Diagnosis criterion for damage monitoring of adhesive joints by a piezoelectric method

Adhesive joints have been widely used for fastening thin adherends because they can distribute the load over a larger area than mechanical joints, require no holes, add very little weight to the structure and have superior fatigue resistance. Since the reliability of an adhesive joint is dependent on many parameters, such as the shape of joint, type of applied load and environment, an accurate prediction of the fatigue life of adhesive joints is seldom possible, which necessitates an in situ damage monitoring of the joints during their operation. Recently, a piezoelectric method using the piezoelectric characteristics of epoxy adhesives has been successfully developed for adhesive joints because it can continuously monitor the damage of adhesively bonded structures without producing any defects induced by inserting a sensor. Therefore, in this study, the damage of adhesive joints was monitored by the piezoelectric method during torsional fatigue tests in order to develop the diagnosis criterion for damage monitoring of adhesive joints by the piezoelectric method. The diagnosis criterion was developed by analyzing damage monitoring signals under various test conditions and adopting normalized parameters.     

Piezoelectric monitoring of the reliability of adhesive joints

Since the reliability of adhesively bonded joints for composite structures is dependent on many parameters such as the shape and dimensions of joints, type of applied load, and environment, so an accurate estimation of the fatigue life of adhesively bonded joints is seldom possible, which necessitates an in-situ reliability monitoring of the joints during the operation of structures. In this study, a self-sensor method for adhesively bonded joints was devised, in which the adhesive used works as a piezoelectric material to send changing signals depending on the integrity of the joint. In order to validate the method, the piezoelectric properties of the adhesive were measured during the fatigue test. Electrically conducting adherends were used as electrodes without embedded sensors, and the adhesively bonded joint was modeled as the equivalent parallel circuit composed of electric charge and capacitance. From the investigation, it was found that the electric charge increased gradually as cracks initiated and propagated in the adhesive layer, and had its maximum value when the adhesively bonded joint failed. So it is feasible to monitor the integrity of the joint during its lifetime. Finally, a relationship between the piezoelectric property of the adhesive and crack propagation was obtained from the experimental results.     

Fatigue damage evaluation of adhesively bonded butt joints with a rubber-modified epoxy adhesive

A damage evolution of adhesively bonded butt joints with a rubber-modified adhesive has been investigated under cyclic loading. An isotropic continuum damage model coupled with a kinetic law of damage evolution was applied to the butt joint. To solve the kinetic law, analytic and numerical methods were tried: the former solution was derived with some simplifications and the latter one was derived rigorously without simplications. On comparing the analytic solutions with the numerical ones, it was confirmed that differences in the two solutions were small. Furthermore, the estimated S-N curves based on the analytic equation agreed well with experimental data.     

Experimental studies on adhesively-bonded scarf joints: influence of natural ageing on progressive damage

This work characterizes the effects of natural ageing on the micro-mechanical behaviour of two adhesively-bonded scarf joints. The samples studied are made of XC18-type steel with different scarf angles (33 and 6°) and the adhesive is an epoxy resin. Contrary to most experimental studies which determine the strength of bonded joints in terms of their failure load, in this study sensitive strain gauges have been used to measure progressive damage of the adhesive joints. The results show that the damage is closely linked to the mechanical and geometrical properties of the test joints and that ageing increases the load thresholds of the first microcracks initiation and the ultimate failure of both adhesively bonded scarf joints.     

