Fracture Of Adhesive Joints Research Articles

Combined computational-experimental investigation of residual stresses and pre-cracking in mode I behaviour of thick adhesively bonded GFRP composite joints

This paper presents a novel Finite Element (FE) simulation approach to examine the mode I fracture of thick adhesive joints used particularly in the trailing edge of the wind turbine blades. The approach involved FE models of the DCB specimens focusing on aspects overlooked in the existing literature. There has been limited investigation on residual stresses caused by thermal mismatch between composites and adhesives. Similarly, the impact of generating notches/pre-cracks in the adhesive layer during the preparation of Double Cantilever Beam (DCB) specimens on residual stresses has received minimal attention. Additionally, the Cohesive Zone Model, commonly used for simulating elastoplastic adhesives, may be inadequate due to its inability to account for the plastic deformation of the adhesive. In the present work, the pre-cracks were virtually generated in DCB FE models so that their effect on the stresses within the joint could be examined, making it a novel contribution to the field. The components were assigned with appropriate thermal expansion coefficients, and a simulation of the cool-down process was conducted to determine the thermal residual stresses. Furthermore, the Drucker-Prager plasticity criteria were used to capture the elastoplastic behaviour of adhesives in the FE simulations. Concurrently, the T-stresses were assessed through numerical investigations. For validation, experiments were conducted on DCB specimens made of two cross-ply composite laminates bonded with a ∼ 10 mm thick layer of an epoxy-based adhesive. A good agreement between computational and experimental results was observed, confirming the effectiveness and reliability of the proposed approach.

An experimental and analytical study of mode I fracture and crack kinking in thick adhesive joints

This study investigates the fracture behavior of thick adhesive joints manufactured with composite adherends and bonded with an epoxy-based structural adhesive common to the wind turbine industry. For that purpose, double cantilever beam specimens with an adhesive thickness of approximately 10 mm and different pre-crack lengths are manufactured and tested under mode I loading. Analytical approaches are compared to assess the energy release rate, including the simple beam theory, modified beam theory, compliance calibration method, and beam on an elastic and elastic-plastic foundation. In order to evaluate the applicability of the analytical approaches, an in-situ measurement method based on Digital Image Correlation is also employed to determine the energy release rate of the thick adhesive joints. The crack propagation angle is determined theoretically using the second-order crack kinking theory. A good correlation is observed between the theoretical predictions and experimental results. Furthermore, it is demonstrated that due to the T-stress, the crack tends to deviate from the middle of the joint and propagate towards the interface. By comparing different data reduction methods to evaluate the energy release rate of thick adhesive joints, recommendations for their fracture analysis are made, pinpointing the beam on an elastic and elastic-plastic foundation as the most suitable model.

A finite-deformation isotropic non-associative viscoplasticity/damage coupled thermodynamic model for ductile fracture of thick adhesive composite joint

This paper develops a finite-deformation isotropic non-associative viscoplasticity/damage coupled model to predict ductilefracture behaviors of thick adhesive composite joint within the framework of irreversible thermodynamics. First, a damage variable is introduced into the elastic constitutive model, along with the Drucker-Prager’s type yielding function and plastic potential function which take into account the variable hydrostatic pressure and non-associative plasticity. An exponential damage potential function is developed to derive the damage evolution law relating to the thermodynamic force. Second, both kinematic hardening and isotropic hardening are considered that are represented by the back stress, hardening stress and their conjugate relationships with the corresponding internal variables, derived by the Helmholtz free energy. Third, an extended version of the Perzyna’s type model is developed by incorporating an over-stress function to derive the consistency plasticity factor for the viscoplasticity/damage coupled model. Fourth, the strain, stress, back stress, thermodynamic force, damage variable and tangent modulus are updated within the corotated configuration in the integration procedure. To simplify numerical computation, the stress and strain at time n + 1 are initially updated using the frozen damage variable and the back stress at time n, and the latter two values are independently updated at time n + 1. Finally, the developed model and numerical algorithm by implicit FEA are employed to predict the strain, stress, back stress, damage and fracture behaviors of the dog-bone MMA specimens under tensile loads and the thick MMA ductile adhesive specimens under shear loads.

