Cleavage behavior of bonds made with adherends capable of plastic yield

The failure behavior of adhesive joints under cleavage stresses depends upon the thickness of the adherend. With thick, rigid adherends failure occurs by rapidly propagated adhesive rupture. Thinner adherends can exhibit plastic flexural yield, the subsequent adhesive failure then being progressive and strain-limited, and occurring only in the region of bond directly adjacent to the yielding adherend. A fairly sharp discontinuity between these two types of behavior occurs over a small range of adherend thickness T. Work to rupture can differ by more than an order of magnitude, for otherwise identical joints having T above or below the transitional range (around T_c). For T > T_c the applied load P causing rupture is proportional to T^1.5 while the moment arm remains constant, as predicted by Yurenka. For T < T_c the turning moment during failure is proportional to T² and is substantially independent of the nature of the adhesive. Empirically, the radius of the yielded adherend after failure is proportional to T. The manner of interaction of various adhesive mechanical properties in defining P in the two ranges and, thereby, T_c, are related to this and other empirical correlations. The initial free moment arm in the joint, L, determines the stability of peel at initiation of adhesive rupture. Reducing L leads ultimately to instability. The change of controlling factors as L → 0 is discussed.     

Peel mechanics for an elastic-plastic adherend

The force required to propagate a 180° bend in an elastic-plastic strip has been calculated from elementary bending theory. Measured forces for Mylar strips of various thicknesses, bent to various degrees, were in good agreement with these calculated values. The corresponding additional stripping force in a peeling experiment will depend upon the thickness of the elastic-plastic adherend, becoming zero both for infinitesimally thin adherends and for those exceeding a critical thickness t_c and passing through a maximum value at intermediate thicknesses. Published data are in good agreement with these conclusions. For a strongly adhering strip, higher peel strengths are found for a peel angle of 180°, compared to 90°, and the effect is greater than can be accounted for solely by plastic yielding of the adherend. It is attributed in part to greater energy dissipation within the adhesive layer.     

The Mechanical Behaviour of Polyimide/Copper Laminates Part 2: Peel Energy Measurements

The mechanical peel behaviour of laminates consisting of polyimide films adhered to copper foil using a modified acrylic adhesive has been studied over a wide range of test rates and temperatures. The laminates were prepared from polyimide films which had been subjected to either a “high-thermal history” or a “low-thermal history” treatment during the production of the film. The measured peel energies of the laminates could be superimposed to give a master curve of peel energy versus the reduced rate of peel test, Ra_T , where R is the rate of peel test and a_T is the time-temperature shift factor. The appropriate shift factors were a function of the test temperature and were mainly deduced from tensile tests conducted on the bulk adhesive. The “high-thermal history” laminates gave higher peel energies and the locus of failure of the laminates was mainly by cohesive fracture through the adhesive layer. At low values of log₁₀ Ra_T , i.e. Low rates of peel and high test temperatures, the “low-thermal history” laminates also failed in the adhesive layer and possessed similar peel energies to those measured for the “high-thermal history” laminates. However, at high log₁₀ Ra_T values, the peel energies measured for the “low-thermal history” laminates were lower and showed a wider scatter. These arose from a different locus of failure occurring in these “low-thermal history” laminates when tested under these conditions. Namely, it was found that most of these laminates failed in a weak boundary layer in the outer regions of the “low-thermal history” polyimide film.     

Substrate constraint and adhesive thickness effects on fracture toughness of adhesive joints

