Partition energy absorption of axially crushed aluminum foam-filled hat sections

The “interaction effect” between aluminum foam and metal column that takes place when foam-filled hat sections (top-hats and double-hats) are axially crushed was investigated in this paper. Based on experimental examination, numerical simulation and analytical models, a systemic approach was developed to partition the energy absorption quantitatively into the foam filler component and the hat section component, and the relative contribution of each component to the overall interaction effect was therefore evaluated. Careful observation of the collapse profile found that the crushed foam filler could be further divided into two main energy-dissipation regions: densified region and extremely densified region. The volume reduction and volumetric strain of each region were empirically estimated. An analytical model pertinent to the collapse profile was thereafter proposed to find the more precise relationship between the volume reduction and volumetric strain of the foam filler. Combined the superfolding element model for hat sections with the current model according to the coupled method, each component energy absorption was subsequently derived, and the influence of some controlling factors was discussed. According to the finite element analysis and the theoretical modeling, when filled with foam, energy absorption was found to be increased both in the hat section and the foam filler, whereas the latter contributes predominantly to the interaction effect. The formation of the extremely densified region in the foam filler accounts for this effect.     

Thermal effects on adhesively bonded composite repair of cracked aluminum panels

This study introduces the two-dimensional finite element analysis involving three layer technique to investigate the adhesively bonded composite repair of cracked metallic structure under thermo-mechanical loading. The thermal loading involves, in this study, the temperature drop such as seen during the bonding process. Three patch materials having different stiffnesses and coefficients of thermal expansion are investigated to analyze the thermal effects on the damage tolerance of the crack in the repaired structure and of the debond in the adhesive bondline. For the single sided repair, the patch material having the maximum mismatch in the coefficient of thermal expansion with that of the cracked aluminum plate provides the better damage tolerance capability for both the crack in the panel and the debond in the adhesive. On the other hand, for double sided repair, the patch material having the minimal mismatch in the coefficient of thermal expansion with that of the cracked plate provides the better damage tolerance capability.     

Isodyne stress analysis of adhesively bonded symmetric joints

The paper presents experimental data on the actual three-dimensional stress states produced by tensile axial forces in components of adhesively bonded symmetric joints. Stress components are determined in lamination planes and in planes at various distances from lamination planes using the methods of isodyne stress analysis.The presented evidence shows that all three normal stress components exist in the components of a joint, and clearly vary with all three coordinates aligned with the length, width, and thickness of the joint. The stress state is pronounceably three dimensional and as such cannot be reliably determined using the analytical and experimental procedures based on the concept of generalized plane stress state. Thus the convenient simplified analytical and experimental procedures of stress analysis should be carefully tested for their admissibility, using as a criterion, the magnitude of acceptable error. The paper illustrates capacity of the method of analytical and optical isodynes.Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 26–June 1.     

Stress-function variational method for interfacial stress analysis of adhesively bonded joints

High interfacial stresses at the free edges of adherends are responsible for the debonding failure of adhesively bonded joints (ABJs). In this paper, a general stress-function variational method is formulated to determinate the interfacial shear and normal (peeling) stresses in ABJs in high accuracy. By extending authors’ prior work in stress analysis of bonded joints (Wu and Jenson, 2011), all the planar stress components in the adherends and adhesive layer of an ABJ are expressed in terms of four unknown interfacial stress functions, which are introduced at the upper and lower surfaces of the adhesive layer. A set of governing ordinary differential equations (ODEs) of the four interfacial stress functions is obtained via minimizing the complimentary strain energy of the ABJ, which is further solved by using eigenfunctions. The obtained semi-analytic stress field can satisfy all the traction boundary conditions (BCs) of the ABJ, especially the stress continuity across the bonding lines and the shear-free condition at the ends of adherends and adhesive layer. As an example, the stress field in an adhesively single-sided strap joint is determined by the present method, whose numerical accuracy and reliability are validated by finite element method (FEM) and compared to existing models in the literature. Parameter studies are performed to examine the dependencies of the interfacial stresses of the exemplified ABJ upon the geometries, moduli and temperature change of the adherends and adhesive layer, respectively. The present method is applicable for scaling analysis of joint strength, optimal design of ABJs, etc.     

Progressive fracture of adhesively bonded composite structures

Progressive damage and fracture of adhesively bonded graphite/epoxy composite structures are evaluated via computational simulation. Load induced damage in both the adhesive bond and the adjoining laminate is considered. An integrated computer code is used for the simulation of structural degradation under loading. Damage initiation, growth, accumulation, and propagation to fracture are included in the simulations. Results show in detail the damage progression sequence and structural fracture resistance during different degradation stages. Design implications with regard to damage tolerance of adhesively bonded joints are examined. Influence of the type of loading as well as adhesive thickness on damage initiation and progression for an adhesively bonded composite structure are investigated.     

