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.     

The Effects of Molecular Weight on the Single Lap Shear Creep and Constant Strain Rate Behavior of Thermoplastic Polyimidesulfone Adhesive

The bonded shear creep and constant strain rate behavior of zero, one, and three percent end capped Thermoplastic Polyimidesulfone adhesive were examined at room and elevated temperatures. End capping was accomplished by the addition of phthalic anhydrides.

The viscoelastic Chase-Goldsmith and elastic nonlinear relations gave a good fit to the experimental stress strain behavior. Ultimate stress levels and the safe levels for creep stresses were found to decrease as molecular weight was reduced.

The primary objective was to determine the effects of molecular weight on the mechanical properties of the adhesive in the bonded form. Viscoelastic and nonlinear elastic constitutive equations were utilized to model the adhesive. Crochet's relation was used to describe the experimental creep failure data. The effects of molecular weight changes on the above mentioned mechanical behavior were assessed.     

The Effects of Cure Conditions on the Relaxation Behavior of Thermosetting Adhesives

The ability to dissipate mechanical energy by plastic (viscous) deformation is an important strength consideration for structural adhesives. The bulk solid viscosity parameter, μ, used in spring-dashpot mechanical-model characterization of polymeric materials, provides a convenient measure of this capability. The viscosity parameter, in turn, can be related to the relaxation time for the material with the use of the elastic modulus.

This paper presents a study of the effects of cure temperature and time on the stress relaxation behavior of Metlbond 1113 modified-epoxy adhesive with carrier cloth. Short term (t=1/2 minute) relaxation data are successfully fitted with the modified Bingham mechanical model to obtain relaxation time and bulk solid viscosity parameter values corresponding to different cure conditions. Experimental results indicate that both the relaxation time and the bulk viscosity values behave in a bell-shaped increasing-decreasing manner with respect to the cure temperature for all cure time values. This behavior is similar to that of adhesive ultimate strength and elastic modulus as observed by us earlier.     

Residual Stress Development in Adhesive Joints Subjected to Thermal Cycling

The effect of thermal cycling on the state of residual stress in thermoviscoelastic polymeric materials bonded to stiff elastic substrates was investigated using numerical techniques, including finite element methods. The work explored the relationship between a cyclic temperature environment, temperature-dependent viscoelastic behavior of polymers, and thermal stresses induced in a bimaterial system. Due to the complexity of developing a closed-form solution for a system with time- and temperature-dependent material properties, and time-varying temperature and coupled boundary conditions, numerical techniques were used to acquire approximate solutions.

The results indicate that residual stresses in an elastic-viscoelastic bimaterial system incrementally shift over time when subjected to thermal cycling. Potentially damaging tensile axial and peel stresses develop over time as a result of viscoelastic response to thermal stresses induced in the polymeric layer. The applied strain energy release rate at the ends of layered or sandwich specimens is shown to increase as axial stress develops. The rate of these changes is dependent upon the thermal cycling profile and the adhesive's thermo-mechancial response. Discussion of the results focuses on the possiblility that the increasing tensile residual stresses induced in an adhesive bond subjected by thermal cycling may lead to damage and debonding, thus reducing bond durability.     

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.     

Nonlinear Analysis of theTorque Transmission Capability of Adhesively Bonded Tubular Lap Joints

Calculated torque transmission capability of adhesively bonded tubular lap joints using linear elastic material properties is usually much less than the experimentally-determined one because the majority of the load transfer of the adhesively bonded joints is accomplished by the nonlinear behavior of rubber-toughened epoxy adhesives.

Although the adhesively bonded tubular double lap joint has better torque transmission capability and reliability than the single lap joint, the nonlinear analytic or numerical analysis for the adhesively bonded tubular double lap joint has not been performed because of numerical complications.

An iterative solution that includes the nonlinear shear behavior of the adhesive was derived using the analytic solution. Since the iterative solution can be obtained very quickly due to the simplicity of the algorithm, it is an attractive method of designing adhesively bonded tubular single and double lap joints.     

Yield in Adhesive Joints and Design of Zones with Constant Elastic Shear Stresses

Yield in adhesive joints has been investigated by several scientists among whom L. J. Hart-Smith¹ especially is to be mentioned.

In the following, a method is demonstrated which is based on a simple elastic-plastic model. It shows the distribution of stresses in the adhesive and gives a total picture of the development of the length of the yield zones and their strain as a function of load.

Methods are given for the design of adhesive joints with constant elastic shear stresses at their ends or throughout their whole length. These stresses are obtained by varying the thickness of the adherends, the adhesive, or a combination of both. The constant elastic shear stress zones can be designed to take into consideration all known factors as temperature and hardening stresses, moments, etc. The characteristic yield properties as well as internal stresses after yield and unloading are determined together with the modified stress distribution for a new load.     