A new crack-tip element for the logarithmic stress-singularity of Mode-III cracks in spring interfaces

A new crack-tip finite element able to improve the accuracy of Finite Element Method (FEM) solutions for cracks growing along the Winkler-type spring interfaces between linear elastic adherents is proposed. The spring model for interface fracture, sometimes called Linear-Elastic (perfectly) Brittle Interface Model (LEBIM), can be used, e.g., to analyse fracture of adhesive joints with a thin adhesive layer. Recently an analytical expression for the asymptotic elastic solution with logarithmic stress-singularity at the interface crack tip considering spring-like interface behaviour under fracture Mode III was deduced by some of the authors. Based on this asymptotic solution, a special 5-node triangular crack-tip finite element is developed. The generated special singular shape functions reproduce the radial behaviour of the first main term and shadow terms of the asymptotic solution. This special element implemented in a FEM code written in Matlab has successfully passed various patch tests with spring boundary conditions. The new element allows to model cracks in spring interfaces without the need of using excessively refined FEM meshes, which is one of the current disadvantages in the use of LEBIM when stiff spring interfaces are considered. Numerical tests carried out by h-refinement of uniform meshes show that the new singular element consistently provides significantly more accurate results than the standard finite elements, especially for stiff interfaces, which could be relevant for practical applications minimizing computational costs. The new element can also be used to solve other problems with logarithmic stress-singularities.

The effect of abrading treatment method on the bonding surface characteristics and fracture behavior of glass fiber-epoxy composite adhesive joints

The effect of the mechanical abrading method on the bonding surface characteristics and fracture response of glass fiber-reinforced polymer (GFRP) composite adhesively bonded joints was investigated. Double cantilever beam specimens were manufactured by bonding GFRP substrates with an epoxy adhesive to evaluate the mode-I adhesive joint fracture response. The bonding surfaces were treated with degreasing and abrading methods utilizing sandpapers with various grit sizes ranging from P60 to P800. The results showed that the sandpaper grit size can considerably change the bonding surface properties comprising the surface energy, roughness, morphology, and water drop contact angle and consequently, it can affect the joint fracture behavior. Reducing the sandpaper grit size continuously increased the surface roughness but there were optimum values for the surface energy and water drop contact angle. The fracture resistance of adhesive joints followed the trend of bonding surface energy as the higher the bonding surface energy, the higher the joint fracture resistance. The fracture energy and load-bearing capacity of adhesive joints were improved by 62 and 34%, respectively, when the joint bonding surfaces were abraded with P240. However, further reducing the sandpaper grit size to P60 caused a decrease in the fracture energy and load-bearing capacity of adhesive joints by 18 and 44%, respectively, compared to the joint with degreased and non-abraded bonding surfaces. Moreover, the abrading method considerably changed the microscopic and macroscopic failure modes of adhesive joints.

Analysis of the adhesively bonded composite double cantilever beam specimen with emphasis on bondline constraint, adherend through-thickness flexibility and fracture process zone relative size

ABSTRACT The double cantilever beam (DCB) specimen is widely used to characterise the mode I fracture of adhesive joints. This paper analyses some particular characteristics of adhesively bonded composite DCB specimens which could affect test results. Three-dimensional (3D) and two-dimensional (2D) finite element analyses (FEA) were conducted in order to evaluate the effects bondline constraint and adherend through-thickness flexibility on the specimen response. Since beam theory-based data reduction schemes are widespread, beam models were also employed to analyze the effects of adherend through-thickness flexibility and fracture process zone relative size. It is shown that, although composite adherends are usually thinner and have much lower transverse moduli than metal adherends, the level of bondline constraint is similarly high. This may: limit the level of adhesive plastic deformations in the fracture process zone; generate high bondline tractions that increase the likelihood of interface failure and interlaminar damage in the composite adherends. The present analyses also show relevant effects of adherend through-thickness flexibility in the adhesive elastic loading stage. Finally, smaller fracture process zones relative to metal adherend DCB specimens were predicted by a beam cohesive zone model. This may explain lower fracture energy values reported with composite adherends in some studies.

