End-notched Flexure Specimens Research Articles

Simulation of mode II fracture propagation in adhesive joints using a meshless technique

Adhesive bonding is extensively used by commanding industries such as automotive and aircraft sectors. Nevertheless, due to the intricate mechanical behaviour of adhesively bonded joints, especially when crack propagation occurs at the adhesive layer, improvement of new numerical techniques to simulate this bonding approach is currently under development. In this work, a recent crack propagation algorithm based on a meshless technique is implemented to analyse mode II fracture propagation in adhesively bonded joints. After the problem domain is discretized with an independent set of field nodes, a background numerical integration mesh is constructed. The crack tip advancement is then simulated by iteratively rearranging the field nodes and integration cells at the crack tip. Radial point interpolation (RPI) functions are constructed using the concept of influence domains, allowing to obtain sparse and stable global matrices. To assess the suitability of the proposed method, End-notched flexure (ENF) specimens were manufactured and tested. The numerical simulation justly reproduces the experimental data provided and, thus, the numerical model can be applied to mode-II shear loadings and industrial applications for design purposes.

A mixed-mode fatigue crack growth model for co-consolidated thermoplastic joints

In this work, a mixed-mode fatigue crack growth model for simulating interfacial fracture of co-consolidated thermoplastic joints was developed. The model is based on the cohesive zone modeling approach and was specifically designed to account for any I + II mode-mixity, requiring only pure mode I and II loading data as input. The fatigue crack growth rate is constantly updated using a function of the energy release rates and the computed mode-mixity ratio. A linear mode-mixity law is applied. Both force-controlled and displacement-controlled loads can be modeled in specimens ranging from coupon-scale sizes to larger structural elements. Implementation of the model was done for the low-melt polyaryletherketone (LM-PAEK) material by developing a user-defined subroutine in the LS-Dyna FE software. To feed the model, mode I and mode II fatigue tests were conducted using double-cantilever beam and end-notch flexure specimens, respectively, while to validate the model mixed-mode single lap shear (SLS) tests were conducted. The model reproduces accurately the mode I and II fatigue crack growth while it predicts also accurately the mixed-mode fatigue crack growth of the SLS specimens.

Characterization and prediction of hygrothermally aged CFRP adhesive joint subjected to mode II load

Carbon fiber composite adhesives joints provide higher specific strength and fatigue life than traditional joints. However, carbon fiber composites and adhesives are polymeric materials that may lose their integrity in hygrothermal environment. Predicting the environmental degradation behavior of composite joints is challenging because of limited understanding of the complex failure behavior. Moreover, the experiments are time-consuming and therefore it is essential to use accelerated aging methods such as the open faced method. However, the challenge is how to incorporate the accelerated fracture test data into the fracture prediction of real joints. To address this, a methodology is presented for predicting mode II cohesive law parameters of degraded CFRP epoxy adhesive joints using a direct method, and an accelerated aging test. End notched flexure (ENF) specimens made with CFRP laminate and epoxy adhesive were used to study the mode II fracture. Accelerated and uniform aging was achieved using open-faced specimens aged at 40 °C and 82% relative humidity (RH). Fracture testing of aged open-faced specimens along with crack-tip images were used to determine the degradation in trapezoidal traction-separation law (TSL) with aging. These variations in trapezoidal TSL with aging were used to develop a 3D finite element (FE) model of a closed ENF specimen that captures the non-uniform degradation across the specimen width. The TSL parameters degraded significantly at the specimen edges compared to width center for the closed ENF specimens. Validation of the FE model with aged closed ENF joint showed good agreement.

Effect of Through-the-Thickness Delamination Position on the R-Curve Behavior of Plain-Woven ENF Specimens.

In this study, the effect of through-the-thickness delamination plane position on the R-curve behavior of end-notch-flexure (ENF) specimens was investigated using experimental and numerical procedures. From the experimental point of view, plain-woven E-glass/epoxy ENF specimens with two different delamination planes, i.e., [012//012] and [017//07], were manufactured by hand lay-up method. Afterward, fracture tests were conducted on the specimens by aiding ASTM standards. The main three parameters of R-curves, including the initiation and propagation of mode II interlaminar fracture toughness and the fracture process zone length, were analyzed. The experimental results revealed that changing the delamination position in ENF specimen has a negligible effect on the initiation and steady steady-state toughness values of delamination. In the numerical part, the virtual crack closure technique (VCCT) was used in order to analyze the imitation delamination toughness as well as the contribution of another mode on the obtained delamination toughness. The numerical results indicated that by choosing an appropriate value of cohesive parameters, the trilinear cohesive zone model (CZM) is capable of predicting the initiation as well as propagation of the ENF specimens. Finally, the damage mechanisms at the delaminated interface were investigated with microscopic images taken using a scanning electron microscope.

