The use of flexible interface theory for fully coupled nonlinear analysis of balanced adhesive single-lap joint

A theoretical model is presented for determining the edge moment factors, the transverse deflections and the interfacial stresses of the balanced adhesive single-lap joint (SLJ). Based on the flexible interface theory, the improved one-dimensional beam model incorporates simultaneously the effects of interfacial compliances, the overlap geometric nonlinearity and the transverse shear deformations for the adherends. On the basis of normal and tangential displacement compatibility condition for the flexible interface, two sets of fully coupled governing equations concerning rotation of transverse normal and longitudinal displacement of adherends are constructed, from which the improved solutions for the edge moment factors, the transverse deflections, and the interfacial stresses can be obtained. The applicability and accuracy of the improved one-dimensional beam model are validated by comparing the present solutions with the results of the classical model, non-linear finite element analysis, and experimental results. Finally, the effects of the interface compliances on the adhesive stresses distributions of the balanced SLJ are studied.     

Analytical solutions for nonlinear analysis of composite single-lap adhesive joints

This paper presents analytical nonlinear solutions for composite single-lap adhesive joints. The ply layups of each composite adherend can be arbitrary, but in the overlap region the ply layups of the upper and lower adherends are assumed to be symmetrical about the adhesive layer. In the present formulation, equilibrium equations of the overlap are derived on the basis of geometrical nonlinear analysis. The governing equations are presented in terms of adherend displacements by taking into account large deflections of the overlap adherends and adhesive shear and peel stresses simultaneously. Closed-form nonlinear solutions for adherend displacements, an edge moment factor and adhesive stresses are formulated and then simplified for practical applications. To verify the present analytical solutions for nonlinear analysis of composite single-lap joints, the geometrically nonlinear 2D finite element analysis is conducted using commercial package MSC/NASTRAN. The numerical results of the edge moment factor, deflections and adhesive stresses predicted by the present solutions correlate well with those of the geometrically nonlinear finite element analysis. This indicates that the present analytical solutions capture key features of geometrical nonlinearity of composite single-lap adhesive joints.     

Closed-form solutions for elastic stress-strain analysis in unbalanced adhesive single-lap joints considering adherend deformations and bond thickness

A theoretical model is developed for the stress analysis in adhesive-bonded single-lap joints under tension, for which the two adherends could have different thicknesses and consist of different materials. A two-dimensional (2D) elasticity theory is adopted in the analysis, which simultaneously incorporates the complete strain-displacement and the complete stress-strain relationships for the adherends and adhesive. The approach provides a unified treatment for any possible adhesive layer flexibility and capable of satisfying the stress-free condition at the ends of the bondline. An explicit closed-form analytical solution is formulated for upper and lower adherends/adhesive stresses (strains) and tensile, shear and bending loads acting on the adherends along the overlap and then simplified for practical applications, and simple design formulae for adhesive stresses are produced. The results predicted by the present full and simplified solutions were compared with the previously theoretical solution by Bigwood and Crocombe (1989) [35], and the 2D geometrically nonlinear finite element model using MSC/NASTRAN. The agreement validates the present formulation and solutions for unbalanced bonded joints. The effects of the stiffness unbalanced parameters on the adhesive stress distributions were also discussed.     

An alternative solution for the edge moment factors of the unbalanced adhesive single-lap joint in tension

An evaluation of the existing theoretical solutions and a proposal of an improved one for edge moment factors of the unbalanced adhesive single-lap joint are performed. Firstly, the existing classical solutions are reviewed and studied in detail. The scope of applications and limitations related to the classical solutions are identified. Meanwhile, the determination for the long and short unbalanced single-lap joint (SLJ) is performed. Then, through removing disadvantages of the existing theoretical solutions, an improved theoretical solution considering the effect of large deflection for overlap is proposed. Meanwhile, the adherends of the overlap regions are treated as individual beams in the improved theoretical solution. The fully-coupled nonlinear formulations for determining adherend displacements (includes axial deformation and transverse deformation) in the overlap and edge moment factors are constructed using the improved theoretical solution. Finally, the results of the existing solutions and the improved theoretical solution are compared with the results of the finite element analysis.     