Effect of Adhesive Thickness on Transverse Low-Speed Impact Behavior of Adhesively Bonded Similar and Dissimilar Clamped Plates

This study investigates the effect of adhesive thickness on the transverse low-speed impact behavior of adhesively bonded similar (Al–Al, St–St) and dissimilar (Al–St, St–Al) clamped plates using the three-dimensional explicit finite element method. The contact force and plastic dissipation histories are studied for various impact energies and adhesive thicknesses. The residual plastic strains in both adhesive layer and the two plates increase with increasing impact energy. The central transverse deflections become maximal in Al–Al, moderate in Al–St, St–Al and minimal in St–St bonded plates. The back plates of all configurations deform noticeably. The stiff steel plate results in a shorter contact time, a higher contact force, a lower plastic dissipation energy and the impact energy is absorbed by the adhesive layer rather than by the front and back plates, whereas Al–Al plates dissipate it as much as the adhesive layer. The total contact time gets longer with increasing impact energy. St–St bonded plates experience larger damaged regions in both plates and adhesive layer than those in Al–Al bonded plates. The adhesive thickness has only a minor effect on the magnitude of the contact force and contact time, whereas a stiffer (St) front or back plate affects considerably the contact force and total contact time. Increasing the adhesive thickness decreases apparently residual plastic strains in plates and the adhesive layer, the central transverse deflection. A thick adhesive layer results in a minor increase in the kinetic energy of impactor, a shorter total contact time, a lower plastic dissipation energy and smaller damaged areas on the back faces of the lower plate, along the adhesive–plate interfaces.     

Transverse Low-Speed Impact Behavior of Adhesively Bonded Similar and Dissimilar Clamped Plates

This study concentrates on the transverse low-speed impact behavior of adhesively bonded similar and dissimilar clamped plates using the three-dimensional explicit finite element method. The contact force and plastic dissipation histories of the adhesively bonded dissimilar plates, such as aluminum–aluminum (Al–Al), aluminum–steel (Al–St), steel–aluminum (St–Al) and steel–steel (St–St) layered structures, were studied for different values of the impactor mass, radius and velocity (impact energies). The residual plastic strains in both adhesive layer and plates increased with increasing impact energies. The impactor radius had only a minor effect on the contact force histories for all configurations. The peak transverse deflection in the impact region was maximal in Al–Al, decreased in Al–St, St–Al plates and became minimal in St–St bonded plates. Impact effect was evident in the back plates of all four configurations. Al–Al plates dissipated impact energy as much as the adhesive layer, whereas the adhesive layer rather than plates absorbed the impact energy in Al–St, St–Al and St–St bonded plates and this state became evident in the St–St bonded plates. The number and locations of the steel plates considerably affected impact force history, impact time as well as the plastic dissipation level; thus, the contact force increased, the contact time shortened and the dissipated energy decreased. As the impact energy was increased the impact period got longer. Damage areas in the adhesive layer were minimal in Al–Al bonded plates but maximal in St–St bonded plates.     

Thermal characteristics of tubular single lap adhesive joints under axial loads

When an adhesive joint is exposed to high environmental temperature, the tensile load capability of the adhesive joint decreases because both the elastic modulus and failure strength of the adhesive decrease. The thermo-mechanical properties of a structural adhesive can be improved by addition of fillers to the adhesive. In this paper, the elastic modulus and failure strength of adhesives as well as the tensile load capability of tubular single lap adhesive joints were experimentally and theoretically investigated with respect to the volume fraction of filler (alumina) and the environmental temperature. Also the tensile modulus of the filler containing epoxy adhesive was predicted using a new equation which considers filler shape, filler content, and environmental temperature. The tensile load capability of the adhesive joint was predicted by using the effective strain obtained from the finite element analysis and a new failure model, from which the relation between the bond length and the crack length was developed with respect to the volume fraction of filler.     

Effect of overlap length on durability of joints bonded with a pressure-sensitive adhesive

In this study, the effect of overlap length on durability of a film type adhesive, Structural Bonding Tape (SBT) 9244, which possesses pressure-sensitive and visco-elastic properties, was investigated. Single-lap joints with 1.62 and 3.2 mm adherend thicknesses and at 12.5, 25 and 50 mm overlap lengths consisting of AA2024-T3 alloy as the adherend were exposed to two environmental conditions for exposure times of up to 90 days. The exposure environments were 100% relative humidity (RH) and 3.5% NaCl solution. At the end of exposure times, the failure surfaces were examined by Scanning Electron Microscopy (SEM) after the strength of joints was determined with the lap shear test. It was observed that with increasing overlap length, not only the failure load increased, but also the degradation rate decreased. In addition, as the metal adherends do not absorb any water and moisture from the environments, the metal adherend thickness had no effect on durability of the adhesively bonded joints.     