Mode-II fracture toughness and crack propagation of pultruded carbon Fiber-Epoxy composites

This study develops a quasi-static mode II fracture toughness test methodology for pultruded carbon fiber-reinforced polymer (CFRP) composites along the fiber direction. The mode II fracture tests using a non-standard End-Notched Flexure (ENF) specimen as the pre-crack cannot be generated during the pultrusion process. A Compliance-Based Beam Method (CBBM) is used for data reduction, which does not require crack growth length monitoring during propagation and accounts for the effects of the Fracture Process Zone (FPZ) based on the equivalent crack growth length concept. When the test procedure is applied to the ENF specimens with different pre-crack sizes, the dependence of fracture behaviors on the pre-crack sizes is revealed according to the R-curves and crack growth rate curves. And the effects of the fracture process zone and damage accumulation development are revealed. Based on the analysis of fracture propagation behavior, the proper pre-crack size of the ENF specimen for testing the mode II fracture toughness of pultruded CFRP is determined, and fracture toughness of the investigated pultruded CFRP is obtained with the test results.

Quasi-static modes I, II and mixed modes I/II fracture toughness of two laminate composites: Part II — micro-computerized tomography and numerical simulations

In Part I of this paper, quasi-static fracture toughness tests were reported which were carried out on two carbon fiber reinforced polymer materials. One laminate was unidirectional and the second was composed of plies fabricated from a twill fabric. In Part II, which is presented here, micro-computerized tomography was performed providing a relationship between the observed experimental behavior and the micromechanical structure of the materials. This was carried out for the double cantilever beam (DCB), mixed mode bending (MMB) and end-notched flexure (ENF) specimens. Load–displacement curves were simulated numerically by means of a cohesive zone model and the finite element method to obtain better insight into the failure mechanisms observed for DCB and ENF specimens.

Quasi-static modes I, II and mixed modes I/II fracture toughness of two laminate composites: Part I — Testing

In Part I of this study, fracture toughness tests were carried out in modes I, II and mixed modes I/II on two laminate composites. Both composites contain carbon fibers in an epoxy matrix. One laminate is unidirectional and the second is composed of plies fabricated from a twill fabric. The tests were carried out using double cantilever beam, end-notched flexure and mixed mode bending specimens according to ASTM and ISO standards. This is an extensive and complete study of the in-plane, quasi-static fracture toughness (both initiation and resistance) of two material systems. In Part II of this study, micro-computerized tomography carried out on some of the specimens is reported. On the basis of these images, the experimental behavior was related to the micromechanical structure of the materials. In addition, load–displacement curves were simulated numerically by means of a cohesive zone model and the finite element method to gain better insight into the failure behavior observed.

Evaluation of mode II fracture toughness under high loading rate conditions for composite bonded joints

Composite bonded joints are widely used in the aircraft components, which are frequently subjected to impact loading. The present paper intends to evaluate the mode II fracture behavior of composite bonded joints under high loading rate conditions. Dynamic loading was applied on the end-notched flexure (ENF) specimen at 10 m/s and 15 m/s via an electromagnetic split Hopkinson pressure bar system. Then the dynamic fracture toughness was evaluated using an experimental-numerical hybrid method according to the virtual crack-closure technique and compared to the fracture toughness under quasi-static loading rate (2 × 10−5 m/s and 2 × 10−4 m/s). Results indicate that the mode II fracture toughness of adhesively bonded composite joints shows a positive rate-dependent trend. The mode II fracture toughness can increase about 31.5% when the loading rate increases to 15 m/s. At last, fracture surface inspections using scanning electron microscopy (SEM) were conducted to reveal the physical mark of such an effect.

