Stepped-lap Joints Research Articles

Numerical bond assessment of carbon-epoxy stepped-lap joints

With the main purpose of obtaining lightweight and durable structures, bonding techniques have improved significantly in several industries. Depending on the type of structure, joining different components with different materials may require different joint geometries, which may perform better or worse. Still, only the bond performance of a very limited number of joint geometries is well known. A lack of knowledge, for instance, about the debonding process of one and two-step joints persists, especially for the latter. The present work intends to mitigate this gap by studying the debonding processes of one and two-step joints made with CFRP and aluminium adherends. To that end, implicit and explicit numerical methods (finite and distinct element methods, respectively), were applied to study different joint geometries and identify which one shows the best bond performance when subjected to a monotonic load consistent with pure fracture mode II. Based on the bond stresses obtained within the interface of the joints, the debonding propagations of the one and two-step joints are analyzed thoroughly. In the case of the one-step bonded joints, the results revealed that when the ratio between the axial stiffness of the adherends is r = 1.0 the load capacity of these joint configurations is maximized. With two-step joints, the load capacity is very sensitive to the relationship between the axial stiffness on the left (ra) and right-hand side (rb). Based on 162 different numerical simulations, the results also suggest that the load capacities of the two-step joint configurations can be maximized when the axial stiffness ra and rb of the joint are equal to 1/3 and 3.0, respectively.

Stress analysis of adhesively-bonded single stepped-lap joints with functionally graded adherends based on the four-parameter fractional viscoelastic model

This paper presents a viscoelastic stress analysis of adhesively-bonded single stepped-lap joints under tension with functionally graded adherends. This analysis is based on the four-parameter fractional viscoelastic model and is considered the shear, peel, and axial stress components in the adhesive layer. The adhesive layer is assumed to exhibit a linear viscoelastic behavior, which is modeled using the fractional Zener model. The adherends is made of functionally graded Al2O3–Ni and are modeled using Timoshenko beam theory. The governing differential equations of the joint are derived in terms of the internal forces and moments in the Laplace domain using the structural, equilibrium, and compatibility equations of the adhesive layer and adherends. The governing equations are solved simultaneously and transformed from the Laplace domain into the time domain via the numerical inverse Laplace method. The results are compared to finite element results obtained from ANSYS Workbench, and a good agreement is observed. The results indicate that the axial stress in the adhesive layer is remarkable compared to the peel and shear stresses and must be considered in studies. Moreover, the variation in stress along the adhesive layer's thickness at both sides of the overlap region is significant.

An improved framework based on four-parameter viscoelastic model for stress analysis of adhesively-bonded single stepped-lap joints

The present study introduces an improved framework to analyze the longitudinal, shear, and peel stresses in the single stepped-lap joints under tensile loading based on a four-parameter viscoelastic model. To model the viscoelastic behavior of adhesive, the standard linear solid model is used. The governing differential equations are derived in the Laplace domain and are simultaneously solved and transformed using the Gaver–Stehfest inverse Laplace method. It was found that a rise in the butt thickness reduces the shear stress and increases the peel stresses. Moreover, an increase in the adhesive thickness reduces the longitudinal stress.

Stress analysis of adhesively-bonded single stepped-lap joints based on three-parameter fractional viscoelastic foundation model

This paper aims to develop a viscoelastic analytical model for adhesively bonded single stepped-lap joints subjected to tensile loading. The adherends are aluminum alloy A6063 and modeled as Timoshenko elastic beams and the adhesive is epoxy type B. A three-parameter fractional viscoelastic foundation (3PFVF) model is proposed to express the governing stresses in the joint and the fractional Zener model is used to model the viscoelastic behavior of the adhesive layer. The proposed 3PFVF model makes it possible to have different peel stresses between the two interfaces of adhesive and adherends. The governing differential equations are derived in the Laplace domain, and then solved and transformed simultaneously in the time domain using the Gaver-Stehfest inverse Laplace transform method. The finite element simulation with ANSYS is applied to validate the proposed method. The results show that a simple fractional viscoelastic model, which has a short differential equation, offers the same results as the classical viscoelastic models, which have higher and more complex differential equations. Moreover, the results show that the maximum shear and peel stresses in the single stepped-lap joints are about 20% less than single-lap joints.