A New Coupled Solution for Interfacial Stresses Analysis in a Repaired Beam with an Adhesively Bonded Prestressed FRP Plate

This paper focuses on a new coupling solution for determining the elastic interfacial shear and normal stresses in an adhesive joint between a strengthening plate and a simply supported beam. The mismatch of the curvatures in the beam and plate is considered by including both the effect of the adherend shear deformations and the prestressed laminates model. This new method leads to the coupling of governing differential equations for the interfacial shear and normal stresses. Most of the other solutions in the literature assume that the beam and plate have an equal curvature to uncouple this effect. In this paper, however, a solution is presented to calculate the interfacial stresses of beams strengthened with a prestressed composite plate having a new rigidity model coupled with the shear lag effect, which are neglected by the previous studies. It is found that the present method can predict accurately stresses in the interior and near the ends of the adhesive layer, where the stress fields can be significantly influenced by the edge effects. A parametric study was carried out to show how the stress concentration and distribution are influenced by the dimensions of the adherends and the material properties of the strengthened beam.     

Investigation of gas-assisted injection molding. Part III: Effect of gas channel design on part bending strength

Numerical simulation and experimental measurements were carried out to investigate the effect of gas channel design on the bending performance of gas-assisted injection molded parts. Plate parts designed with various channel geometries were gas-assisted injection molded. Part flexible strength were measured via bending tests. It was found that part stiffness basically increases linearly with the inertia moment of the plate. The gas channel introduces an additional moment of inertia, the amount of which is determined by the shape and the dimension of the channel section as well as the hollowed core geometry. An analysis algorithm based on DKT/VRT elements superimposed with beam elements representing gas channels of various section geometries was developed to evaluate part bending behavior. An equivalent diameter was assigned to the beam element so that both the original gas channel and the circular beam have the same moment of inertia. The analyzed results from this model of 2 1/2-D characteristics were also verified with both 3-D and 2 1/2-D analyses using ANSYS. The present simulations show reasonable accuracy as compared with experimental measurements and predictions from ANSYS. This investigation also indicates that it may be feasible to use the same CAE finite element model implemented for process simulation of gas-assisted injection when performing part structural analysis as well as warpage calculation, resulting in great computational efficiency for industrial application.     

Non-linear stress and failure analyses of adhesively-bonded joints subjected to a bending moment

In this paper, the mechanical behavior of the Single-Lap Joints (SLJs) bonded with two different adhesives (FM 73 and SBT 9244) under a bending moment was analyzed, both experimentally and numerically. Four-point bending experiments for the joints with different overlap lengths were carried out and fracture surfaces of the SLJs were examined with a Scanning Electron Microscope (SEM). After the stress analysis in the SLJs was performed via a finite element method by considering the material non-linearities of the adhesives and adherend (AA2024-T3), the Finite Element Analysis (FEA) results were compared with experimental results. Finally, the stress analyses and experimental results show that the failure in the SLJs subjected to a bending moment probably initiates from the overlap region on the adhesive–upper adherend interface in tension and propagates towards the centre of the overlap. Also, in the joint subjected to a bending moment, it is seen that the load carried by the SLJ with SBT 9244 adhesive with increasing overlap length is more than that of the SLJ with FM 73 adhesive, although in the bulk form FM 73 adhesive is about three times stronger than SBT 9244 adhesive.     

