Finite element analysis of adhesive joints in four-point bending load

Nonlinear finite element analysis (FEA) was applied to the adhesively bonded Single Lap Joint (SLJ) in bending load. Two adhesives, one stiff and one flexible, with very different mechanical behaviors, and hard steel as adherend with four different thicknesses, were analyzed for the joint configuration. For comparison, experimental work was also undertaken. It was shown that adherend thickness played an important part in the joint performance; while the stiff adhesive gave stronger joint strength when using thick adherends, the opposite was the case for the flexible adhesive when using thin adherends. These results were related to the mechanical behaviors of the adhesives used. It was shown that the results from the FEA and the experimental works were in a good agreement.     

FINITE ELEMENT ANALYSIS OF ADHESIVE JOINTS IN FOUR-POINT BENDING LOAD

Nonlinear finite element analysis (FEA) was applied to the adhesively bonded Single Lap Joint (SLJ) in bending load. Two adhesives, one stiff and one flexible, with very different mechanical behaviors, and hard steel as adherend with four different thicknesses, were analyzed for the joint configuration. For comparison, experimental work was also undertaken. It was shown that adherend thickness played an important part in the joint performance; while the stiff adhesive gave stronger joint strength when using thick adherends, the opposite was the case for the flexible adhesive when using thin adherends. These results were related to the mechanical behaviors of the adhesives used. It was shown that the results from the FEA and the experimental works were in a good agreement.     

An investigation on the initiation and propagation of damaged zones in adhesively bonded lap joints

In this study, the initiation and propagation of damaged zones in the adhesive layer and adherends of adhesively bonded single and double lap joints were investigated considering the geometrical non-linearity and the non-linear material behaviour of the adhesive and adherends. The modified von Mises criteria for adherends and Raghava and Cadell's failure criteria (J. Mater. Sci. 8, 225 (1973) [1]) including the effects of the hydrostatic stress states for the epoxy adhesive were used to determine the damaged adhesive and adherend zones which exceeded the specified ultimate strains. The stiffness of all finite elements corresponding to these zones was reduced so that they could not contribute to the overall stiffness of the adhesive joint. This approach simplifies to observe the initiation and propagation of the damaged zones in both the adhesive layer and adherends. A tensile load caused first the damaged adhesive zones to appear at the right free end of the adhesive-lower adherend interface and at the left free end of the adhesive-upper adherend interface, and then to propagate through the adhesive regions near the adhesive-adherend interfaces (interfacial failure). In the bending test, the damaged zone initiated at the left free end of the adhesive-upper adherend interface in tension, and similarly propagated through the adhesive regions close to the adhesive-adherend interface (interfacial failure). In the double-lap joint subjected to a tensile load, the damaged adhesive zones initiated first at the right free end of the adhesive-middle adherend interface and then propagated through the adhesive region near the adhesive-adherend interface. After the damaged zone reached a specific length it also grew through the adhesive thickness, and the adhesive joint failed. The SEM micrographs of fracture surfaces around the free edges of the overlap region indicated that the failure was interfacial. An additional damaged zone growth was observed in the side adhesive regions due to lateral straining, called the Poisson effect.     

Effect of Mechanical Surface Treatment on the Static Strength of Adhesive Lap Joints

This work deals with an experimental investigation on the effect of mechanical surface treatments of adhesive bonded joints. The behaviour of an adhesively bonded joint can be considered good if cohesive failure is achieved, while when interfacial failure occurs the performances are normally much worse. A key parameter which drives the failure type is the surface treatment applied to the adherends. This work analyzes, by means of a structured experimental campaign, which surface mechanical treatment gives the best performance. The design of the experimental approach used involves different materials, joint geometries, and surface treatments. The results are investigated in terms of force, energy, and stresses in the joints and the performance of the several mechanical treatments tested is assessed, showing that a simple correlation with the surface roughness is not sufficient to predict the best joint performances. The reliable results obtained prove that sandpapering or sandblasting the adherends gives a strong improvement in terms of performance and leads to a higher probability of cohesive failure.     