Interfacial failure of circular or tubular hybrid bonded joints: A theoretical description

In different industries, the bonding technique has gained several advances in recent years. However, due to the specificity of each industry, the bonded joints may present different configurations. For instance, in the case of metallic truss bridges, the use of Carbon Fibre Reinforced Polymers (CFRP) bonded on the steel surface members may require circular or even tubular transitions between these materials. Although the bonded transitions between a metal and a composite material have been deeply studied with flat surfaces the information on circular or tubular hybrid bonded joints is still scarce. Therefore, the present study aims to mitigate some of this lack of knowledge by proposing an analytical solution able to describe the interfacial debonding process between a circular or tubular bonded transition between two materials. The proposed model also aims to simulate the interfacial debonding of double butt (or stepped) lap joints. Under these circumstances, a bilinear local adhesive model is adopted which required the quantification of the elastic and the softened stiffnesses as well as the pure Mode II fracture energy. The Finite Element Method (FEM) is used for the validation of the proposed model. The behaviour of the adhesive joint between materials is numerically modelled through the Cohesive Zone Modelling (CZM) in which the same bilinear shape used in the analytical solutions is adopted. Different situations were analyzed thoroughly and the numerical simulations tracked very closely the analytical results obtained from the proposed closed-form solutions.

Analysis of Intensity of Singular Stress Field at the Stepped-Lap Joint

Analysis of Intensity of Singular Stress Field at the Stepped-Lap Joint

Composite stepped-lap adhesive joint analysis by cohesive zone modelling

The use of adhesive bonds has increased significantly in recent years and is now a predominant bonding technique in the aeronautical and automotive industries. Cohesive Zone Models (CZM), used together with the Finite Element Method (FEM), are a viable tool to predict the strength (Pm) of adhesive joints. The CZM combines strength criteria for damage initiation and fracture mechanics concepts for crack propagation. The main objective of this study is to numerically and experimentally evaluate the mechanical performance of adhesively-bonded stepped-lap joints with carbon-fiber reinforced plastic (CFRP) substrates under tensile loading. The influence of different overlap lengths (LO) and a ductile adhesive was also investigated. Experimental data was gathered and compared with numerical CZM results obtained using Abaqus®. A study of peel (σy) and shear (τxy) stresses in the adhesive layer was performed. A significant geometry effect was found on the maximum load (Pm) of the stepped-lap joints, with benefit for large LO; however, delamination should be taken into account mostly for the longer LO. The CZM technique was revealed to be a suitable tool in determining the behavior of composite stepped-lap joints.

Adhesive strength evaluation of stepped-lap joint based on the intensity of singular stress field (ISSF)

Adhesive strength evaluation of stepped-lap joint based on the intensity of singular stress field (ISSF)

The effect of joint configuration on the strength and stress distributions of dissimilar adhesively bonded joints

The recent increase in the use of adhesively bonded joints (ABJs) made from dissimilar adherends demands the acquisition of a better understanding of the strength and behaviour of these joints, including their failure mechanisms. Several studies have reported on such joints individually, however few have compared the performances of dissimilar ABJs with varying configurations and design parameters, in order to determine the optimal design configuration for hybrid structures. In this work, a comparative study using experimental methods and finite element analysis was conducted, focusing on four joint configurations (scarf joints, stepped-lap joints, half-lap splice joints and single-lap joints), with the aim of evaluating the ways in which their performances differ. In addition, the effects of overlap length (L0) and the mechanical properties of the adherends on the overall success of each joint were particularly closely analysed and compared. The results showed that the scarf joint provided the best performance of all the designs discussed, and it was found that increasing the overlap length was only significantly beneficial for certain joint configurations and adherend combinations. When the overlap length was increased from 12.5 mm to 25 mm, the failure load increased by 47.50% and 21.25% for the scarf and the stepped-lap joints, respectively. In comparison, the percentage increases for the half-lap splice and single-lap joints under the same conditions were less than 10%. Moreover, the mechanical properties of the adherends considerably affected the failure mechanisms of the dissimilar joints, and for all four joint configurations, the failure was initiated by a crack at the adherend-adhesive interface adjacent to the adherend with a lower modulus.

