End-notched Flexure Research Articles

Hygrothermal effect on the strain energy release rates and mode mixity of asymmetric delaminations in generally layered beams

An analytical framework is presented to calculate the mode I and II components of the strain energy release rate (SERR) of a delamination between two generally layered sub-laminates, considering the residual hygrothermal stresses effect. First, the sub-laminates are modeled as Timoshenko beams, the crack tip is assumed rotationally flexible and the mode partitioning is based on the global method. Next, SERR and mode mixity are obtained for an arbitrarily loaded delaminated beam and reduced for some typical delamination fracture tests. An asymmetrically delaminated fiber metal laminate (FML) is analyzed under double cantilever beam (DCB) and end-notched flexure (ENF) configurations. For the ENF configuration, the inherent contact problem was analytically approached. We demonstrate that the thermal effect on the SERR and mode mixity of the FML, rather ignored so far in the literature, can be non-negligible. Finally, the analytical results are validated against numerical predictions using the finite element method.

Effect of notch length and pre-crack size on mode II fracture energy of brittle adhesives

In this study, the effects of notch length and pre-crack size on mode II fracture energy of brittle adhesives are investigated. These effects are not considered by the direct beam theory (DBT) and the compliance-based beam method (CBBM) for the end-notched flexure (ENF) specimens. The sum of the lengths of the notch and the pre-crack are known as the pre-crack size in common data reduction schemes. In the current work, experiments were performed on ENF adhesive joints using digital image correlation (DIC) technique. Then, the fracture energy was obtained experimentally based on the J-integral method, the classic beam theory, and the compliance-based beam method. Numerical analyses were carried out to measure the stress distribution ahead of the pre-crack tip. Based on the obtained results, it is shown that there is a specific pre-crack length and notch size in which the pure mode II condition in an ENF test is obtained. Other combinations of the notch to pre-crake size ratio result in mixed mode conditions where the obtained fracture energy significantly changes.

Evaluation of a trilinear traction-separation law for mode II delamination using the effective crack method

Mode II delamination testing for measuring the critical strain-energy release rate has reached a high level of maturity with the recent publication of ISO and ASTM standards. Cohesive zone modelling has also become a well-established design tool implemented in many commercial finite element analysis codes. The particularly large fracture process zone in mode II delamination increases the relevance of the traction-separation law. This paper proposes a fairly simple inverse method to evaluate an approximate trilinear traction-separation law from quasi-static end-notched flexure test results. The method employs an analytical beam cohesive zone model and consists of evaluating the parameters that fit the effective crack length versus strain-energy release rate curve. Preliminary studies showed that specific features of the latter curve were quite sensitive to some model parameters. Therefore, accurate approximate trilinear traction-separation laws could be obtained without the extensive numerical calculations typical of inverse methods.

Thermally modified (TM) beech wood: compression properties, fracture toughness and cohesive law in mode II obtained from the three-point end-notched flexure (3ENF) test

Abstract The fracture properties of thermally modified beech (Fagus sylvatica) wood (TMW) at 180° and 200°C were evaluated in mode II using the three-point end-notched flexure (3ENF) scheme assisted by three-dimensional (3D) stereovision equipment for obtaining displacements and strains. The compliance-based beam method (CBBM) provided the strain energy release rates (G II) of TMW and cohesive laws for both native wood (W) and TMW. Based on the CBBM and equivalent crack length approach (ECLA), G II was obtained directly from the force-deflection data. The thermal modification (TM) process reduced the compressive strength by 4.4% and increased the compressive elastic modulus by 38.3%, whereas G II was reduced substantially by 40.8% and 67.9% at TM180°C and TM200°C, respectively. TM also increased wood brittleness that was visible on the displacement slip reduction. The resulting mean cohesive models can be used for numerical analyses. The fracture properties of TMW have to be taken into consideration for constructional wood application, when cyclic loading may lead to microcracking and material fatigue.