Non-linear Modeling of Tubular Adhesive Scarf Joints Loaded in Tension

In this paper, a simple analytical model is developed to determine the adhesive shear strain distribution of a tubular adhesive scarf joint loaded in tension. The approach is an extension of the original well-recognized Volkersen's shear lag analysis for a shear loaded joint, which is frequently applied to adhesively-bonded joints. A mathematical representation consisting of linear and exponential functions is employed to model the elastic–plastic behavior commonly observed in structural adhesives. The governing equation is found to be in the form of a non-linear second-degree ordinary differential equation with variable coefficients. A numerical method required for solving this equation is also introduced. Numerical predictions of shear strain distributions are compared with results from non-linear Finite Element Analysis (FEA), utilizing the commercially available software, ANSYS 5.6, a general-purpose software system. It is shown that both the linear and non-linear approximate solutions are closely comparable with the FEA results for a 10°-scarf angle and elastic isotropic adherends. In concurrence with previous work on flat adherends, the present work demonstrates that the scarf joint develops more uniform shear stress and strain distributions with a consequent reduction in peak values than those for the conventional lap joint. In contrast, the conventional lap joint with the equivalent bonded surface area experiences a more substantial elastic trough, which can provide a more stable configuration for, sustained long term loading applications.     

Development of a Computer Program for the Design of Adhesive Joints

Adhesive joints are increasingly being used due to their improved mechanical performance and a better understanding of the mechanics of failure. To predict the joint strength, one must have the stress distribution and a suitable failure criterion. The literature contains many closed-form solutions for the stress distribution. However, the models are sometimes difficult to implement and use. The objective of the present work was to compile existing models of increasing complexity into user friendly software. Three main situations were considered: elastic adherends and adhesive, elastic adherends with nonlinear adhesive and nonlinear analyses for both adherends and adhesive. The adherends were both isotropic (metals) and anisotropic (composites). The joints considered are the single and double lap joints for most of the models. However, a sandwich model initially proposed by Crocombe can be used for any type of joint provided the boundary conditions are known. For each model proposed the compatible failure criteria are included to enable the user not only to have the stress distribution but also the failure load for a given joint/load scenario. Experimental tests corresponding to the three cases described above were carried out to validate the models implemented.     

Single and dual adhesive bond strength analysis of single lap joint between dissimilar adherends

The emerging trends for joining of aircraft structural parts made up of different materials are essential for structural optimization. Adhesively bonded joints are widely used in the aircraft structural constructions for joining of the similar and dissimilar materials. The bond strength mainly depends on the type of adhesive and its properties. Dual adhesive bonded single lap joint concept is preferred where there is large difference in properties of the two dissimilar adherends and demanding environmental conditions. In this work, Araldite-2015 ductile and AV138 brittle adhesives have been used separately between the dissimilar adherends such as, CFRP and aluminium adherends. In the dual adhesive case, the ductile adhesive Araldite-2015 has been used at the ends of the overlap because of high shear and peel strength, whereas in the middle of the bonded region the brittle adhesive AV138 has been used at different dimensions. The bond strength and corresponding failure patterns have been evaluated. The Digital Image Correlation (DIC) method has been used to monitor the relative displacements between the dissimilar adherends. Finite element analysis (FEA) has been carried-out using ABAQUS software. The variation of peel and shear stresses along the single and dual adhesive bond length have been captured. Comparison of experimental and numerical studies have been carried-out and the results of numerical values are closely matching with the experimental values. From the studies it is found that, the use of dual adhesive helps in increasing the bond strength.     

