Optimal Design of the Adhesively-Bonded Tubular Single Lap Joint

In this paper, a method for the optimal design of the adhesively-bonded tubular single lap joint was proposed based on the failure model of the adhesively-bonded tubular single lap joint. The failure model incorporated the nonlinear mechanical behavior of the adhesive as well as the different failure modes in which the adhesive failure mode changed from bulk shear failure, via transient failure, to interfacial failure between the adhesive and the adherend, according to the magnitudes of the residual thermal stresses induced by fabrication.

The effects of the design parameters for the adhesively-bonded tubular single lap joint, such as the thicknesses of adhesive layer and adherends, the bonding length, and the scarfs of adherends, on the torque transmission capability and the efficiency of the adhesive joint were investigated.     

Strength Analysis of Adhesively-Bonded Tubular Single Lap Steel-Steel Joints Under Axial Loads Considering Residual Thermal Stresses

The static tensile load bearing capability of adhesively-bonded tubular single lap joints calculated using linear mechanical adhesive properties is usually far less than the experimentally-determined one because the majority of the load transfer of adhesively-bonded joints is accomplished by the nonlinear behavior of the rubber-toughened epoxy adhesive

In this paper, both the nonlinear mechanical properties and the residual thermal stresses in the adhesive resulting from joint fabrication were included in the stress calculation of adhesively-bonded joints. The nonlinear tensile properties of the adhesive were approximated by an exponential equation which was represented by the initial tensile modulus and ultimate tensile strength of the adhesive.

From the tensile tests and the stress analyses of adhesively-bonded joints, a failure model for adhesively-bonded tubular single lap joints under axial loads was proposed.     

Influence of Fabrication Residual Thermal Stresses on Rubber-toughened Adhesive Tubular Single Lap Steel-Steel Joints under Tensile Load

The tensile load bearing capability of adhesively-bonded tubular single lap joints which is calculated under the assumption of linear mechanical adhesive properties is usually much less than the experimentally-determined because the majority of the load transfer of adhesively-bonded joints is accomplished by the nonlinear behavior of rubber-toughened epoxy adhesives. Also, as the adhesive thickness increases, the calculated tensile load bearing capability with the linear mechanical adhesive properties increases, while, on the contrary, the experimentally-determined tensile load bearing capability decreases.

In this paper, the stress analysis of adhesively-bonded tubular single lap steel-steel joints under tensile load was performed taking into account the nonlinear mechanical properties and fabrication residual thermal stresses of the adhesive. The nonlinear tensile properties of the adhesive were approximated by an exponential equation which was represented by the initial tensile modulus and ultimate tensile strength of the adhesive.

Using the results of stress analysis, the failure criterion for the adhesively-bonded tubular single lap steel-steel joints under tensile load was developed, which can be used to predict the load-bearing capability of the joint. From the failure criterion, it was found that the fracture of the adhesively-bonded joint was much influenced by the fabrication residual thermal stresses.     

An Iterative Solution for the Torque Transmission Capability of Adhesively-Bonded Tubular Single Lap Joints with Nonlinear Shear Properties

The adhesively-bonded tubular single lap joint shows large nonlinear behavior in the load-displacement relationship, because structural adhesives for the joint are usually rubber-toughened, which endows adhesives with nonlinear shear properties. Since the majority of load transfer of the adhesively-bonded tubular single lap joint is accomplished by the nonlinear behavior of the adhesive, its torque transmission capability should be calculated using nonlinear shear properties. However, both the analytic and numerical analyses become complicated if the nonlinear shear properties of the adhesive are included during the calculation of torque transmission capabilities.

In this paper, in order to obtain the torque transmission capabilities easily, an iterative solution which includes the nonlinear shear properties of the adhesive was derived using the analytic solution with the linear shear properties of the adhesive. Since the iterative solution can be obtained very quickly due to its simplicity, it has been found that it can be used in the design of the adhesively-bonded tubular single lap joint.     

Development of a Failure Model for the Adhesively Bonded Tubular Single Lap Joint

The accurate calculation of the stresses and torque capacities of adhesively bonded joints is not possible without understanding the failure phenomena of the adhesive joints and the nonlinear behavior of the adhesive.

In this paper, an adhesive failure model of the adhesively bonded tubular single lap joint with steel-steel adherends was proposed to predict the torque capacity accurately.

The model incorporated the nonlinear behavior of the adhesive and the different failure modes in which the adhesive failure mode changed from bulk shear failure, via transient failure, to interfacial failure between the adhesive and the adherend, according to the magnitudes of the residual thermally-induced stresses from fabrication.     

Torque Transmission Capabilities of Bonded Polygonal Lap Joints for Carbon Fiber Epoxy Composites

Although carbon fiber epoxy composite materials have excellent properties for structures, the joint in composite materials often reduces the efficiency of the composite structure because the joint is often the weakest area in the composite structure.

