顶端受集中力偶的双材料平面界面接合楔体的对数奇异应力场

应用复变函数方法,通过构造复函数形式的特解序列,从理论上研究了顶端受集中力偶的双材料平面界面接合楔体的应力场,给出了相应的经典解,发现其存在一次和二次佯谬,相应的应力具有(Inr)／r2和(In2r)／r2的奇异性。     

Singular stress field near the edge of interface of bonded dissimilar materials with an interlayer

For bonded dissimilar materials, the free-edge stress singularity usually prevails near the intersection of the free-surface and the interface. When two materials are bonded by using an adhesive, an interlayer develops between the two bonded materials. When a ceramic and a metal are bonded, the residual stress develops because of difference in the coefficient of thermal expansion. An interlayer may be inserted between the two materials to defuse the residual stress. Stress field near the intersection of the interface and free-surface in the presence of the interlayer is then very important for evaluating the strength of bonded dissimilar materials.In this study, stress distributions on the interface of bonded dissimilar materials with an interlayer were calculated by using the boundary element method to investigate the effect of the interlayer on the stress distribution. The relation between the free-edge singular stress fields of bonded dissimilar materials with and without an interlayer was investigated numerically. It was found that the influence of the interlayer on the stress distributions was confined within a small area of the order of interlayer thickness around the intersection of the interface and the free-surface when the interlayer was very thin. The stress distribution near the intersection of the interface and the free-surface was controlled by the free-edge stress singularity of the bonded dissimilar materials without the interlayer. In this case, the interlayer can be called free-edge singularity-controlled interlayer. If a stress distribution on the interface is known for one thickness of an interlayer h, stress distributions on the interface for other values of h can be estimated.     

Paradox solution on elastic wedge dissimilar materials

According to the Hellinger-Reissner variational principle and introducing proper transformation of variables , the problem on elastic wedge dissimilar materials can be led to Hamiltonian system, so the solution of the problem can be got by employing the separation of variables method and symplectic eigenfunction expansion under symplectic space, which consists of original variables and their dual variables . The eigenvalue - 1 is a special one of all symplectic eigenvalue for Hamiltonian system in polar coordinate . In general, the eigenvalue - 1 is a single eigenvalue, and the classical solution of an elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is got directly by solving the eigenfunction vector for eigenvalue - 1. But the eigenvalue - 1 becomes a double eigenvalue when the vertex angles and modulus of the materials satisfy certain definite relationships and the classical solution for the stress distribution becomes infinite at this moment, that is, the para     

Problems on collinear cracks between bonded dissimilar materials under concentrated loads

Following Ref. [6], this paper deals with the problem on collinear cracks between bonded dissimilar materials under a concentrated force and moment at an arbitrary point. Several typical solutions of complex stress functions in closed form are formulated and the stress intensity factors are given. These solutions include a series of results of previous researchers, and redress some errors in the researches of problems containing semi-infinite cracks^[3],[4].     

Residual stress analysis of joints of ceramics and metals

Development of reliable bonding techniques for ceramics and metals is considered to be very important for more useful applications of ceramics to machinery parts. However, a high thermal stress concentration occurs at the corner of bonded interface in ceramics during the bonding process. This occurs because of the difference in thermal properties of the bond materials and reduces the strength of the bonded joint considerably.The authors have been investigating various methods for effectively decreasing this stress concentration. In this paper, they present theoretical and experimental evidence that the stress concentration can be successfully diminished by varying the apex angle of joints. It is found that the tensile strength of joints increases as the apex angle of metals decreases from 90 deg to 45 deg. It also increases with increasing the apex angle of metals. Numerical calculations confirm these experimental results and the proposed procedure may be useful in the design and manufacture dissimilar joints.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

Problems of collinear cracks between bonded dissimilar materials under antiplane concentrated forces

In this paper problems of cullinear cracks between bonded dissimilar materials underantiplane concentrated forces are dealt with.General solutions of the problems areformulated by applying extended Schwarz principle integrated with the analysis of thesingularity of complex stress functions.Closed-form solutions of several typical problemsare obtained and the stress intensity factors are given.These solutions include a series oforiginal results and some results of previous researches.It is found that under symmetricalloads the solutions for the dissimilar materials are the same as those for the homogeneousmaterials.     

直角结合异材界面端应力强度系数的经验公式

由不同材料结合而成的材料(简称异材或双材料)的力学性能及其可靠性评价是工程中亟待解决的问题。表征界面端奇异应力场大小的应力强度系数是结合异材强度评价的依据，本文针对工程中最常见的直角结合异材，通过对大量不同材料组合的异材的边界元数值分析，提出了界面端应力强度系数的近似计算公式，无量纲化后的应力强度系数的值只与异材Dundurs参数a，卢有关，该公式具有较高的精度，可以作为一般工程上的应力强度系数的计算以及异材结构设计的依据。     

The curved bar subjected to an arbitrarily distributed loading: Another paradox in the two-dimensional theory of elasticity

The problem of the curved bar subjected to an arbitrarily distributed loading on the surfacesr=a andr=b is solved by using the method of complex functions and expanding the boundary conditions atr=a andr=b into Fourier series. Then another paradox in the two-dimensional theory of elasticity is discovered, i. e., the classical solution becomes infinite when the curved bar is subjected to a uniform loading or when the angle included between the two ends of the curved bar 2 is equal to 2 and the curved bar is subjected to a sine or cosine loading. In this paper the paradox is resolved successfully and the solutions for the paradox are obtained. Moreover, the modified classical solution which remains bounded as 2 approaches 2 is provided.     

