A study on the strength of adhesively bonded joints with different adherends

In this study, mechanical properties of adhesively bonded single-lap joint (SLJ) geometry with different configurations of lower and upper adherends under tensile loading were investigated experimentally and numerically. The adherends were AA2024-T3 aluminum and carbon/epoxy composite with 16 laminates while, the adhesive was a two-part liquid, structural adhesive DP 460. In experimental studies, four different types of single-lap joints were produced and used namely; composite–composite (Type-I) with lower and upper adherends of the same thicknesses and four different stacking sequences, composite–aluminum (Type-II) with lower and upper adherends of the same thicknesses and four different stacking sequences, composite–aluminum (Type-III) with lower adherend (composite) of the same thickness but upper adherend of three different thicknesses, aluminum–aluminum (Type-IV) with lower adherend of the same thickness but upper adherend of three different thicknesses, composite–composite (Type-V) with [0]₁₆ stacking sequences and three different overlap length, aluminum–aluminum (Type-VI) with three different overlap length. In the numerical analysis, the composite adherends were assumed to behave as linearly elastic materials while the adhesive layer and aluminum adherend were assumed to be nonlinear. The results obtained from experimental and numerical analyses showed that composite adherends with different fiber orientation sequence, different adherend thicknesses and overlap length affected the failure load of the joint and stress distributions in the SLJ.     

Characteristics of plasma surface treated composite adhesive joints at high environmental temperature

When an adhesive joint is exposed to high environmental temperature, the load transmission capability of the adhesive joint decreases because the stiffness and strength of structural adhesive decrease. The load transmission capability of adhesive joint at high environmental temperature can be improved by increasing the surface free energy of adherends with surface pretreatments.

In this paper, a capacitively coupled radio frequency plasma system was designed for the surface treatment of carbon/epoxy composites. The suitable plasma surface treatment conditions were experimentally investigated with respect to gas flow rate, vacuum pressure, power intensity, and surface treatment time through measurement of surface free energy by investigating strength of single lap composite adhesive joint. The surface free energy and adhesive joint strength were investigated with respect to the surface characteristics of the carbon/epoxy composite adherend measured with atomic force microscope. Also the failure mode of the composite adhesive joint was studied with respect to surface treatment and environmental temperature.     

Investigation of elastic stresses in an adhesively bonded single lap joint with functionally graded adherends in tension

In this study three-dimensional elastic stress state of an adhesively bonded single lap joint with functionally graded adherends in tension was investigated. The adherends compose of a functionally gradient layer between a pure ceramic (Al₂O₃) layer and a pure metal (Ni) layer. Stress concentrations are observed along the free edges of the adhesive layer and through the corresponding zones in the upper and lower adherends. The adhesive layer experiences stress concentrations along the left and right free edges in the horizontal plane, and the normal stresses and the shear stress σ_xy are critical. Whereas the middle overlap region has a uniform low stress distribution the zones in the upper adherend corresponding to the left free edge of the adhesive layer and the zones in the lower adherend corresponding to the right free edge of the adhesive layer are subjected to higher stresses. The normal stress σ_xx among the normal stresses and the shear stress σ_xy among the shear stresses are dominant in both upper and lower adherends. The normal stress σ_xx changes uniformly from compression in the ceramic layer to tension in the metal layer through the upper plate-thickness and from tension in the ceramic layer to compression in the metal layer through the lower plate-thickness. In the adhesive layer, the normal stress σ_yy becomes peak at the left free edge of the upper adherend–adhesive interface and at the right free edge of the lower adherend–adhesive interface and then decreases uniformly across the adhesive layer towards the other adherend–adhesive interface. The functionally gradient region across the adherend thickness was modelled using the layers with the mechanical properties calculated based on the power law. However, a layer number larger than 20 has a minor effect on the through-thickness profiles and magnitudes of von Mises and normal stresses in both the adherends and the adhesive. In addition, increasing the ceramic phase in the material composition (compositional gradient exponent n) of the functionally gradient region does not affect the through-thickness profiles of von Mises and normal stresses in the adherends and adhesive whereas their magnitudes in the ceramic rich layer of both adherends and along the adherend–adhesive interfaces increase considerably. On the contrary, the layer number and compositional gradient exponent have an evident effect on the through-thickness profiles and magnitudes of the critical stress components in the adherends and adhesive layer of the functionally graded adhesively bonded joints.     