Strength assessment of adhesively bonded tile claddings

A simplified analytical approach for the assessment of bonding strength in tiled flooring is formulated and discussed. The approach is conceived for application to a specific type of failure mechanism, usually activated by differential elongation/shortening between tiles and substrate, of the type induced by thermal gradients or fresh concrete maturation. It is discussed how the failure mechanism, promoted by eccentric tile compression, can be studied as a Mode I cohesive crack propagation through the adhesive layer and a closed form estimate of the ultimate tile compression is provided. Based on closed-form solutions for the problem of stress transfer between substrate and tile through shear of the adhesive, simple formulas for the estimation of the tile compression are also derived.     

Stress analysis of adhesively bonded sandwich pipe joints subjected to torsional loading

Composite pipes are becoming popular in the offshore oil and gas industry. These pipes are connected to one-another by various configurations of joints. The joints are usually the weakest link in the system. In this investigation we examine the response of various joint configurations subjected to torsion, one of the most common loading conditions in piping systems. Specifically, the theoretical analysis used to evaluate the stress field in the adhesive layers of tubular and socket type bonded sandwich lap joints is presented here. The two adherends of the joints may have different thickness and materials, and the adhesive layer may be flexible or brittle. The analysis is based on the general composite shell theory. The stress concentrations at and near the end of the joints as functions of various parameters, such as the overlap length, and thickness of the adhesive layer are studied. The effects of different adherend thickness ratios, adhesive thickness and overlap length are also studied. Results obtained from the proposed analytical solutions agree well with the results obtained from finite element analysis and those obtained by other workers.     

Numerical simulation of debonding of adhesively bonded joint

This paper describes a numerical method to simulate the debonding of adhesively bonded joints. Assuming that the adhesive thickness and the adhesive Young’s modulus are small with respect to the characteristic length of the joint and to the Young’s modulus of the adherents, a simplified model is derived in the case of large displacements using the asymptotic expansion technique. Then, the problem of the crack growth is stated, in the case of a stable growth, as the search of the local minima of the total energy of the joint, sum of the mechanical energy and the Griffith’s fracture energy. This is made using the Newton’s method. To this end, the expressions of the first and second derivatives of the mechanical energy with respect to a crack front displacement are derived analytically. Finally, numerical examples are presented, highlighting the unstable character of the crack growth at initiation.     

Strength of cylinder joint adhesively bonded by coupling

Summary A method of joining two metal cylindrical shafts with adhesive coupling is proposed. Two cylindrical shafts with the same diameter are connected by bonding through a cylindrical coupling with epoxy resin. The strength of the shaft joint under tensile loading and torsional loading is investigated analytically and experimentally. The stress and strain distributions of the shaft joint is analyzed by the finite element method. The analyzed strain distributions in the joint are compared with experimental values. The joint strength is predicted by applying the strength laws of shafts, coupling, adhesive layer and adhesive interface between shaft and adhesive coupling. The effects of the coupling dimension on the joint strength are examined. It is shown that the adhesive shaft joint can transfer the load by which the cylindrical shafts are plastically deformed.This paper was refined by the author, K. Ikegami, during statying at Technische Universität München under the support of Deutscher Akademischer Austauschdients. The author is grateful to Professor Lippmann of Technische Universität München who is the host professor of the support.     

An analytical investigation on thermomechanical stress analysis of adhesively bonded joints undergoing heat conduction

Thermomechanical loading, in the same way that mechanical loading can cause significant stress violations, may give rise to significant stress variations and concentrations and in some circumstances can result in structural destruction or even failure. This clearly shows the importance of accurate stress analysis of thermal-loaded structures. This paper presents three-dimensional thermomechanical stress analysis of heterogeneous adhesively bonded joints undergoing steady-state one-dimensional heat conduction using the full layerwise theory. In this approach, the fully coupled three-dimensional governing equilibrium equations are derived generally for an orthotropic joint based on the use of variational calculus and the principle of minimum total potential energy. The through-thickness temperature distribution is determined using the equivalent thermal-resistant model and is rewritten in the layerwise form. The governing equations of equilibrium then are analytically solved using the state space approach. The accurate results presented in this study are compared and verified via analytical as well as numerical investigations, and the study shows rapid converging solutions.     

Interfacial transient thermal fracture of adhesively bonded dissimilar materials

The effect of a transient thermal load on an interface crack in adhesively bonded dissimilar materials was experimentally studied by using photothermoelasticity. It is determined that the effect of the thermal load is to cause mostly shearing deformations at the crack tip. For two configurations, a horizontal crack (normal to the heat flow direction) and a vertical crack (parallel to the heat flow direction), it is shown that increasing the adhesive thickness results in steady-state and maximum transient strain-energy release rates and stress-intensity factors of smaller magnitudes. It is also found that the ratio of mode I to mode II stressintensity factors for the vertical crack is larger than the one for the horizontal crack.     

