Compliance-based Beam Method Research Articles

The double cantilever beam test applied to mode I fracture characterization of polyamide 12 processed by selective laser sintering technology

In recent years, parts produced by Selective Laser Sintering (SLS) technology have aroused growing interest due to their valuable potential for end-use applications. However, to ensure the applicability of SLS products for advanced structural purposes, an accurate characterization of their mechanical behaviour is essential, which includes the assessment of fracture performance. Thus, cohesive zone modelling that allows mimicking damage initiation and propagation in quasi-brittle materials is used in this work to identify the cohesive laws of Polyamide 12 parts sintered by SLS with different values of energy density. This has been accomplished with success in this work for pure mode I loading employing the Double Cantilever Beam (DCB) test. In this context, experimental data is used to evaluate the critical energy release rate under quasi-static loading, by means of the Compliance-Based Beam Method (CBBM). The identification of the cohesive laws comprises finite element analysis to achieve accurate agreement with the experimental load-displacement curves obtained under quasi-static loading. The experimental protocols are duly validated for the tested conditions, which includes a developed numerical procedure combined with experimental data.

Experiments on the mode II fracture toughness in ENF tests of CFRP curved beams

The purpose of this study is to establish end-notched flexure (ENF) tests of curved beam specimens cut from tanks or cylinders. To provide data reduction methods for experiments, a compliance-based beam method (CBBM) for curved beams in ENF tests is proposed based on the previously established Euler–Bernoulli curved beam theory formulations of ENF tests. ENF tests were conducted using curved beam specimens with three different curvature radii, and the results were in good agreement with the curved beam theory. In addition, the fracture toughness values obtained from the proposed CBBM for curved beams were validated using three-dimensional finite element (FE) analysis. The results revealed that the FE analysis with the measured fracture toughness agreed well with the experimental load–displacement curves, verifying the validity of the obtained fracture toughness values for curved beams.

Influence of Laser Treatment on End Notched Flexure Bonded Joints in Carbon Fiber Reinforced Polymer: Experimental and Numerical Results.

Surface pretreatment for bonding is one of the most important steps for the manufacturing of a reliable bonded joint. In this paper, the effectiveness of an innovative pretreatment by CO2 pulsed laser for bonding Carbon Fiber Reinforced Polymer (CFRP) was investigated. End Notched Flexure (ENF) specimens were made with different densities of laser treatment, and the respective fracture toughness was obtained through the Compliance-Based Beam Method (CBBM). Furthermore, a cohesive model for simulating debonding processes was illustrated, and the cohesive parameters were obtained by an inverse method. The achieved results represent a fundamental step for the development of a numerical model useful for the determination of laser texturing as a function of the applied local stress into the bonded joint.

Evaluation of [formula omitted]-curves and cohesive law in mode I of European beech

This work addresses the determination of the cohesive laws in Mode I and tangential–longitudinal (TL) crack propagation system of Fagus Sylvatica L. This species is one of the ever-growing and most widely used hardwood species in Europe for engineered timber products. Double Cantilever Beam (DCB) tests are performed. The strain energy release rate (GI) is derived from the R-curves by applying the Compliance-Based Beam Method (CBBM), which has the advantage of not requiring the measurement of the crack length during propagation, but only the global load–displacement curves. The cohesive law of the material is determined from the relationship between GI, and the crack tip opening displacement (CTOD) monitored for each specimen using Digital Image Correlation (DIC). Numerical finite element models are developed by implementing the average cohesive law through Cohesive Zone Models (CZM). An average GI value of 0.46 kJ/m2 is obtained for this species. The numerical load–displacement curves are consistent with the experimental results, which demonstrates the suitability of the method for the identification of the cohesive laws in beech. The fracture properties obtained are essential in the development of advanced and reliable numerical models in timber engineering design using this species.

Experimental and numerical investigation of the traction-separation law of mode II fracture in single-edge ultrasonic welding in polypropylene composite reinforced by glass fibers

The use of welded joints in composite structures with reinforced fibers has rapidly increased owing to their advantages in terms of strength-to-weight ratio, design flexibility and ease of production. Herein, the generalized progressive damage model is numerically and experimentally studied to predict the degradation process in end notch flexure (ENF) composite specimens welded by the ultrasonic method. In numerical modeling, a trapezoidal traction-separation model that expresses the embedded process zone (EPZ) is developed using three data reduction methods of the compliance calibration method (CCM), classical beam theory (CBT) and compliance-based beam method (CBBM), and formulated by combining failure and damage mechanics. Finally, the force-displacement diagrams obtained from experimental investigations and the force-displacement diagrams extracted from numerical modeling are compared. The results demonstrate that the models extracted using CBBM and CBT methods make accurate predictions compared to the CCM method.