Strength prediction of tubular composite adhesive joints under torsion

This paper addresses prediction of the strength of tubular adhesive joints with composite adherends by combining thermal and mechanical analyses. A finite element analysis was used to calculate the residual thermal stresses generated by cooling down from the adhesive cure temperature, and a nonlinear analysis incorporating the nonlinear adhesive behavior was performed to accurately estimate the mechanical stresses in the adhesive. Joint failure was estimated by three failure criteria: interfacial failure, adhesive bulk failure, and adherend failure. The distributions of residual thermal stresses were investigated for various stacking angles. The effect of residual thermal stresses on joint strength was also taken into consideration. The results indicate that the residual thermal stresses, depending on the stacking angle, have a significant influence on the failure mode and strength of adhesive joints when a subsequent mechanical load is applied. Good agreement is also obtained between the predicted joint strength and the available experimental data.     

Singular intensity factors at bimaterial anisotropic interfaces

The singular intensity factors at bimaterial anisotropic interfaces in bonded joints with composite adherends are found by using a hybrid method based on numerical and elasticity solutions. The method is applicable to the solution of problems having complex geometry, loading and boundary conditions, which is the case in typical composite structures. Results are given in terms of the singular intensity factor, which is a generalization of the stress intensity factor commonly used with cracks. Both closed and open wedges, which are found, respectively, in bonded joints with or without adhesive fillets, are considered. Equivalent singular intensity factors in modes I, II and III are defined, and the results indicate that the mode III factor, which arises due to out-of-plane coupling, is negligible in all cases studied. Moreover, use of the Erdogan–Sih failure criterion indicates that the direction of crack propagation in lap joints with fillets remains constant beyond a very small region near the point of singularity, while for joints without fillets crack initiation always occurs in a direction parallel to the adhesive–adherend interface.     

End effects in scarf joints

Scarf joints with small scarf angles are especially sensitive to stiffness mismatch between adherends and to adherend tip bluntness. Pre-assembly breakage of an adherend tip where it is only a few microns thick can cause significant reduction in joint strength. Mathematically, the reason for such sensitivity is that the solutions to the governing differential equation develop boundary layer character when the scarf angles are small. The boundary layers are regions with large adhesive stresses. Experimental strength data for laminated composite adherends agree with the results of this analysis.     

New designs of adhesive joints for thick composite laminates

New joint designs are proposed for adhesive bonding of thick multilayered composite adherends. The objective is to reduce or eliminate the failure modes associated with delamination and tensile and/or shear failure of the surface plies that are often observed in lap joints, and provide for a better stress distribution in the adhesive. In contrast to lap-joint designs, which transfer in-plane tensile stresses and other loads from the adherends to doubler plates by out-of-plane shearing of the surface plies, the new joint configurations transfer most of the load by in-plane shear and normal stresses, through bonded inserts or interlocking interfaces which have the same thickness as the laminate adherends. Doublers will transfer a calculated percentage of the load. Finite-element evaluations of the internal stresses in laminates, joined in both the conventional lap method and the new manner, suggest that the proposed load-transfer mechanism may improve joint efficiency by substantially increasing the size of adhesively bonded areas, and by making the stresses in the adherends nearly uniform through the thickness of the laminate. Some of the designs allow for selected ratios of shear to normal stresses in the adhesive layers. The stress concentrations often found in conventional designs, in the adherend surface plies and the adhesive layer at the leading edges of the doublers, are substantially reduced.     