Progressive failure of bamboo-steel adhesive bonding interface subjected low-energy impact and tension in sequence

Bamboo–steel composite structure is a newly developed structure, composed of bamboo plywood and cold-formed thin-walled steel bonded by structural adhesive. This paper configured a three-dimensional (3D) numerical model to characterize the progressive failure of bamboo–steel adhesive bonding interface subjected low-energy impact and tension in sequence. A 3D cohesive zone model (CZM) with reloading trapezoid softening law was adopted to characterize the debonding behavior of the bamboo–steel interface. Investigations on the debonding damage propagation of the bamboo–steel interface subjected low-energy impact and tension after impact were completed, and the influence factors of the residual tensile strength were studied.     

An improved four-parameter model on stress analysis of adhesive layer in plated beam

The prediction of stresses in an adhesive layer is helpful in revealing the mechanism of debonding failure in plated beams. This study proposes an improved analytical model for the stress analysis of an adhesive layer in a plated beam. The beam and the soffit plate are individually modelled as a single Timoshenko sub-beam with separate rotations, while the adhesive layer is modelled as a two-dimensional elastic continuum in plane stress, which considers different adherend-adhesive interface stresses. The internal forces of the adhesive layer are assumed to satisfy the Timoshenko beam theory, and the shear deformation and bending moment of the adhesive layer can be considered. The internal forces and displacements of the adhesive layer are fully considered in the displacement compatibility equations, and deformable interfaces are assembled so that the effect of interface stresses on local deformation is captured. Based on equilibrium equations and displacement continuity, the governing differential equations of beam forces are derived, and then the analytical solutions of interface stresses and stresses along the thickness of the adhesive layer are obtained. Comparisons of the results of the finite-element analysis and the existing four-parameter model solutions show that the present model is reasonable. The influence of adhesive thickness on stress distributions in adhesive layers is also investigated.     

Buckling analysis of a taper‐taper adhesive‐bonded composite joint

An analytical model of the behavior of an adhesive‐bonded taper‐taper composite joint under axial compressive loading has been developed using the Ritz Method. The model was based on laminated beam theory. A Fourier series was used to represent the transverse displacement variable and the Ritz Method was used to derive an eigenvalue equation for adhesively bonded taper‐taper composite joint. The smallest eigenvalue is the critical buckling load. Finite element analyses were performed on two unidirectional laminated beam joints with various taper angles to verify the analytical model. The effect of varying the taper angle, adhesive thickness, and adhesive modulus on the critical buckling load was investigated analytically.     

Two dimensional analysis for an adhesively bonded composite single-lap joint based on flexible interface theory

An improved two-dimensional model based on flexible interface theory is proposed for an adhesively bonded composite single-lap joint. In the modified model, the adherends are treated as a Timoshenko beam, and the adhesive layer is assumed to be an Euler–Bernoulli beam. The peel stress and shear stress across the adhesive thickness varied. Additionally, the zero shear stress condition at the free end of the adhesive layer was satisfied. Based on the displacement compatibility condition of a flexible interface, the governing differential equations for the internal forces are derived. The stress distributions of the adhesive layer can be obtained by solving the governing differential equations. A comparison of the results between the modified model, existing classical models, and finite element results indicate that the improved two-dimensional model can determine the stress distribution of the adhesive with high accuracy. Finally, the effects of the thickness ratio, Young’s modulus ratio, and interfacial compliance on the stress distribution of the adhesive are studied using the improved model.     

Kissing bond detection in structural adhesive joints using nonlinear dynamic characteristics

In this paper, the effect of kissing bond on nonlinear dynamic behavior of structures with flexible adhesive joint is investigated. Bilinear characteristic due to opening and closing in kissing bond region results in nonlinear dynamic behavior of the structure such as harmonic distortion in response to harmonic excitation. So, the higher-order harmonics can be considered as Nonlinear Damage Indicator Functions (NDIF) for the purpose of damage identification. A two-dimensional (2D) finite element model of a beam connected to a rigid support via a flexible adhesive layer is used to investigate the efficiency of the proposed NDIFs in kissing bond detection. Kissing bond is introduced to the model via contact elements. NDIFs are extracted for the finite element model using single tone stepped-sine test simulation. Parameters such as amplitude of excitation, size and location of kissing bond region as well as friction between kissing surfaces, are studied. The results proved that the NDIFs are sensitive to the size and location of kissing bond. Consequently, in an experimental damage identification procedure, NDIFs can be used as an indicator of kissing bond type damages in adhesive joints.     