In this paper, the effects of the adhesive thickness and the adherend surface roughness on the static and fatigue strengths of adhesively-bonded tubular polygonal lap joints have been investigated by experimental methods. The dependencies of the static and fatigue strengths on the stacking sequences of the composite adherends were observed.

From the experimental investigations, it was found that the fatigue strength of the circular adhesively-bounded joints was quite dependent on the surface roughness of the adherends and that polygonal adhesively-bonded joints had better fatigue strength characteristics than circular adhesively-bonded joints.     

Torque Transmission Capabilities of Bonded Polygonal Lap Joints for Carbon Fiber Epoxy Composites

Although carbon fiber epoxy composite materials have excellent properties for structures, the joint in composite materials often reduces the efficiency of the composite structure because the joint is often the weakest area in the composite structure.

In this paper, the effects of the adhesive thickness and the adherend surface roughness on the static and fatigue strengths of adhesively-bonded tubular polygonal lap joints have been investigated by experimental methods. The dependencies of the static and fatigue strengths on the stacking sequences of the composite adherends were observed.

From the experimental investigations, it was found that the fatigue strength of the circular adhesively-bounded joints was quite dependent on the surface roughness of the adherends and that polygonal adhesively-bonded joints had better fatigue strength characteristics than circular adhesively-bonded joints.     

The Torque Transmission Capabilities of the Adhesively-Bonded Tubular Single Lap Joint and the Double Lap Joint

With the wide application of fiber-reinforced composite materials in aircraft, space structures and robot arms, the design and manufacture of composite joints have become a very important research area because they are often the weakest areas in composite structures.

In this paper, the stress and torque transmission capabilities of the adhesively-bonded tubular single lap joint and the double lap joint were experimentally tested. In order to compare the experimental results with the calculated results, the stress and torque transmission capabilities were analyzed by the 3-dimensional finite element method taking into consideration the nonlinear properties of the adhesive.

From the experiments it was found that the torque transmission capabilities of the adhesively-bonded double lap joint was 2.7 times as large as that of the single lap joint. Also, it was found that the fatigue limit of the double lap joint was 16 times as large as that of the single lap joint.     

Development of a Fatigue Failure Model for the Adhesively Bonded Tubular Single Lap Joint under Dynamic Torsional Loading

The adhesively bonded tubular single lap joint shows nonlinear torque transmission capability and deformation characteristics under static torsional loading because of nonlinear properties of the adhesive. However, the dynamic or fatigue torque transmission capability can be calculated with linear, analysis because the stress-strain relation under torsional fatigue loading is linear, due to the small dynamic transmission capability compared with the static torque transmission capability.

In this paper, a failure model for the adhesively bonded tubular single lap joint under torsional fatigue loading was developed with respect to the adhesive thickness, which is the critical factor for the static torque transmission capability. Also, a design method for the adhesively bonded tubular single lap joint under torsional fatigue loading was proposed.     

Development of a Fatigue Failure Model for the Adhesively Bonded Tubular Single Lap Joint under Dynamic Torsional Loading

The adhesively bonded tubular single lap joint shows nonlinear torque transmission capability and deformation characteristics under static torsional loading because of nonlinear properties of the adhesive. However, the dynamic or fatigue torque transmission capability can be calculated with linear, analysis because the stress-strain relation under torsional fatigue loading is linear, due to the small dynamic transmission capability compared with the static torque transmission capability.

In this paper, a failure model for the adhesively bonded tubular single lap joint under torsional fatigue loading was developed with respect to the adhesive thickness, which is the critical factor for the static torque transmission capability. Also, a design method for the adhesively bonded tubular single lap joint under torsional fatigue loading was proposed.     

Transverse cracking of a simple lap joint under axial load

The failure mode of axially loaded simple, single lap joints formed between thin adherends which are flexible in bending is conventionally described as one of axial peeling. We have observed – using high-speed photography – that it is also possible for failure to be preceded by the separation front, or crack, moving in a transverse direction, i.e. perpendicular to the direction of the axial load. A simple energy balance analysis suggests that the critical load for transverse failure is the same as that for axial separation for both flexible lap joints, where the bulk of the stored elastic energy lies in the adhesive, and structural lap joints in which the energy stored in the adherends dominates. The initiation of the failure is dependent on a local increases in either stress or strain energy to some critical values. In the case of a flexible joint, this will occur within the adhesive layer and the critical site will be close to one of the corners of the joint overlap from which the separation front can proceed either axially or transversely. These conclusions are supported by a finite element analysis of a joint formed between adherends of finite width by a low modulus adhesive.     

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.     

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.     