Optimization of adhesively-bonded single lap joints by adherend notching

The effect of adherend notching on the strength and deformation behavior of single lap joints was investigated. First, a parametric study was conducted using finite element analysis (FEA). This initial part of the research into the effect of notches on joint behavior involved determination of the optimum notch location and notch dimensions. This was done by using FEA in a series of models with different notch positions and geometries. The results of this parametric study were used to select the most promising lap geometries for further study. Next, more detailed FEA were conducted on the selected lap geometries. These data were compared with the experimental single-lap shear test results to assess the applicability of different failure criteria. Three different model adhesives were used: a rubber toughened film epoxy with nylon carrier, a styrene-butadiene-styrene block copolymer based deformable 'gel' adhesive, and a two-part, metal filled brittle epoxy adhesive. The FEA for single lap joints containing 'top notches' on the unbonded, top side of the adherends, at locations corresponding to the overlap ends, and bonded with the two-part metal filled epoxy provided the best agreement with the experimental results. The experimental results showed a 29% increase in joint strength with the introduction of the notches, which matched very well with the 27% decrease in the peak peel stress observed by the FEA results. For this brittle adhesive, the peel stress is almost certainly the governing failure stress. This was confirmed by matching of the FEA peak peel stress ratios with the experimental load ratios, for both the notched and unnotched specimens.     

Metallic multi-material adhesive joint testing and modeling for vehicle lightweighting

While adhesive bonding has been shown to be a beneficial technique to join multi-material automotive bodies-in-white, quantitatively assessing the effect of adherend response on the ultimate strength of adhesively bonded joints is necessary for accurate joint design.In the current study, thin adherend single lap shear testing was carried out using three sheet metals used to replace mild steel when lightweighting automotive structures: hot stamped Usibor® 1500 AS ultra-high strength steel (UHSS), aluminum (AA5182), and magnesium (ZEK 100). Six combinations of single and multi-material samples were bonded with a one-part toughed structural epoxy adhesive and experimentally tested to measure the force, displacement across the bond line, and joint rotation during loading. Finite element models of each test were analyzed using LS-DYNA to quantitatively assess the effects of the mode mixity on ultimate joint failure. The adherends were modeled with shell elements and a cohesive zone model was implemented using bulk material properties for the adhesive to allow full three-dimensional analysis of the test, while still being computationally efficient.The UHSS-UHSS joint strength (27.2 MPa; SD 0.6 MPa) was significantly higher than all other material combinations, with joint strengths between 17.9 MPa (SD 0.9 MPa) and 23.9 MPa (SD 1.4 MPa). The models predicted the test response (average R2 of 0.86) including the bending deformation of the adherends, which led to mixed mode loading of the adhesive. The critical cohesive element in the UHSS-UHSS simulation predicted 85% Mode II loading at failure while the other material combinations predicted between 41% and 53% Mode II loading at failure, explaining the higher failure strength in the UHSS-UHSS joint.This study presents a computational method to predict adhesive joint response and failure in multi-material structures, and highlights the importance of the adherend bending stiffness and on joint rotation and ultimate joint strength.     

Experimental and numerical analysis on load capacity and failure process of T-joint: Effect produced by the bond-line length

Aim of this work is to analyze the load capacity of the adhesive-bonded T-joints under tension load. And the work presents an experimental investigation into the effect produced by the bond-line length on adhesive bonded T-joints made of steel and aluminum. The experimental results showed that the bond-line length did not have any effect on the ultimate load of T-joints; however, by increasing the bond-line length the energy absorbed capacity of T-joints increased significantly. A concept, balanced and imbalanced joints, was proposed to illustrate the influence caused by stiffness ratio (R) between two adherends of T-joints. And it can be found that the ratio R had a significant effect on the ultimate load. In order to model the adhesive between joint components and simulate the damage propagation, a cohesive zone model based analysis was carried out using finite element method in ABAQUS program. Also, failure process of adhesive can be modeled. One can observe that only the upper end of adhesive layer transmits the load in the beginning. And after the damage occurs, it will propagate along the bond line from the upper end to the lower end.     