Numerical Study of Adhesive Single-Lap Joints with Composite Adherends Subjected to Combined Tension–Torsion Loads

The present investigation focuses on modifying the strength of single-lap adhesively bonded joints under tension–torsion loading with the use of three-dimensional finite element (FE) modeling. A single-lap adhesively bonded joint is reinforced by fibers and analyzed by means of ABAQUS-6.9.1 FE code. The adherends are considered to be made of orthotropic materials, while the adhesive is neat resin or reinforced by various types of fibers. The carbon and glass unidirectional fibers are used for adhesive reinforcement. In the FE modeling, the behavior of all the members is assumed to be linear elastic. The ultimate bond strength is increased as the fiber volume fraction in the adhesive is increased. By changing the properties and the behavior of the adhesive from neat resin (isotropic) to fiber composite adhesive (orthotropic) and with various fiber volume fractions and by changing the orientation of the fibers in the adhesive region with respect to the global axes, the bond strength in tension–torsion loadings are changed. Also, the excessive adhesive layer is modeled and its effect on the joint strength is investigated.     

Experimental and numerical analysis of single-lap joints for the automotive industry

Lap joints are used extensively in the manufacture of cars. In order to determine the effect of using a structural adhesive instead of spot-welding, a detailed series of tests and finite element analyses were conducted using a range of loadings. The adhesive was a toughened epoxy and the adherend was mild steel typical of that used in the manufacture of car bodyshells. The lap joints were tested in tension (which creates shear across the bondline), four-point loading (pure bending) and three-point loading (bending plus shear). Various parameters were investigated such as the overlap length, the bondline thickness and the spew fillet. The major finding is that three-point bending and tension loading are very similar in the way in which they affect the adhesive while the four-point bend test does not cause failure because the steel yields before the joint fails. A failure criterion has been proposed based on the tensile load and bending moment applied to the joint.     

Analytical solutions for adhesively bonded composite single-lap joints under mechanical loadings using full layerwise theory

In this paper, analytical solutions for adhesively bonded composite single-lap joints (SLJs) are presented within the framework of the full layerwise theory (FLWT). The adhesively bonded composite SLJ is divided into a large number of mathematical plies through the thickness and three regions along its length. The equilibrium equations of each region are obtained using the principle of minimum total potential energy. The three sets of fully-coupled governing equations then are simultaneously solved by introducing the state space variables. The effects of adhesive thickness and loading conditions including uniaxial tension and bending moment on the interfacial peel and shear stress as well as the von Mises stress distributions along the length and through the thickness of the adhesive layer are studied. The present results, which are verified via analytical, experimental, and numerical investigations available in the literature, can be introduced as scaling solutions to verify the authenticity of other methods.     

Numerical/experimental assessment of 3D-printed shape-memory polymeric beams

The main objective of this article is to present different computational tools to replicate thermomechanical shape-memory responses of beam-like structures fabricated by three-dimensional (3D) printing technology. To simulate thermomechanical behaviors of shape-memory polymer (SMP) beams, one-dimensional (1D) finite element model (FEM) building with MATLAB and 3D FEM by means of COMSOL Multiphysics are established. All governing equations are developed based on a 3D thermomechanical SMP constitutive model. 1D FEM is derived on the basis of the Euler–Bernoulli beam theory and linear geometrical assumption. The 3D SMP constitutive model is implemented into geometrically nonlinear COMSOL Multiphysics software through a user-defined material subroutine to provide a powerful 3D simulation tool. Comparative studies on FEMs of MATLAB and COMSOL Multiphysics reveal that geometrically linear assumption is appropriate for models in large/small deformation under tension/bending. 1D analytical solution for deflection of an SMP beam employing Euler–Bernoulli beam theory is also developed. An experiment is conducted to demonstrate a full shape-memory cycle of SMPs. It is experimentally shown that a 3D-printed beam recovers the deformation incurred by external loads upon heating over the transition temperature. The accuracy of the 3D FEM in COMSOL Multiphysics is checked with analytical solutions and experimental data. It is found that simulation results of the program are in good agreement with characteristics observed in the experiment and analytical solutions. The developed computational tools are expected to be instrumental in the design of simple/complicated SMP structures. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47422.     