Parameters prediction of cohesive zone model for simulating composite/adhesive delamination in hygrothermal environments

In this paper, moisture parameters of adhesive SY-14M-III and composite T800/AC531 were firstly measured, which were used for the following moisture diffusion investigations. Then, double cantilever beam (DCB) tests and end notched flexure (ENF) tests were conducted in four environments, and relevant progressive damage models considering cohesive zone models were established. The results show that the models are efficient by comparison of experimental and numerical results, and eight pairs of cohesive parameters (interface strength and interface stiffness) corresponding to the specified fracture energy release rates were obtained. Finally, a modified Tsai prediction method of cohesive zone model for simulating composite/adhesive delamination in hygrothermal environments was proposed based on an assumption of the composite/adhesive moisture diffusion process, which can be as a reference or basic data for numerical analysis of adhesively bonded composite structures.

Enhancing the predictive capabilities of a composite plasticity model using cohesive zone modeling

One of the challenges in building a predictive numerical model for laminated composites is the ability to accurately model delamination. In this paper, a modular orthotropic plasticity model that is made of three sub-models – deformation, damage and failure, is used in conjunction with a delamination model to predict the behavior of an impact event involving a unidirectional laminated composite. Both the composite and delamination constitutive models are built entirely using experimentally obtained data. The delamination model that uses cohesive zone elements, is built using data obtained from double cantilever beam (DCB) and end-notched flexure (ENF) tests. An impact validation test is simulated, and the results are compared both qualitatively and quantitatively with experimental results to validate the both the cohesive zone element (CZE) parameters and the composite material model. The paper concludes with a summary of the work and ongoing work to improve experimental procedures and the constitutive model.

Fracture modelling of adhesively-bonded joints by an inverse method

Nowadays, any structure must have strength, robustness and lightness, which has increased the industrial interest and research efforts in adhesive joining, mainly in the improvement of strength and fracture properties of adhesives. Thus, in recent years, the use of adhesive joints in industrial applications has gradually grown, replacing some traditional bonding methods, since they have advantages such as reduced stress concentrations, reduced weight and cost, and ease of processing/manufacturing. In this work, the cohesive laws of three adhesives, Araldite® AV138, Araldite® 2015 and Sikaforce® 7752, were obtained by the application of an inverse adjustment method between the numerical and experimental load-displacement curves (P-d) of Double-Cantilever Beam (DCB) tests for tensile characterization and End-Notched Flexure (ENF) tests for shear characterization. Next, these laws were validated with experimental data of single-lap joints (SLJ) and double-lap joints (DLJ), using Abaqus®. For the Araldite® AV138 and Araldite® 2015, in tension and shear, the triangular law accurately predicted the behaviour of the SLJ and DLJ. For the Sikaforce® 7752, the triangular law did not suitably fit the experimental results. It was considered that, due to its ductility, the Sikaforce® 7752 is best modelled with a trapezoidal law.

Experimental and numerical analysis on the cohesive behavior of an automotive adhesive improved by MWCNT subjected to mode I and II loadings

This paper presents the effect of multi-walled carbon nanotubes (MWCNT) incorporation in the fracture and damage behavior of an epoxy adhesive. In this regard, the fracture energies and cohesive behavior of the neat and reinforced adhesives are obtained by testing Double Cantilever Beam (DCB) and End-Notched Flexure (ENF) specimens in mode I and mode II, respectively. The cohesive behavior is studied by extracting traction-separation law (TSL) corresponding to each and every adhesive using direct method. In order to validate the extracted TSL, an experimental test and numerical simulation on Single Lap Joint (SLJ) specimens are conducted. The good agreement between experimental and numerical load-displacement responses proves the accuracy and precision of TSLs. The results revealed that in pure modes, the fracture toughness of the epoxy adhesive is improved by adding MWCNTs up to a critical %wt. Afterwards, incorporating excess additive would weaken the adhesive. Similarly, load-displacement responses of SLJs indicates that the highest improvement of the joint energy would be achieved using the same critical %wt and result in an enhancement of over 80%.

