Dissimilar material joints with and without free-edge stress singularities: Part II. An integrated numerical analysis

Numerical investigations were conducted on plane and axisymmetric convex joints of polycarbonate—aluminum and poly(methyl methacrylate)—aluminum interfaces to gain a better understanding of the stress state along the interface and also to aid an experimental study conducted on the same issue. Two-dimensional plane—stress investigations of convex joints revealed the successful elimination of the free-edge stress singulatities along the specimen width although stress singularities, along the thickness direction, persisted. A convex axisymmetric design, with the same material combination and joining angles, proves to be a better design in order to achieve an overall elimination of free-edge stress singularities of dissimilar materials and structures.     

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.     

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.     

多材料交接点裂纹无摩擦奇性应力场

在文献「１」基础上，针对工程中难于求解的多材料交接点裂纹尖应力奇性分析问题，在于哈密顿原理，通过分离变量与共轭辛本征函数地求解，利用材料间的界面连接条件与坐标变换关系，建立了应力奇性与本征函数求解的解析表达式。由于采取裂纹面接触区模型，因而不再发生振荡奇异性。     

Analysis of bi-material interface cracks with complex weighting functions and non-standard quadrature

A boundary element formulation is developed to determine the complex stress intensity factors associated with cracks on the interface between dissimilar materials. This represents an extension of the methodology developed previously by the authors for determination of free-edge generalized stress intensity factors on bi-material interfaces, which employs displacements and weighted tractions as primary variables. However, in the present work, the characteristic oscillating stress singularity is addressed through the introduction of complex weighting functions for both displacements and tractions, along with corresponding non-standard numerical quadrature formulas. As a result, this boundary-only approach provides extremely accurate mesh-insensitive solutions for a range of two-dimensional interface crack problems. A number of computational examples are considered to assess the performance of the method in comparison with analytical solutions and previous work on the subject. As a final application, the method is applied to study the scaling behavior of epoxy–metal butt joints.     

Hertz contact at finite friction and arbitrary profiles

Axisymmetric contact at finite Coulomb friction and arbitrary profiles is examined analytically and numerically for dissimilar linear elastic solids. Invariance and generality are aimed at and an incremental procedure is developed resulting in a reduced benchmark problem corresponding to a rigid flat indentation of an elastic half-space. The reduced problem, being independent of loading and contact region, was solved by a finite element method based on a stationary contact contour and characterized by high accuracy. Subsequently, a tailored cumulative superposition procedure was developed to resolve the original problem to determine global and local field values. Save for the influence of the coefficients of friction and contraction ratio, it is shown that at partial slip the evolving relative stick-slip contour is independent of any convex and smooth contact profile at monotonic loading. For flat and conical profiles with rounded edges and apices, results are illustrated for relations between force, depth and contact contours together with surface stress distributions. The solution for dissimilar solids in a full space is transformed to a half-space problem and solved for a combination of material parameters in order to first determine interface traction distributions. Subsequently, full field values for the two solids were computed individually. In order to predict initiation of fracture and plastic flow, results are reported for the location and magnitude of maximum tensile stress and effective stress, respectively, for a range of geometrical and material parameters. In two illustrations, predicted results are compared with experimental findings related to initiation of brittle fracture and load-depth relations at nanoindentation.     

高锁螺栓连接件动态拉伸响应与失效机理

飞机坠撞过程中结构的变形模式和吸能对乘员保护具有重要意义，而连接结构的载荷传递和失效形式是影响飞机结构变形的重要因素之一。为了获取航空高锁螺栓连接件在坠撞载荷下的动态响应和失效机理，基于抗剪型平头高锁螺栓设计了2种材料（2024-T3和7050-T7451）的单钉单搭接连接件，利用高速液压伺服材料试验机进行4种速度（0.01、0.10、1.00和3.00 m/s）下的拉伸测试，得到连接件的动态响应、极限载荷、能量吸收和失效模式随速度的变化规律，并分析了连接件的失效机理。结果表明，连接件的失效模式受母材和高锁螺栓/螺母材料强度影响较大，而受加载速度影响较小；当速度从0.01 m/s增加到3.00 m/s时，2024-T3连接件的极限载荷和能量吸收分别增加了2.17%和34.43%，7050-T7451连接件的极限载荷和能量吸收分别增加了5.53%和6.58%。     

结合材料界面端的三维应力奇异性

本文利用特殊有限元方法，开发了一个用来求解结合材料界面端三维应力奇异性问题的数值分析程序。该方法只需对界面端的角度方向进行离散即可求得应力奇异性。结合材料的应力奇异性取决于两种材料的材料常数和界面端形状。选用三个材料参数作为变量，用来研究结合材料三维应力奇异性随材料常数的变化规律。文中计算了几种重要而且常见的情况，并以此为基础建立了数据库。同时，还分析了应力奇异性随界面端形状的变化规律，并得到了应力函数的分布图。     

Upper bound of the limit load for a tensile cylinder with a soft welded (soldered) joint containing a crack

The limit load is one of the main characteristics in estimating the performance of different structures, in particular, structures with soft welded (soldered) joints. In some cases, the difference between the yield strengths of the main material and the joint material is so great that plastic strain is localized in a thin joint. With some features of such strain distribution taken into account, an upper bound of the limit load of a tensile axisymmetric sample with a crack in a welded (soldered) joint is obtained.     

