On flaw size and distribution in lap joints

By using adhesive as the bonding substance between metals or polymeric materials, simple structural joints can be made to bear relatively high loads. Applications have increasingly been made in substituting adhesive joints for conventional mechanical fastenings, especially in the aircraft and aerospace industries where weight is a predominant factor. In order to design a most effective adhesive-bonded joint, an understanding of the stress distribution along the joint is as important as the physical properties of the bonding agent. One of the most common and widely used adhesive joints is the single lap joint.Recent investigations using various analytical models have revealed that the cause of failure in an idealized ‘defect free’ lap joint is primarily due to the localized effect of high stress concentration at the lap ends. With the presence of flaw like defects in the adhesive layer, the load transfer from adherend to adhesive is expected to be different from the idealized joint. In addition, localized stress concentrations induced by irregular adhesive defects that may be found in practical engineering applications can further reduce fracture strength of such an imperfect joint.This paper is intended to describe an investigation into the effect of internal adhesive flaw size and distribution on the fracture behaviour of adhesive-bonded lap joints. The finite element method is used to gain a quantitative understanding of the localized shear stress distributions due to the presence of the internal flaws along the bonding layer. It is observed that the reduction in the fracture strength is relatively small when a flaw is located in the central portion of the bonding length. However, a flaw located near the lap ends of the adhesive joint can cause marked reduction in the fracture strength, due to its interaction with the high stress concentration at the lap ends.     

胶层吸湿对单搭接接头影响的数值模拟

在建立胶桔剂吸涅本构模型的基础上,用弹塑性有限元法研究了聚丙烯酸酯胶层吸涅程度对单搭接接头上胶层中应力分布的影响.结果表明:随着胶层吸湿程度增加,单搭接接头上胶瘤处的峰值应力显著降低.对水分从搭接区两侧渗入胶层的总宽度变化时胶层中的应力分布作了研究,发现随渗入总宽度的增加,胶层中的等效应力Seqv峰值下降.因水分渗入后引起胶层溶胀,在胶瘤过渡到中间胶层的拐角处会产生严重变形,可能导致该处发生脱粘.     

Stress analysis of adhesively bonded sandwich pipe joints subjected to torsional loading

Composite pipes are becoming popular in the offshore oil and gas industry. These pipes are connected to one-another by various configurations of joints. The joints are usually the weakest link in the system. In this investigation we examine the response of various joint configurations subjected to torsion, one of the most common loading conditions in piping systems. Specifically, the theoretical analysis used to evaluate the stress field in the adhesive layers of tubular and socket type bonded sandwich lap joints is presented here. The two adherends of the joints may have different thickness and materials, and the adhesive layer may be flexible or brittle. The analysis is based on the general composite shell theory. The stress concentrations at and near the end of the joints as functions of various parameters, such as the overlap length, and thickness of the adhesive layer are studied. The effects of different adherend thickness ratios, adhesive thickness and overlap length are also studied. Results obtained from the proposed analytical solutions agree well with the results obtained from finite element analysis and those obtained by other workers.     

Analytical solutions for adhesive composite joints considering large deflection and transverse shear deformation in adherends

This paper presents a novel formulation and analytical solutions for adhesively bonded composite single lap joints by taking into account the transverse shear deformation and large deflection in adherends. On the basis of geometrically nonlinear analysis for infinitesimal elements of adherends and adhesive, the equilibrium equations of adherends are formulated. By using the Timoshenko beam theory, the governing differential equations are expressed in terms of the adherend displacements and then analytically solved for the force boundary conditions prescribed at both overlap ends. The obtained solutions are applied to single lap joints, whose adherends can be isotropic adherends or composite laminates with symmetrical lay-ups. A new formula for adhesive peel stress is obtained, and it can accurately predict peel stress in the bondline. The closed-form analytical solutions are then simplified for the purpose of practical applications, and a new simple expression for the edge moment factor is developed. The numerical results predicted by the present full and simplified solutions are compared with those calculated by geometrically nonlinear finite element analysis using MSC/NASTRAN. The agreement noted validates the present novel formulation and solutions for adhesively bonded composite joints. The simplified shear and peel stresses at the overlap ends are used to derive energy release rates. The present predictions for the failure load of single lap joints are compared with those available in the literature.     

