Temperature and Loading Rate Effects on the Fracture Behaviour of Adhesively Bonded GFRP Nylon-6,6

The combined effect of varying test temperature and loading rate on the Mode II fracture toughness of plasma-treated GFRP Nylon-6,6 composites bonded using a silica-reinforced epoxy adhesive has been studied. End notch flexure tests have shown that the adhesive system used in this study offers a wide range of fracture energies that are extremely sensitive to changes in temperature and loading rate. Increasing the test temperature resulted in a substantial reduction in the Mode II fracture toughness of the adhesive, with the value of G_IIc at 60°C being approximately one-half of the room temperature value. In contrast, increasing the crosshead displacement rate at a given temperature has been shown to increase the value of G_IIc by up to 250%. Compression tests performed on bulk adhesive specimens revealed similar trends in the value of [sgrave]_y with temperature and loading rate. In addition, it was found that the plasma treatment employed in this study resulted in stable crack propagation through the adhesive layer under all testing conditions.

A more detailed understanding of the effect of varying temperature and loading rate on the failure mechanisms occurring at the crack tip was achieved using the double end notch flexure (DENF) geometry, which was considered in tandem with the fracture surface morphologies. Here, changes in the degree of matrix shear yielding and particle-matrix debonding were used to explain the trends in [sgrave]_y and G_IIc.     

Fracture toughness of adhesive joints. I. Relationship between strain energy release rates in three different fracture modes and adhesive strengths

The three strain energy release rates, G_IC, G_IIC, and G_IIIC, of adhesive joints can be attributed to their ability to resist crack propagation of solids in the adhesive layer. The dependencies of G_IC, G_IIC, and G_IIIC on crack lengths for various adhesive joints were determined using the double-cantilever beam specimen by a compliance method. The two types of adhesive strengths, i.e., adhesive tensile strength and adhesive shear strength, corresponding to G_IC and G_IIC, respectively, were carried out at room temperature and 65% RH with a crosshead speed of 10 mm/min. The G_IC, G_IIC, and G_IIIC were dependent upon crack length and had constant values irrespective of geometric parameters of the specimen over the crack length of five times adherend thickness, 0.65 (= crack length over half a length of span) and eight times adherend thickness, respectively. In the region of the crack length, we determined the following increasing order of fracture toughness: G_IC < G_IIIC < G_IIC. A positive correlation was found between adhesive tensile strength and G_IC. A significant relation between adhesive shear strength and G_IIC was not found in this work. Further studies are needed to clarify the relation between adhesive shear strength and G_IIC with general adhesives. © 1994 John Wiley & Sons, Inc.     

Fracture toughness of adhesive joints. III. Temperature and rate dependencies of mode II fracture toughness and adhesive shear strength

Adhesive strength shows temperature and rate dependencies that reflect viscoelastic properties of an adhesive. Similarly, a critical strain energy release rate is expected to show temperature and rate dependencies because deformation and fracture of the adhesive occur at the time of the measurement of the strain energy release rate, which is a kind of fracture mechanical parameter for adhesive joints. In this study, the critical strain energy release rate (G_IIC) of a plane-shear mode was measured over a wide range of temperatures and rates, and then a master curve was obtained by applying the temperature-rate superposition principle to the obtained data. The relation between G_IIC and adhesive shear strength was also investigated. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 835–841, 1997.     

Fracture toughness of adhesive joints. II. Temperature and rate dependencies of mode I fracture toughness and adhesive tensile strength

It has been known that adhesive strength shows temperature and rate dependencies reflecting visoelastic properties of an adhesive. Similarly, a critical strain energy release rate is expected to show temperature and time dependencies deformation and fracture of the adhesive occurs at the time of measurement of the critical strain energy release rate, which is a kind of fracture mechanical parameter for adhesive joints. The term “critical strain energy release rate” has usually been called “fracture toughness.” In this study, the critical strain energy release rate (G_IC) of the opening mode was called mode I fracture toughness. G_IC was measured over a wide range of temperatures and rates, and then a master curve was obtained by applying the temperature–rate superposition principle to the obtained data. Also, on the relation between G_IC and adhesive tensile strength is discussed. © 1995 John Wiley & Sons, Inc.     