接合残余应力在界面端的应力奇异性

接合残余应力对异种接合材料强度的影响很大，正确地分析接合残余应力在界面端附近的分布及其奇异特性，是研究异材强度评价方法的关键问题之一，本文利用弹性学中的Ｇｏｕｒｓａｔ公式和有关微分方程解的理论，求得了平面近似下的界面端附近的残余应力场及其应力奇异性，与单纯的外力作用时的情况不同，残余应力在界面端有可能出现对数型的应力奇异性，并且不能仅用Ｄｕｎｄｅｒｓ的异材参数来描述。     

与界面相交的裂纹尖端的应力奇异性分析

为了确定与结合材料的界面相交的裂纹尖端附近的应力奇异性次数，提出了一种基于最小势能原理的一维特殊有限元法，以奇异点为原点半径r0的扇形奇异区域，可以简化为一维线性领域，即一条以代表结合材料的两个自由表面为端点的线段。对该一维线性领域作网格划分，采用三节点一维等参数二次单元。数值计算结果与已有理论解的比较表明，该方法具有很高的精度和效率，最后，利用文中给出的方法，得到了各向异性结合材料中与界面以任意角相交的裂纹尖端的奇异性次数随裂纹的变化规律。     

极坐标哈密顿体系约当型与弹性楔的佯谬解

讨论了极坐标弹性平面哈密顿体系的当型,并通过约当型的求解,直接给出了相关弹性楔体佯谬问题的解,从理论上阐明了经典弹性力学中某些佯谬问题的出现是由于其对应的是哈密顿体系中特殊的约当型解,同时也很自然地为该类问题提供了一个通用,有效的求解方法。     

Problems on circular-arc cracks between dissimilar materials under antiplane concentrated forces

This paper deals with the problems of circular-arc crack between bonded dissimilar materials under antiplane concentrated forces. By applying the analytic continuation technique and the analyzing method of the Singularity in complex functions, we obtain universal solutions for the problems. For several typical cases the closed form solutions are obtained and the stress intensity factors are devived From these solutions, we provide a series of particular results, some of which coincide with those in Ref.(7).     

The wedge subjected to general tractions: A paradox resolved

A wedge subjected to tractions in proportion tor ⁿ (n≥0), is considered. The stresses in the solutions of the classical theory of elasticity become infinite when the angle of the wedge is ρ or 2ρ. The paradox has been resolved by Dempsey^[4] and T.C.T. Ting^[5] whenn=0. The purpose of this paper is to resolve the paradox whenn>0.     

A unified definition for stress intensity factors of interface corners and cracks

Based upon linear fracture mechanics, it is well known that the singular order of stresses near the crack tip in homogeneous materials is a constant value −1/2, which is nothing to do with the material properties. For the interface cracks between two dissimilar materials, the near tip stresses are oscillatory due to the order of singularity being −1/2 ± iε and −1/2. The oscillation index ε is a constant related to the elastic properties of both materials. While for the general interface corners, their singular orders depend on the corner angle as well as the elastic properties of the materials. Owing to the difference of the singular orders of homogeneous cracks, interface cracks and interface corners, their associated stress intensity factors are usually defined separately and even not compatibly. Since homogenous cracks and interface cracks are just special cases of interface corners, in order to build a direct connection among them a unified definition for their stress intensity factors is proposed in this paper. Based upon the analytical solutions obtained previously for the multibonded anisotropic wedges, the near tip solutions for the general interface corners have been divided into five different categories depending on whether the singular order is distinct or repeated, real or complex. To provide a stable and efficient computing approach for the general mixed-mode stress intensity factors, the path-independent H-integral based on reciprocal theorem of Betti and Rayleigh is established in this paper. The complementary solutions needed for calculation of H-integral are also provided in this paper. To illustrate our results, several different kinds of examples are shown such as cracks in homogenous isotropic or anisotropic materials, central or edge notches in isotropic materials, interface cracks and interface corners between two dissimilar materials.     