Fatigue strength of welded joints based on local, semi-local and nominal approaches

Analysis based on the so-called “local approach” is made to estimate the fatigue strength of welded joints. Numerical analyses or strain gauges are employed for finding the stress and/or strain state in the vicinity of the weld toe. The notch stress intensity factor (NSIF) approach applied to fillet welded joints, as far as the opening angle between the weld and the main plate surface is constant (e.g. 135°, typical for many fillet welds), is able to rationalise the fatigue strength data both for different joint geometries and absolute dimensions. The NSIF approach has been previously developed as an extension of the Linear Elastic Fracture Mechanics (LEFM) to open V-notches and is based on the exponential local stress field around the V-notch tip. Several different “local approaches”, although simpler and more practical than the NSIF, are based on the stress (or strain) values determined beyond the exponential local one. To distinguish such approaches from the NSIF based one, we define the former as semi-local or nominal approaches while the latter is a local approach. The paper underlines that the local approaches, differently from the other ones, are able to unify in a single scatter band the fatigue strength data obtained from welded joints having different geometry and absolute dimensions.     

The plane solution for bending of joined dissimilar elastic semi-infinite strips

The problem is reduced to a system of two singular integral equations for determining the interface slope and shear stress. The dominant part of the system is analyzed to determine the order of the stress singularity and its dependence on the elastic constants. After removing logarithmic singularities from the right hand sides we solve these equations numerically for several chosen composites and the interface slope and traction are exhibited graphically. The solution should be relevant in studying adhesive joints by means of a bending test.     

Balanced and unbalanced patching of cracked lap joints using weighted adhesive plate element

First order shear deformation theory is applied to analyze the behavior of one-side (unbalanced) and two-side (balanced) patched lap joints containing initial through cracks. The joints are made of adherends bonded together by adhesives. An adhesive interface plate element is introduced; it consists of an adhesive layer weighted by influence of the adherend. The thin adhesive layer is assumed to behave elastically and modelled as a simple tension-shear spring. The mathematical model contains layers of adherend and weighted adhesive layer.Finite elements are employed to model the adherend with an 8-node isoparametric plate element and interface layer with a 16-node plate element. Numerical results are obtained for one-side and two-side patches the width of which could be narrower or wider than the crack length. The former leads to bulging and possible peeling while the latter provides better bonding. Stresses and crack-tip stress intensity factors are calculated for different patch thickness. Effectiveness of the weighted adhesive layer model is exhibited by comparing the present results with those found in previous work where the adhesive is modelled as an individual layer.     

Direct Measurement of the Cohesive Law of Adhesives Using a Rigid Double Cantilever Beam Technique

Engineering adhesive joints are being increasingly used in industry because of the advantages they offer over other joining methods such as fastening or welding. The development and the use of adhesives in a design environment require accurate mechanical tests in order to measure their strength and toughness. Standard techniques such as the shear lap test are commonly used to measure shear strength, but the results they produce generally depend on geometry and on initial defects within the bond line. Fracture tests such as the double cantilever beam (DCB) tests overcome these limitations, but rely on elasticity models and assumptions to determine toughness. In this study, we present a novel technique to directly determine the mode I fracture toughness of engineering adhesive joints as well as their full cohesive law, without any initial assumption on its shape. Our new method is remarkably simple in terms of experimental setup, execution and analysis. It is similar to the standard double cantilever beam (DCB) test with the difference that the material and dimensions of the beams are chosen so that they are assumed to be rigid compared to the bond line. In this rigid DCB (RDCB) technique the crack opening is known everywhere along the interface, which we use to compute the cohesive law of the adhesive directly from the load-displacement data obtained from experiment and the geometry of the RDCB specimen. The RDCB method is validated and applied to three typical commercial adhesives (polyurethane, epoxy, and silicone), to determine their cohesive law and fracture toughness.     

