiffness matrices of the thin nonhomogeneous layer are combined to obtain the total stiffness matrix for an arbitrary functionally graded multilayered system. It is shown that the round-off error for the stiffness-matrix recursive algorithm is higher than that for the transfer matrices. To optimize the recursive procedure, a computationally stable hybrid method is proposed which first starts the recursive computation with the transfer matrices and then, as the thickness increases, transits to the stiffness matrix recursive algorithm. Numerical results show this solution to be stable and efficient. As an application example, we calculate the surface wave velocity dispersion for a functionally graded coating on a semispace.     

Thermal fracture of a functionally graded/homogeneous bimaterial with system of cracks

The thermal fracture of a bimaterial consisting of a homogeneous material and a functionally graded material (FGM) with a system of internal cracks and an interface crack is investigated. The bimaterial is subjected to a heat flux. The thermal properties of FGM are assumed to be continues functions of the thickness coordinate, while the elastic properties are constants. The method of the solution is based on the singular integral equations. For a special case where the interface crack is much larger than the internal cracks in the FGM the asymptotic analytical solution of the problem is obtained as series in a small parameter (the ratio between sizes of the internal and interface crack) and the thermal stress intensity factors (TSIFs) are derived as functions of geometry of the problem and material characteristics. A parametric analysis of the effects of the location and orientation of the cracks and of the inhomogeneity parameter of FGM’s thermal conductivity on the TSIFs is performed. The results are applicable to such kinds FGMs as ceramic/ceramic FGMs, e.g., TiC/SiC, MoSi₂/Al₂O₃ and MoSi₂/SiC, and also some ceramic/metal FGMs.     

Investigation of stresses in he orthogonal cutting of fiber-reinforced plastics

A photoelastic study was conducted to examine the stress fields in the cutting process of fiber-reinforced plastics (FRPs). Force measurements were made and used in the analysis of the stress fields. Machined surfaces of workpieces with fibers oriented away from the cutting direction showed that the fibers were machined by shearing and tensile fracture; and when fibers were inclined towards the cutting tool, the fibers failed by shearing and bending. In addition, fiber-matrix debonding was observed to be maximum for fibers oriented at 45 deg towards the tool's path. Fiber orientation was shown to have an influence on the machining forces and stresses.Paper was presented at the 1994 SEM Spring Conference held in Baltimore, MD on June 6–9.     

Cylindrical interface crack in a hollow layered functionally graded cylinder under static torsion

A hollow functionally graded composite cylinder under static torsion, which consists of an inner and outer elastic circular tube with a cylindrical interface crack, is studied in this work. By utilizing Fourier integral transform method, the mixed boundary value problem is reduced to a Cauchy singular integral equation, from which the numerical results of the stress intensity factor are obtained by the Lobatto–Chebyshev quadrature technique. Numerical results demonstrate the coupled effects of geometrical, physical, and functionally graded parameters on the interfacial fracture behavior.