The adhesive thickness effect on fracture behaviour of adhesive joints has been studied using the boundary effect model recently developed for specimen size effect on fracture properties of concrete, and the essential work of fracture model for ligament (uncracked region) effect on largescale yield of bulk metals and polymers. The leading common mechanism responsible for the nonlinear elastic fracture mechanics behaviours, such as adhesive thickness effect of adhesive joints, specimen size effect of brittle heterogeneous materials and notch dependence of deeply notched metal and polymer specimens, is discussed. These two fracture mechanics models show that the height variation of a fracture process zone (FPZ) or a plastic zone is directly responsible for any change in fracture energy measurements such as the specific fracture energy G _f and the critical strain energy release rate G _c. Both models show that G _f is rapidly reduced when the crack-tip approaches the back-face boundary of a specimen because only a limited FPZ or plastic zone height h _FPZ can be developed in the boundary region. In the case of a thin adhesive joint, the development of a plastic zone height is limited by the thickness of the adhesive sandwiched between the upper and lower adherends or substrates. Consequently, a linear relationship between the adhesive joint toughness and adhesive thickness is established. Test results on adhesive joints from the literature are analysed and compared with the new adhesive joint failure model based on the two well-established fracture mechanics models developed for other material systems.     

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).     

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.     

Three-dimensional finite element analysis of single-lap adhesive joints subjected to impact bending moments

This paper deals with the stress wave propagations and stress distributions in single-lap adhesive joints subjected to impact bending moments with small strain rate. The elastic stress wave propagation and the stress distribution in single-lap adhesive joints of similar adherends subjected to impact bending moments are analyzed using three-dimensional finite-element method (FEM). A three-point impact bending moment is applied to the joint by dropping a weight. FEM code employed is DYNA3D. The effects of Young's modulus of the adherends, the lap length, the adherend thickness and the adhesive thickness on the stress wave propagation at the interfaces are examined. It is found that the maximum value of the maximum principal stress, σ₁, appears at the interface between the adhesive and the upper surface of upper adherend which is impacted. The maximum stress, σ₁, increases as Young's modulus of adherends, the lap length and the adhered thickness increase. It is also found that the maximum stress, σ₁ increases with decreasing adhesive thickness. In addition, experiments were carried out to measure the strain response of single-lap joints subjected to impact bending moments using strain gauges. A fairy good agreement was observed between the numerical and experimental results.     

Peel mechanics of adhesive joints

A review is given of the mechanics of peeling rupture of an adhesive joint, consisting of a flexible adhering strip peled away from a layer of adhesive. Attention is drawn to a number of anomalous results that cannot be accounted for solely, in terms of the thermodynamic work of formation of two new surfaces. The work of detachment is found to be generally much larger than the theoretically-predicted amount. Moreover, the value obtained is greater for thicker layers of adhesive, and for detachment at a peel angle of 180° rather than at 90°. Also, it is found to increase with increasing thickness of the adhering strip, passing through a maximum value in some cases and then decreasing as the strip thickness is increased still further. All of these effects are attributed to dissipative processes, for example, plastic yielding, in one or both of the adhering layers as they are peeled apart. Some quantitative relationships are given for the additional peel forces arising from plastic yielding of the adherend or the adhesive.     

Impact of geometry on the critical values of the stress intensity factor of adhesively bonded joints

Several studies have dealt with the application of the generalized stress intensity factor (GISF) on the failure load prediction of adhesive joints. However, the effect of geometry on the critical value of the GSIF (H_c) is complex and limits its application. Due to the effect of multiple geometrical features and the limited success in the field of adhesive joints, a statistical analysis is a possibility. This paper investigates the impact of different geometrical features on the H_c in single lap adhesive joints. To achieve this, the statistical response surface methodology (RSM) was used to design the experiments and for the statistical analysis. According to the RSM, 31 arrangements of single lap joints were manufactured and tested. In this analysis, the adhesive thickness, adherend thickness, overlap length and also the free length, each in five different levels, were considered. The effect of linear, quadratic and two-way interactions of the geometrical parameters on the H_c and failure load were also studied. It was shown that H_c is most affected by the overlap length. Variation of H_c in term of the free length is by far higher at lower adhesive thicknesses. Also, the effect of substrate thickness on H_c is more considerable for thinner bondlines. The interactions of overlap length/free length and overlap length/adhesive thickness affect the failure load more considerably than the other studied interactions. The effect of free length on the failure load increases with the bondline thickness, while the effect of substrate thickness is stronger for a lower adhesive thickness.     