Obtaining strain-rate dependent traction-separation law parameters of epoxy adhesive joints and predicting fracture for dissimilar bonding adherends

This study investigated the mode I fracture behavior of double cantilever beam (DCB) epoxy adhesive joints with similar adherends on the both sides (i.e., aluminum-aluminum or copper-copper) at different strain rates; i.e., quasi-static (∼10 −3 s −1 ), low (∼7 s −1 ) and intermediate (∼14 s −1 ) rates. The fracture energy of the DCB joint in Al-adhesive-Al specimens decreased (i.e., by ∼62%, p = 0.0013) with an increase in the applied strain rate from quasi-static to low values, while it remained almost unchanged with further increase of stain rate to intermediate range (p > 0.05). For Cu-adhesive-Cu cases, however, the fracture energy was found to be almost insensitive to the applied strain rate over the range tested (p > 0.05). A cohesive zone model (CZM) was built and strain-rate dependent parameters of traction-separation (TS) law were obtained. These parameters were then used to predict the fracture of epoxy adhesive joints bonded with dissimilar substrates (i.e., copper-aluminum). Predicted fracture loads of the Cu-adhesive-Al cases obtained from the stain-rate dependent model were in reasonable agreement with measured forces (i.e., from ∼0 to 24%) at a given strain rate. Therefore, once TS law parameters for Al-adhesive and Cu-adhesive interfaces were determined, the CZM could predict the fracture of the joint bonded with Al and Cu on its sides. • Fracture tests were performed on 5 cm long, 250 μm thick epoxy adhesive joints at different strain rates. • Fracture energy of the Al–Al joints decreased significantly by increasing strain rate from quasi-static to low values. • By increase in the strain rate, J ci of Cu–Cu joints did not change significantly. • TS law parameters of Al–Al and Cu–Cu joints were determined by a CZM. • Fracture of Cu–Al joints were predicted using TS law parameters in a CZM at various strain rates.

Fracture and dynamic mechanical analysis of seawater aged aluminum-BFRP hybrid adhesive joints

Adhesively bonded hybrid FRP-aluminium structures have recently become an efficient solution for marine engineering applications. However, polymer adhesives' bond performance is sensitive to the marine environment due to polymer and interfacial degradation. This study aims to develop mode I, mode II delamination toughness, and Tg data as a comprehensive design guideline for hybrid BFRP-aluminum modified-adhesively bonded joints subjected to seawater aging. The hybrid joints were exposed to long-term seawater aging (for 6 months) to reveal their fracture and thermomechanical performances. Besides, the adhesive was reinforced with HNTs to increase fracture resistance with additional nano-scale toughening mechanisms and to delay the water absorption. After the long-term aging, reinforced adhesively bonded joints exhibited ∼36% higher fracture toughness than neat adhesively bonded joints. Moreover, DMA was conducted on miniaturized SLJ samples, which revealed that HNT modified adhesive joints showed ∼11.5 °C higher Tg. The calculated aging rates also proved the effectiveness of HNTs modification on the epoxy adhesive’s aging performance since the HNT reinforced adhesive represented 43% lower aging rates in terms of storage modulus. It is considered that experimental results will help comprehend long-term aging influences on the composite-aluminum hybrid designs’ fracture and thermomechanical performances. These exciting findings will pave the way for the safe use of high stiffness and cost-effective aluminum-BFRP hybrid structures for the marine industry.