Strength model of adhesive-bonded double-lap joints under cantilevered bending

The objective of this study was to develop mathematical relations for predicting the strength of adhesive-bonded double-lap joints under cantilevered bending. Based on the strength of composite materials theory, two models were proposed to predict the stress-strain distribution and vertical deflection of the laminates and the adhesive under this loading condition. The first model was based on the basic beam theory with the assumption that every cross section in a plane before bending remains plane after the bending load is applied. In the other model, a strain gap between each bonded surface is assumed. Based on the second model and the predicted peel failure mode, the effects of shear modulus of the adhesive, joint length, and adhesive thickness on the joint strength were evaluated. Scotchply composite laminates were used as the adherends of the double-lap joints in the experimental investigation. An Instron machine fitted with a special apparatus was used for conducting the experiments. By the attachment of strain gages to the adherends and through the use of a dial indicator, the theoretical models were verified experimentally.     

碳纤维传动轴刚度不平衡胶接接头的失效行为研究

建立了碳纤维传动轴刚度不平衡胶接接头的有限元模型,对扭转载荷下刚度不平衡胶接接头的失效行为进行分析,预测了胶接接头的失效扭矩和失效模式,并进行扭转实验证明有限元分析方法的有效性,最后研究了被粘物剪切模量比和壁厚比对刚度不平衡胶接接头失效行为的影响,为工程上碳纤维传动轴胶接接头的设计提供了参考。     

Failure behavior of adhesive bonded interface between steel and bamboo plywood

Bamboo–steel composite structure is constructed with bamboo plywood and cold-formed thin-walled steel, which are bonded by structural adhesive. To investigate the failure behavior of the adhesive bonded interface between bamboo plywood and steel, both experimental and numerical analyses were performed. An adhesive bonded member was designed to observe the failure behavior through the variation of stress distribution on steel sheet under tension. Further analysis of failure behavior was carried out by the numerical model through the stress analysis at the adhesive bonded interfaces. The experimental and numerical analyses revealed the failure mainly occurred at the adhesive bonding interface, caused by the stress concentration at the end of the overlap. The influences of modulus of elasticity of bamboo plywood in the parallel to grain direction and the thickness of steel sheet on the stress distribution at the adhesive bonding interface were investigated, which indicated the stress distribution had a major effect on the load-carrying capacity of the composite structural member. It also suggests enlarging the geometry properly and choosing the bamboo plywood with large modulus of elasticity in the parallel to grain direction are effective to increase the load-carrying capacity.     

Mechanical response of beams of a nonlinear viscoelastic material

A constitutive equation for nonlinear viscoelasticity is used to model the mechanical response of solid polymers such as polycarbonate. The nonlinearity arises from a reduced time which causes stress relaxation to accelerate with increasing strain. The constitutive equation can account for the occurrence of yield in a homogeneous uniaxial constant strain rate test. The constitutive equation is used in a study of the pure bending of beams. It is assumed that the classical assumption of beam theory is valid, i.e., plane sections remains plane. At each fixed time, the strains vary linearly through the depth of the beam. At a fixed material element the strain varies in time with the curvature. This spatial variation of the strains combined with the nonlinear dependence of the reduced time on strain leads to a significantly different response from that given by traditional beam theory. The implications of this for the bending moment history, stress distributions, and other factors that relate to beam design are discussed.