Thermal residual stresses in an adhesively-bonded functionally graded single-lap joint

This study investigates three-dimensional thermal residual stresses occurring in an adhesively-bonded functionally graded single-lap joint subjected to a uniform cooling. The adherends are composed of a through-the-thickness functionally graded region between Al₂O₃ ceramic and Ni metal layers. Their mechanical properties were calculated using a power law for the volume fraction of the metal phase and a 3D layered finite element was implemented. In a free single-lap joint the normal stress σ_xx was dominant through the overlap region of the upper and lower adherends and along the adhesive free edges, whereas the transverse shear stress σ_xy concentrations appeared only along the free edges. The peel stress σ_yy and the transverse shear stress σ_xy became dominant along the free edges of the adhesive layer. In addition, the von Mises stress decreased uniformly through the adherend thickness from compressive in the top ceramic-rich layer to tensile in the bottom metal-rich layer. In addition, the layer number had only a minor effect on the through-the-thickness stress profiles after a layer number of 50, except for the peak stress values in the ceramic layer. In a single-lap joint fixed at two edges both adherends underwent considerable normal stress σ_xx concentrations varying from compressive in the top ceramic-rich layer to tensile in the bottom metal-rich layer along the free edges of both adherend–adhesive interfaces, whereas the peel stress σ_yy and transverse shear stress σ_xy reached peak levels along the left and right free edges of the adhesive layer. The layer number and the compositional gradient exponent had only minor effects on the through-the-thickness von Mises stress profiles but considerably affected the peak stress levels. The free edges of adhesive–adherend interfaces and the corresponding adherend regions are the most critical regions, and the adherend edge conditions play more important role in the critical adherend and adhesive stresses. Therefore, the first initiation of the joint failure can be expected along the left and right free edges of the upper and lower adherend–adhesive interfaces.     

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.     

Mode-l Fracture Behaviour of Adhesive Joints. Part I. Relationship Between Fracture Energy and Bond Thickness

The fracture properties of adhesive joints of aluminium were investigated using a rubber-modified tough epoxy resin system (G_IC = 2.76 kJ/m²) as adhesive material. Compact tension (CT) adhesive joints were manufactured for a wide range of bond thickness t (from 0.05mm to 10mm) and fracture tests conducted under static load. Scanning electron microscopy (SEM) was used to examine the fracture surface morphology. A large deformation elastic- plastic finite element model was developed to evaluate the J-integral value for different bond thickness. The fracture energy, J_c , was found to be highly dependent on the bond thickness and was lower than that of the bulk adhesive. As the bond thickness was increased J_c also increased, though not monotonically, towards the fracture energy of the bulk adhesive. This result was caused by the complicated interactions between the stress and strain fields, plastic deformation of the adhesive around the crack tip, constraint from the adherends and the failure path. It was shown that values of J_c as a function of bond thickness correlated well with the variation of plastic zone height. Scanning electron micrographs from the fracture surfaces of the CT adhesive joints illustrated that the failure path was mainly cohesive through the centre-plane of the adhesive layer. Brittle fracture mechanisms were observed for thin bonds (0.04mm < t< 0.5 mm) but tough fracture mechanisms were identified for thick bonds (t > 1 mm).     

Shear and peel stress analysis of an adhesively bonded scarf joint

The shear and peel stress distributions in a scarf joint made of two isotropic adherends with blunt adherend tips are analysed using a linear elastic analysis. The limits of the analysis with respect to adherend tip thickness have been investigated. A finite difference method is used to solve the differential equations for the shear and peel stress distributions over the joint. The boundary conditions used limit the analysis to the two adherends having the same thicknesses, lengths, and material properties. The adherends are modelled as plates with extensional and bending stiffnesses bonded together with an elastic interlayer. The stresses across the adhesive layer are assumed to be constant. The current analysis applied to cases known from the literature shows good agreement with the shear stresses but the peel stresses are overestimated.     