胶层吸湿对单搭接接头影响的数值模拟

在建立胶桔剂吸涅本构模型的基础上,用弹塑性有限元法研究了聚丙烯酸酯胶层吸涅程度对单搭接接头上胶层中应力分布的影响.结果表明:随着胶层吸湿程度增加,单搭接接头上胶瘤处的峰值应力显著降低.对水分从搭接区两侧渗入胶层的总宽度变化时胶层中的应力分布作了研究,发现随渗入总宽度的增加,胶层中的等效应力Seqv峰值下降.因水分渗入后引起胶层溶胀,在胶瘤过渡到中间胶层的拐角处会产生严重变形,可能导致该处发生脱粘.     

A theoretical analysis for the dynamic axial crushing behaviour of aluminium foam-filled hat sections

A theoretical analysis was performed to predict the dynamic axial crushing behaviour of aluminium foam-filled top hat and double hat sections made from mild steel material. The deformation mode from the test results was used to create a deformation model for the theoretical analysis. According to the energy method and the superfolding element theory, the mean dynamic crushing loads of the aluminium foam-filled hat sections and the interactive effect between the aluminium foam and hat sections were theoretically predicted. The mean dynamic crushing loads and the interactive effect predicted by this theoretical analysis were in good agreement with the experimental results. The theoretical prediction results showed that the interactive effect was mainly from the aluminium foam.     

Dislocation approach to study interaction of adhesively bonded weak zones

The problem of interaction between crack-like interface defects subjected to a remote tensile stresses in an elastic bi-plane is considered using a model of an adhesively bonded asymmetric weak zone. In this model, the opening displacements are prescribed by a basis function which contains free parameters and automatically accounts for the asymmetry and the “true” stress–strain field behavior near the tips. The corresponding adhesive forces which can be very different by physical origin, are determined a posteriori. The limiting situations: transformation of one of the defects to the nucleus of a cohesive crack or the rupture of an obstacle between the weak zones are analytically described.     

A simple continuum damage model for adhesively bonded butt joints

The present work is concerned with the study of the damage behavior of adhesive joints consisting of an epoxy adhesive layer bonding aluminium alloy substrates. A model for butt joints, developed within the framework of Continuum Damage Mechanics, that accounts for the effect of the thickness of the adhesive layer on the strength of the system is proposed and analyzed. The predicted values of rupture stress for different values of the thickness of the adhesive layer are compared with experimental data, showing a good agreement.     

Linear and higher order displacement theories for adhesively bonded lap joints

This work presents an adhesive model for stress analysis of bonded lap joints, which can be applied to model thin and thick adhesive layers. In this theory, linear variations of displacement components along the adhesive thickness are firstly assumed, and the longitudinal strain and the Poisson's effect of the adhesive are modeled. A differential form of the equilibrium equations for the adherends is analytically solved by means of compatible relations of the adhesive deformation. The derived shear and peel stresses are compared with the classical adhesive model of continuous springs with constant shear and peel stresses, and validated with two-dimensional finite element results of the geometrically nonlinear analysis using a commercial package. The numerical results show that the present linear displacement theory can be applied to both thin and moderately thick adhesive layers. The present formulation of the linear displacement theory is then extended to the higher order displacement theory for stress analysis of a thick adhesive, whose numerical results are also compared with those of the finite element computation.     

The dynamic stress intensity factor analysis of adhesively bonded material interface crack with damage under shear loading

This paper studies the dynamic stress intensity factor (DSIF) at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters.     

A continuum based modelling approach for adhesively bonded piezo-transducers for EMI technique

In the electro-mechanical impedance (EMI) technique, which is based on induced strain actuation through piezoelectric ceramic (PZT) patch, the knowledge of shear stress distribution in the adhesive bond layer between the patch and the host structure is very pertinent for reliable health monitoring of structures. The analytical derivation of continuum based shear lag model covered in this paper aims to provide an improved and more accurate model for shear force interaction between the host structure and the PZT patch (assumed square for simplicity) through the adhesive bond layer, taking care of all the piezo, structural and adhesive effects rigorously and simultaneously. Further, it eliminates the hassle of determining the equivalent impedance of the structure and the actuator separately, as required in the previous models, which was approximate in nature. The results are compared with the previous models to highlight the higher accuracy of the new approach. Based on the new model, a continuum based interaction term has been derived for quantification of the shear lag and inertia effects.     

Cohesive zone model for high-cycle fatigue of adhesively bonded joints under mode I loading

A cohesive zone model adequate for simulating the behaviour of adhesively bonded joints subjected to high-cycle fatigue and pure mode I loading is presented. The bilinear cohesive zone law with linear softening relationship was considered. The main advantage of the proposed formulation is the use of a unique damage parameter accounting for cumulative damage resulting from static and fatigue loading. The method was implemented in a user subroutine of the commercial finite element software Abaqus®. Two-dimensional numerical simulations of the double cantilever beam test using different representative combinations of the modified Paris law coefficients were performed. It was verified that the results of the model simulate with excellent agreement the several Paris laws used as input, thus demonstrating the good performance of the method as a predictive tool.