Evaluation of Mode-II Fracture Energy of Adhesive Joints with Different Bond Thickness

A study on the mode-II edge-sliding fracture behaviour of aluminium-adhesive joints was carried out. Compact pure shear (CPS) adhesive joints of different bond thickness were produced using a rubber-modified epoxy resin as the adhesive. An analytical model was developed to calculate the stress distribution along the bond line of the joint. A crack-closure technique was used to evaluate the mode-II strain energy release rate. G _II, as a function of the adhesive bond thickness. The results indicated that for a given applied load, G _II increased gradually with the bond thickness. A finite element model (FEM) was also developed to evaluate the stress state along the bond line and the strain energy release rate of the CPS specimens. Consistent results were obtained between the theoretical model and finite element analysis. Scanning electron micrographs of the fracture surface illustrated a mainly interfacial fracture path between the adherends and the adhesive for all adhesive joint specimens. The critical fracture load increased very rapidly with bond thickness in the range 0.02 mm to 0.1 mm but remained constant thereafter. However, the mode-II critical fracture energy rose more gradually as the bond thickness was increased.     

Effect of Bond Thickness on Fracture Behaviour in Adhesive Joints

To study the effects of bond thickness on the fracture behaviour of adhesive joints, experimental investigation and finite element analysis have been carried out for compact tension (CT) and double-cantilever-beam (DCB) specimens with different bond thickness. Fractography and fracture toughness exhibited apparent variations with bond thickness. Numerical results indicate that the crack tip stress fields are affected by bond thickness due to the restriction of plastic deformation by the adherends. At the same J level, a higher opening stress was observed in the joint with a smaller bond thickness (h). Beyond the crack tip region, a self-similar stress field can be described by the normalized loading parameter, J/hσ₀. The relationship between J and crack tip opening displacement, δ, is dependent on the bond thickness. The strong dependence of toughness upon bond thickness is a result of the competition between two different fracture mechanisms. For small bond thickness, toughness is linearly proportional to bond thickness due to the high constraint. After reaching a critical bond thickness, the toughness decreases with further increase of bond thickness due to the rapid opening (blunting) of the crack tip with loading. A simple model has been proposed to predict the variation of toughness with bond thickness.     

Evaluation of Mode-II Fracture Energy of Adhesive Joints with Different Bond Thickness

A study on the mode-II edge-sliding fracture behaviour of aluminium-adhesive joints was carried out. Compact pure shear (CPS) adhesive joints of different bond thickness were produced using a rubber-modified epoxy resin as the adhesive. An analytical model was developed to calculate the stress distribution along the bond line of the joint. A crack-closure technique was used to evaluate the mode-II strain energy release rate. G_II, as a function of the adhesive bond thickness. The results indicated that for a given applied load, G_II increased gradually with the bond thickness. A finite element model (FEM) was also developed to evaluate the stress state along the bond line and the strain energy release rate of the CPS specimens. Consistent results were obtained between the theoretical model and finite element analysis. Scanning electron micrographs of the fracture surface illustrated a mainly interfacial fracture path between the adherends and the adhesive for all adhesive joint specimens. The critical fracture load increased very rapidly with bond thickness in the range 0.02 mm to 0.1 mm but remained constant thereafter. However, the mode-II critical fracture energy rose more gradually as the bond thickness was increased.     

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.     

Fracture behaviour of a rubber nano-modified structural epoxy adhesive: Bond gap effects and fracture damage zone

This paper critically examined the fracture behaviour of a rubber-modified, structural epoxy adhesive with various bond gap thicknesses ranging from 0.05 mm to 6 mm. The main and very novel contribution is direct measurement of the fracture process zone, plastic deformation zone and intrinsic fracture energy dissipated in the fracture process zone. The shape and size of the fracture process zone and plastic deformation zone were identified using scanning electron microscopy, transmission electron microscope and transmission optical microscope. As the bond gap thickness increased, the fracture energy increased steadily from 2365 J/m² for 0.05 mm bond gap thickness to 6289 J/m² of 1.6 mm bond gap thickness, and then plateaued. The thickness and failure strain of the fracture process zone remained essentially constant, being approximately 0.052 mm and 0.55 respectively, for different bond gap thicknesses. The intrinsic fracture energy (dissipated in the fracture process zone) appeared to be a material property, which remained approximately 2738 J/m². The plastic deformation zone extended through the entire bond gap in thickness and occupied a significant length for all bond gap thicknesses. The effect of bond gap thickness on the fracture energy of the adhesive joints is hence directly attributed to the variation of the plastic deformation energy (dissipated in the plastic deformation zone) with bond gap thickness.     