A Closed-form Solution for the Torque Transmission Capability of the Adhesively Bonded Tubular Double Lap Joint

The adhesively bonded tubular double lap joint has better torque transmission capability and reliability in bonding than the single lap joint.

In this paper, an analytic solution for the torque transmission capability and stress distribution of the adhesively bonded tubular double lap joint was derived assuming linear properties of the adhesive.

From the analytic solution, it was found that the torque transmission capability of the double lap joint was more than 40% larger than that of the single lap joint.     

Two Dimensional Displacement-Stress Distributions in Adhesive Bonded Composite Structures

Computerized analysis of composite structures formed by the adhesive bonding of materials is presented. The adhesive is considered to be a part of a linearly elastic system whose components are individually characterized by two bulk property elastic constants. Solution is obtained by finite difference minimization of the internal energy distribution in a discretized, piecewise homogeneous continuum. The plane-stress, plane-strain problems are considered, and yield displacement and stress distributions for the composite system. Displacement and/or stress boundary conditions are allowed. Acute contour angles are not allowed. This is the only restriction for otherwise arbitrary plane geometries.

Results are presented for typical lap shear specimens as well as for a particular case of a butt joint in which a void exists in the adhesive layer.     

Relationship between Viscoelastic and Peeling Properties of Model Adhesives. Part 1. Cohesive Fracture

The viscoelastic and peeling properties of polybutadiene/tackifying resin compatible blends have been studied in detail. Viscoelastic properties have been described through the variations of the complex shear modulus, G*(ω), as a function of frequency, ω and peeling properties through the variations of peeling force (F) as a function of peeling rate (V).

After showing the objective character of the peeling curves obtained, the variations of the peeling force and peeling geometry have been studied as a function of volume fraction of the tackifying resin.

In this first paper, the analysis is focused on the first domain of the peeling curves, i.e. the cohesive fracture region. In this region, the peeling properties have been related to the viscoelastic properties in the terminal region of relaxation. It is shown that the longest relaxation time, τ_o, is a reducing parameter of the peeling curves, so a peeling master curve-which is independent of temperature, resin volume fraction and polymer molecular weight-may be defined. Furthermore, the variations of the test geometry as a function of peeling rate have been investigated: the variations of the radius of curvature of the aluminium foil have been analyzed with respect to the viscoelastic behavior of the adhesive, which in fact governs the test geometry.

A detailed analysis of all these features leads to a model which allows one to calculate the peeling curves in the cohesive domain from the adhesive formulation.     

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.     

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.     

Peel Analysis Using the Finite Element Method

Large displacement finite element analysis and subsequent experimental work has been used to investigate the adhesive peel test; at this stage, only elastic behaviour has been considered.

Both non-cracked and cracked configurations have been analysed, representing initial and continuous failure of the peel test. Analysis of the former indicated that initial failure was caused by the adhesive principal stresses driving a crack towards the interface with the flexible adherend. Investigation of the cracked configuration has shown that the amount of mode II loading at the crack tip is significant and is essentially independent of peel angle, load and adhesive or adherend modulus, only decreasing as the adhesive becomes incompressible. Failure (propagation) has been shown to occur at a critical applied bending moment for a particular adherend and adhesive, independent of peel angle. Further, the strength (load)'measured by the peel test is not proportional to the actual strength of the adhesive, a small increase in the adhesive strength causing a much larger increase in the applied peel load.     

Analysis of tubular adhesive joints with a functionally modulus graded bondline subjected to axial loads

The strength and lifetime of adhesively bonded joints can be significantly improved by reducing the stress concentration at the ends of overlap and distributing the stresses uniformly over the entire bondline. The ideal way of achieving this is by employing a modulus graded bondline adhesive. This study presents a theoretical framework for the stress analysis of adhesively bonded tubular lap joint based on a variational principle which minimizes the complementary energy of the bonded system. The joint consists of similar or dissimilar adherends and a functionally modulus graded bondline (FMGB) adhesive. The varying modulus of the adhesive along the bondlength is expressed by suitable functions which are smooth and continuous. The axisymmetric elastic analysis reveals that the peel and shear stress peaks in the FMGB are much smaller and the stress distribution is more uniform along its length than those of mono-modulus bondline (MMB) adhesive joints under the same axial tensile load. A parametric evaluation has been conducted by varying the material and geometric properties of the joint in order to study their effect on stress distribution in the bondline. Furthermore, the results suggest that the peel and shear strengths can be optimized by spatially controlling the modulus of the adhesive.     