Direct evaluation of mode I cohesive law of eucalyptus bonded joints

Eucalyptus globulus L. is a hardwood species with high mechanical properties and great potential for engineered timber products. In the development of glued laminated products using high density wood species such as eucalyptus, bonded joints (e.g. finger-joints) could be a weak point and therefore require special analysis. Numerical cohesive zone models in the framework of fracture mechanics can be applied to accurately simulate the brittle failure behaviour of such bonded joints. These models require assuming a cohesive law that relates cohesive forces and displacements ahead of the crack tip to predict the crack growth along a fracture process zone. In the present research, the fracture cohesive laws in mode I loading of Eucalyptus globulus L. bonded joints using one-component polyurethane adhesive (1C-PUR) are directly identified by coupling Double Cantilever Beam tests (DCB) with full-field displacements at the crack tip (w) measured by Digital Image Correlation (DIC). The Compliance-Based Beam Method (CBBM) is applied as data reduction scheme to evaluate the strain energy release rate (G) from the Resistance-curves of the specimens considering an equivalent crack length. Cohesive laws are determined by fitting a logistic function to the experimental data curve (G-w). It is found that that eucalyptus bonded joints have high values for mode I fracture properties, in the same range of those obtained for eucalyptus solid wood in previous research by the authors.

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.

Effects of mean load on interlaminar fracture behavior of carbon-epoxy prepreg fabric laminates under Mode I fatigue loading

Mode I delamination fatigue crack growth behavior was investigated in a carbon-epoxy prepreg fabric laminate by evaluating the mean load effects. The fatigue crack growth rate was determined as a function of the maximum Mode I strain energy release rate considering an exponential fitting function according to the Compliance Based Beam Method (CBBM). Classical data reduction techniques were combined with the proposed method, indicating less scatter on results and satisfying basic assumptions of smoothness and continuity for the fatigue crack growth process. The delamination growth rate curve proved to be strongly affected by the applied mean load as the fatigue onset delamination. The number of cycles to onset is higher for lower load levels and, considering the stable propagation region, a higher delamination growth rate was reported for higher load levels. The fractographic analysis has confirmed the effects of cyclic loading and the mean load levels on fracture surfaces. For a higher mean load, failure mechanisms expose static aspects and substantial presence of microcracks at fiber imprints, while, under lower mean load were noticed significant wear and plasticity and featureless fiber tracks.

Direct Evaluation of Mixed Mode I+II Cohesive Laws of Wood by Coupling MMB Test with DIC.

Governing cohesive laws in mixed mode I+II loading of Pinus pinaster Ait. are directly identified by coupling the mixed mode bending test with full-field displacements measured at the crack tip by Digital Image Correlation (DIC). A sequence of mixed mode ratios is studied. The proposed data reduction relies on: (i) the compliance-based beam method for evaluating strain energy release rate; (ii) the local measurement of displacements to compute the crack tip opening displacement; and (iii) an uncoupled approach for the reconstruction of the cohesive laws and its mode I and mode II components. Quantitative parameters are extracted from the set of cohesive laws components in function of the global phase angle. Linear functions were adjusted to reflect the observed trends and the pure modes (I and II) fracture parameters were estimated by extrapolation. Results show that the obtained assessments agree with previous experimental measurements addressing pure modes (I and II) loadings on this wood species, which reveals the appropriateness of the proposed methodology to evaluate the cohesive law under mixed mode loading and its components.

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.