Mechanics of crack growth in epoxide resins

Experiments have been conducted employing tapereddouble-cantilever-beam joints with different epoxide adhesives. Depending on the adhesive employed, crack propagation occurred either (a) in a continuous stable manner with crack propagation velocities in the range 10^?4 to 5 m/s and values of the adhesive fracture energy, G_Ic, being almost independent of the crack velocity, or (b) intermittently in an unstable manner when the initial crack velocity was never less than about 20 m/s and, in some instances, rose to about 450 m/s; values of G_Ic (initiation) increased rapidly with increasing velocity. It is proposed that the amount of localized plastic deformation arising from shear yielding that occurs at the crack tip prior to crack propagation is controlling. Secondly, the longterm strength of stressed, structural adhesive joints has been investigated. The fracture of these joints over eight decades of time is uniquely described by a critical plastic zone size developed at the crack tip at failure.     

Numerical assessment of the Double-Cantilever Beam and Tapered Double-Cantilever Beam tests for the GIC determination of adhesive layers

ABSTRACT

Fracture mechanics-based techniques have become very popular in the failure prediction of adhesive joints. The most commonly used is cohesive zone modeling (CZM). For both conventional fracture mechanics and CZM, the most important parameters are the tensile and shear critical strain energy release rates (G_IC and G_IIC, respectively). The most common tests to estimate G_IC are the Double-Cantilever Beam (DCB) and the Tapered Double-Cantilever Beam (TDCB) tests. The main objective of this work is to compare the DCB and TDCB tests to obtain the G_IC of adhesive joints. Three adhesives with varying ductilities were used to verify their influence on the precision of the typical methods of data reduction. For both tests, methods that do not need the measurement of crack length (a) were tested. A CZM analysis was considered to reproduce the experimental load–displacement (P-δ) curves and obtain the tensile CZM laws of each tested adhesive, to test the suitability of the data reduction methods, and to study the effect of the CZM parameters on the outcome of the simulations. The CZM models accurately reproduced the experimental tests and confirmed that the data reduction methods for the TDCB test tend to underestimate G_IC for ductile adhesives.     

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.     

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.     

Influence of rheological properties of adhesive polymer on strain energy release rate of mode II and adhesive shear strength

It is well known that adhesive strength shows temperature and rate dependencies reflecting viscoelastic properties of an adhesive used. Specifically, a mechanical relaxation mechanism around the glass transition temperature (T_g) has a strong effect on the adhesive strength, which involves deformation of the adhesive layer. In addition, it is very interesting to know how viscoelastic properties of the adhesive affect the value of strain energy release rate since deformation and failure of the adhesive occur at the measurement of strain energy release rate for adhesive joints. In this study, adhesive tensile strength and strain energy release rate (G_IIC) in plain-shearing mode were measured under a constant experimental condition using adhesives consisting of two types of epoxy resins; the influence of viscoelastic properties on these two values was investigated, and we discuss the relationship between the adhesive shear strength and G_IIC. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 525–536, 1997     

Numerical simulation of the ENF test for the mode-II fracture characterization of bonded joints

In this work, the End Notched Flexure (ENF) test is analyzed in order to obtain the critical strain energy release rate in mode-II fracture of bonded joints. A cohesive model based on specially developed interface elements, including a linear softening damage process, is employed. The adequacy of the experimental ENF test is evaluated by numerical simulation. The objective is to compare the critical strain energy release rate in mode-II (G _{II c} ) obtained by different data reduction schemes with the real value which is an inputted parameter in the cohesive model. The effect of the Fracture Process Zone (FPZ) ahead of the crack tip is evaluated. A crack equivalent concept is proposed in order to account for the energy dissipated in the FPZ. A data reduction scheme avoiding the need to measure crack length is proposed. A good agreement with the inputted value of G _{II c} was obtained.     

A Rate-Dependent Cohesive Zone Model for Adhesively Bonded Joints Loaded in Mode I

The present work investigates the rate-dependent failure behaviour of structural adhesive joints loaded in mode I. Butt joint and tapered double cantilever beam (TDCB) specimens were tested at velocities ranging over more than six orders of magnitude. A rate-dependent extension of the bi-linear cohesive zone model is proposed and implemented into the finite element code LS-DYNA via an user-defined subroutine. The parameters for the implemented cohesive zone model are found directly by evaluation of experimental data. The comparison of simulations with experimental results for different specimen types and test velocities validates the proposed model. The critical energy release rate of adhesively bonded joints is usually measured in (tapered) double cantilever beam tests, and evaluated using the Irwin–Kies equation. In this paper a different evaluation method is proposed, which provides additional information on the energy dissipated during crack initiation. The results of this method agree with the results obtained using the Irwin–Kies equation. The investigations have focussed on thin adhesive layers. Parameter identification and validation have been performed using the crash-optimized adhesive Terokal 5077 from Henkel.     