Numerical and experimental analysis of bonded joints with combined loading

The metallic materials bonding using structural adhesives has become an increasingly used process, presenting advantages when compared to other fastening methods such as screws and rivets. The aim of this paper is the numerical evaluation of bonded joints with combined loading (traction and shear) using the finite element method, comparing the results obtained with the experiments performed at the same configurations. Considering adhesive joints with the same bonded area, but with different linear dimensions, the mechanical strength may be different, which characterizes the shape factor. In this way, the analyzes considered the bonded area shape factor in nine different configurations, being modified both the height and the width of the joint, considering two points of force application for each group. For the numerical simulation, the cohesive zone models (CZM) were used, which use the concepts of linear elastic fracture mechanics (LEFM). These models consider that one or multiple interfaces or regions of fracture may be artificially introduced into the structures, which is done through the separation-traction laws. For this purpose, DCB (double cantilever beam) and ENF (end notched flexure) tests were performed, measuring this way the essential cohesive properties to the numerical modeling, especially the critical energy release in I and II modes (normal and shear, respectively). The influence of some cohesive properties on the maximum load of the bonded joint was investigated. The good numerical and experimental concordance in different configurations studied confirms that the CZM provide consistent results with the bonded joint experiments for the presented conditions of adhesive thickness, surface treatment and load application point, not only in single lap joints, but also in combined loading joints, whose investigation was done in this work.

Enhanced Failure Load Bearing in Adhesively Bonded Strap Repairs: Numerical Analysis and Experimental Results

Adhesively bonded repairs are frequently used to repair aluminum structures due to their attractive options compared to traditional methods such as welding or riveting. A new method of increasing the repair’s strength against uniaxial tensile loads is used in this study. For this purpose, standard single-strap (SS) and double-strap (DS) repairs were produced with aluminum patch. In the first step, an epoxy-based adhesive was employed to create SS and DS repairs using neat adhesive and 0.5 wt.% reduced graphene oxide (RGO)-reinforced adhesive. Afterward, samples of SS and DS joints with the reinforced adhesive were manufactured to study the effect of the added RGO. Uniaxial tensile tests were conducted and above 30% enhancement in the ultimate load was observed in the joints bonded with reinforced adhesive. The repaired joints were analyzed by finite element (FE) method using cohesive zone modeling technique to obtain failure loads. For this purpose, two sets of tests (a) double cantilever beam and (b) end notch flexure tests were implemented to estimate the cohesive zone model CZM parameters. Comparing the results obtained from experiments and the numerical simulations shows that FE models accurately predict the failure load in the reinforced and unreinforced repaired joints.

Experimental investigation of Mode II fracture properties of parallel strand bamboo composite by end notched flexure test

Parallel strand bamboo (PSB) is a high-strength bamboo composite that has been used in construction in recent years. Crack growth is a major concern in the design of PSB components for building structures. This study investigated the mode II fracture properties of PSB composite under in-plane shear action, starting from the end notched flexure (ENF) test as the prototype of specimens. The compliance based beam method (CBBM) was used to analyze the crack propagation process. The results showed that crack propagation of mode II fracture of PSB was self-similar cracking with cracks parallel to the strand. The fracture process contained two stages: the development of the Fracture Process Zone (FPZ) and the crack propagation stage. The critical energy release rate GIIc was a constant independent of the initial crack length, with a mean value of 2.61 N/mm; the mean value of fracture toughness KIIc was 4436 kN·m-3/2, which is greater than those of commonly used timber products. The R-curve showed a gradual increase before crack extension due to the development of the FPZ but became approximately horizontal during crack propagation.

Application of continuum decohesive finite element to progressive failure analysis of composite materials

The continuum decohesive finite element (CDFE) is a novel finite element technique combining continuum and cohesive crack modeling seamlessly. In CDFE, the transition from a continuum to non-continuum is modeled physically by introducing pairs of dummy nodes to account for the crack separations. A static condensation algorithm is applied to solve for and preserve the separations. In this paper, CDFE has firstly been applied to the modeling of transverse crack growth in a representative volume element (RVE) of composite materials. Microscopic cracks initiate separately and coalesce into a macroscopic transverse crack. In this case, mode I cracking is dominant and the maximum principal stress criterion is used for crack angles. The second problem set is the delamination toughness tests, including a double cantilever beam (DCB) test, an end notched flexure (ENF) test and mixed mode bending (MMB) tests of three mixed mode ratios. In these cases, the crack plane is well-defined and mode mixity is encountered. For better numerical stability, the CDFE inner-element discretization scheme is modified and a novel mixed mode cohesive formulation is implemented. Through analyses, the capability of CDFE to deal with general progressive failure problems of composite materials is shown.