带凸缘弯曲梁应力集中区内表面裂纹应力强度因子的研究

用三维光弹性冻结应力实验技术与修正的多点超定法相结合研究了带凸缘弯曲梁应力集中区内表面裂纹的应力强度因子。分析了不同过渡圆弧的应力集中对两种表面裂纹(半圆形表面裂纹与前缘直线表面裂纹)的影响。用实验方法得到了应力强度因子放大系数的数值.结果表明,应力集中对浅裂纹的影响是更大的,是不可忽视的,但放大系数随表面裂纹的几何形状变化很小。这些对管节点的断裂力学评估提供了有价值的实验依据.     

Dimensionless parameters in symmetric double lap joints: An orthotropic solution for thermomechanical loading

Two thermomechanical analytical models are developed for orthotropic double lap joints with a view to identifying key dimensionless parameters that describe the behavior of the joint under combined thermal–mechanical loads. The solutions, based on the principle of virtual work, differ in the complexity of the assumed stress field. The first solution is similar to Volkersen [Volkersen, O., 1938. Die niektraftverteilung in zugbeanspruchten mit konstanten laschenquerschritten. Luftfahrtforschung 15, 41–47] with the addition of orthotropic and thermal effects. The second solution, extending the work of Davies [Davies, G.A.O., 1982. Virtual Work in Structural Analysis, John Wiley & Sons, New York] captures the peel stress as well as the traction free boundary condition at the adhesive edge. Relevant non-dimensional parameters are identified in terms of geometric, material, and load quantities. A dimensionless load ratio is identified which dictates the shape of the stress distribution. This ratio can also be used to quickly determine the dominant loading mechanism. Dimensionless stress plots are presented for representative lap joints.     

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.     

Linear and higher order displacement theories for adhesively bonded lap joints

This work presents an adhesive model for stress analysis of bonded lap joints, which can be applied to model thin and thick adhesive layers. In this theory, linear variations of displacement components along the adhesive thickness are firstly assumed, and the longitudinal strain and the Poisson's effect of the adhesive are modeled. A differential form of the equilibrium equations for the adherends is analytically solved by means of compatible relations of the adhesive deformation. The derived shear and peel stresses are compared with the classical adhesive model of continuous springs with constant shear and peel stresses, and validated with two-dimensional finite element results of the geometrically nonlinear analysis using a commercial package. The numerical results show that the present linear displacement theory can be applied to both thin and moderately thick adhesive layers. The present formulation of the linear displacement theory is then extended to the higher order displacement theory for stress analysis of a thick adhesive, whose numerical results are also compared with those of the finite element computation.     

Stress singularity analysis around the singular point on the stress singularity line in three-dimensional joints

The characteristics of the stress fields around a singular point on the stress singularity line of dissimilar materials in three-dimensional joints are investigated using BEM. Contour for the order of stress singularity around the point is mapped on Dundurs’ parameters plane using eigen value analysis by FEM. The results in 3D joints are compared with those in 2D joints having the same cross section and material combination. The order of stress singularity around the singular point on the stress singularity line in 3D joints is almost identical with that in 2D joints in the singularity region. However, the zero boundary of singularity in 3D joints is slightly different from that in 2D joints. Furthermore, the multiple root of p = 1 exists in the eigen value analysis by FEM. Therefore, logarithmic singularity possibly occurs around the singular point on the stress singularity line. Then, the stress distributions around this point are expressed by the combination of the r^λ term and logarithmic singularity terms. Finally, the characteristics of the stress intensity factors of the r^λ term and logarithmic singularity terms around the singular points are investigated.     