Evaluation of Fatigue Damage in Adhesive Bonding: Part 1: Bulk Adhesive

The measurement of fatigue damage in adhesive bonding has been investigated. Bulk adhesive was used in this study for two reasons: the stress distribution of adhesives in bulk is simpler to investigate than adhesives in joints; and the specimen dimensions met fatigue test standards. Bulk adhesive was made from a film type of epoxy resin. In general, the characteristics and the behaviour of bulk adhesive may differ from adhesive in joint because of the presence of voids and the constraints imposed by the substrates. Low cycle fatigue tests with a load amplitude ratio of 0.1 at a frequency of 5 Hz were performed to determine the damage as a function of the number of cycles. Damage curves, i.e., the evolution of the damage variable as a function of number of cycles, were derived and plotted using an isotropic damage equation. Damage was evaluated using the decrease of stress range during the lifecycles of a constant displacement amplitude test. It was found that the damage curves were well fitted by a low cycle, fatigue damage evolution law equation. This equation was derived from a dissipation potential function. Curve fitting was performed using the robust least square technique rather than ordinary linear least square technique because damage curves have extreme points (usually near the failure point). It was found that the fitting process would not converge for adhesive fractures at high cycle values (N _f > 9000). Two damage constants A and β were found from the fitting process. Each fatigue set of data, at a certain level of von-Mises stress range for the undamaged state or at the stabilized hardened state, (Δσ*_eq), had a different set of damage parameters A and β. Linear regression of these points was used to express A and β as a function of Δσ*_eq. Using these expressions, damage curves for different levels of Δσ*_eq could be predicted.     

Electrically conductive adhesive and soldered joints under compression

Compression of soldered and conductive adhesive joints resulted in both reversible and irreversible changes in the contact electrical resistivity. At a low stress (as low as 0.02 and 0.005 MPa for soldered and adhesive joints, respectively), the resistivity increased with almost complete reversibility as the compressive stress increased. At an intermediate stress (as low as 0.03 MPa) for both soldered and adhesive joints, the resistivity decreased with partial or complete reversibility as the stress increased. At a high stress (as high as 0.21 MPa) for the soldered joint only, the resistivity increased slightly with increasing stress. The resistivity of the soldered joint at no load increased irreversibly and gradually as stress cycling progressed, even at the lowest stress amplitude of 0.12 MPa. However, the resistivity of the adhesive joint at no load decreased irreversibly and gradually as stress cycling progressed, even at the lowest stress amplitude of 0.009 MPa.     

Modeling of cohesive failure processes in structural adhesive bonded joints

This paper presents an approach to predicting the strength of joints bonded by structural adhesives using a finite element method. The material properties of a commercial structural adhesive and the strength of single-lap joints and scarf joints of aluminum bonded by this adhesive were experimentally measured to provide input for and comparison with the finite element model. Criteria based on maximum strain and stress were used to characterize the cohesive failure within the adhesive and adherend failure observed in this study. In addition to its simplicity, the approach described in this paper is capable of analyzing the entire deformation and failure process of adhesive joints in which different fracture modes may dominate and both adhesive and adherends may undergo inelastic deformation. It was shown that the finite element predictions of the joint strength generally agreed well with the experimental measurements.     