Effects of Film Thickness on The Work of Fracture Between Adhesives and Glass

In this investigation, the fracture energy of joints consisting of soda lime glass sandwiched around either an acrylate or poly(vinyl butyral) (PVB) was studied. This was accomplished for various adhesive thicknesses with the use of a tapered double cantilever beam specimen loaded in mode I. For adhesive thicknesses varying between 0.03 mm and 0.80 mm, the fracture energies ranged from 15 to 95 Pam for the glassy acrylate joints and from 375 to 1060 Pam for the more rubbery PVB joints. While the fracture energy was relatively independent of thickness for the acrylate joints, there was an increasing trend in toughness for the PVB joints. The fracture energy of the acrylate joints was modeled with a process zone model with reasonable results while the fracture energy of the PVB joints was modeled with constraints on the plastic zone. Scanning electron microscopy and measured bulk adhesive properties provided necessary input into the models.     

Mode-l Fracture Behaviour of Adhesive Joints. Part II. Stress Analysis and Constraint Parameters

The constraint effect on the fracture behaviour of a rubber-modified epoxy was investigated using compact tension (CT) adhesive joints. An elastic-plastic finite element analysis was conducted to evaluate the stress distribution ahead of the crack tip in the bulk adhesive and adhesive joints of different bond thickness. The models with sharp and finite radius crack tips were evaluated in the analyses. The constraint effect of adherends on the stress triaxiality ahead of the crack tip in the adhesive joints were discussed. The constraint parameters were investigated using the J-Q theory and the J-CTOD relationship. It was found that as the adhesive thickness was increased, the stress triaxiality ahead of the crack tip was relieved by the remarkable deformation of the adhesive material. Similarly, the crack tip constraint was reduced with increasing bond thickness so that the fracture energy increased towards the value of the bulk adhesive. A higher constraint was associated with a lower fracture energy and vice versa. Furthermore, the J-integral did not have a unique relationship with the crack-tip opening displacement (CTOD) for different adhesive bond thickness, as this depends on the constraint around the crack tip. The results of this study will help improve reliability assessment of adhesive joints in engineering applications.     

Fracture toughness of acrylonitrile-butadiene-styrene by J-integral methods

The fracture toughness of acrylonitrile-butadiene-styrene (ABS) was determined by three J-integral methods, ASTM E813-81, E813-87, and by hysteresis. The critical J values (J_1c) obtained are fairly independent of the specimen thickness, ranging from 10 to 15 mm. ASTM E813-81 and hysteresis methods result in comparable J_1c values, whereas the ASTM E813-87 was ～40% to 50% higher. The critical displacement determined from the plots of hysteresis (energy or ratio) and the true crack grow length vs. displacement are close. This indicates the critical displacement determined by the hysteresis method is indeed the displacement at onset of crack initiation, and the corresponding J_1c represents a physical event of crack initiation. The elastic storage energy. The input energy minus the hysteresis energy, is the most important factor in determining the onset of crack initiation. The critical elastic storage energy (at the beginning of crack growth) was found close to the J_1c obtained from the E813-81 or the hysteresis method.     

Fracture toughening behavior and mechanical properties of polyphenylene oxide/high-impact polystyrene blends

Blends of a poly(phenylene oxide) (PPO) with high-impact polystyrene (HIPS) were injection molded. The static mechanical properties and fracture toughness of the blends were determined by means of the uniaxial tension, Brinell hardness and three-point-bending measurements. From the static mechanical test results, it was shown that the yield strength, Young's modulus and hardness values of the PPO/HIPS blends were considerably higher than those of their PPO and HIPS component polymers. Dynamic mechanical measurements indicated that the PPO/HIPS blends appear to be miscible as shown by the existence of a single glass transition temperature. Furthermore, the J integral method based on ASTM E813-89 procedure was used to characterize the fracture toughness of PPO/HIPS blends. The J integral analysis indicated that the PPO specimen exhibited the lowest fracture toughness (J_c). The PPO containing 50 wt% HIPS blend had the highest J_c. SEM observations revealed that the crack growth zone of the pure PPO is relatively smooth. However, cavitation of the elastomeric particles and shear band formation were observed in the deformed zones ahead of the crack tip of the PPO with 50 wt% HIPS blend. The cavitation and shear band formation would dissipate bulk strain energy and their formation was responsible for the highest J_c value observed in this blend.     