The Stress State of Three-Dimensional Bodies with Nonsmooth Inclusions

The stress state of a three-dimensional body with inclusions bounded by surfaces with singular lines (sets of corner points) and a conical point is studied. By determining the asymptotics of displacements and stresses at the singularities of interfaces and using the generalized elastic potentials of single and double layers, the problem posed is reduced to a system of singular integral equations. The results obtained are used to analyze the stress state of a body with a circular conical inclusion     

Fully-coupled nonlinear analysis of single lap adhesive joints

This paper presents novel closed-form and accurate solutions for the edge moment factor and adhesive stresses for single lap adhesive bonded joints. In the present analysis of single lap joints, both large deflections of adherends and adhesive shear and peel strains are taken into account in the formulation of two sets of nonlinear governing equations for both longitudinal and transverse deflections of adherends. Closed-form solutions for the edge moment factor and the adhesive stresses are obtained by solving the two sets of fully-coupled nonlinear governing equations. Simplified and accurate formula for the edge moment factor is also derived via an approximation process. A comprehensive numerical validation was conducted by comparing the present solutions and those developed by Goland and Reissner, Hart-Smith and Oplinger with the results of nonlinear finite element analyses. Numerical results demonstrate that the present solutions for the edge moment factor (including the simplified formula) and the adhesive stresses appear to be the best as they agree extremely well with the finite element analysis results for all ranges of material and geometrical parameters.     

Stress distribution in a lap joint under tension-shear

This paper deals with the elastostatic load transfer of a tensile load in a model of an adhesive lap joint (tension-shear problem). The adhesive layer is regarded as infinitesimally thin and the displacement and traction vectors in the adherends are assumed to be continuous across the bond. The problem is reduced to a pair of Fredholm integral equations of the second kind which involve the mean angle between the deformed bond line and the tensile load. This angle, in turn, is determined by means of a scheme due to Goland and Reissner. Numerical results for the bond line stresses and the stress intensity factors at the ends of the bonded region are presented.     

Vibration Analysis for Damage Detection in Metal-to-Metal Adhesive Joints

Vibration based non-destructive evaluation shows promise for damage detection in metal-to-metal adhesive joints. This research investigates an experimental technique to diagnose damage in single-lap adhesive joints subject to cyclical tensile loading. Vibration analysis reveals that damage can be correlated with changes in identified modal damping ratios. Constant amplitude forcing functions are employed to eliminate amplitude-dependent nonlinearities in the dynamic response profiles. Damping estimates obtained from time-domain analyses correlate well with damage magnitudes. Finite element modal analysis of the lap joints supports the experimental results.     

On the Iwan models for lap-type bolted joints

The paper presents mathematical modeling of the non-linear constitutive relation for bolted joints in the framework of the Kragelsky-Demkin theory of rough contact. It is shown that this approach, which maintains the tribology-related features of bolted joint interfaces, leads to a singular Iwan distribution density. In particular, we show that the Iwan density is expressed in terms of the height distribution density of the surface asperities, whereas its singular exponent is determined by the shape exponent of the surface asperities. Following this, constitutive relations for lap joints and the corresponding backbone (force-deflection) curves are obtained. Finally, Masing's hypothesis is applied and Goodman's relation for energy dissipation is recovered in order to describe the effects of cyclic loading. The two cases of a rough surface in contact with a flat surface and of two contacting rough surfaces are treated separately.     

Scattering of harmonic elastic waves by a plane interface crack with linear adhesive tips in a layered half space

In this paper, the scattering of elastic waves by an interface crack with linear adhesive tips in a layered half space is considered. By use of integral transform and integral equation methods, the singular integral equations of this problem are derived, which are transformed into a set of algebraic equations by means of contour integration and Chebyshev polynomials expanding technique. The numerical results of the adhesive region and stress amplitudes are given in this paper.     

尖端具有线性粘着力作用的加层空间的界面裂纹对稳态弹性波的散射

本文研究一类粘着型界面裂纹的弹性波散射问题．文中利用积分变换和积分方程方法推导了确定这类问题的奇异积分方程组．采用围道积分技术和切比雪夫多项式展开技术，得到了待定系数的非线性代数方程组．最后本文给出裂纹尖端粘着区的大小和界面应力的数值结果．