Is there any contradiction between the stress and energy failure criteria in micromechanical tests? Part III. Experimental observation of crack propagation in the microbond test

A direct observation of crack propagation in the microbond test was carried out for five different fiber/polymer matrix systems. This technique appeared to be a very effective tool for interface characterization. Experimental plots of the force required for further crack propagation as a function of debond length were analyzed using both energy-based and stress-based models of debonding. The fracture mechanics analysis was used to construct families of crack resistance or R-curves which showed the variation of energy release rate, G, with the debond length, and included the effect of interfacial friction in debonded regions. For the first time, analogs of the R-curves were created within the scope of the stress-based model to present the local shear stress near the crack tip, τ, as a function of crack length. In both models, the behavior of the interfacial parameter (G or τ) strongly depends on the assumed value of the interfacial frictional stress (τ_f). However, for each matrix/fiber system there exists such a τ_f value for which the investigated parameter is nearly constant over the whole region of stable crack propagation (70–90% of the embedded length). Moreover, these best-fit τ_f values for each specimen appeared to be practically the same for both energy-based and stress-based approaches. Thus, both interfacial toughness, G _ic, and local interfacial shear strength, τ_d, adequately characterize the strength of a fiber/matrix interface. Extrapolation of R-curves and their analogs to zero crack length allows measurement of the interfacial parameters with good accuracy.     

Study of effect of specimen thickness,gelatin concentration,normal force and sliding velocity on the stick-slip vibrations of gelatin hydrogel

Abstract

Soft solids undergo stick-slip instability which is characterized by the velocity weakening effect where interfacial shear stress decreases with sliding velocity. Soft solids show the hysteresis of energy release rate (G) during the stick and slip phase of a stick-slip cycle. In the present study, the effect of specimen thickness on G is studied by conducting the direct shear sliding experiments on gelatin hydrogel and glass substrate. Interfacial shear stress and corresponding crack lengths obtained during the slide-hold-slide (SHS) experiments are used to determine G analytically. Significance of specimen thickness, normal stress, gelatin concentration and sliding velocity on the hysteresis of G during a stick-slip cycle is discussed in detail. Increase in the specimen thickness, normal stress and gelatin concentration lead to an increase in the hysteresis of G as well as tendency of stick-slip instability. However, increase in the sliding velocity leads to decrease in hysteresis.     

Evolution of crack path and fracture surface with degradation in rubber-toughened epoxy adhesive joints: Application to open-faced specimens

The crack path and fracture surface in the mixed-mode fracture of two different rubber-toughened epoxy adhesives were evaluated using double-layered open-faced double cantilever beam (ODCB) specimens in which the primary adhesive layer had been environmentally aged. The crack path in the mixed-mode fracture of unaged ODCB specimens was unexpectedly in the secondary adhesive layer, and several hypotheses were examined to explain this. It was concluded that a reduced residual stress in the secondary adhesive layer produced stable crack growth in the secondary layer instead of the expected path in the primary layer. The average crack path depth, fracture surface roughness and maximum elevation in the fracture surface profiles were then measured using optical profilometry as a function of the degree of aging. The results showed a strong relationship between all these parameters and the critical strain energy release rate, G_cs, irrespective of the type of adhesive. In the case of adhesive A where significant irreversible degradation was observed, all these parameters varied approximately linearly with G_cs. In the case of adhesive B, aging did not result in permanent degradation (G_cs was unchanged) and so all these fracture surface parameters also remained unchanged after aging. The results indicate that quantifying fracture surface parameters as a post-failure analysis can be of use in the estimation of the fracture toughness at which a practical joint fails.     

The effect of temperature and loading rate on the mode II interlaminar fracture properties of a carbon fiber reinforced phenolic

The combined effect of varying loading rate and test temperature on the mode II Interlaminar fracture properties of a carbon fiber reinforced phenolic resin has been investigated. End notch flexure tests at room temperature have shown that this composite offers a relatively modest value of G_IIc^NL at non‐linearity and that its interlaminar fracture toughness decreases with increasing loading rate. As the test temperature is increased, the quasistatic value of G_IIc^NL increases steadily and the reduction in G_IIc^NL with loading rate becomes less dramatic. At temperatures approaching the glass transition temperature of the phenolic matrix, the interlaminar fracture toughness of the composite begins to increase sharply with crosshead displacement rate. A more detailed understanding of the effect of varying the test conditions on the failure mechanisms occurring at the crack tip of these interlaminar fracture specimens has been achieved using the double end notch flexure (DENF) geometry.     