Accuracy of cohesive laws with different shape for the shear behaviour prediction of bonded joints

The use of adhesive bonding as a joining technique is increasingly being used in many industries because of its convenience and high efficiency. Cohesive Zone Models (CZM) are a powerful tool for the strength prediction of bonded joints, but they require an accurate estimation of the tensile and shear cohesive laws of the adhesive layer. This work evaluated the shear fracture toughness (J_IIC) and CZM laws of bonded joints for three adhesives with distinct ductility. The End-Notched Flexure (ENF) test geometry was used. The experimental work consisted of the shear fracture characterization of the bond by the J-integral. Additionally, by this technique, the precise shape of the cohesive law was defined. For the J-integral, digital image correlation was used for the evaluation of the adhesive layer shear displacement at the crack tip during the test, coupled to a Matlab sub-routine for extraction of this parameter automatically. Finite Element Method (FEM) simulations were carried out in Abaqus® to assess the accuracy of triangular, trapezoidal and linear-exponential CZM laws in predicting the experimental behaviour of the ENF tests. As output of this work, fracture data is provided in shear for the selected adhesives, allowing the subsequent strength prediction of bonded joints.     

Elastoplastic Fracture Behavior of Structural Adhesives Under Monotonic Loading

Elastic-plastic fracture behavior of a structural adhesive in the bulk and bonded forms is discussed. The model adhesive chosen, Metlbond 1113 (with scrim carrier cloth) and 1113-2 (neat resin) solid film adhesives exhibit a relatively brittle material behavior to justify the use of LEFM methods.

The solid film adhesives are first cast in the form of tensile coupons to determine the bulk fracture properties with the use of single-edge-cracked specimen geometry. K_Ic evaluation is done using the procedure suggested by the ASTM standard. A K-calibration method based on application of boundary collocation procedure to the William's stress function is utilized to relate the measured critical loads to the K_Ic values. The yield stresses and elastic moduli values in the bulk tensile mode are also evaluated. The availability of K_Ic à _y E and v (Poisson's ratio) values makes the calculation of crack tip plastic zone radii (r_yc ) and fracture energy (G_Ic ) values possible on the basis of Irwin's theory. The bulk casting procedure is done under different cure (temperature, time and cool-down) conditions to determine optimum properties.

The fracture behavior of the same adhesives in the bonded form is studied with the use of Independently Loaded Mixed Mode Specimen (ILMMS) geometry. This specimen allows independent measurement of P_I and P_II (and consequently G_I and G_II ) values. Since the fracture energy values are affected by the thickness of the adherend and the bondline, an experimental program is executed first by varying these geometrical parameters to determine the plane strain conditions. The relationship between the bondline thickness and the crack tip plastic zone radius values calculated earlier is also studied. Expressions developed on the basis of LEFM assumptions are utilized to calculate G_Ic and G_IIC values in the bonded form. The G_IC values obtained in this manner are compared to the bulk G_IC values obtained earlier.

With the availability of P_I and P_II (G_I and G_II ) values that result in failure in the bonded form, the fracture condition (i.e. the fracture failure criterion) in mixed mode (modes I and II) loading is determined for adhesively bonded joints. The use of both 1113 and 1113-2 adhesives also reveals the effects of the carrier cloth on the mechanical phenomena cited above.     

Comparison of laboratory techniques for evaluating the fracture toughness of glassy polymers

Several test methods were employed to determine polymer fracture toughness (??_Ic, the opening-mode strain energy release rate) at room temperature. The materials used included DGEBA epoxies and those modified by the addition of CTBN elastomers. Double-cantilever beam specimens were used to determine the fracture toughness both of bulk resins and of an adhesive layer bonded between two aluminum half-beams. The adhesive fracture toughness of a 0.025-cm bond was slightly less than the bulk ??_Ic value, attributed to the bond thickness effect. Fracture toughness of bulk resins was also evaluated by using both rectangular and round compact tension specimens. The results, when compared with those obtained with the bulk double-cantilever beams, are quite acceptable. The thickness of compact tension specimens, ranging from 0.64 to 1.0 cm, might not give pure plane-strain conditions, and thus some plane-stress contribution to ??_Ic should be expected for the tougher materials. Izod impact tests were also carried out to determine sample fracture toughness at high loading rate.     

Fracture toughness of PC/PBT blend based on J-integral methods

The fracture toughness of a polycarbonate/poly(butylene terephthalate) (PC/PBT) blend was determined using three different J-integral methods, ASTM E813-81, E813-87, and hysteresis energy. The critical J values (J_1c) obtained are largely independent of the cross-head speed (range from 0.5 to 50 mm/min). ASTM E813-81 and hysteresis energy methods result in comparable J_1c values, while the E813-87 method estimates J_1c to be 60–80% higher. The critical displacement determined from the plots of hysteresis (energy and ratio) and the true crack growth length vs. displacement is very close. This indicates that the critical displacement determined by the hysteresis energy method is indeed the displacement at the onset of crack initiation and the corresponding J_1c represents a physical event of crack initiation. © 1995 John Wiley & Sons, Inc.     

