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.     

Dynamic fracture of imperfectly bonded lap joints

Summary Dynamic photoelasticity in conjunction with linear elastic fracture mechanics was utilized to study the dynamic behavior of imperfectly bonded single lap joints. Transient phenomena of propagation, reflection and diffraction of explosively generated plane elastic stress field disturbances about the tips of a crack located at the interface between the two adherends are investigated in detail. Fracture mechanics aspects of dynamic initiation under stress wave loading in similar and dissimilar lap joints are discussed.

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Dynamisches Verhalten von imperfekt geklebten, einfach überlappten Klebeverbindungen

Übersicht Das dynamische Verhalten von imperfekt geklebten einfach-überlappten Klebeverbindungen wird mit Hilfe der dynamischen Spannungsoptik im Rahmen der linear-elastischen Bruchmechanik untersucht. Die zeitlich schnell veränderlichen Vorgänge bei der Ausbreitung, Reflexion, Brechung und Beugung von explosiv erzeugten ebenen elastischen Störungen des Spannungsfeldes um die Rißspitze einer an der Trennfläche zweier (verschiedener) Materialien liegenden rißähnlichen Klebeimperfektion werden im Detail behandelt. Bruchmechanische Aspekte der dynamischen Rißinitiation an Klebefehlern unter Spannungs-wellenbelastung in monolithischen und kompositen Lappverbindungen werden diskutiert.

     

Study of multi-site damage of fuselage lap joints

The downturn in the world economy coupled with the cost of new aircrafts has meant that there are now ageing fleets whose continued airworthiness requires special attention to corrosion treatments, repair design, fatigue and fracture analysis, and improved crack detection techniques. To assist in this goal the present paper first summarises recent Australian efforts into the development of a simple experimental test specimen which is capable of reproducing the crack growth and failure mechanisms seen in the fuselage lap splice of a wide bodied transport aircraft. The development of a composite repair to overcome these phenomena is then discussed.     

Understanding crack growth in fuselage lap joints

The problem of multi-site damage and multiple interacting cracks is one experienced by many aircraft manufacturers and operators. This paper focuses on understanding the phenomena, and on developing a predictive capability that can form the engineering framework for maintaining continued airworthiness. To this end the present paper uses a simple formulation based on the Frost–Dugdale crack growth law to study the problem of cracking at fastener holes in fuselage lap joints and shows that the predicted crack growth history is in good agreement with both experimental results and with fleet data.     

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.     

Bonded lap joints of composite laminates with tapered edges

This study presents a semi-analytical solution method to analyze the geometrically nonlinear response of bonded composite lap joints with tapered and/or non tapered adherend edges under uniaxial tension. The solution method provides the transverse shear and normal stresses in the adhesives and in-plane stress resultants and bending moments in the adherends. The method utilizes the principle of virtual work in conjunction with von Karman’s nonlinear plate theory to model the adherends and the shear lag model to represent the kinematics of the thin adhesive layers between the adherends. Furthermore, the method accounts for the bilinear elastic material behavior of the adhesive while maintaining a linear stress–strain relationship in the adherends. In order to account for the stiffness changes due to thickness variation of the adherends along the tapered edges, the in-plane and bending stiffness matrices of the adherents are varied as a function of thickness along the tapered region. The combination of these complexities results in a system of nonlinear governing equilibrium equations. This approach represents a computationally efficient alternative to finite element method. The numerical results present the effects of taper angle, adherend overlap length, and the bilinear adhesive material on the stress fields in the adherends, as well as the adhesives of a single- and double-lap joint.     

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 in adhesive-bonded joints for orthotropic plates

In the current paper we present the tensile force, the edge moment and edge transverse force acting on the single-lap joint and get the moment reduction factork for orthotropic plates. We use the variational method based on the principle of complementary energy. Considering Hooke's law for orthotropic materials, carrying out the variationV=0 and using the Euler-Poisson's equation we establish all the expressions of stresses in the joint for orthotropic plates. All numerical calculations can be made on a computer.     

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 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.     

Strength of adhesive-bonded lap joints with respect to change of temperature and fatigue

The theoretical analyses of the stress distribution in bonded joints are of little help to the practical designer. An approximate solution yields an expression for the “average” ultimate shear stress in terms of two constants. This paper shows how these constants can easily be determined experimentally and gives test results which show their temperature dependence and their variation under fatigue-loading conditions. The constants are essential characteristics of a given adhesive and can be used to design any glued joint using this adhesive.     

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.     

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.     

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.     

The strain energy release rates in adhesively bonded balanced and unbalanced specimens and lap joints

An analytical model is developed to determine the strain energy release rate in adhesive joints of various configurations such as the double-cantilever beam and single-lap joints. The model is based on asymptotic analysis of adhesive layer stresses and Irwin’s crack closure integral. Closed-form solutions are presented for balanced and unbalanced joints under mode I, II and mixed-mode I/II that take into account the influence of the shear force on the adhesive stresses, and its influence on the strain energy release rate. The accuracy of the model is tested against the classical beam theory expressions for double-cantilever beam and end-notch flexure specimens. In fact, classical beam theory’s expressions are found to be the lower bound of the proposed model solutions, and the two methods converge as the adhesive layer thickness decreases. Analysis of single-lap joints reveals the influence of edge shear forces on the total strain energy release rate, and more importantly on the ratio between modes I and II. Results from the proposed analytical model are in good agreement with finite element results and with analytical models found in the literature.     

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.     

Velocity analysis of mechanisms with ball joints

A procedure is developed for analyzing velocities in spatial mechanisms with ball joints has been designed for practical computerization. The correspondence between the calculated velocities in a ball joint and the time changes of the physical displacements is clarified. The methodology is demonstrated using the RSPC mechanism which has seen commercial application as a washing-machine agitator mechanism.     

Analysis of adhesive lap joint

This paper is to solve the interlaminar stresses of adhesive lap joint by the energy method without considering the adhesive layer. The joint is made of two identical narrow plates. Two cases are discussed: one is for the isotropic material and the other is for orthotropic material. Because of the different materials forming the joint, the length of distribution and the magnitude of the interlaminar, stresses for the two cases will be very different.Projects supported by the Science Fund of Chines Academy of Sciences (1986–1988).     

Isodyne stress analysis of adhesively bonded symmetric joints

The paper presents experimental data on the actual three-dimensional stress states produced by tensile axial forces in components of adhesively bonded symmetric joints. Stress components are determined in lamination planes and in planes at various distances from lamination planes using the methods of isodyne stress analysis.The presented evidence shows that all three normal stress components exist in the components of a joint, and clearly vary with all three coordinates aligned with the length, width, and thickness of the joint. The stress state is pronounceably three dimensional and as such cannot be reliably determined using the analytical and experimental procedures based on the concept of generalized plane stress state. Thus the convenient simplified analytical and experimental procedures of stress analysis should be carefully tested for their admissibility, using as a criterion, the magnitude of acceptable error. The paper illustrates capacity of the method of analytical and optical isodynes.Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 26–June 1.