The effect of thin film adhesives on mode II interlaminar fracture toughness in carbon fiber composites with shape memory alloy inserts

A single sheet of nickel-titanium (NiTi) shape memory alloy (SMA) was introduced within an IM7/8552 polymer matrix composite (PMC) panel in conjunction with multiple thin film adhesives to promote the interfacial bond strength between the SMA and PMC. End notched flexure (ENF) testing was performed in accordance to ASTM D7905 method for evaluation of mode II interlaminar fracture toughness (GIIC) of unidirectional fiber-reinforced polymer matrix composites. Acoustic emissions (AE) were monitored during testing with two acoustic sensors attached to the specimens. The composite panels examined using scanning electron microscopy techniques after part failure. GIIC values for the control composite samples were found to be higher than those of samples with embedded SMA sheets. The presence of adhesives bonded to SMA sheets further diminished the GIIC values. AE values revealed poor bonding of the panels, with little to no signals during testing.

Comparison of different test configurations for the shear fracture toughness evaluation of a ductile adhesive

Cohesive zone modelling (CZM) is widely used for predicting the strength of adhesive joints. The key variable for crack path modelling is the critical strain energy release rate (GC), which can be separated into the tensile (GIC) and shear (GIIC) components. In shear, the End Notched Flexure (ENF) test is widespread. However, other test methods exist and could be a viable replacement. This work aims to make a numerical evaluation between the ENF and Four-Point End Notched Flexure (4ENF) tests to determine GIIC of a ductile adhesive (SikaForce® 7752) and to provide shear CZM laws for further application in design. An inverse technique was used to obtain the shear CZM laws of the adhesive. It was concluded that the GIIC values obtained by the ENF and 4ENF tests are in good agreement. The numerical analysis led to unique shear CZM laws for both tests, with similar results.

Mode II fracture toughness of asymmetric metal-composite adhesive joints

The paper presents an experimental investigation of the mode II fracture toughness behavior of dissimilar metal-composite adhesive joints using the end-notched flexure (ENF) test. The adhesive joint under study consists of a thin titanium sheet joined with a thin CFRP laminate and is envisioned tobe applied in the hybrid laminar flow control system of future aircraft. Four different industrial technologies for the manufacturing of the joint areevaluated; co-bonding with and without adhesive and secondary bonding using either a thermoset or a thermoplastic composite. The vacuum-assisted resin transfer molding (VARTM) technique is employed for the manufacturing of the titanium-CFRP joint. After manufacturing, the joint is stiffened from its both sides with two aluminum backing beams to prevent large deformations during the subsequent ENF tests. Towards the fracture toughness determination from the experimental data, an analytical model recently reported by the authors is applied; that model considers the bending-extension coupling of each sub-laminate of the joint as well as the effect of the manufacturing-induced residual thermal stresses. The load-displacement behaviors, failure patterns, and fracture toughness performances for each of the four manufacturing options (MO) investigated are presented and compared.

Fracture envelope estimation of a structural adhesive by dedicated fracture tests

Cohesive zone modelling (CZM) is widespread for the strength analysis of bonded joints. The fracture toughness (GC) is required to use CZM. A scarcely studied mixed-mode test is the Asymmetric Tapered Double-Cantilever Beam (ATDCB), which merges a Tapered Double-Cantilever Beam (TDCB) adherend with a Double-Cantilever Beam (DCB) adherend. This work addresses the ATDCB test to estimate the fracture envelope of a structural adhesive. TDCB and End-Notched Flexure (ENF) tests were also performed to acquire the tensile (GIC) and shear fracture toughness (GIIC), respectively. Numerically, mixed-mode CZM laws were constructed based on the obtained data, and the results were compared with experiments, to validate the CZM laws and the mixed mode propagation criterion. As a result, the best damage propagation criterion for mixed mode was estimated and validated.