Effect of Pressure Cycling on Fracture Energy of Polyurethane/Aluminum Adhesive Bonds

An experimental study was conducted to investigate the effect of pressure-cycling on adhesive bond fracture energy of polyurethane/aluminum adhesive bond joints. Initially, two types of peel tests were conducted to characterize adhesive bond strength and challenges associated with pre-mature polyurethane cracking and failure during these tests are discussed. A modified double cantilever beam (MDCB) specimen configuration was specially designed and opening-mode loading conditions were employed to determine the interfacial adhesive bond energy (G_C). The test specimens were pressure-cycled in water-filled tanks for 1 to 4 weeks with an increment of 1 week. The G_C of pressure-cycled specimens was compared with both control and water-soaked samples (without pressure-cycling). The results indicated that pressure-cycling decreased G_C values to those of the control and water-soaked samples: hence, prolonged pressure-cycling could be problematic to polymer/metal adhesive bonds of hardware installed outboard of submarine pressure hulls.     

Fracture toughness of poly(lactic acid)/ ethylene acrylate copolymer/wood‐flour composite ternary blends

A fracture mechanics analysis based on the J‐integral method was adopted to determine the resistance of composites with various concentrations of wood‐flour and ethylene acrylate copolymer (EAC) to crack initiation (J_in) and complete fracture (J_f). The J_in and J_f energies of unmodified poly(lactic acid) (PLA)/wood‐flour composites showed the deleterious effect of incorporating wood fibers into the plastic matrix by significantly decreasing the fracture toughness of PLA as the wood‐flour content increased. The reduced fracture toughness of the matrix induced by adding brittle wood‐flour into PLA was well recovered by impact modification of the composites with EAC. Microscopic morphological studies revealed that the major mechanisms of toughening were through the EAC existing as separate domains in the bulk matrix of the composites which tended to act as stress concentrators that initiated local yielding of the matrix around crack tips and enhanced the toughness of the composites. © 2012 Society of Chemical Industry     

Fracture of adhesive joints and laminated composites

The mechanisms of resin controlled failure in adhesive joints and composites (delamination and transverse cracking) are examined. An in-situ failure model based on the fracture mechanics principles is applied here to describe the failure processes involved. The model centers on the crack tip plastic zone developed in the thin resin layer between the fibers or the adherends. The plastic zone in the resin layer is heavily influenced by a dominant slow varying stress distribution, approximated to be r^?m/2 dependent with m ? 1 (r is the distance from the crack tip). The adhesive or composite fracture toughness G*_IC can then be expressed as a function of several resin properties of comparable importance: modulus E, yield stress σ_y, resin G_IC and residual stress. The relative significance of the resin properties on the adhesive or composite fracture is discussed. The effects of temperature, loading rate, and resin toughening on such failure as a result of the corresponding variations in resin properties are also addressed.     

Fracture toughness of an epoxy system

The fracture toughness of epoxy used in the bulk and adhesive form was measured by a previously developed technique. The uniform double cantilever-beam specimen, which was described earlier, was modified to a tapered beam, which simplified the experimental procedure and calculations for obtaining toughness measurements. by varying the ratio of hardener to resin and post-cure temperature on a single epoxy system (DER 332-TEPA), it was found that the toughness of the epoxy used in either bulk or bond form varied by a factor of approximately five. A particular combination of composition and post-curing temperature generally yielded higher toughness in the bulk than in the bond form. This was not always the case, however. At high post-cure temperatures, where the bonds were very tough, their toughness exceeded that of the bulk material. Hence, it does not appear possible to predict joint toughness from bulk toughness measurements. The toughness of joints was found to be a single-valued function of tensile modulus. For the bulk material, on the other hand, the toughness obtained on the epoxy having a specific modulus depended on the combination of composition and post-cure temperature. Joint toughness for any combination of composition and post-cure temperature depended only on the cracking rate. If the epoxy was the type that caused cracks to jump rapidly, the epoxy was tough and vice versa. For a particular epoxy system, toughness was increased by driving the crack at an increasing rate.     

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.     

Effect of molecular weight between crosslinks on the fracture behavior of rubber‐toughened epoxy adhesives

The effect of molecular weight between crosslinks, M_c, on the fracture behavior of rubber‐toughened epoxy adhesives was investigated and compared with the behavior of the bulk resins. In the liquid rubber‐toughened bulk system, fracture energy increased with increasing M_c. However, in the liquid rubber‐toughened adhesive system, with increasing M_c, the locus of joint fracture had a transition from cohesive failure, break in the bond layer, to interfacial failure, rupture of the bond layer from the surface of the substrate. Specimens fractured by cohesive failure exhibited larger fracture energies than those by interfacial failure. The occurrence of transition from cohesive to interfacial failure seemed to be caused by the increase in the ductility of matrix, the mismatch of elastic constant, and the agglomeration of rubber particles at the metal/epoxy interface. When core‐shell rubber, which did not agglomerate at the interface, was used as a toughening agent, fracture energy increased with M_c. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 38–48, 2001