A new quantitative acoustic emission model for damage characterization of composite laminates using original waveforms

The correlation between acoustic characteristics and mechanical behaviors shows great significance for health monitoring and characterization. This paper develops a new quantitative model based on the modified Mel-frequency cepstral analysis and statistical methods so as to link acoustic emission (AE) features with mechanical behaviors of end-notched flexure (ENF) composite laminates. First, the Mel-frequency cepstral analysis in automatic speech recognition is modified to adapt to AE sensors and signals. Second, the modified Mel-frequency cepstral coefficients (MFCCs) are extracted from original waveforms of AE hits for damage characterization of composites. MFCC0 is taken as an effective feature to qualitatively discriminate damage stages and to identify the pre-failure critical point. The decreasing patterns of MFCC1 and MFCC2 for ENF specimens can be clearly observed with the loading time by using the simple moving average method. Third, pencil lead breaks are repeatedly conducted on the healthy specimen to verify the pattern in the degraded specimen. Finally, a further investigation based on the cumulative moving average method demonstrates that MFCC1 and MFCC2 are quadratic and linear functions of the load ratio or the deflection ratio, respectively. In addition, the latter is more suitable to be an indicator of damage accumulation of composite laminates.

High-resolution in situ characterization of micromechanisms in CFRP laminates under mode II loading

Micromechanisms in carbon fiber reinforced plastics (CFRPs) were studied by in situ mode II fracture toughness tests using a high-resolution optical microscope. The fracture toughness tests on four-point bend end notched flexure specimens were interrupted between the proportional limit and the plateau region, followed by postmortem examination using a high-resolution X-ray computed tomography system to identify three-dimensional microdamage. The observations sequentially captured the formation of damage zone, which composed of plastic zone, fiber/matrix debonding, and microcracks. The microscopic failure process was correlated with the macroscopic behavior of CFRP laminates during mode II fracture toughness tests.

Fracture toughness assessment of CF-PEEK composites consolidated using hot gas torch assisted automated fibre placement

This paper address the challenges in using traditional film inserts specific to hot gas torch (HGT) assisted and in-situ consolidated automated fibre placement (AFP) manufactured double cantilever beam (DCB) and end notched flexure (ENF) specimens using carbon fibre (CF) reinforced polyetheretherketone (PEEK) prepregs. Traditional films suffer from thermal degradation, wrinkling and distortion under the consolidation roller. In this study, steel shim inserts with different thicknesses (25 and 50 µm) were used to manufacture the DCB and ENF specimens for fracture toughness evaluation. The processing parameters for in-situ consolidation were selected based on prior optimisation studies on short beam tests. In-situ consolidated specimens suffer from high void content which can affect the mechanical properties. Hence, optical micrography was used to investigate on the void contents in the manufactured specimens. Microhardness measurement is proposed as an AFP manufacturing quality assessment tool for DCB and ENF specimens which were taken from different regions of composite laminates. A manufacturing methodology for producing high quality DCB and ENF specimens by hot gas torch assisted in-situ consolidation using AFP is proposed in this paper that provide comparable results with those specimens manufactured using traditional methods.

Dynamic mode II interlaminar fracture toughness of electrically modified carbon/epoxy composites

This work investigates mode II delamination toughness of unidirectional carbon/epoxy laminates with enhanced electrical conductivity through different loading rates. The electrical modification was realized through interleaving a tough veil loaded with silver nanowires (AgNWs) into the laminate. A benchmarking against non-modified carbon/epoxy laminates was carried out to examine the influence of the modification of the material delamination toughness. End-notched flexure (ENF) specimens were subjected to loading rates ranging from quasi-static up to 5.5 m/s using servo-hydraulic load frame and modified Hopkinson bar apparatus. The strain energy release rate was determined by applying the compliance based beam method (CBBM), ruling out a necessity of the crack length measurement, generating complete R-curves. The findings demonstrated a notable increase, nearly 79%, on the critical strain energy release rate of the modified laminates, in comparison with that of the reference ones, carried out under the quasi-static loading condition. With respect to the influence of loading rate on mode II interlaminar fracture toughness values, the non-modified carbon/epoxy laminates demonstrated a marginal increase, whereas showing no notable effect on the interleaved ones.

Theory of dynamic mode-II delamination in end-notched flexure tests

The dynamic mode-II energy release rate of the end-notched flexure (ENF) test with applied time-dependent displacement is derived for the first time with the effect of vibration included. A dynamic Euler-Bernoulli beam theory is employed together with a deflection condition to simulate contact. To investigate the dynamic effect and the relative dynamic contribution from each vibration mode, a dynamic factor and a spatial factor are defined. It is found that the contribution of the ith vibration mode is dependent on the spatial factor (which is a function of the delamination length and the total length of the ENF specimen) and that certain vibration modes are dominant (depending on the delamination-length ratio). In addition, for a given spatial factor, there may be a certain vibration mode with a zero contribution to the ERR. The developed theory is verified against results from finite-element-method simulation for two cases of ENF tests and they are in excellent agreement. This work now allows the loading rate-dependent mode-II delamination toughness of layered materials to be determined using ENF tests. In addition, it provides understanding of the structural dynamic response in the presence of mode-II delamination and can guide the design of structures to mitigate the vibration-driven delamination.