Effect of bond thickness on creep lifetime of adhesive joints under mode I

An experimental investigation has been carried out on double cantilever beam specimens with different bond thicknesses to study the effect of bond thickness on lifetime of adhesive joints under mode I. This paper describes an approach to predict the rate of crack propagation. The approach is based on principles of linear elastic fracture mechanics and uses elevated temperature to accelerate the crack propagation under constant loads. The fracture energy of the joint is studied as a function of bond thickness. The results from short-term tests are analyzed and a simple model has been proposed to predict the variation of two kinetic parameters of the Paris law with bond thickness.     

Simulation of Mixed-Mode I/II Fatigue Crack Propagation in Adhesive Joints with a Modified Cohesive Zone Model

A model to predict fatigue crack growth in bonded joints under mixed mode I/II conditions is developed in this work. The model is implemented in the finite element software ABAQUS using the related USDFLD subroutine. The present model is based on the cohesive zone (CZ) concept, where damage develops according to the value of the opening/sliding at the bondline under static loading, and according to a cyclic damage accumulation law under fatigue loading. The damage accumulation law is obtained by distributing the cyclic crack area increment over the process zone ahead of the crack tip, where the cyclic crack area increment is calculated according to a Paris-like law that relates the crack growth rate to the applied loading. In this way, the experimental crack growth rate is related directly to damage evolution in the cohesive zone, i.e., no additional parameters have to be tuned besides the quasi-static cohesive zone parameters.     

Fatigue and failure behaviors of silver-filled electronically-conductive adhesive joints subjected to elevated humidity

Conductive adhesives are used in electronics packaging applications for hybrid, die-attach and display assemblies. There are a number of issues of concern in the design of joints bonded using electronically-conductive adhesives (ECAs). An important issue is the cyclic fatigue behavior of conductive adhesive joints under elevated humidity environments, in which failures may occur due to cyclic mechanical and/or thermal stresses. This paper addresses the effect of elevated humidity levels on the fatigue and failure behaviors of ECAs. For this purpose, joints were prepared using stainless-steel adherend specimens and a commercial ECA, and tested under monotonic and cyclic fatigue conditions, at two humidity levels, namely 20% and 90% relative humidity at 28°C. Furthermore, joint failure mechanisms were analyzed using optical techniques, and joint conductivity measurements. Load versus number of cycles (P–N) curves were generated using these specimens at three different load ratios (R), namely 0.1, 0.5 and 0.9, at a cyclic frequency of 150 Hz. The P–N curves were parallel and the failure modes were found to be predominantly interfacial, accompanied by a significant decrease in joint conductivity.     

Analysis of stresses in adhesive joints applicable to IC chips using symbolic manipulation and the numerical method

In this study, a concentrated force is applied to both adherends bonded by an adhesive under pin–pin boundary conditions. First a mathematical model is derived with governing equations and boundary conditions. These complicated, and analytically problematic, coupled equations are solved numerically using symbolic manipulation and singular value decomposition (SVD). Also discussed are the effects of major factors, including the relative thickness of adherends, joint length and the action point of the concentrated force on the peel and shear stresses in the adhesive layer. This study identifies the conditions under which the upper adherend without breakage can be fully separated from the lower adherend. Particularly, it is found that the thickness of the lower adherend should be greater than ten times that of the adhesive layer but less than one-third that of the upper adherend, the adhesive layer should be relatively thin (h _a ≤ 0.01 mm), and the adhesive joint should be relatively short (thickness to length ratio γ ₁ ≥ 0.08).     

Damping characteristics of machine structures assembled by bonding: a beam in which two steel strips are partially joined by an adhesive

Machine structures assembled by adhesive bonding are expected to possess a high damping capacity because of the high damping capacity of the adhesive. In this study, the damping characteristics of a beam in which two steel strips were partially joined by an adhesive have been investigated. The primary aim of this study was to clarify the damping characteristics of adhesively bonded structures and to establish an estimation method for the damping capacity. In the analysis, strain energy distributions in the adhesively bonded beam in motion are analyzed by the finite element method. Then the damping capacity of the beam is derived using the strain energies and damping ratios of the two materials, i.e. the steel strips and the adhesive, which were obtained beforehand in independent experiments. The validity of the proposed estimation method for the damping capacity and the effects of the thickness of the adhesive and vibration modes on the damping capacity were confirmed by experiments. Satisfactory agreement was shown by comparing the estimated values of the damping capacity of the beam with the experimental results. Furthermore, the temperature dependence of the damping capacity was examined.     