Non-linear Modeling of Tubular Adhesive Scarf Joints Loaded in Tension

In this paper, a simple analytical model is developed to determine the adhesive shear strain distribution of a tubular adhesive scarf joint loaded in tension. The approach is an extension of the original well-recognized Volkersen's shear lag analysis for a shear loaded joint, which is frequently applied to adhesively-bonded joints. A mathematical representation consisting of linear and exponential functions is employed to model the elastic-plastic behavior commonly observed in structural adhesives. The governing equation is found to be in the form of a non-linear second-degree ordinary differential equation with variable coefficients. A numerical method required for solving this equation is also introduced. Numerical predictions of shear strain distributions are compared with results from non-linear Finite Element Analysis (FEA), utilizing the commercially available software, ANSYS 5.6, a general-purpose software system. It is shown that both the linear and non-linear approximate solutions are closely comparable with the FEA results for a 10°-scarf angle and elastic isotropic adherends. In concurrence with previous work on flat adherends, the present work demonstrates that the scarf joint develops more uniform shear stress and strain distributions with a consequent reduction in peak values than those for the conventional lap joint. In contrast, the conventional lap joint with the equivalent bonded surface area experiences a more substantial elastic trough, which can provide a more stable configuration for, sustained long term loading applications.     

Geometrical Optimization of the Overlap in Mixed Adhesive Lap Joints

The aim of this research is to optimize the geometry of the overlap in mixed adhesive single- and double-lap joints using a modified version of Bees and Genetic Algorithms (BA and GA). Accounting for adherends Poisson's ratio in the deduced equilibrium equations, the proposed shear lag model gives a more accurate approximation of joint failure load in comparison with Volkersen's solution. The objective functions used in this work are used separately to maximize the load bearing capacity f and the specific strength (f/w) of the joint. This procedure is applied to optimize aeronautical adhesively bonded assemblies, while taking manufacturing constraints into account. The employed constraints are the application of yield criterion on adherends as well as geometrical constraint on the overlap length. The proposed straightforward procedure provides 18 optimal configurations amid a wide range of changes for optimization variables, among which the designer can take a choice, depending on his/her goal. The efficiency of the two employed algorithms, BA and GA, in searching for the optimum geometrical design of the mixed adhesive joints have also been investigated. The results show the more robust and efficient performance of the modified version of BA over GA in such kinds of engineering problems.     

A Two-dimensional Stress Analysis and Strength of Single-lap Adhesive Joints of Dissimilar Adherends Subjected to External Bending Moments

The stress distributions of single-lap adhesive joints of dissimilar adherends subjected to external bending moments are analyzed as a three-body contact problem by using a two-dimensional theory of elasticity (plane strain). In the analysis, dissimilar adherends and an adhesive are replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli of adherends, the adherend thickness ratio and the adherend length ratio between dissimilar adherends on the stress distributions at the interfaces are examined. The results show that the stress singularity occurs at the ends of the interfaces, and its intensity is greater at the interface of the adherend with smaller Young's modulus. It is also noted that the singular stress is greater at the interface of the thinner adherend. It is found that the effect of the adherend length ratio on the stress singularity at the interfaces is very small. Joint strength is predicted by using the interface stress and it was measured by experiments. From the analysis and the experiments, it is found that the joint strength increases as Young's modulus of adherends and the adherend thickness increase while the effect of the adherend lengths on the joint strength is small. For verification of the analysis, a finite element analysis (FEA) is carried out. A fairly good agreement of the interface stress distribution is seen between the analytical and the FEA results.     

The interrelationships between electronically conductive adhesive formulations,substrate and filler surface properties,and joint performance. Part I: the effects of adhesive thickness

Electronically conductive adhesives (ECAs) have received a great deal of attention for interconnection applications in recent years. Even though ECAs have excellent potential for being efficient and less costly alternative to solder joining in electronic components, they still possess a number of problems with respect to durability and design to meet specific needs. One of the issues that requires understanding is regarding the optimum adhesive thickness (AT) to be used. This study addresses this issue in relation to the formulations of the conductive adhesives and their interactions with adherend surfaces. For this purpose, two different adherends varying in surface characteristics were utilized along with three different conductive adhesive formulations with varying particle loadings, and shapes and sizes of conductive nickel fillers. Joints were also prepared with two different AT values, to gain insight into the influence of AT on the joint strength, deformation and joint conductivity. As the AT was increased, only a small reduction in failure load and ultimate displacement values were observed with unetched adherends. With etched adherends, however, a small increase in joint stretchability was evident with higher adhesive thickness tested at a lower crosshead speed. When the AT was increased, we also noted a corresponding increase in the initial joint resistance.     