Experimental and XIGA-CZM based Mode-II and mixed-mode interlaminar fracture model for unidirectional aerospace-grade composites

This article presents a fracture model for evaluation of Mode-II and Mixed-Mode (Mode-I + II) interlaminar fracture properties of unidirectional laminated composites. Mode-II and Mixed-Mode (Mode-I + II) interlaminar fracture tests have been carried out on End-Notched Flexure and Mixed-Mode bending specimens, respectively. The non pre-craked specimens are tested under pure Mode-II and Mixed-Mode loading conditions for the estimation of energy required to initiate crack growth from the natural crack tip. Pre-cracked specimens have been tested under pure Mode-II loading conditions to investigate the nature of delamination propagation from the sharp crack tip. A new set of interfacial fracture properties has been evaluated for AS4/914 laminates. An expression has been developed to correlate the experimentally obtained energy release rate (ERR) and equivalent crack growth (Δa) using a compliance based beam method. The curve-fitted expression between ERR and Δa is further introduced to the cohesive zone model for numerical modelling. Fractured surfaces at the final fracture load point in non pre-cracked specimens during Mode-II fracture tests are examined using scanning electron microscopy technique. Numerical simulations of crack initiation and propagation for all fracture tests have been performed using a combined formulation of fracture mechanics and damage mechanics. The introduction of experimentally obtained interlaminar interfacial properties into a combined formulation of extended isogeometric analysis and cohesive zone model shows a good agreement with experimentally obtained results.

Modelling prediction on the degradation in mode II fracture energy of structural adhesive subjected to hygrothermal ageing

ABSTRACT In this work, the effect of hot-humid environment on the mode II fracture energy (G IIc) of the selected structural adhesive was experimentally evaluated through End-Notched Flexure (ENF) testing as well as corresponding finite element (FE) modelling approach. The ready-cured ENF samples were first immersed in distilled water and 5% NaCl solution under 50°C for different durations, and then removed from the hot-wet environment for mode II loading up to failure. Degradation was observed in the experimentally measured G IIc for adhesives immersed in both aqueous environments, while a further decrease was found in the samples immersed in distilled water, possibly due to the fact that more water was absorbed than saltwater immersion. A two-step FE modelling approach was developed to simulate the water absorption process under-elevated temperature (Step 1) and subsequent mode II loading test after hygrothermal ageing (Step 2) of ENF specimens. User subroutines were developed to accurately simulate the water ingress process in the adhesive layer and properly transfer the moisture distribution data between the two FE models. The feasibility of the established FE modelling was then successfully validated through comparison between the experimental and numerical results.

On the R-curve and cohesive law of glass/epoxy end-notch flexure specimens with 0//θ interface fiber angles

In the current paper, the effects of interface fiber angles on the characteristics of R-curve and the cohesive law shape of end-notch-flexure specimens are investigated using numerical and empirical methods. To this aim, laminated composites manufactured by E-glass/epoxy with 0//θ interface where θ = 0, 15, 45, 60, and 90 were fabricated and tested. The mode II laminated fracture toughness and the cohesive shear traction-separation model were obtained irrespective of the impact of the remote-ply orientation. The empirical results showed that as the interface fiber angle rises, the crack growth behavior in the samples becomes more stable which is evident in the augmented length of the steady-state fracture process zone. Furthermore, the maximum bearable load of specimens drops considerably. Also, the delamination toughness propagation is approximately identical for all specimens. This is the case even if the initiation of delamination toughness is significantly reduced by increasing the interface fiber angle. After parameter identification of the cohesive zone model and conducting numerical analyses, it was demonstrated that this model with the proposed linear-exponential softening behavior can estimate the load-displacement response of samples that display a pronounced R-curve behavior.