Effects of interfacial friction on flaw tolerant adhesion between two dissimilar elastic solids

Flaw tolerance refers to a state in which a pre-existing crack-like flaw does not propagate even as the material is stretched to failure near its theoretical strength. Such an optimal scenario can be achieved when the characteristic length scale is reduced to below a critical value. So far, the critical conditions to achieve flaw tolerance have been discussed mostly for homogeneous materials or for two dissimilar materials in frictionless or perfectly bonded adhesion. In this paper, we consider the role of friction in flaw tolerant adhesion between two dissimilar elastic solids. We adopt a frictional contact model in which slip is allowed wherever the shear stress along the interface reaches a threshold value defined as the friction strength. The critical length scale for flaw tolerance is derived analytically for a penny-shaped crack and for an external circular crack. Compared to the cases of frictionless contact, we find that interfacial friction can reduce the critical length scales for flaw tolerance by up to 12.5%.     

圆形界面裂纹反平面问题的基本奇异解

本文研究反平面集中力作用下,不同弹性材料的圆形界面上有多条裂纹的问题。运用复变函数的解析延拓技术与奇性主部分析方法,首次获得该问题的一般解答,求出了几种典型情况的封闭解;算出了应力强度因子,并由此导出一系列特殊结果,其中几个与已有文献完全吻合。     

Mode III stress intensity factors in an interfacial crack in dissimilar bonded materials

The antiplane shear deformation problem of two edge-bonded dissimilar isotropic wedges is considered. In the case when the sum of the two apex angles is equal to 2π, the problem reduces to that of two edge-bonded dissimilar materials with an interfacial crack subjected to concentrated antiplane shear tractions on the crack faces. An explicit expression is extracted for the stress intensity factor at the crack tip. In the special cases of different combinations of the apex angles, the obtained expression for the stress intensity factor may be simplified and relations of a simpler form are given for the stress intensity factor. It is shown that the stress intensity factor is dependent on the material properties as well as the geometry and loading. However, in special cases of equal apex angles as well as the case of similar materials the dependency of the stress intensity factor on the material properties disappears.     

The accuracy of some formulae for the interconversion of creep and stress-relaxation data

The accuracy of the approximation formulaeJ (t) ~ 1/G (t) andd lnJ (t)/d lnt ~ —d lnG (t)/d lnt, which interconnect stress-relaxation modulusG (t) and creep complianceJ (t) and their double logarithmic rates are investigated. For glassy polymers, the errors in the first formula are less than 1–2%, and in the second, they are generally in the order of a few percent, too. Similar estimates can also be found for the real parts of the analogous complex functionsJ ^* () andG ^* ().     

Mechanics of crack propagation in materials with initial (residual) stresses (review)

Major results on the mechanics of crack propagation in materials with initial (residual) stresses are analyzed. The case of straight cracks of constant width that propagate at a constant speed in a material with initial (residual) stresses acting along the cracks is examined. The results were obtained, based on linearized solid mechanics, in a universal form for isotropic and orthotropic, compressible and incompressible elastic materials with an arbitrary elastic potential in the cases of finite (large) and small initial strains. The stresses and displacements in the linearized theory are expressed in terms of analytical functions of complex variables when solving dynamic plane and antiplane problems. These complex variables depend on the crack propagation rate and the material properties. The exact solutions analyzed were obtained for growing (mode I, II, III) cracks and the case of wedging by using methods of complex variable theory, such as Riemann–Hilbert problem methods and the Keldysh–Sedov formula. As the initial (residual) stresses tend to zero, these exact solutions of linearized solid mechanics transform into the respective exact solutions of classical linear solid mechanics based on the Muskhelishvili, Lekhnitskii, and Galin complex representations. New mechanical effects in the dynamic problems under consideration are analyzed. The influence of initial (residual) stresses and crack propagation rate is established. In addition, the following two related problems are briefly analyzed within the framework of linearized solid mechanics: growing cracks at the interface of two materials with initial (residual) stresses and brittle fracture under compression along cracks     

On the influence of low initial pressure and detonation stochastic nature on Mach reflection of gaseous detonation waves

The two-dimensional, time-dependent and reactive Navier–Stokes equations were solved to obtain an insight into Mach reflection of gaseous detonation in a stoichiometric hydrogen-oxygen mixture diluted by 25 % argon. This mixture generates a mode-7 detonation wave under an initial pressure of 8.00 kPa. Chemical kinetics was simulated by an eight-species, forty-eight-reaction mechanism. It was found that a Mach reflection mode always occurs for a planar detonation wave or planar air shock wave sweeping over wedges with apex angles ranging from \(5^\circ \) to \(50^\circ \) . However, for cellular detonation waves, regular reflection always occurs first, which then transforms into Mach reflection. This phenomenon is more evident for detonations ignited under low initial pressure. Low initial pressure may lead to a curved wave front, that determines the reflection mode. The stochastic nature of boundary shape and transition distance, during deflagration-to-detonation transition, leads to relative disorder of detonation cell location and cell shape. Consequently, when a detonation wave hits the wedge apex, there appears a stochastic variation of triple point origin and variation of the angle between the triple point trajectory and the wedge surface. As the wedge apex angle increases, the distance between the triple point trajectory origin and the wedge apex increases, and the angle between the triple point trajectory and the wedge surface decreases exponentially.