Mechanical behavior of interlocking multi-stepped double scarf adhesive joints including void and disbond effects

Surface topographical effects on the mechanical behavior of interlocking multi-stepped double scarf adhesive joints under tensile load were studied. For this purpose, finite element analysis (FEA) of the joint geometry at 10 different step angles was carried out. In the second stage, the effects of substrate voids and adhesive delaminations on the interfacial strength were studied for the scarf angle of 32.2° by FEA simulation as well as experimentally. For the cases of the missing steps (voids) and delamination (absence of bonding induced by release agent) the ratios of maximum stresses (principal, von Mises, normal, shear and transverse) between the completely bonded and altered (void or delaminated) joints were compared with the failure load ratios for the same joints to interpret the mechanism of failure. The results revealed that except for the normal stress, the maximum stress ratios reach a maximum value and then decrease with increasing scarf angle. FEA analysis with the voids showed that the strength of the joint not only depends on their size, but also on their location in the joint. When the experimental results were compared with the FEA using the stress ratio between the unmodified (completely bonded) and modified (void or disbond) cases, the results indicated that the normal stress dominates the failure behavior of the 32.2° scarf angle joint. Comparison of the experimental results for the void, and disbond cases revealed that the disbond cases can possess higher joint strength in comparison to the void cases. This finding could not be predicted by FEA, and was attributed to the presence of friction at the interface subsequent to delamination.     

Experimental study of the influence of adhesive reinforcement in lap joints for composite structures subjected to mechanical loads

The paper deals with experimental investigations on reinforcing the adhesive in single lap joints subjected to mechanical loads such as tensile, bending, impact and fatigue. The adhesive used for bonding was an epoxy reinforced with unidirectional and chopped glass fibres as well as micro-glass powder. The adherends were glass reinforced composite laminates. The bonding surfaces were prepared before joining. In the case of unidirectional fibres in the adhesive region, the fibre orientations considered were 0°, 45° and 90°. The volume fraction of fibres in the adhesive layer in all the cases was 30%. The volume fractions of micro-glass powder were 20%, 30% and 40%. The tensile, bending, impact and fatigue tests on the prepared specimens were conducted according to ASTM standards. The results show that except the 90° unidirectional orientation, reinforcing the adhesive with glass fibres or powder increases the joint strength. The use of volume fraction of 30% of micro-glass powder gave the best performance in the above loading conditions. The fatigue life increased by 125%, the ultimate joint strength in tension increased by 72%, the bending ultimate joint strength increased by 112% and the impact joint strength increased by 63%. The microstructure of the debonded area was examined and three modes of failure could be observed namely cohesive failure, light fibre-tear failure and thin layer cohesive failure.     

Effect of adhesive free-end geometry on the initiation and propagation of damaged zones in adhesively bonded lap joints