Stress-function variational method for stress analysis of bonded joints under mechanical and thermal loads

High interfacial stresses near the ends of adherends are responsible for debonding failure of bonded joints used extensively in structural engineering and microelectronics packaging. This paper proposes a stress-function variational method for determination of the interfacial stresses in a single-sided strap joint subjected to mechanical and thermal loads. During the process, two interfacial shear and normal (peeling) stress functions are introduced, and the planar stresses of adherends of the joints are expressed in terms of the stress functions according to the static equilibrium equations. Two coupled governing ordinary differential equations (ODEs) of the stress functions are obtained through minimizing the complementary strain energy of the joints and solved explicitly in terms of eigenfunctions. The stress field of the joints based on this method can satisfy all the traction boundary conditions (BCs), especially the shear-free condition near the adherend ends. Compared to results based on finite element method (FEM) and other analytic methods in the literature, the present variational method is capable of predicting highly accurate interfacial stresses. Dependencies of the interfacial stresses upon the adherend geometries, moduli and temperature are examined. Results gained in this study are applicable to scaling analysis of joint strength and examination of solutions given by other methods. The present formalism can be extended conveniently to mechanical and thermomechanical stress analysis of other bonded structures such as adhesively bonded joints, composite joints, and recently developed flexible electronics, among others.     

Analytical investigation of thermal and mechanical load effects on stress distribution in adhesive layer of double-lap metal-composite bonded joints

Significant thermal stresses are induced in the adhesive layers of a metal-composite bonded joint owing to the large temperature change associated with the difference in the coefficients of thermal expansions of metals and composite adherends. In this study, a theoretical analysis of shear and peel stresses in adhesive layers of a double-lap metal-composite bonded joint is carried out to evaluate the effects of thermal and mechanical loads on the stress distribution in the adhesive layer. The effects of temperature change and adhesive thickness on the shear and peel stresses in the adhesive layer of the bonded joint, with and without external forces, are examined based on the theoretical analysis. The results calculated for the condition involving a mechanical load application to the bonded joint and a decrease in temperature indicate that the absolute value of the shear and peel stresses peak at both ends of the adhesive layer, and that the absolute value of the peak stresses increases in the case of a thinner adhesive layer. When mechanical and thermal loads are simultaneously applied to a double-lap joint, shear and peel stresses synergistically increase at one end of the adhesive layer and decrease with an offset at the other end.     

Composite-to-metal tubular lap joints: strength and fatigue resistance

The axial strength and fatigue resistance of thick-walled, adhesively bonded E-glass composite-to-aluminum tubular lap joints have been measured for tensile and compressive loadings. The joint specimen bonds a 63 mm OD aluminium tube within each end of a 300 mm long, 6 mm thick E-glass/epoxy tube. Untapered, 12.5 mm thick aluminium adherends were used in all but four of the joint specimens. The aluminum adherends in the remaining four specimens were tapered to a thickness of 1 mm at the inner bond end (the bond end where the aluminum adherend terminates). For all loadings, joint failure initiates at the inner bond end as a crack grows in the adhesive adjacent to the interface. Test results for a tension-tension fatigue loading indicate that fatigue can severely degrade joint performance. Interestingly, measured tensile strength and fatigue resistance for joints with untapered adherends is substantially greater than compressive strength and fatigue resistance.The joint specimen has been analyzed in two different ways: one approach models the adhesive as an uncracked, elastic-perfectly plastic material, while the other approach uses a linear elastic fracture mechanics methodology. Results for the uncracked, elastic-plastic adhesive model indicate that observed bond failure occurs in the region of highest calculated stresses, extensive bond yielding occurs at load levels well below that required to fail the joint, and a tensile peel stress is generated by a compressive joint loading when the aluminum adherends are untapered. This latter result is consistent with the observed joint tensile-compressive strength differential. Results of the linear elastic fracture mechanics analysis of a joint with untapered aluminum adherends are also consistent with the observed differential strength effect since a mode I crack loading is predicted for a compressive joint loading. Calculations and a limited number of tests suggest that it may be possible to selectively control the differential strength effect by tapering the aluminum adherends. The effect of adherend material and thickness on fracture mechanics parameters is also investigated. The paper concludes by examining the applicability of linear elastic fracture mechanics to the joints tested.     