A beam model for the fracture of adhesive joints with dissimilar metal adherends

The natural ability to join different materials is one of the main advantages of adhesive joints. It is thus important to characterize the fracture resistance of adhesive joints with dissimilar materials, as they are increasingly used in relevant industrial applications. There are, however, well-known problems in data analysis of such tests, especially where mode partitioning is concerned. A beam model is here developed for mixed-mode I-II fracture testing on adhesive joints with dissimilar metal adherends. The model predicts quite accurately the strain-energy release rate, the mode-mix and the load-point displacements with fully closed-form equations. Therefore, it can be the basis of future data reduction schemes for fracture tests. Furthermore, it is shown that a wide range of mode-mix combinations can be achieved with simple well-known tests on dissimilar metal adherend joints. They could thus be an interesting alternative to developed mixed-mode I-II tests that require complex test fixtures.

Mode I creep fracture of rubber-like adhesive joints at constant crack driving force

This work contributes to the description of time-dependent mechanical mode I creep fracture of viscoelastic adhesive joints under pure peel loading at finite deformations. The focus is on the dependency of crack resistance and resulting crack propagation rate on the forming of minor cracks beside the macroscopic major crack tip. In this work, Double Cantilever Beam tests were carried out at polyurethane-based flexible adhesive joints. The experiments were externally controlled on a constant J-integral, which was calculated in-situ from measured data to obtain a constant crack driving force and a statically loaded crack tip, respectively. The resulting creep crack propagation was investigated using two cameras targeting both sides of the specimen. With help of image processing and the beam compliance method, crack extension and crack propagation rate were determined. The respective results were used to draw comparisons between these two methods. The slight difference between the methods was attributed to the appearance of minor cracks, which seemed to reduce the stress intensity at the macroscopic crack tip, yielding a lower crack propagation rate.

Examination of plastic region size and two singular stress field on the ISSF adhesive strength evaluation method

In an adhesive joint under certain conditions, the adhesive joint strength is larger than the bulk adhesive strength. In this study, the fracture of adhesive joints by using the elastic-plastic behavior is considered. Then, the validity of evaluating the adhesive strength by two ISSFs based on the elastic analysis is discussed. Even when the butt joint strength is larger than the bulk adhesive strength, the small-scale yielding is occurred. Therefore, it is shown that the ISSF strength evaluation method is appropriate.

On characterization of cohesive zone model (CZM) based upon digital image correlation (DIC) method

Cohesive zone model (CZM) has been extensively applied in numerical simulation of interfacial fracture behaviors such as composite delamination and fracture of adhesive joints. Accurate and efficient identification of CZM parameters signifies an important research topic to enable reliable analysis and design of these structures. This paper aims to derive the actual traction-separation law of CZM by means of experimental measurement with only digital image correlation (DIC) technique. A double cantilever beam (DCB) specimen was employed for experimental tests and a semi-empirical analytical model was developed to associate the traction-separation law with the global loading response. Explicit formulae of the initial stiffness, maximum traction stress and damage evolution were derived. In this study, the DCB specimens bonded with a ductile adhesive layer of Araldite® 2015 were fabricated and experimentally tested. The displacement distribution of the adhesive layer was quantified as the fundamental data for identification of CZM parameters. The initial stiffness, maximum traction stress and damage evolution of CZM were identified accurately. Based upon the extracted CZM parameters in the present work, a finite element (FE) model was developed and verified with the experimental results. Furthermore, a FE model with a traditional linear damage evolution was also established for comparison, thereby demonstrating the effectiveness of the proposed method for extracting the traction-separation law of CZM. By employing the present approach, the real traction-separation law can be better presented and accurate simulation of adhesive joint can be achieved.