Prediction of the tensile load-bearing capacity of a co-cured single lap joint considering residual thermal stresses

In this paper, stress distributions in a co-cured single lap joint subjected to a tensile load were investigated using the finite element analysis. Residual thermal stresses, which resulted from the curing process of the co-cured single lap joint, were also considered. Since the adhesive layer in the co-cured single lap joint was about 10 μm thick, very thin compared with the thickness of both adherends, the interface between the steel and composite adherends was assumed to be perfectly bonded. The co-cured single lap joint was analyzed with respect to several bond parameters such as the bond length and stacking sequence of the composite adherend. The failure mechanism of the co-cured single lap joint was partial cohesive failure in the composite material, which was significantly affected by the interfacial tensile stress at the free edge of the co-cured single lap joint. Interfacial tensile stress was a primary factor that caused interfacial delamination between the steel and composite adherends in the co-cured single lap joint. Finally, tensile load-bearing capacities calculated from the Ye-delamination failure criterion were compared with the experimental results, and relatively good agreement was found.     

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.     

Failure behaviour of the single lap joints of angle-plied composites under three point bending tests

Abstract

In this paper, the response of adhesively-bonded single lap joints (SLJs) with angle-plied composite adherends subjected to flexural loading was investigated. The experiments were carried out for the adherends, glass reinforced polymer matrix, with three kinds of stacking sequence. A three-dimensional finite element (FE) model was developed using ABAQUS/Explicit. The three dimensional Hashin failure criterion with an appropriate damage evolution law was used to characterize the damage inside a ply. Cohesive zone elements were used to model the damage in the adhesive layer (AF163-2K) and the interply failure, that is, the delamination. The developed numerical model was verified with the performed experiments. The SLJs of [±20]_5s and [±45]_5s failed due to failure in the adhesive layer and the delamination between the plies, whereas that of [±10]_5s failed mainly due to the former failure. The intralaminar damage was not noticed for any case. The influence of the fiber angle of plies in the adherends, adherend thickness, overlap length, and the thickness of adhesive layer on the damage in the adhesive layer and the delamination were investigated in terms of the competition between these two failures and activation of different failure modes in each thoroughly.     

An Experimental Study of Fatigue Strength for Adhesively Bonded Tubular Single Lap Joints

In this paper, manufacturing technology of the tubular single lap adhesive joint was studied to obtain reliable and optimal joint quality. In addition, a surface preparation method and a bonding process for the joint were devised. The effect of the adhesive thickness and the adherend roughness on the fatigue strength of the joint was experimentally investigated. From experiments, it has been found that the fatigue strength of the joint increased as the adhesive thickness decreased and the optimal arithmetic surface roughness of the adherends was about 2 μm.     

The effects of surface roughness and bond thickness on the fatigue life of adhesively bonded tubular single lap joints

Since the surface roughness of adherends greatly affects the strength of adhesively bonded joints, the effect of surface roughness on the fatigue life of adhesively bonded tubular single lap joints was investigated analytically and experimentally by a fatigue torsion test. The stiffness of the interfacial layer between the adherends and the adhesive was modelled as a normal statistical distribution function of the surface roughness of the adherends. From the investigation, it was found that the optimum surface roughness of the adherends for the fatigue strength of tubular single lap joints was dependent on the bond thickness and applied load.     

Numerical analysis of the strength and interfacial properties of adhesive joints with graded adherends

The strength and interfacial behavior of single lap joints with graded adherends subjected to uniaxial tensile loading are investigated in the present paper. A bilinear cohesive zone model coupled with the finite element method is adopted to describe the damage and failure process of the adhesive layer. The peak loading, the rotation angle between the overlap of the joint and the horizontal direction, as well as the failure energy are investigated comprehensively. It is interesting to find that adopting different variation law in the graded adherends may result in varying strength of adhesive joints. By means of choosing proper material and geometry parameters of adhesive joints, the peak loading, the rotation angle and the failure energy of joints can be greatly improved. What is more, the strength of the SLJ is found to depend much more on the property of the soft part near the adhesive layer. The results should be helpful to guide the design of novel structures of adhesive joints in present and potential applications.     

Analysis of the Tubular Single Lap Joint with Nonlinear Adhesive Properties

The majority of the load transfer of an adhesively-bonded joint is accomplished by the nonlinear behavior of the adhesive. In this paper, the torque transmission capability and shear stress distribution of the tubular single lap joint were calculated by incorporating the nonlinear shear properties of the adhesive. The nonlinear shear properties were represented by three different mathematical models such as two-parameter exponential, linear perfectly-plastic and multilinear strain-softening approximations.

From the analyses and experiments, it was found that all the analyses with nonlinear approximations predicted the torque transmission capabilities accurately, but the two-parameter exponential approximation gave the best predictions with the simplest form for use in numerical calculation.