Design analysis of end notch flexure sandwich specimen with honeycomb core

Laminate beam theory based design analysis of the sandwich End Notch Flexure (ENF) test specimen is presented. The analysis is specifically considering specimens with honeycomb core, prone to in-plane compression failure of the core, other undesirable failure modes such as face indentation and core shear failure are analyzed. In addition, crack stability and energy dissipation due to frictional sliding between the crack surfaces are analyzed. Parametric analysis of ENF specimens with a range of face and core thickness, is presented to guide the design. In-plane compression failure of the core, but shorten the range of crack lengths were stable growth occurs. A thicker face will also increase the critical load for crack propagation and by so elevate the risk for indentation and core shear failures. Increased core density is beneficial for preventing indentation and core shear failures, but may increase the risk for in-plane compression failure of the core. The thickness of the core does not strongly influence the critical load for crack propagation. A thicker core increases frictional energy loss, but reduces the risk for core shear failure. A thicker core, however, makes the ENF specimen more prone to in-plane compression failure. ENF sandwich specimens with foam and honeycomb core were tested. The test results support the design analysis.

Determination of the shear traction-separation law of adhesive layers using the end-notched flexure specimen

Cohesive zone modelling is increasingly applied to predict the strength of structural adhesive joints. A method is here proposed to determine the bondline shear traction-separation law needed for cohesive zone models. The method combines an effective crack length approach derived from a beam model and an existing J-integral analysis of the end-notched flexure specimen. The resulting work done by the tractions versus separation curves can be easily processed with direct or mixed direct-inverse approaches. Application to some published experimental results demonstrates the potential of the method while highlighting the importance of adherend material and specimen geometry selection.

Mode II fracture energy characterization of brittle adhesives using compliance calibration method

AbstractThe end‐notched flexure (ENF) test is widely used for measuring the Mode II critical strain energy release rate of adhesively bonded joints (ABJs). Unstable crack growth in ENF joints with brittle adhesives is a common phenomenon. Classic data reduction methods like the direct beam theory (DBT) and the compliance‐based beam method (CBBM) usually result in unacceptable scatter when crack grows unstable. In this study, the application of a compliance calibration method (CCM) for ENF adhesive joints with a brittle adhesive is experimentally investigated. For this purpose, ENF specimens were manufactured and tested. Different data reduction methods were considered for treating the results. Afterwards, the obtained fracture energies were used as an input parameter in a finite element (FE) analysis with a cohesive zone model to evaluate the validity of the experimental data. It is shown that the fracture loads obtained by the CCM have the best agreement with the experimental ones comparing with the other data reduction approaches. To study the effect of geometry on the CCM results, ENF specimens with different adhesive thicknesses, substrate thicknesses and span lengths were also considered in this study, and some general conclusions are made about the geometrical parameters effect on the Mode II fracture energy.

On the extent of fracture toughness transfer from 1D/2D nanomodified epoxy matrices to glass fibre composites

In this study, the effects of adding nanofillers to an epoxy resin (EP) used as a matrix in glass fibre-reinforced plastic (GFRP) composites have been investigated. Both 1D and 2D nanofillers were used, specifically (1) carbon nanotubes (CNTs), (2) few-layer graphene nanoplatelets (GNPs), as well as hybrid combinations of (3) CNTs and boron nitride nanosheets, and (4) GNPs and boron nitride nanotubes (BNNTs). Tensile tests have shown improvements in the transverse stiffness normal to the fibre direction of up to about 25% for the GFRPs using the ‘EP + CNT’ and the ‘EP + BNNT + GNP’ matrices, compared to the composites with the unmodified epoxy (‘EP’). Mode I and mode II fracture toughness tests were conducted using double cantilever beam (DCB) and end-notched flexure (ENF) tests, respectively. In the quasi-static mode I tests, the values of the initiation interlaminar fracture toughness, G_{text{IC}}^{text{C}} , of the GFRP composites showed that the transfer of matrix toughness to the corresponding GFRP composite is greatest for the GFRP composite with the GNPs in the matrix. Here, a coefficient of toughness transfer (CTT), defined as the ratio of mode I initiation interlaminar toughness for the composite to the bulk polymer matrix toughness, of 0.68 was recorded. The highest absolute values of the mode I interlaminar fracture toughness at crack initiation were achieved for the GFRP composites with the epoxy matrix modified with the hybrid combinations of nanofillers. The highest value of the CTT during steady-state crack propagation was ~ 2 for all the different types of GFRPs. Fractographic analysis of the composite surfaces from the DCB and ENF specimens showed that failure was by a combination of cohesive (through the matrix) and interfacial (along the fibre/matrix interface) modes, depending on the type of nanofillers used.