Singularities in auxetic elastic bimaterials

In this paper we study the effects of negative Poisson's ratios on elastic problems containing singularities. Materials with a negative Poisson's ratio are termed auxetic. We present a brief review of such materials. The elasticity problem of a bimateral wedge is presented, then two particular cases of this problem are investigated: the free-edge problem and the interface crack problem. We study the effect on the stress singularity due to one portion of the bimaterial becoming auxetic. We find that the auxetic material has a significant effect on the singularity order, even causing the singularity to vanish for certain values of the elastic constants.     

Determining material true stress–strain curve from tensile specimens with rectangular cross-section

The uniaxial true stress logarithmic strain curve for a thick section can be determined from the load–diameter reduction record of a round tensile specimen. The correction of the true stress for necking can be performed by using the well-known Bridgman equation. For thin sections, it is more practical to use specimens with rectangular cross-section. However, there is no established method to determine the complete true stress–logarithmic strain relation from a rectangular specimen. In this paper, an extensive three-dimensional numerical study has been carried out on the diffuse necking behaviour of tensile specimens made of isotropic materials with rectangular cross-section, and an approximate relation is established between the area reduction of the minimum cross-section and the measured thickness reduction. It is found that the area reduction can be normalized by the uniaxial strain at maximum load which represents the material hardening and also the section aspect ratio. Furthermore, for the same material, specimens with different aspect ratio give exactly the same true average stress–logarithmic strain curve. This finding implies that Bridgmans correction can still be used for necking correction of the true average stress obtained from rectangular specimens. Based on this finding, a method for determining the true stress–logarithmic strain relation from the load–thickness reduction curve of specimens with rectangular cross-section is proposed.     

Stress analysis of an orthotropic material under diametral compression

The diametral compression test is commonly used to determine the tensile strength of brittle materials. For isotropic materials a simple relation based on specimen geometry and the applied load at failure is used to calculate the tensile strength. Previous to this work the effect of material orthotropy and material orientation on the specimen stress state had not been completely determined. In this study, both isotropic and orthotropic specimens were analyzed using a finite element analysis and experimentally verified by strain gage and photoelastic measurements. Further, this work investigated the effect of the applied load area on the specimen stress state. Results of this work show that there is a significant difference between the theoretical calculations based on the assumption of material isotropy when compared to an orthotropic material. This difference can be as much as 45 percent depending on the degree of orthotropy and the orientation. It was also determined that the applied load area and material orientation significantly influence the specimen stress state. An applied load area of 8 percent of the circumference was found to reduce the stresses in the applied load region.     

Plane-strain crack tip field and a dual-parameter fracture-criterion for non-linear fracture mechanics

Hancock and Cowling measured the critical crack tip opening displacements, δ_f, at fracture initiation in HY-80 steel specimens of six different configurations. δ_f varied from 90 μm in a deeply double-edge-cracked tensile panel to 900 μm in a single-edge-cracked tensile panel.McMeeking and Parks, and Shih and German have shown by their finite element calculations that the characteristics of the plane strain crack tip fields in both large scale yielding and general yielding are strongly dependent on specimen geometry and load level.In this study, the plane strain crack tip fields in the specimens tested by Hancock and Cowling were calculated using the finite element method. The crack tip triaxial tensile stress field is strongly affected by specimen geometric constraint, and the state of the triaxial tensile stress in a crack tip region is monitored by the ratio between the local tensile stress and the effective stress, i.e., ( ), at a distance x=2δ from the crack tip. The values of ( ) vary from 3.1 for the double-edge-cracked tensile panel to 1.7 for the single-edge-cracked tensile panel. The δ_f measured by Hancock and Cowling correlates very well with the ratio ( ). δ_f is a measure of the fracture ductility of the material ahead of the crack tip, and the ductility decreases with an increase in the triaxial tensile stress, i.e., the ratio ( ).     

Finite Fracture Mechanics model for mixed mode fracture in adhesive joints

Up to now the failure load assessment of bonded joints is still not fully understood. This work provides a new approach for assessing the crack initiation load of bonded joints. A failure model for single lap joints is proposed that is based on Finite Fracture Mechanics. Only two basic fracture parameters are required: the tensile strength and the fracture toughness of the adhesive. A coupled stress and energy criterion proposed in 2002 by Leguillon is used to model crack initiation in the adhesive layer. The theory of this criterion is outlined in detail, its relationship to other failure criteria is discussed and an overview of applications found in literature is given. An enhanced weak interface model that predicts a linear variation of the shear stresses in the adhesive layer is utilized to model the single lap joint. To compare joint designs and to reveal the limitations of the given approach a dimensionless brittleness number for mixed-mode loading is proposed. Along with a detailed discussion of the results for exemplary joint designs a comparison to experimental results from literature is performed. The two necessary fracture parameters are each taken from standard test results published in literature. A good agreement of the failure load predictions with the experimental results is observed. A remarkable outcome is that the presented failure model renders the adhesive thickness effect correctly. The paper concludes with a discussion of the limitations of the approach and the effect of material parameters.     