Bulk and Interphase Effects in Aged Structural Joints

Although structural adhesives are becoming widespread in numerous applications, one important limitation at present is the long term behaviour of bonded assemblies under conditions of high humidity, especially at elevated temperatures. This study presents a comparison between bulk properties of a structural epoxy resin and its behaviour in a torsional joint consisting of a hollowed-out cylinder bonded to a plate—both substrates being in stainless steel. Exposure to ca. 100% relative humidity at 70°C leads to modification of the bulk properties of the polymer, notably reduction of its elastic modulus. Although this may explain some differences in behaviour of the torsional joint, premature failure is attributed to weaknesses in the interphase zone.

Auger Electron Spectroscopy (AES) has been employed to investigate both unbonded steel surfaces and fracture zones. Although prolonged exposure to water leads to a more extensive degree of (apparently) adhesive failure at the interface polymer/metal, AES has shown the presence of non-negligible quantities of carbon, attributed to residual polymer. Failure would seem to occur, at least partly, in a weak interphase of the polymer, near, but not at, the interface.

Various possible causes are evoked. For dry failure, residual polymer may be due to the topography of the metal surface and/or local modification of the adhesive during cure. In the case of aged joints, in addition there are potential effects due to swelling and differential stresses, secondary bond failure and molecular chain scission within the polymer, all provoked by the presence of water.     

Theoretical and Experimental Analysis of the Scarf Joint Bonded Structure: Influence of the Adhesive Thickness on the Micro-mechanical Behavior

In this work, we have studied the influence of the adhesive thickness on the micro-mechanical behavior of a scarf joint bonded structure loaded in uniaxial tension. Adherends are made of mild steel containing 0.18% Carbon (French Standard XC18), the adhesive is a two-component epoxy resin with a 5800 MPa elastic modulus. The experimental method is based on strain gauge measurements and acoustic emission. It makes it possible to determine the following zones:

—the areas of the joint where the start of microcracks occurs (threshold Fd);

—the areas where crack propagation occurs (threshold Fg) up to the failure (threshold Fr). The experimental results confirm the good correlation between the different thresholds. They also show that there is an optimal adhesive thickness close to 0.1 mm, which confers to the scarf joint the greatest resistance to microcrack initiation and crack extension. We have compared our experimental measurements with the main theories in this domain to determine their limits and their fields of application, particularly in the angular singularities regions near the ends of the lap.     

混合胶接劈裂接头胶层中应力分布的数值分析

采用ANSYS有限元分析软件,对由两种弹性模量相差悬殊的丙烯酸酯和环氧树脂胶粘剂连接的劈裂接头胶层中部的应力分布进行数值分析和讨论。结果表明:对于采用单一胶连接的劈裂接头来说,采用弹性模量较低的胶粘剂更为有利;混合胶劈裂接头因其存在应力集中程度较高,会导致接头的强度降低。     

The Stresses in an Adhesive Layer

A simple method has been developed for calculating the stresses near the ends of a parallel-sided adhesive layer. The method can be applied to adhesive layers having aspect ratios of 10 or greater, and Poisson's ratios of 0.49 or less. For a layer subject to uniform boundary conditions of displacement at the adhering surfaces, the stress fields at distances greater than about five layer thicknesses from the free surfaces are uniform. The stress field throughout the layer is uniquely determined by the stresses in the uniform stress region. If the stress field is expressed by functions of reduced coordinates of position, obtained by dividing the cartesian coordinates by the layer thickness, these functions are for practical purposes independent of the aspect ratio or the thickness.

The method has been used to calculate shrinkage stresses, the stresses in a joint under tension perpendicular to the plane of the adhesive layer, and the stresses in a joint under shear. The features of the stress fields are described, and where necessary, shown in the form of graphs or contour plots.     

Stresses in an Adhesive Bond at an Adhesive/Adherend Interface Under Load

Triaxial stresses were determined by X-ray diffraction immediately adjacent to the adhesive/adherend interface of a single lap adhesive bond while under a tensile load. One adherend was a Be strip that was relatively transparent to the X-rays; the X-ray beam passed through this and the layer of FM-73M adhesive to diffract from the surface of the other adherend which was of 6061 aluminium alloy suitably annealed. The thicknesses of the Be and Al were made such that their stiffness in tension was matched.

Measured stresses were compared with stresses calculated using the Texgap-2D finite element code for a nominally identical joint and at a depth of 0.033 mm into the Al adherend which coincided with the average depth from which the X-ray data were obtained. The comparison showed a general agreement in trends and magnitudes except at the extremities of the bond. In particular the measured peel stress was found to be substantially larger at one extremity than the calculated peel stress. Possible causes of the discrepancies are discussed.