In this study the effect of adhesive free-end geometry on the initiation and propagation of damaged zones in adhesively bonded single- and double-lap joints was investigated considering the material non-linear behaviour of both adhesive and adherends and the geometrical non-linearity. The damaged adhesive and adherend zones exceeding the specified ultimate strains were determined based on the modified von Mises criterion for adherends and the failure criterion, including the effects of the hydrostatic stress states for the epoxy adhesives proposed by Raghava and Cadell. The stiffness of each finite element in the damaged zones was reduced to a negligible value, thus not contributing to the overall stiffness of the adhesive joint. This simple method provides useful information on the initiation and propagation of damaged zones in both the adhesive layer and adherends. The damaged adhesive zones due to a tensile load were observed to initiate around the rounded adherend corners inside the adhesive fillets and to propagate first towards both the free surface of the adhesive fillet and across the adhesive layer, and later along the adherend–adhesive interface. The damaged adhesive zones initiate at the left free-end of the adhesive-upper adherend interface and at the right free-end of the adhesive-lower adherend interface and propagate along these interfaces in the large adhesive fillets. In the bending test, the damaged adhesive zones appeared only at the left free-end in tension of the adhesive-upper adherend interface for the large adhesive fillets, but around the lower adherend corner for the smaller adhesive fillets. Later, it propagated with a similar mechanism as in the tensile load. In a double-lap joint subjected to a tensile load, the damaged zone appeared around the upper adherend corner inside the right adhesive fillet in tension, and propagated first towards the free surface of the adhesive fillet and through the adhesive layer towards the adhesive-middle adherend interface, and later along this interface. For all loading conditions, increasing the adhesive fillet size caused the damaged zone initiation to occur at a larger load level. The SEM micrographs of fracture surfaces around the adhesive fillets showed that the damaged zones initiated around the adherend corner inside the adhesive fillet and propagated through the adhesive fillets.     

Three-dimensional finite element analysis of stress response in adhesive butt joints subjected to impact bending moments

The stress wave propagation and the stress distribution in adhesive butt joints of T-shaped similar adherends subjected to impact bending moments are calculated using a three-dimensional finite-element method (FEM). An impact bending moment is applied to a joint by dropping a weight. The FEM code employed is DYNA3D. The effects of the Young's modulus of adherends, the adhesive thickness, and the web length of T-shaped adherends on the stress wave propagation at the interfaces are examined. It is found that the highest stress occurs at the interfaces. In the case of T-shaped adherends, it is seen that the maximum principal stress at the interfaces increases as Young's modulus of the adherends increases. In the special case where the web length of T-shaped adherends equals the flange length, the maximum principal stress at the interfaces increases as Young's modulus of the adherends decreases. The maximum principal stress at the interfaces increases as the adherend thickness decreases. The characteristics of the T-shaped adhesive joints subjected to static bending moments are also examined by FEM and compared with those under impact bending moments. Furthermore, strain response of adhesive butt joints was measured using strain gauges. A fairly good agreement is observed between the numerical and the experimental results.     

Stress analysis and strength evaluation of single-lap band adhesive joints of dissimilar adherends subjected to external bending moments

Single-lap band adhesive joints of dissimilar adherends subjected to external bending moments are analyzed as a four-body contact problem using a two-dimensional theory of elasticity (plane strain state). In the analysis, the upper and lower adherends and the adhesive which are bonded in two regions are replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli of the adherends, the ratio of the adherend thicknesses, and the ratio of the band length to the half lap length on the stress distributions at the interfaces are examined. A method for estimating the joint strength is proposed using the interface stress and strain obtained by the analysis. An elasto-plastic finite element analysis (EP-FEA) was conducted for predicting the joint strength more exactly. Experiments to measure strains and the joint strength were also carried out. The results show that the strength of a single-lap band adhesive joint is almost the same as that of a single-lap adhesive joint in which the two adherends are completely bonded at the interfaces. Thus, the single-lap band adhesive joints are useful in the design of single-lap joints.     

Failure load prediction of structural adhesive joints Part 1: Analytical method

This paper describes an analytical method for calculating the strain energy release rate of cracked adhesive joints. The calculations proceed from a knowledge of the reactions in the adherends at the end of the joint overlap. For joints with equal adherends, a simple method exists for determining the Mode I and Mode II components of the energy release rate. The equations make it relatively easy to apply fracture mechanics failure criteria to arbitrarily loaded adhesive joints. In a subsequent paper, it is shown that by treating uncracked joints as having a crack, with the crack tip coinciding with the location of the spew fillet, the load required to propagate a crack in a cracked joint serves as a reliable conservative estimate of the load required to propagate a crack in an uncracked joint. The present method is suitable, therefore, for failure load predictions of structural adhesive joints in design applications.