Structural health monitoring of adhesive joints under pure mode I loading using the electrical impedance measurement

The addition of Multi-wall carbon nanotubes (MWCNTs) or functionalized-graphene nanoplatelets (f-GNPs) into the epoxy resin create an electrical conductive networks which can be employed for structural health monitoring (SHM) in sensitive adhesive joints. The opening fracture mode (Mode I) loading condition, as one of the important fracture modes in adhesive joints was precisely evaluated in this study. The study aims to investigate the crack extension in the adhesive joint (Fracture mechanics) under mode I loading by both smart adhesives and proper measurement technique. In order to provide high sensing capability in the adhesive joint, several aluminum to aluminum adhesive joints were prepared by dispersion of 2.5 wt% MWCNTs or 12 wt% f-GNPs into the epoxy adhesive, respectively. Considering the electrical impedance changes simultaneously with the mechanical response of the adhesive joints, novel outcomes were obtained. Almost linear trend has been observed in the impedance curve for the strain value of 0.57. During crack growth, the conductive network in epoxy matrix near the crack tip would be break and thus the electrical impedance would be increased. In addition, the electrical impedance curve has exhibited several sharp increases, which are attributed to the rapid crack growth.

Thermo-fracture analysis of composite-aluminum bonded joints at low temperatures: Experimental and numerical analyses

Adhesive joints have found extensive applications in aerospace structures because of important advantages such as uniform stress distribution, thermal, acoustic and electrical insulation as well as capability of joining dissimilar materials. These joints in aerospace structures frequently experience severe low temperatures. Lack of experimental data in this field motivated the study of the fracture of adhesive joint at low temperatures in this paper. Fracture parameters of carbon-fibre-reinforced polymer-based composites (CFRP) and aluminum bonded joints were investigated in a temperature range of −80 to +22 °C. In order to understand the mechanical behavior of different components of the bonded joint, firstly, the components (adhesive, composite, and aluminum) were characterized by conducting tensile tests. Subsequently, specimens of cracked bonded joint were tested at low temperatures in different loading modes (mode I, mode II, and mixed mode I/II). The finite element model of the bonded joint was developed in order to obtain the dimensionless functions of stress intensity factors at lower temperatures. The results showed that a reduction in temperature down to a particular value contributes to improved critical stress intensity factors, while any further reduction in the temperature tends to lower the critical stress intensity factors, eventually leading to decreased fracture energy absorption capacity of the structure. In the final section of this paper, a study on fracture surfaces and fracture mechanisms was performed via macroscopic and scanning electron microscopic (SEM) analyses.

The deformation process of amorphous polymers and adhesive lap-shear joints formed thereof as studied by the emission of charged particles in high-vacuum technique

The emission of charged particles in high vacuum (at a pressure of 10−5 Pa) has been investigated during the deformation process of the monolithic bulk samples of amorphous polystyrene (PS) and poly(2,6-dimethyl-p-phenylene ether) (PPE), and of homo- and hetero-adhesive single lap-shear joints PPE–PPE and PS–PPE, respectively. The adhesive joints were formed by holding in contact the two bulk samples of PPE or the samples of PS and PPE at a small contact pressure of 0.03 MPa at the self-healing temperatures well below (by 100 K or even lower) of the PPE bulk glass transition temperature. It has been shown that the mechanoemission of charged particles has occurred at the moment of fracture (time interval < 1 ms) both of the PS and PPE bulk samples and of the PPE–PPE and PS–PPE adhesive joints and continued after the adhesive joint fracture. It has been found that, upon the adhesive joints fracture, the emission of negative ions has not been observed while electrons have been emitted. The fracture mechanisms of the bulk samples and of adhesive joints have been discussed. An equation relating the concentration of the broken chemical bonds to the intensity of the charged particles has been proposed.