Delamination damage analyses of adhesively bonded lap shear joints in laminated FRP composites

Three-dimensional non-linear finite ele- ment analyses have been carried out to evaluate the out-of-plane stresses in the adhesive layer existing between the lap and the strap adherends of the Lap Shear Joint (LSJ) in laminated FRP composites for varied delamination lengths. The delaminations are presumed to be pre-embedded in the thin resin rich layer existing between the first and second plies of the strap adherend. Sublaminate technique has been used to model the LSJ with the delamination. Contact finite element analyses have been performed in order to avoid interpenetration of delaminated surfaces. The effects of varied delamination lengths on the peel and interlaminar shear stresses and the individual modes of Energy Release Rate (ERR) in the delamination zones are highlighted in this paper. It is seen that three-dimensional effects exist near the free edges of the overlap end of the joint. The delamination propagation significantly affects the stress distributions in the adhesive layer existing between the lap and the strap adherends of the LSJ. The variations of interlaminar stresses and ERRs on both the delamination fronts are found to be significantly different and thus, indicate that the propagation of delamination does not occur at same rate at the two delamination fronts. This may throw some light to the evaluation of structural integrity of the LSJ in the presence of pre-embedded delaminations.     

Strain energy release rate determination of prescribed cracks in adhesively-bonded single-lap composite joints with thick bondlines

An analytical model for determining the strain energy release rate due to a prescribed crack in an adhesively-bonded, single-lap composite joint with thick bondlines and subjected to axial tension is presented. An existing analytical model for determining the adhesive stresses within the joint is used as the foundation for the strain energy release rate calculation. In the stress model, the governing equations of displacements within the adherends are formulated using the first-order laminated plate theory. In order to simulate the thick bondlines, the field equations of the adhesive are formulated using the linear elastic theory to allow non-uniform stress distributions through the thickness. Based on the adhesive stress distributions, the equivalent crack tip forces are obtained and the strain energy release rate due to the crack extension is determined by using the virtual crack closure technique (VCCT). The specimen geometry of ASTM D3165 standard test is followed in the derivation. The system of second-order differential equations is solved to provide the adherend and adhesive stresses using the symbolic computational tool, Maple 7. Finite element analyses using J-integral as well as VCCT are performed to verify the developed analytical model. Finite element analyses are conducted using the commercial finite element analysis software ABAQUS™. The strain energy release rates determined using the analytical method correlate well with the results from the finite element analyses. It can be seen that the same prescribed crack has a higher strain energy release rate for the joints with thicker bondlines. This explains the reason that joints with thick bondlines tend to have a lower load carrying capacity.     

Analysis of tongue and groove joints for thick laminates

A finite element evaluation of local stresses in the adhesive and adherends is presented for a tongue-and-groove joint of a homogenized thick composite laminate to steel plate. The quasi-isotropic laminate is made of glass fabric/vinyl ester plies. Most results are obtained for elastic response of the Dexter-Hysol 9338 adhesive that was used in recent experiments (Compos Sci Technol 61 (2001) 1123–1142). A non-linearly viscoelastic adhesive is also considered, with illustrative properties taken from experiments on the FM-73 system. Both in-plane force resultants and out-of-plane moments are included in the applied loads. Scaling of the elastic results with regard to plate thickness shows that for given levels of overall stresses applied to the adherend plates, the stresses supported by the adhesive do not depend on plate thickness. Adhesive stress relaxation is shown to be relatively small, and occurring in a short time period.     

