Thermal and geometrically non-linear stress analyses of an adhesively bonded composite tee joint

Adhesive bonding technique is used successfully for joining the carbon fibre reinforced plastics to metals or composite structures. A good design of adhesive joint with either simple or more complex geometry requires its stress and deformation states to be known for different boundary conditions. In case the adhesive joint is subjected to thermal loads, the thermal and mechanical mismatches of the adhesive and adherends cause thermal stresses. The plate-end conditions may also result in the adhesive joint to undergo large displacements and rotations whereas the adhesive and adherends deform elastically (small strain). In this study, the thermal and geometrically non-linear stress analyses of an adhesively bonded composite tee joint with single support plus an angled reinforcement made of unidirectional CFRPs were carried out using the non-linear finite element method. In the stress analysis, the effects of the large displacements were considered using the small displacement–large displacement theory. The stress states in the plates and the adhesive layer of the tee joint configurations bonded to a rigid base and a composite plate were investigated. An initial uniform temperature distribution was attributed to the adhesive joint for a stress free state, and then variable thermal boundary conditions, i.e. air flows with different velocity and temperature were specified along the outer surfaces of the tee joints. The thermal analysis showed that a non-uniform temperature distribution occurred in the tee joints, and high heat fluxes took place along the free surfaces of the adhesive fillets at the adhesive free ends. Later, the geometrical non-linear thermal-stress analysis of the tee joint was carried out for the final temperature distribution and two edge conditions applied to the edges of the vertical and horizontal plates (HP). High stress concentrations occurred around the rounded adherend corners inside the adhesive fillets at the adhesive free ends, and along the adhesive–composite adherend interfaces due to their thermal–mechanical mismatches. The most critical joint regions were adhesive fillets subjected to high thermal gradients, the middle region of HP, the region of the vertical plate corresponding to the free end of the vertical adhesive layer–left support interface. In addition, the support length had a small effect of reducing the peak stresses at the critical adherend and adhesive locations.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Influence of adherend’s delamination on the response of single lap and socket tubular adhesively bonded joints subjected to torsion

Tubular adhesively bonded joints are widely used in many industries such as the oil-and-gas, aerospace and automotive. Such joints are often used to mate dissimilar materials. Composite materials, because of their superior specific strength and stiffness and high resistance to corrosion, have also been widely used to form tubular components. When composites are mated to other materials (such as metals) by adhesives, the stress concentration in the adhesive layer becomes even more exasperated due to the mismatch in the mechanical properties of the mating adherends, thus posing further challenges. Moreover, the presence of a delamination in the composite adherend can significantly influence the stress distribution within the adhesive layer; therefore, the assessment of the adhesive layer stresses in the presence of a delamination is of importance, thus forms the main objective of the present work.     

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.     

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.     

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.     

胶接接头界面理论及其表面处理技术研究进展

胶接是用胶粘剂将被粘物表面连接在一起,形成可承受外载的胶接接头的过程,是涉及材料粘附、高分子材料老化机理、表面技术、力学性能测试等多个学科领域的边缘学科.介绍了与胶接接头界面紧密相关的弱界面层理论和润湿理论等领域的研究进展,总结了胶接接头表面处理方面的主要方法.     

Strength and failure modes of bonded single lap joints between cross-ply adherends

Adhesively bonded joints with cross-ply adherends having a 0° or 90° surface layer have been manufactured and tested. The stresses in the joint were determined using a continuum method of analysis and large displacement finite element analysis was also undertaken. A numerical crack simulation was used to determine approximately stress/strain redistribution after initial cracking. Numerical predictions are compared with joint experimental performance and failure modes.     

The J-integral for single-lap joint using the stress field from the mixed variational principle

The closed-form solution for the J-integral of a single-lap joint is presented based on the stress field derived from Reissner’s mixed variational principle. In an adhesive-bonded joint, loads are carried by the surface of the adherends in shear through an adhesive layer, and thus, the shear effect is important. To improve the accuracy of shear response in fracture analysis, all transverse effects of the shear and peel stresses are considered, and then the constitutive equations and the equilibrium equations are derived from the variational principle. The obtained J-integral gives additional terms on the transverse shear part of the total integral compared with the results from previous conventional analysis, and illustrative examples are provided to show the effects of the current approach. Also, the formulation proposed in this paper can deal with non-identical adherends and laminates easily.     

刚度非平衡胶接接头的二维应力分析

建立一种通用的分析刚度非平衡胶接接头应力的二维弹性理论。该理论通过使用完整的几何方程和完整的本构方程,不但考虑被粘体的弯曲、拉伸、剪切效应和胶层的剪切和撕扯行为,而且严格满足包括接头端头处胶层剪应力为零的所有边界条件,适用于被粘体/胶层厚度和材料属性的任何组合。与二维线弹性有限元分析对比表明:该理论解有很好的精度。最后对刚度不平衡程度对胶层应力分布的影响进行参数研究。     

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.     

Interfacial shear stress in FRP-plated RC beams under symmetric loads

A recently popular method for retrofitting reinforced concrete (RC) beams is to bond fibre-reinforced polymer (FRP) plates to their soffits. An important failure mode of such plated beams is debonding of the FRP plates from the concrete due to high level interfacial stresses near the plate ends. A closed-form rigorous solution for the interfacial stresses in simply supported beams bonded with thin plates and subjected to arbitrary loads has been found, in which a non-uniform stress distribution in the adhesive layer was taken into account. This paper uses the rigorous solution to investigate the impact of symmetric loading configurations on the interfacial shear stress distributions, and concludes that the bending moments on the cross sections at the plate ends play a significant role in terms of stress concentration, while the shear forces on the same cross-section contribute little to the concentration. On the basis of this observation, this paper proposes a simplified approximate solution to the shear stress along the interface between concrete and adhesive layer. Compared with the rigorous and other approximate solutions, the simplified solution exhibits sufficient accuracy in terms of stress distribution and stress concentration localized near the plate ends. Due to its compact feature, the simplified solution is more suitable for engineering applications using a portable calculator and to be adopted in the codes of practices.     

Fracture and yield behavior of adhesively bonded joints under triaxial stress conditions

Most of adhesively bonded joints are under complicatedly distributed triaxial stress in the adhesive layer. For the estimating of the strength of adhesively bonded joints, it is crucial to clarify behavior of yield and failure of the adhesives layer under triaxial stress conditions. Two types of the adhesively bonded joints were used in this study: One is the scarf joint which is under considerably uniform normal and shear stresses in the adhesive layer, where their combination ratio can be varied with scarf angle. The other is the butt joint with thin wall tube in which considerably uniform pure shear can be realized in the adhesive layer under torsional load conditions. These joints can cover the stress triaxiality in adhesive layers of most joints in industrial application. The effect of stress triaxiality on the yield and fracture stresses in the adhesive layer were investigated using the joints bonded by three kinds of adhesives in heterogeneous and homogeneous systems. The results showed that both the yield and failure criterion depend on the stress triaxiality and that the fracture mechanism of the homogeneous adhesive is different from that of the heterogeneous one. From these experimental results, a method of estimating the yield and failure stresses was proposed in terms of a stress triaxiality parameter.