Analysis of automotive mixed‐adhesive joints weakened by moist conditions: Experimental characterization and numerical simulation using cohesive zone model

AbstractThis paper is mostly concerned with an experimental and numerical study to clarify the behaviour and failure in the mono‐adhesive joints and mixed‐adhesive joints under different environmental conditions (dry [E0], 75.3% relative humidity [E1], 84.2% relative humidity [E2], and submerged in tap water [E3] at 25°C) and different strain rates (1 and 100 mm/min). Experimental investigations are compared with the numerical analysis, which is carried out by bilinear cohesive zone model (CZM). Through this work, degradations of cohesive parameters are calculated by using open‐faced double cantilever beam (DCB) and end notch flexure (ENF) specimens. The experimental data show that the cohesive parameters of Araldite 2015 have negative correlation to moisture content. Although Araldite AV138 parameters experience a decrease in mode I, in mode II, its cohesive parameter increases. First, it is found that the decrease in experimental failure load of mixed‐adhesive joints with regard to the dry condition is recorded as 32.6%, 54%, and 59.1% for E1, E2, and E3 conditions, respectively. Following this further, single lap joint (SLJ) that has non‐uniform moisture content distribution is modelled by engaging specific CZM parameters related to the specific moisture content. The results show a good agreement between experimental and numerical data.

Simultaneous extraction of tensile and shear interactions at interfaces

A simple beam analysis is developed that accounts for the tensile and shear interactions between the surfaces of two beams that have been brought into contact. The generally coupled differential equations for the relative normal and tangential displacements between the interacting surfaces and the normal and shear components of the traction between the two surfaces are decoupled when a balance condition involving the bending stiffness and height of each beam is satisfied. This condition also allows the normal and shear components of the J-integral and the crack tip displacement to be obtained from measurements of the applied loads along with load point displacement and rotation of each beam. As a result, the derivative of each component of the J-integral with respect to its associated crack tip displacement simultaneously provides both the normal and shear traction–separation relations at any value of the mode-mix without invoking any assumption on the particular form. As an application of this method, the normal and shear traction–separation relations for a silicon/epoxy interface were determined over nominal mode-mixes ranging from −53° to 87.5° using non-symmetric end-loaded split (ELS) and end-notched flexure (ENF) specimens. It is found that many of the assumptions made previously in developing traction–separation relations based on potential or damage-based approaches do not apply to this particular interface, which should motivate future theoretical developments.

Interlaminar fracture toughness of a plain weave flax/epoxy composite

ABSTRACTIn recent decades, flax fibre has become a popular natural resource as reinforcement in polymeric composites. However, the pure mode characterisation of flax fibre composites is rather limited. Furthermore, the mixed-mode delamination is not yet available. Nevertheless, delamination behaviour is important to be characterised as it is a major problem in composite laminates. This study examined the delamination behaviour of a woven flax/epoxy composite. Specimens were tested using mode I double cantilever beam, mode II end-notched flexure and mixed-mode I+II single leg bending tests. Results showed that the mode I, mode II and mixed-mode I+II fracture toughness were 363.23, 962.17 and 649.06 N m−1, respectively. When the fracture toughness values were fitted using Benzeggagh–Kenane criterion, it was found that the best-fit material parameter η was attained at 0.88. This information is useful to estimate the variation of fracture toughness with the mode ratio. Finally, through scanning electron micrographs, it was noticed that fibre/matrix debonding was the major fracture mechanism in all loading modes. In conclusion, the findings from this study suggested that the composite was suitable to be used for structural applications under mixed-mode loading.

Effect of unstable crack growth on mode II interlaminar fracture toughness of a thermoplastic PEEK composite

An end notched flexure (ENF) test was used to study the effect of growth stability on mode II interlaminar fracture toughness (GIIC) of a carbon/PEEK composite. The instability of the ENF test was used to induce both stable and unstable crack growth with a static loading. Two techniques were used to evaluate mode II fracture toughness: the traditional compliance method and the infra-red thermography technique. The compliance technique has the advantage of being simple and it has already been confirmed for standard tests. Nevertheless its results may be inaccurate for unstable crack growth propagation. The infra-red thermography technique enables fracture toughness to be accurately measured for non-standard tests in which the crack growth may be unstable.Both methods are complementary and this study came to the conclusion that GIIC is sensitive to crack growth velocity. Fracture toughness showed a low value for crack growth start and unstable propagation, and a high value for stable crack growth. The transition between a ductile fracture mode (for low crack growth velocity) and a brittle fracture mode (for high crack growth velocity) explained the important variability in GIIC values.