纤维端部的界面裂纹分析

基于弹性力学空间轴对称问题的通解,研究了短纤维增强复合材料中纤维端部的轴对称币形和柱形界面裂纹尖端的应力奇异性,得到了裂纹尖端附近的奇异应力场．研究结果表明,这两种轴对称界面裂纹尖端的应力奇异性相同,并且与平面应变状态下相应模型的应力奇异性一致,材料性能对裂纹尖端附近奇异应力场的影响可用三个组合参数描述     

Hertzian fracture at unloading

Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally. Initiation of cone cracks has been observed and failure loads together with contact and fracture radii determined at monotonically increasing load but also during unloading phases. Contact of dissimilar elastic solids under decreasing load may cause crack inception triggered by finite interface friction and accordingly the coefficient of friction was determined by two different methods. In order to make relevant predictions of experimental findings, a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. It was found that at continued loading it is possible to specify in advance how the contact domain divides into invariant regions of stick and slip. The maximum tensile stress was found to occur at the free surface just outside the contact contour, the relative distance depending on the different elastic compliance properties and the coefficient of friction. In contrast, at unloading invariance properties are lost and stick/slip regions proved to be severely history dependant and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. Predictions of loads to cause crack initiation during full cycles were made based on a critical stress fracture criterion and proved to be favourable as compared to the experimental results.     

Dissimilar ultrasonic spot welding of Mg-Al and Mg-high strength low alloy steel

Sound dissimilar lap joints were achieved via ultrasonic spot welding (USW), which is a solid-state joining technique. The addition of Sn interlayer during USW effectively blocked the formation of brittle al₁₂Mg₁₇ intermetallic compound in the Mg-Al dissimilar joints without interlayer, and led to the presence of a distinctive composite-like Sn and Mg₂Sn eutectic structure in both Mg-Al and Mg-high strength low alloy (HSLA) steel joints. The lap shear strength of both types of dissimilar joints with a Sn interlayer was significantly higher than that of the corresponding dissimilar joints without interlayer. Failure during the tensile lap shear tests occurred mainly in the mode of cohesive failure in the Mg-Al dissimilar joints and in the mode of partial cohesive failure and partial nugget pull-out in the Mg-HSLA steel dissimilar joints.     

Design and validation of a new fixture for the shear testing of cellular solids

The design and validation of a new fixture for the shear testing of cellular solids are presented. The fixture is an extended version of a picture-frame shear fixture (EPF) and is suited for comparatively thick rectangular block specimens. The stress state in the specimen is analyzed using a detailed finite element model. The finite element model is based on a 3D CAD model and incorporates friction in the revolute joints. Using specimens with low stiffness, a nearly pure and uniform shear stress state is induced in the specimen. A correction factor for the shear stress is derived which takes into account the friction in the joints and the nonuniformity of the shear stress distribution in the gauge section. The shear response of the polymer foam Rohacell^® 200 WF is determined in order to demonstrate the capabilities of the EPF. The strain state is analyzed by means of digital image correlation and is detected to be very pure and uniform on the specimen’s surface, as predicted by the numerical analysis. The shear modulus obtained with the EPF is in good agreement with the calculated shear modulus derived from tensile tests on the same material. In addition, there is only little scatter of the strength values over the tested specimens which further confirms the accuracy of the new fixture.     

梁柱不同混凝土强度的高层框架节点试验和有限元分析

高层框架结构设计时，梁板与柱常常会采用不同的混凝土强度等级，柱的混凝土强度等级往往高于梁板。对于梁柱的节点，一般多采用与柱相同的强度等级，这给施工带来很大麻烦，如果采用与梁板相同强度等级混凝土时。虽然方便了施工，但降低了节点的抗震性能。本文的研究是通过对此类节点采取加强措施，以弥补混凝土强度等级降低的不利影响。通过节点模型试验，研究其受力性能及破坏机理，验证加强措施的有效性。并在试验研究的基础上，用有限元方法对受力复杂的节点进行分析，结果表明节点区混凝土存在应力集中和应力扩散现象以及存在混凝土侧向受拉的现象．证实了梁加腋和增设X型钢筋后节点受力性能得到了改善和加强。这些研究成果对目前高层建筑梁柱节点采用不同混凝土强度等级的设计、施工提供了有益的参考。     

Three-dimensional investigation of thick single-lap bolted joints

Stresses in single-lap bolted joints of thick plates are complex and difficult to analyze. Previous studies involving stresses through the thickness of bolted joints have been limited to finite element method (FEM) simulations and have been implemented only for the joining of relatively thin plates. In this paper we report on several experimental and numerical analyses that were conducted to evaluate the stress distribution inside thick bolted plates along the bearing plane normal to the plate surface. Experimental analysis was conducted via embedded-polariscope photoelasticity and embedded resistance strain gages. The FEM analysis was performed with the ABAQUS commercial code using material properties and other data obtained experimentally as input. Experimental and numerical results agreed reasonably well, and are believed to depict the behavior of the joint under load well enough to assist in development of improved joint design.