Wood-adhesive bond loaded in mode II: experimental and numerical analysis using elasto-plastic and fracture mechanics models

Abstract The goal of the study was to analyze fracture properties of adhesive bond using a three-point end-notched flexure test and the compliance-based beam method. Critical strain energy release rates (G IIc ) and cohesive laws were obtained for adhesive bonds made of European beech (Fagus sylvatica L.) and adhesives such as EPI, MUF, PRF and PUR. The experiments were assisted with FE analyses employing three different material models of wood: elastic (Elas), symmetric elasto-plastic (EP) and elasto-plastic with different compressive and tensile yield stresses parallel to fiber (EP+). The highest mean G IIc was achieved for PUR (5.40 Nmm−1) and then decreased as follows: 2.33, 1.80, 1.59 Nmm−1 for MUF, EPI, and PRF, respectively. The failure of bondline was brittle and occurred at bondline for EPI, MUF and PRF, and ductile and commonly occurring in wood for PUR adhesive. The FE simulations employing cohesive models agreed well with the experimental findings for all adhesives. FE model with Elas material was found accurate enough for EPI, MUF and PRF adhesives. For PUR adhesive, the model EP+ was found to be the most accurate in prediction of maximal force. The impact of friction between lamellas may be up to 4.2% when varying friction coefficient from 0 to 1. The impact of the grain angle distortion (α) with respect to longitudinal specimen axis showed its high influence on resulting stiffness and maximal force. It was found that three-point end-notched test is suitable for EPI, MUF, and PRF, while it is less appropriate for a bond with PUR adhesive due to notable plastic behavior.

Experimental Investigation of Delamination in Composite Continuous Fiber-Reinforced Plastic Laminates with Elastic Couplings.

This paper presents an experimental evaluation of influence of the elastic couplings on the fracture toughness as well as on delamination initiation and propagation in carbon/epoxy composite laminates. For this purpose the mode I double cantilever beam (DCB) tests according to the American Society for Testing and Materials (ASTM) D5528 Standard were performed on specimens with different delamination interfaces and specific lay-ups composition exhibiting the bending-twisting (BT) and the bending-extension (BE) couplings. The critical strain energy release rates (mode I c-SERR, GIC) were calculated by using the classical methods, namely: the modified beam theory (MBT), the compliance calibration (CCM) and the modified compliance calibration (MCC). In order to evaluate an accuracy of the different methods, the values of c-SERR obtained by using standardized data reduction schemes were compared with values calculated by using the compliance based beam method (CBBM). All the methods give rise to comparable values of the GIC, which makes the CBBM an appealing choice, since it does not depend on crack length monitoring during the test. Initiation and propagation of delamination were investigated by using the acoustic emission (AE) technique. Moreover, the scanning electron microscope (SEM) analysis were performed after the experimental tests in order to investigate a fracture surface at delamination plane.

An experimental analysis of the end-notched flexure composite laminates beams with elastic couplings

This paper presents an experimental study of the composite beams with elastic couplings subjected to the end-notched flexure (ENF) test. The object of research were carbon/epoxy composite laminates with specific stacking sequences exhibiting the bending–extension and the bending–twisting couplings. In addition, multidirectional laminates with different delamination interfaces were tested. Influence of elastic coupling phenomena on behavior of laminates subjected to the bending moment as well as on fracture toughness and delamination surfaces after the ENF tests was discussed. All experiments were performed according to the ASTM D7905 Standard. Determination of crack initiation was supported by the acoustic emission technique. Data analysis of the ENF test was performed by using both the direct beam theory and the corrected beam theory. Results obtained by using the classical data reduction schemes were compared with the compliance-based beam method (CBBM). Greater values of the fracture toughness obtained by using the non-standardized methods can be explained by the effect of the fracture process zone which was taken into account in the CBBM calculation scheme. Delamination surfaces of coupled laminates after the ENF tests were investigated by using the scanning electron microscopy. Results revealed that the effect of elastic couplings might influenced on intense bridging phenomena, more extensive fracture process zone and contribution of the mode III in total delamination resistance. Nevertheless, application of the standardized ENF procedure to determination of the fracture toughness of laminates exhibiting elastic couplings is still possible, provided assistance of additional data reduction schemes and techniques or numerical analysis.