Adhesively-bonded joints in metallic alloys, polymers and composite materials: Mechanical and environmental durability performance

The factors affecting the mechanical and environmental durability (or stability), and performance of the adhesively bonded joints in various adherends including metallic alloys, polymers and composite materials are studied in detail. The primary function of a joint is to transfer load from one structural member to another. In most bonded joints the load transfer takes place through interfacial shear. At present, the use of adhesive bonded joints are largely applied to secondary non-critical structures. Whereas the use of adhesive bonding in primary structural applications has been somewhat limited because of the difficulty in defining and predicting joint strength, and designing the joint geometry to optimize strength and reliability. The determination of adhesive joint strength is complicated primarily by the nature of the polymeric material itself. Since these problems are mainly mechanical in nature, stress analysis is required to understand how the force loads are distributed along the adherends and adhesive layer. Most structural engineers consider the durability or stability of a joint to be fatigue related. This is only partly true for adhesive bonds as most durability issues are driven by environmental resistance rather than fatigue loads. The environmental resistance of an adhesive bond is determined by the chemical bonds formed during cure of the adhesive and the resistance of the chemical bonds to environmental degradation. Environmental resistance is fundamental to the durability of a bonded joint or repair. Most in-service failures are caused by environmental degradation of the interface between the bonding surface and the adhesive. Although the use of adhesive bonding is increasing rapidly, there are still important issues which need to be addressed in joint analysis, design, durability, and performance considerations. Therefore, the study of joints usually involves consideration of (a) joint geometries, (b) materials (i.e., adhesives and adherends), (c) loading conditions (i.e., static and dynamic loadings), (d) failure modes (i.e., cohesive, adhesive or mixed failure modes), and (e) temperature and moisture or environmental effects (humidity, solvents, corrosion, temperature extremes, thermal cyling etc.). Therefore, in the present paper the adhesive joints are critically assessed in terms of these factors which affect the durability and performance of them.There are two basic mathematical approaches for the analysis of adhesively bonded joints: (a) closed-form or analytical model and (b) numerical solutions (i.e., finite element analysis, FEA). In the closed-form approach, a set of differential equations and boundary conditions is formulated. The solutions of these equations are analytical expressions which give values of stresses at any point of joint. The analytical approach for the solution of complex stress distributions in the joints has been progressively refined until recent times. In the second approach, solutions of differential equations are obtained by numerical methods or the continuum is represented by a discrete model at the outset. The solution of these equations gives displacements at the determined points from which strains and stresses can be obtained for any point within the model. Among the numerical methods, finite element analysis (FEA) has been extensively used with success. The two- and three-dimensional finite element analyses approaches have been extensively applied by many workers to analyse the adhesive joints considering the linear and geometric nonlinearities.     

Analysis of composite-to-metal joints with bondline flaws

Stress analysis techniques have been developed for load transfer in metal-to-composite adhesively bonded joints with bondline flaws such as variable bondline thickness and debond in the adhesive layer. Two joint configurations, namely, single-step-lap bonded joint and smoothly tapered scarf joint, have been investigated. The problem is formulated on the basis of the assumptions that both the metal and the composite are under generalized plane stress conditions and that the adhesive acts as a shear spring. Differential equations are obtained for the load transfered from the metallic layer to the composite layer. Numerical results are obtained for the force and stress in the composite layer, the stress in the metal and the stress in the adhesive. The influence of bondline flaw location on the stresses in the adhesive and the adherends has been investigated.     