An analytical model for interfacial stresses in double-lap bonded joints

Due to their many advantages, adhesively bonded joints are widely used to join components in composite structures. However, premature failure due to debonding and peeling of the joint is the major concern for this technique. Existing analytical models suffer from two major drawbacks: 1) not satisfying zero-shear stress boundary conditions at the adhesive layer’s free edges^[1] and 2) failure to distinguish the peel stress along two adherend/adhesive interfaces^[2]. In this study, we develop a novel three parameter elastic foundation (3PEF) model to analyze a representative adhesively bonded joint, the symmetric double-lap joint, which is believed to have relatively low peel stresses. Explicit closed-form expressions of shear and peel stresses along two adhesive/adherend interfaces are yielded. This new model overcomes the existing model’s major drawbacks by satisfying all boundary conditions and predicting various peeling stresses along two adherend/adhesive interfaces. It not only reaches excellent agreement with existing solutions and numerical results based on finite element analysis but also correctly predicts the failure mode of an experimentally tested double-lap joint. This new model therefore reveals the peel stresses’ significant role in the failure of the double-lap joint, but the classical 2PEF model cannot create it.     

Analytical Peel Load Prediction as a Function of Adhesive Stress Concentration

Peel data for two epoxy adhesives and a recent model of the adhesive stresses in the peel geometry are used to investigate the effectiveness of two constitutive models and several adhesive failure criteria. The failure criteria are based on either the critical strain energy-release rate or the critical von Mises strain at the peel root, both taken as functions of the “loading zone length” (LZL), defined as a measure of the degree of stress concentration at the root of the peeling adherend. The peel model uses LZL as an independent parameter that captures the effects of the peel angle, adherend thickness, and the mechanical properties of the adhesive and adherend. Both the energy- and strain-based failure criteria can be used to predict the steady-state peel load with an average absolute error of less than 10% over the range of conditions that were examined.     

On the intralaminar and interlaminar stress analysis of adhesive joints in plated beams

An improved bimaterial adhesive joint model is proposed for the intralaminar and interlaminar stress analysis of adhesively-bonded interfaces in plated beams with thin or moderately thick adhesive layer. To overcome the limitations or unreasonable assumptions in the existing theoretical joint models, both the shear and normal stresses along two adherend–adhesive interfaces are assumed to be different in the present model, and the adhesive layer is modeled as a simplified 2-D elastic continuum. Deformable interfaces are assembled to establish the continuity conditions between the adherend–adhesive interfaces, and the local deformations near the end of the adhesive layer are fully captured. The longitudinal and transverse displacements of the adhesive layer are introduced as two new independent parameters, and the missing “degrees of freedom” in the conventional elastic foundation models are retrieved. Differential governing equation of an adhesively-bonded bi-layer beam is established, and explicit closed-form expressions of beam forces and interface stresses are derived. Comparisons of the present solution with the existing elastic foundation models as well as the full 2-D continuum elastic solutions by the finite element analysis are conducted to validate the presented model. Parametric studies are then conducted to reveal the roles of the adhesive thickness and local interface deformations on the stress distributions both along the adherend–adhesive interfaces (interlaminar) and through the adhesive layer thickness (intralaminar), from which a feasible measure to reduce the strain or stress concentrations is obtained. The present improved adhesive joint model in plated beams sheds light on the effect of adhesive layer thickness in bimaterial bonding assembly and provides a better understanding of potential interface debonding initiation and its propagation path.     

Analysis of adhesively-bonded T-joints by experimentation and cohesive zone models

Within the scope of adhesively-bonded joints, one of the joint types having industrial application is the T-joint, for example, in marine applications (joining of panels to the hull and connecting the glass-fibre composite hull with anti-flood panels) and aeronautical applications (wing panels, fuselage sections). This work aims to experimentally and numerically study, by cohesive zone models (CZM), the behaviour of T-joints under peel loads. The experimentally evaluated adhesives are the Araldite^® AV138 (high ultimate strength but brittle) and Araldite^® 2015 (less stress to failure but ductile and more flexible). The joint strength is evaluated with different L-shaped adherends’ thickness (t_P2). With the numerical analysis, the stress distributions, damage evolution and strength are studied. Additionally, a purely numerical study compared joints with or without adhesive filling at the curvature of the L-shaped adherends, and an extremely ductile adhesive (Sikaforce^® 7752) was additionally evaluated. The experimental tests validated the numerical results and showed that CZM is an accurate technique for the study of T-joints. It was also shown that the geometry of the L-parts, the presence of filler adhesive and the type of adhesive have a direct influence on the joint strength. In fact, in this particular joint configuration, the ductile but with lower ultimate strength adhesive Sikaforce^® 7752 clearly outperforms the two adhesives with higher mechanical properties but less ductility.     