Material and adhesive effect in adhesively-bonded composite stepped-lap joints

Adhesive bonding is a predominant bonding technique in the aeronautical and automotive industries. Cohesive zone models, used together with the finite element method, are a viable tool to predict the strength of adhesive joints. The main objective of this study is to evaluate experimentally and numerically (by cohesive zone model) the mechanical performance of carbon-fiber reinforced polymer stepped-lap bonded joints submitted to tensile loads, for different overlap lengths ( LO) and adhesives. The failure mode analysis showed a predominant failure type for all adhesives and good correspondence with the numerical predictions. Normalized peel ( σy) and shear ( τxy) stresses in the adhesive highly increased with LO, which then reflected on different maximum load ( Pm) evolution with LO, depending on the adhesive's ductility. The damage variable SDEG (stiffness degradation) was also evaluated and emphasized on the smaller damage zone at Pm for the brittle adhesive. A significant geometry and material effect were found on Pm of the stepped-lap joints, with benefit for large LO. In this regard, cohesive zone model revealed to be a suitable tool in determining the behavior of different joints. Comparison with joints with aluminum showed that, provided that no carbon-fiber reinforced polymer delamination occurs, stepped-lap joints between carbon-fiber reinforced polymer adherends give better results due to the higher composite stiffness.

Experimental and numerical analysis of dual-adhesive stepped-lap aluminum joints

The use of adhesive bonds has attracted considerable interest from the scientific community. Stepped-lap joints have the advantage of decreasing stress gradients along the bond length, although the outer steps still encounter stress levels above the steps in the inner zone of the joint. One possible way to reduce this stress gradient is to combine this type of joint with the use of two adhesives. This work consists of an experimental and numerical evaluation of stepped-lap dual-adhesive joints between aluminum adherends, for various overlap lengths ( LO), and comparison with stepped-lap single-adhesive joints. The adhesives Araldite® AV138, Araldite® 2015, and Sikaforce® 7752 were evaluated. Numerically, cohesive zone models with a triangular damage law were applied in the joint behavior prediction. The analysis of the results is presented in the form of failure modes, stress analysis, damage variable analysis, load–displacement ( P–δ) curves and maximum load ( Pm), and energy required to failure ( U). It was concluded that, in general, cohesive zone model presented precise predictions. In general, no significant increase in strength was achieved with dual-adhesive joint but, on the other hand, significant energy increases were obtained.

Experimental Study of Stepped-Lap Scarf Joint Repair for Spar Cap Damage of Wind Turbine Blade in Service

The objective of this paper was to design configuration parameters for a stepped-lap scarf joint repair, which can be used for spar cap damage of a wind turbine blade in service and to realize the post-repair monitoring. Two experimental studies were included. First, tensile test for the unidirectional tape specimens with a large aspect ratio repaired using a multiple stepped-lap scarf joint method was carried out. The results showed that the reinforcement layer could effectively improve the load-carrying capacity of the repaired zone. The stepped-lap joint surface was identified as the weak part of the spar cap repair, which should be monitored. Second, by embedding carbon nanotube buckypaper sensors on the stepped-lap joint surface of the repaired specimens, quasi-static tensile tests and fatigue tests were carried out. According to the resistance response of the sensors, the quasi-static tensile test confirmed the failure processes, namely the stiffness turning point, damage evolution, crack propagation, and fracture. The fatigue test could accurately identify the progressive failure, namely the initial damage, damage accumulation, initial cracking, and crack propagation to structural failure. The above tests provided an important configuration parameter basis for evaluating the spar cap repair scheme and presented a promising method for the health monitoring of a spar cap after repair.

Numerical modelling and experimental validation of step bonded joints

For the joint strength prediction of bonded joints, Fracture Mechanics-based techniques are often used. In this context, the tensile and shear toughness of the adhesives are two of the most important parameters to predict the joint behavior. The Finite Element Method has been used for strength prediction in the last decades. Cohesive zone modelling coupled to a FEM analysis is generally accepted as an accurate method. More recently, the Extended Finite Element Method (XFEM) has emerged. This work aims to validate the XFEM to predict the behavior of stepped-lap joints bonded with the adhesive Araldite® 2015. Peel and shear stresses in the bondline were evaluated, which allows an analysis of the behavior of the adhesive under different geometrical conditions. For the XFEM strength prediction, different damage initiation criteria were used based on either stresses or strains. The damage law shape was also evaluated, namely the linear and exponential damage propagation laws. The XFEM was found to be adequate to predict the joint strength using the Quadratic Stress and Maximum Stress damage initiation criteria.