Shear testing of thick adhesive layers using the ENF-specimen

An existing experimental method to determine cohesive laws for adhesive layers loaded in shear is further developed. The method is based on differentiation of the energy release rate (ERR) with respect to the adhesive shear deformation at the crack tip. The test geometry used is an ENF-specimen for which the adherends are assumed to deform linearly elastic. The original method is expanded to account for situations where the thickness of the adhesive layer is not negligible as compared to the adherend thickness. To this end, a novel mathematical expression for the energy release rate (ERR) is derived. No assumptions on the form of the cohesive law are made; it is implicitly included in the derivation. The expression for the ERR contains the applied load and the shear deformation of the adhesive layer at the initial position of the crack tip, in addition to geometrical properties and the elastic modulus of the adherend material. Numerical simulations are performed to verify the accuracy of the mathematical expression for the ERR. Preliminary results from experiments performed on an epoxy adhesive are presented. The cohesive law of the adhesive layer is extracted by using a blunted crack tip. Verifying simulations confirm that the local pre-fracture behavior is accurately captured.     

Investigation of load transfer between the fiber and the matrix in pull-out tests with fibers having different diameters

Single-fiber pull-out tests were used for investigation of the interfacial bond strength or toughness and load transfer between polymeric matrices and glass fibers having different diameters. The interfacial bond strength was well characterized by an ultimate interfacial shear strength (τ_ult) whose values were nearly independent of the fiber diameter. The same experiments were also analyzed by fracture mechanics methods to determine the interfacial toughness (G_ic). The critical energy release rate (G_ic) was a good material property for constant fiber diameter, but G_ic for initiation of debonding typically became smaller as the fiber diameter became larger. It was also possible to measure an effective shear-lag parameter, β, characterizing the load transfer efficiency between the fiber and the matrix. β decreased considerably with the fiber radius; this decrease scaled roughly as expected from elasticity theory. The measured results for β were used to calculate the radius of matrix material surrounding the fiber that was significantly affected by the presence of the fiber. The ratio of this radius to the fiber radius (R_m/r _f) was a function of the fiber diameter.     

Comparison of Analytical,Numerical, and Experimental Methods in Deriving Fracture Toughness Properties of Adhesives Using Bonded Double Lap Joint Specimens

Stress and fracture analysis of bonded double lap joint (DLJ) specimens have been investigated in this paper. Numerical and analytical methods have been used to obtain shear- and peel-stress distributions in the DLJ. The generalized analytical solution for the peel stress was calculated for various forms of the DLJ geometry and, by using crack closure integral (CCI) and by means of the J-integral approach, the analytical strain energy-release rate, G, was calculated. Experimental fracture tests have also been conducted to validate the results. The specimens were made of steel substrates bonded by an adhesive and loaded under tension. Specimens with cracks on both sides and at either end of the DLJ interface were tested to compare the fracture behavior for the two crack positions where tensile and compressive peel stresses exist. Tests confirmed that the substrates essentially behave elastically. Therefore, a linear elastic solution for the bonded region of the DLJ was developed. The fracture energy parameter, G, calculated from the elastic experimental compliance for different crack lengths, was compared with numerical and analytical calculations using the experimental fracture loads. The stresses from analytical analysis were also compared with those from the finite element results. The strain energy-release rate for fracture, G _f , for the adhesive has been shown to have no R-curve resistance, was relatively independent of crack length, and compared well with those obtained from numerical and analytical solutions. However, it was found that fracture energy for the crack starter in the position where the peel stress was tensile was about 20% lower than where the crack was positioned at the side, where the peel stress was found to be compressive.     

Fatigue Crack Growth Rates in Adhesive Joints Tested at Different Frequencies

Mode I fatigue crack growth tests were conducted on joints bonded with a filled adhesive (A) at 20 Hz and 2 Hz and on joints bonded with a filled and toughened adhesive (B) at 20 Hz, 2 Hz, 0.2 Hz and 0.02 Hz. Strain energy release rate, G, and J-integral were evaluated based on elastic and elastoplastic finite element analyses (FEA) of the joints bonded with adhesive A and B, respectively. For the configurations considered, J was found to be path-independent and did not differ much from G. The fatigue crack growth rate (FCGR), da/dN, in the joints bonded with adhesive A was relatively independent of frequency while it increased with decreasing frequency at given δ for the joints bonded with adhesive B. The fatigue processes in both adhesives involved the cracking of the filler particles and subsequent linkage of the resultant microcracks. The process zone in adhesive B is larger than that in adhesive A and it increases with decreasing frequency. It is suggested that this variation in process zone size can account for the observed fatigue behaviour. The fatigue crack growth velocity, da/dt, was also calculated for the joints bonded with adhesive B and the variation of da/dt with test frequency at given δG is much smaller than the variation in da/dN, suggesting a creep effect in the fatigue crack growth.