The effect of environment on the fatigue of bonded composite joints. Part 1: testing and fractography

In this work, the effect that test environment and pre-conditioning had on the fatigue behaviour of CFRP/epoxy lap–strap joints was investigated. It was shown that the fatigue resistance of the lap–strap joints did not vary significantly until the glass transition temperature, T_g, was approached, at which point a considerable reduction in the fatigue threshold load was observed. It was also noted that absorbed moisture resulted in a significant reduction in the T_g of the adhesive. This must be taken into account when selecting an adhesive to operate at elevated temperatures. The locus of failure of the joints was seen to be highly temperature dependent, transferring from primarily in the composite adherend at low temperatures to primarily in the adhesive at elevated temperatures. It was also seen that as the crack propagated along the lap–strap joint, the resolution of the forces at the crack tip tended to drive it into the strap adherend, which could result in complex mixed mode fracture surfaces.     

金属胶接接头残余应力计算及数值分析

利用Baker模型和弹塑性有限元方法研究了胶接接头搭接区残余应力的分布.结果表明,因胶粘荆的线膨胀系数比被粘物高得多,胶层固化时被粘物阻碍了胶层的收缩,故胶层中为残余拉伸应力,被粘物中为残余压缩应力,胶层中的残余应力远大于被粘物中的残余应力.利用Baker模型和有限元计算远离自由端的胶层中的残余应力,两者吻合.被粘物中的残余应力呈中心对称,等效应力经多项式拟合后呈抛物线分布.     

Structural design of single lap joints with delaminated FRP composite adherends

This paper deals with the structural design of single lap joints (SLJs) with delaminated adherends using fracture mechanics principles. The interlaminar stresses and Strain Energy Release Rate (SERR) are considered as damage characterizing parameters used for designing the SLJ when delamination damages are pre-embedded in both the adherends at similar positions. Three dimensional geometrically non-linear finite element analyses (FEAs) of SLJ with delaminated adherends have been performed to determine the interlaminar and SERR values along the delamination fronts by simulating the simultaneous interaction delamination damages when pre-embedded at similar positions in both the adherends. SERR values are evaluated using Modified Crack Closure Technique (MCCI) which is based on energy principle. The delaminations are assumed to be of linear front, and have been considered to be embedded in both the laminated FRP composite adherends beneath the surface ply of the adhesively bonded SLJ. The delamination damages are presumed either to pre-exist or get evolved at the interlaminar locations. Such delaminations have been modelled using the sublaminate technique. The critical issues of modelling pre-embedded delamination damages are discussed in detail. The numerical results presented in this paper are based on the validated FE model compared with the available literature. Based on the present analyses, the structural design recommendations have been made for the SLJ when pre-embedded delamination damages are present in both the adherends. It is observed from the stress based design that the delamination damage when present in the bottom adherend is more detrimental for failure of SLJ compared to that for the case when it is present in the top adherend. Also, SERR based design reveals that the opening mode predominantly governs the propagation of delamination damage for all positions of the pre-embedded delaminations in both the adherends of the SLJ.     

Analysis of singular regions in bonded joints

Singular regions in bonded joints with geometric and material stress singularities are studied by expressing the displacement and stress fields in the neighborhood of the singularity by means of eigenfunction expansions which are in terms of unknown coefficients. These coefficients are found by matching displacements with those from a finite element analysis at points remote from the singularity. Expressions for the eigenfunction expansions are given explicitly for bonded joints with and without fillets (closed and open wedges). The results are not limited to stress intensity factors at the point of singularity, but can include stress values at any point near the singularity. It was found that two singular terms exist in all cases, and that, for joints with adhesive fillets and E ₁/E ₂>7, failure is governed by the term associated with the second lowest eigenvalue, while the lowest eigenvalue controls the failure of joints without fillets. It was also found that the calculation of stresses using only the singular terms provided a good approximation to the actual stresses over a distance of about one-fifth the adhesive thickness. The method was also used in conjunction with the Erdogan–Sih maximum stress failure criterion to determine the initial angle of crack propagation for bonded joints with and without fillets. This revealed that the direction of the maximum principal stress in the adhesive, which is also the direction of crack propagation, for joints with fillets remains essentially constant beyond a very small region near the point of singularity, while for joints without fillets crack propagation always occurs in a direction parallel to the adhesive/adherend interface.