A modified analytical model for stress analysis of adhesively bonded stepped-lap joints under tensile load

A modified analytical model with closed-form solution is proposed in this study to investigate interfacial shear and normal stresses in adhesively bonded double-lap joints with stepped outer adherend, subjected to tensile loading. By extending some researchers' prior related works, explicit expressions for adhesive interfacial shear and normal stresses are derived, with considerations of shear deformation in the adherends and plasticity in the adhesive layer. Continuity conditions are introduced to fit the variation of the outer adherend thicknesses. To obtain unknown constants of general solutions for adhesive normal stress, some approximate boundary conditions are reconstructed and several simplifications are imposed. The adhesive stress distributions along the bondline are obtained to investigate the effects of joint's material properties and geometric parameters. Adhesive with elastic-perfect plastic behavior is also considered in the analyses. The results obtained from the present model show an excellent agreement with corresponding finite element results. The present method is applicable to implement parametric analysis and optimal design for adhesively bonded double-lap joint.

An Experimental Investigation of the Mechanical Behavior of GFRP Co‐cured Joints

Co‐cured parts usually have their application where large monolithic composite structures are desired. This study evaluated the mechanical response in monotonic tensile test of bidirectional glass fiber reinforced polymer (GFRP) co‐cured joints manufactured by Vacuum Assisted Resin Infusion – VARTM. All joints were designed with the same number of fiber plies and joint length, varying only the joint geometry. Three geometries were studied: single lap joint (SLJ), stepped lap joint (STJ), and a new concept proposed in this study called interspersed lap joint (ILJ), the latter provides higher shear area and interfacial contact area per layer. Tensile test pointed STJ as presenting 77% of the monolithic GFRP tensile strength, the highest ultimate tensile strength among the studied joints. Void content and failure analysis showed high levels of porosity in the joint region for the ILJ, and also a weak bond between the adherents, which may result in a poor mechanical performance. In summary, simple modifications, such as plies disposal prior infusion can benefit the mechanical properties achieved for co‐cured joints.

Extended finite element modelling of aluminium stepped-adhesive joints

ABSTRACTFor the joint strength prediction of bonded joints, Fracture Mechanics-based techniques are often used. In this context, the tensile and shear toughness of the adhesives are two of the most important parameters to predict the joint behaviour. The Finite Element Method has been used for strength prediction in the last decades. Cohesive zone modelling coupled to a FEM analysis is generally accepted as an accurate method. More recently, the Extended Finite Element Method (XFEM) has emerged. This work aims to validate the XFEM to predict the behaviour of stepped-lap joints with different overlap lengths. Three adhesives, Araldite® AV138, Araldite® 2015 and Sikaforce® 7752, whose properties are quite different, were tested. Peel and shear stresses in the bondline were analysed, which allows an analysis of the behaviour of the three adhesives under different geometrical conditions. For the XFEM strength prediction, different damage initiation criteria were used, based either on stresses or strains. The damage law shape was also evaluated, namely the linear and exponential damage propagation laws. The XFEM was found to be adequate to predict the joint strength using the Quadratic Stress and Maximum Stress damage initiation criteria.

Comparative evaluation of adhesively-bonded single-lap and stepped-lap joints

Several adhesive joint configurations are available, namely butt joints, single-lap joints (SLJ), double-lap joints and scarf joints. Stepped-lap joints, which are not so studied, consist of a finite number of steps in the bonded area, possessing stress concentrations at all step edges instead of only at the bonded length edges. Stepped-lap joints increase the maximum load (Pm) over SLJ. The present study experimentally and numerically evaluates the static tensile strength of SLJ and stepped-lap joints bonded with the moderately ductile adhesive Araldite® 2015, considering varying values of overlap length (LO). A Finite Element Method (FEM) analysis was carried out to compare through-thickness normal (σy) and shear (τxy) stresses in the bondline between joint configurations. Additionally, a Cohesive Zone Modelling (CZM) analysis was considered to study the failure modes and to evaluate the CZM technique’s accuracy. Between SLJ and stepped-lap joints, the improved stress distributions of the stepped-lap joints resulted in higher joint performance, especially for higher LO. The CZM model revealed to be accurate in predicting Pm.