Effect of residual stresses on fatigue crack growth behavior of aluminum substrate repaired with a bonded composite patch

Composite patches bonded to cracked metallic aircraft structures have been shown to be a highly cost-effective method for extending the service life of the structures. The fatigue crack growth behavior of pre-cracked 7075-T6 aluminum substrate with the 12.7-mm V-notch crack repaired with boron/epoxy composite patches was investigated. 1-ply, 2-ply, 3-ply and 4-ply composite patches were studied. The residual stresses due to mismatch of the coefficients of thermal expansion between the aluminum plate and boron/epoxy composite patch were calculated based on the classical equation. The effects of the residual stresses and patch layers on fatigue lifetime, fatigue crack growth rate, and fatigue failure mode of the repaired plates were examined experimentally. A modified analytical model, based on Rose's analytical solution and Paris power law, was developed for this research. This model considered the residual stress effect and successfully predicted the fatigue lifetime of the patched plates. Results showed that the composite patch had two competing impacts on the structure. The composite patch could cause residual tensile stress in the aluminum substrate, which could consequently increase the crack growth rate. Moreover, reinforcement with the composite patch could also retard the crack propagation in the aluminum plate. If a 4-ply composite patch was used, it resulted in high residual stresses and effectively would not extend the fatigue lifetime of cracked aluminum plates.     

Strength and finite element analyses of single-lap joints with adhesively-bonded columns

This paper introduces a novel approach to increase the loading ability of adhesive joints by incorporating adhesively-bonded columns. Strengths of single-lap adhesive joints with adhesively-bonded columns were measured experimentally. Stress and strain distributions at selective positions in the adhesive layer were analyzed using the Finite Element Method (FEM). Failure mechanisms of the joints were analyzed. It was found that the metal-adhesive columns increased the joint strength and also the joint strength increased with increasing length of the metal-adhesive columns. Therefore, using metal-adhesive columns in adhesive joints is an effective approach for enhancing the strength of bulk adhesive joints.     

Evaluation of Fatigue Damage in Adhesive Bonding: Part 2: Single Lap Joint

The damage parameters for crack initiation in a single lap joint (SLJ) are determined by combining continuous damage mechanics, finite element analysis (FEA) and experimental fatigue data. Even though a SLJ has a simple configuration, the stresses in the adhesive region are quite complex and exhibit multi-axial states. Such a condition leads to the need to introduce a general value for the triaxiality function in the damage evolution law rather than using a triaxiality function which equals unity, as in the case of a uni-axial stress state, e.g., the bulk adhesive test specimen presented in Part 1 of this paper. The effect of stress singularity, due to the presence of corners at edges, also contributes to the complex state of stress and to the variability of the triaxiality function along the adhesive layer in a SLJ. The damage parameters A and β determined in Part 1 for bulk adhesive are now extended to take into account the multi-axial stress state in the adhesive layer, as calculated from FEA.     

Theoretical and experimental studies for the failure criterion of adhesively bonded joints

The objective of this work was to develop a criterion for predicting the failure strength of joints bonded by ductile adhesives. To obtain the criterion, first, fracture tests were carried out on T-peel joints and single-lap joints with various joint geometries, adhesives, and adherend materials. Then using the fracture loads obtained in the tests, a finite element analysis was performed by which the stresses in the adhesive joints were calculated. It is concluded that the failure of an adhesively bonded joint occurs when the maximum of the ratio of the mean to effective stresses exceeds a certain value, which can be considered a new material constant of a ductile adhesive.