Determination of the impact tensile strength of structural adhesive butt joints with a modified split Hopkinson pressure bar

The impact tensile strength of structural adhesive butt joints was determined with a modified split Hopkinson pressure bar using hat-shaped specimens. A typical two-part structural epoxy adhesive (Scotch weld^® DP-460) and two different adherend materials (Al alloy 7075-T6 and commercially pure titanium) were used in the adhesion tests. The impact tensile strength of adhesive butt joints with similar adherends was evaluated from the peak value of the applied tensile stress history. The corresponding static tensile strengths were measured on an Instron testing machine using joint specimens of the same geometry as those used in the impact tests. An axisymmetric finite element analysis was performed to investigate the static elastic stress distributions in the adhesive layer of the joint specimens. The effects of loading rate, adherend material and adhesive thickness on the joint tensile strength were examined. The joint tensile strength was clearly observed to increase with the loading rate up to an order of 10⁶ MPa/s, and decrease gradually with the adhesive thickness up to nearly 180 μm, depending on the adherend materials used. The loading rate dependence of the tensile strength was herein discussed in terms of the dominant failure modes in the joint specimens after static and impact testing.     

The Adhesively Bonded Aluminium Joint: The Effect of Pretreatment on Durability

The interface in aluminium bonded structures can be revealed by ultramicrotomy and subsequently studied by transmission electron microscopy. By these means, the more usual surface pretreatments encountered, have been characterised in depth.

A similar examination has been effected following exposure of bonded joints (floating roller peel specimens) to 85% relative humidity at 70°C. Although a drop in peel performance is noted over the exposure time, interfacial examination reveals little damage to the adhesive or adherend. Possible mechanisms for bond strength reduction are discussed: subtle undermining of the alumina film and disruption of physico-chemical bonds across the interface. Both are initiated by moisture reaching the alumina film, either passing along the interface itself or travelling through the adhesive matrix. Also considered are the effects of surface pretreatment and “oxide” penetration, by the adhesive, on durability.

The effect of priming the adherend surface prior to bonding, using a heavily strontium chromate filled adhesive primer, is mentioned and its possible influence on durability is briefly discussed.     

Peel Adhesion: Influence of Surface Energies and Adhesive Rheology

The adhesion properties of polymers are known to be influenced by both intermolecular forces operative at the interface and the rheological history of both bonding and unbonding. Recent adsorption and viscoelastic theories of adhesion and cohesion are implemented in a comprehensive examination of these phenomena. Eight peel force “master curves” extending over 14 decades of reduced rate and representing glassy state to flow region rheology are superimposed to provide a composite response envelope. Each master curve represents rate-temperature reduced adhesion of an alkyl acrylate adhesive (γ_c = 26 dyne/cm) to substrates ranging from low adhesion fluorinated polymers (γ_c = 15 to 17 dyne/cm) to polar poly-amide surfaces (γ_c = 45 dyne/cm) and glass. The rate dependent transition from interfacial to cohesive failure, a subject not treated by adsorption theory, is shown to be coincident with the onset of entanglement slippage within the polymeric adhesive. Thermodynamic criteria of polymer adhesion are shown to be applicable only to the flow region of polymeric response. This study indicates that measured surface tensions or calculated surface energies of polymeric solids do not properly account for the contributions of three dimensional network structure of the polymeric bulk phase to its total work of cohesion. Evidence of true interfacial failure of a polymer-polymer bond is supported by critical surface tension measurements.