Design of laser-textured surfaces to enhance the strength of adhesively bonded joints

This paper tries to relate the laser treatment process parameters to the morphological properties of laser-treated aluminum alloy surfaces and the adhesive joint fracture load in butt joint configuration to describe their pivotal role as surface roughness design parameters. In these contexts, the role of the individual process parameter and energy density on the surface and joint characteristics were experimentally investigated. Surface roughness was modeled and validated to demonstrate that it is designable and controllable. Moreover, to globally understand the effect of the laser parameters on joint fracture load, experimental results were analyzed following a DoE framework. This study shows that laser-treatment parameters contribute significantly to surface roughness control. Model-based surface morphology and the consequent average surface roughness can be accurately predicted, i.e., groove characteristics of the surface can be accurately controlled by regulating the laser-treatment parameters. Optimal laser parameters allow designing a surface that maximizes the adhesive joint fracture load.

Analysis of the fracture process zone and effective crack length in the adhesively bonded end-notched flexure specimen

ABSTRACTThe mode II fracture of adhesive joints is well-known to involve large fracture process zones. Their effect in fracture energy measurements can be taken into account by the effective crack length approach. Moreover, fracture process zones can be simulated by cohesive zone models, which are increasingly used for structural analysis of adhesive joints. This paper aimed at evaluating the influence of the traction-separation law on the fracture process zone and on the effective crack length in end-notched flexure tests. Novel analytical cohesive zone models were developed for the bilinear and trapezoidal traction-separation laws. The latter were shown to affect significantly the energy dissipation rate versus effective crack length curve prior to crack initiation. Therefore, this effect seems to provide a simple approach for evaluating approximate traction-separation laws. The models here developed are easy to apply and provide simple approximate expressions useful for specimen selection.

Modelling load transfer and mixed-mode fracture of ductile adhesive composite joints

A new general computational framework for the stress and effective strength analysis of ductile adhesive composite joints is proposed. Composite adherends are modelled using First Order Shear Deformation Theory accounting for bending-extension coupling and an asymptotic approach for the bondline within deformation theory of plasticity is employed. The governing one-dimensional boundary value problem is solved using an efficient finite-difference scheme in Matlab. Based on the proposed stress solution, different failure criteria motivated either by strength criteria or fracture mechanics are implemented and benchmarked against experimental data for an effective joint strength assessment.A comparison to numerical finite element analyses demonstrates the model's ability to render the adhesive stress field accurately. The impact of different stress-strain curve approximations and effective stress quantities within deformation theory of plasticity are studied and discussed. Finally, effective joint strength predictions are compared to experimental data from literature. The paper concludes with a discussion on distinct failure criteria for elastic-plastic adhesive joints and recommendations for reliable accurate joint strength predictions.

Elastic-plastic analysis of the adhesively bonded end-notched flexure specimen

The end-notched flexure (ENF) specimen has often been employed to characterise the mode II fracture of adhesive joints. This paper reports a beam model for ENF specimens with metal adherends and typical bondline thickness values. The initial formulation adopting adhesive linear elasticity predicted accurately the shear stress distribution, the compliance and the strain-energy release rate. The adhesive elastic-perfectly plastic behaviour subsequently introduced generated a plastic zone whose size could be predicted by a closed-form expression. The model provides a basis for selecting specimen geometries that enable accurate fracture energy measurements from a corrected beam theory with effective crack length scheme.

Crack front morphology near the free edges in double and single cantilever beam fracture experiments

We analyse edge effects in two common adhesive joint fracture configurations, namely the single and the double cantilever beam tests. Several experiments were performed studying the crack front vicinity for deflection and crack front morphology using light scanning and microscopy techniques. To understand the findings a finite element model is used to determine the energy release rate at the crack front, particularly in the vicinity of free edges. Two approaches - an inverse procedure and a direct method - are compared. Using the inverse procedure, the local values of energy release rate along the experimentally obtained crack front are investigated. With this approach, the fracture criterion is however not necessarily fulfilled at each node along the crack front. In the direct method, a mixed-mode fracture criterion is used to determine the shape of the crack front at steady-state propagation. Qualitatively, the direct method stays in good agreement with experimental findings, showing that the free edges are likely to affect crack front morphology. A full match between the experimental results and numerical simulations can be achieved by using the Poisson's ratio as a fitting parameter.