Comparison of different adhesively-bonded joint types for mechanical structures

Adhesively-bonded joints are widely used to join structural components. The most common joint types are single-lap joints (SLJ), double-lap joints (DLJ), stepped-lap joints and scarf joints. Several factors influence the behaviour and strength of an adhesive joint, namely the type of adhesive (brittle or ductile, strong or weak) and joint geometry. One of the most important parameters that affects the joint strength is the overlap length (LO). A comparative study that involves several joint geometries and uses adhesives with different characteristics was carried out to check which type of adhesive is most suitable for a particular joint geometry. For this purpose, SLJ, DLJ, stepped-lap joints and scarf joints were chosen for testing with three adhesives. The experimental results were compared with numerical results obtained from Abaqus® using an integrated cohesive zone modelling module. Initially, a stress analysis was carried out to compare the different joint geometries. With this work, it was concluded that the optimal joint type significantly depends on the type of adhesive used, such that less strong and ductile adhesives are more suitable for joint geometries that exhibit large stress variations, while stronger but more brittle adhesives are recommended for joint geometries with more uniform stresses.

Crack growth analysis of adhesively-bonded stepped joints in aluminium structures

Adhesive bonding has become a promising joining technique, by satisfying the needs of diverse industrial fields. Several joint configurations are available for the designer, and the most common and exhaustively studied are single-lap, double-lap and scarf joints (Petrie in Handbook of adhesives and sealants. McGraw-Hill, New York, 2000; Moreira and Campilho in Eng Struct 101:99–110, 2015). Stepped-lap joints consist of a finite number of steps in the bonded region, and they are characterized by having stress concentrations at the end of each step rather than only at the bonded length edges, which leads to a higher load transfer through the interior part of the overlap compared to lap joints and, consequently, to a higher performance. The present work experimentally and numerically evaluates the static tensile strength of stepped-lap joints bonded with three adhesives, Araldite® AV138 (brittle), Araldite® 2015 (moderately ductile) and Sikaforce® 7752 (ductile), considering different overlap lengths (LO). A finite element analysis was undertaken to compare through-thickness normal (σy) and shear (τxy) stresses in the adhesive layer between joint configurations. Additionally, a cohesive zone model (CZM) analysis was considered to study the failure modes and the CZM damage variable during failure and to evaluate the CZM technique’s accuracy. It was possible to conclude that the recommended adhesive depends on the joint geometry, since strong and brittle adhesives are better for small LO, while for higher LO ductile adhesives with less strength can give better results. The CZM technique was accurate in the strength prediction, although with slight under-predictions for highly ductile adhesives.

Comparison on damage tolerance of scarf and stepped-lap bonded composite joints under quasi-static loading

Scarf or stepped-lap repairs are desirable for composite structures in aerospace, especially where a flush finish is required. Damage tolerance is a critical issue in the repair design. This paper investigates and compares the damage tolerance of scarf and stepped-lap joints (repairs) under quasi-static loading using finite element analysis (FEA). The damage was represented by a flaw embedded in the bondline between composite adherents. 3D FE models were built for both scarf and stepped-lap joints. Both linear and nonlinear adhesive properties were simulated under room temperature (RT) and hot-wet (HW) conditions. The flaws with varying length and width were imbedded in the bondline, so that the sensitivity of damage tolerance to the flaw size can be analysed and compared between scarf and stepped-lap joints. Other parameters, which may affect the damage tolerance of both joints, include flaw location, number of steps of stepped-lap joint, stacking sequence of laminate adherend, out-of-plane boundary conditions and the presence of an external doubler. The results showed that the stepped-lap joint exhibited better damage tolerance than the scarf joint with linear elastic adhesive. The damage tolerance of both joints became similar when the adhesive became nonlinear under RT or HW conditions. The damage tolerance of both joints can be improved by attaching composite doubler reinforcement or constraining the out-of-plane movement.