Durability study of flexible bonded joints: The effect of sustained loads in mode I fracture tests

Adhesives in bonded structures are exposed both to external loads and environmental conditions; durability studies are currently needed to assess their service lifetime. Conditioning strategies differ in considering external load conditions (such as stressed or not stressed) for the durability analysis of double cantilever beam (DCB) bonded joints. Different test procedures such as ASTM D3762 (wedge testing) or ISO-25217 (DCB testing) exist to characterise the evolution of the fracture strength and toughness found in bonded joints. These methods depend on crack-length measurements, however, and achieving an accurate visual determination may be difficult due to the large fracture process zones (FPZs) that develop in the adhesive layer, especially in flexible or degraded bonded joints. To compensate, crack-length-independent data-reduction methods such as the compliance-based beam method (CBBM) or the J-integral method can be used, but experimental research is lacking on the suitability of these methods in ageing tests. A lack of consensus also exists in testing methodologies to evaluate the durability of bonded joints, especially when examining flexible bonded joints. The present work evaluates the influence of damage on fracture toughness within flexible bonded joints exposed to service conditions. Wedge tests and DCB tests are conducted using DCB specimens bonded with a flexible structural adhesive, proving that the degradation of flexible bonded joints exposed to environmental conditions is significantly accelerated when external loads act on them. The findings show that crack length estimation is affected due to environmental effects and thus, that crack-length-dependent test methods are not applicable in ageing tests.

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.

Experimental Evaluation of Mode II fracture Properties of Eucalyptus globulus L.

Eucalyptus globulus Labill is a hardwood species of broad growth in temperate climates, which is receiving increasing interest for structural applications due to its high mechanical properties. Knowing the fracture behaviour is crucial to predict, through finite element models, the load carrying capacity of engineering designs with possibility of brittle failures such as elements with holes, notches, or certain types of joints. This behaviour can be adequately modelled on a macroscopic scale by the constitutive cohesive law. A direct identification of the cohesive law of Eucalyptus globulus L. in Mode II was performed by combining end-notched flexure (ENF) tests with digital image correlation (DIC) for radial-longitudinal crack propagation system. The critical strain energy release for this fracture mode, which represents the material toughness to crack-growth, was determined by applying the Compliance Based Beam Method (CBBM) as data reduction scheme and resulted in a mean value of 1.54 N/mm.

Adhesive thickness effects on the mixed-mode fracture toughness of bonded joints

ABSTRACTAiming to predict the strength of bonded joints by techniques such as cohesive zone models (CZM), it is highly relevant to estimate the adhesive strength and fracture toughness (GC). Here, the tensile and shear fracture toughness (GIC and GIIC, respectively) and the corresponding mixed-mode behaviour acquire special relevancy. However, it is known that these parameters are highly dependent on the adhesive thickness (tA). The present work experimentally addresses the tA effect on the mixed-mode behaviour of bonded joints, namely on the tensile and shear fracture energies (GI and GII, respectively), using the Single-Leg Bending (SLB) test. Different data reduction schemes were applied. With this purpose, the respective resistance curves (R-curves) were calculated, which enabled plotting the respective fracture envelope for a sample tA by the knowledge of the pure-mode GIC and GIIC. Overall, it was possible to obtain a good agreement between methods for the mixed-mode GI and GII calculation and to estimate the most suitable fracture envelope of the adhesive for a given tA. The compliance-based beam method (CBBM) was found to be particularly suited to perform data reduction, since it accounts for the adhesives’ ductility and it is not affected by crack length (a) measuring errors.

On the effect of adhesive thickness on mode I fracture energy - an experimental and modelling study using a trapezoidal cohesive zone model

ABSTRACTIn this paper, a combined experimental-numerical method was proposed to study the effect of adhesive thickness on mode I fracture energy of the adhesive layer, using Double Cantilever Beam (DCB) testing and Cohesive Zone Modelling (CZM). A Trapezoidal Cohesive Zone Model (TCZM) was introduced in tabular form into commercial Finite Element (FE) package to simulate the crack propagation behaviour in the adhesive layer and include the ductile characteristics of the selected adhesive. In order to overcome the difficulty in the accurate monitoring and measurement of crack length during loading, the Compliance-Based Beam Method (CBBM) was adopted to deduce the mode I strain energy release rate data. The load–displacement curve, Resistance curve (R curve), and mode I fracture energy data obtained from both experiment and simulation were analysed to validate the established FE model. It was observed that adhesive thickness has a significant influence on the ductile fracture behaviour of adhesive under mode I loading. The mode I fracture energy increases initially, and then decreases with the increase of adhesive layer thickness in the selected thickness range, while obvious transition was also observed in the perspective of micro-scale failure mechanism of the fracture surface through Scanning Electron Microscopy (SEM).

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.

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.