Compliance Calibration Method Research Articles

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.

Stress-driven nonlocal integral model with discontinuity for size-dependent buckling and bending of cracked nanobeams using Laplace transform

Due to the frequent occurrence of cracks as structures age, examining the size-dependent responses of cracked micro/nanobeams is critical for safely designing and optimizing high-tech devices such as those used in MEMS/NEMS. With this understanding, we present the size-dependent bending and buckling studies of cracked nanobeams with different boundary edges adopting the well-posed stress-driven nonlocal integral model with discontinuity. Since the presence of a crack, the beam is divided into two segments connected by a rotary spring and a linear spring, whose elastic coefficients can be determined through compliance calibration methods. We propose an efficient method to solve the original integral model directly by converting the integral form of the nonlocal constitutive equation into a general equation through the Laplace transform technique, equipped with three extra constraint conditions. Subsequently, the governing equations of two beam segments are solved by considering the standard boundary and compatibility conditions as well as the extra constraint conditions, while the bending deformation and buckling loads of various bounded nanobeams are presented analytically in the presence of a crack. After verifying the derived formulation, the influence of crack length and location as well as nonlocality on the beam deflections and buckling loads of the first several modes are investigated in detail. Communicated by Rossana Dimitri.

Application of the effective crack length method to model delamination of unidirectional composite laminates under Mode II shear loadings

Damage modelling of composite material delamination is an intense field of research to understand the complex composite failure behaviour and predict the residual strength of damaged structures. One of the widely employed methods to simulate delamination is the cohesive zone modelling (CZM) technique. To successfully utilize this approach, accurate characterisation of the interlaminar fracture toughness is crucial, while the composite delamination is dominated by Mode I and Mode II fracture in most cases. Numerous studies have been conducted on composite materials delamination under Mode I loadings using double cantilever beam (DCB) tests. Accordingly, the ASTM standard testing procedure and data reduction scheme to obtain Mode I fracture toughness (GIc) have been well established and widely accepted. However, it is still challenging to characterize the composite Mode II delamination resistance due to the susceptibility problems inherent to the existing testing methods and the lack of robust data reduction schemes to accurately identify the initial crack tip and monitor the crack growth. This study attempts to find a reliable solution to obtain the Mode II fracture toughness (GIIC) and an effective modelling strategy to simulate Mode II delamination in laminated composites. First, we reviewed the existing testing set-ups and surveyed the data reduction schemes conventionally used to obtain GIIC. The advantages and drawbacks of the three most used test methods, and particularly the standard end-notched flexure (ENF) test (ASTM D7905/D7905M) and the end-loaded split (ELS) test (ISO 15114:2014) were examined. Second, the advantages of the effective-crack-length-based data reduction schemes against the classical data reduction schemes were empirically studied with the ENF tests conducted on G40-800/5276-1 carbon-fibre reinforced composite laminate coupons. Although many studies have studied the accuracy of the effective-crack-length-based approaches from different aspects, there is a lack of direct comparison between the numerical results and experimental data. Our modelling study demonstrates that among the five data reduction schemes that are examined, the compliance calibration method (CCM) required by ASTM D7905 yields the most conservative GIIC values, which is suitable for establishing material property for a design purpose. The compliance-based beam method (CBBM) may generate the least conservative GIIC values, which are deemed to be the most accurate ones for modelling and simulation validation purposes. Finite element (FE) modelling of the ENF tests using the CZM technique was carried out and comprehensive parametric studies were conducted to achieve an efficient and robust strategy for delamination modelling of composite laminates under Mode II shear loadings.

Fracture mechanical stability of DCB and 4ENF tests complemented with linear springs

In this work the stability of the DCB and 4ENF fracture specimens is analyzed using some beam theories and the compliance calibration method. The main goal is that the systems are complemented with linear springs and it is investigated how the springs influence the stability of crack propagation from the theoretical standpoint. Large number of experiments were carried out including crack initiation tests providing the experimental load displacement responses, the compliance datasets and the qualitative observation of crack initiation. Apart from the analytical method the compliance calibration method was employed to evaluate the experimental data and to determine the fit curves of the compliance datasets, the R-curves and finally the bifurcation curves or in other words the critical displacement and crack length relationships including several additional spring stiffnesses for both test configurations. The results indicate that - as expected - the smaller the spring stiffness is the worst the stability of the DCB specimen will be, leading to the possibility of destabilization. On the contrary the analysis and experiments confirm that the 4ENF test cannot be destabilized independently of the stiffness of additional springs.

Experimental study on Mode Ⅰ fracture characteristics of laminated flattened-bamboo lumber combined with VIC-3D system

According to ASTM E399, Mode I fracture tests were conducted on compact tension (CT) specimens of laminated flattened-bamboo lumber (LFBL) loaded parallel to grain, in combination with the optical measurement system VIC-3D (video image correlate, 3D) to observe the evolution of strains and crack propagation. In the test results, the average fracture toughness of the specimen gradually decreased as the ratio of initial crack length to specimen width increased, and after the ratio reached 0.45, the fracture toughness value tended to be stable; the fracture toughness tests could only be considered valid if the thickness of the specimen was greater than or equal to 25 mm. Compared to large-thickness specimens, small-thickness specimens had a lower degree of brittleness; microscopic failure modes were classified as ground-tissue cracking and fiber damage. During the test, the tension-strain field was always concentrated at the tip of the extending crack. When the cracks extended to equal length, the specimens were in the same state, indicating that crack extension followed a self-consistent pattern. Furthermore, the compliance calibration method was used to develop the equation for the function of crack length-compliance.

Initiation and propagation fracture toughness of injection-moulded short fibre composites under different environmental conditions

Injection-moulded short-fibre composites combine lightweight and manufacturability; however, their fracture behaviour and how it is affected by the microstructure and environmental conditions are yet to be fully characterised. The initiation and propagation fracture toughnesses of injection-moulded short glass-fibre reinforced polyamide 6.6 composites were characterised through compact tension testing under the combined effect of fibre orientation, moisture level and temperature. Full R-curves were calculated using either an FE-based compliance calibration method, or the J-integral method based on full-field measurements from Digital Image Correlation; both data reduction methods provided consistent propagation values for the fracture toughness, although only the J-integral method can characterise the initiation toughness and the shape of R-curves reliably. This work revealed that the material became tougher with increasing fibre orientation along the loading direction, increasing moisture content, and/or increasing temperature; the corresponding increase in toughness was related to changes in failure and toughening mechanisms, identified through fractography. FE simulations of the compact tension tests have demonstrated the need to consider both initiation and propagation values of fracture toughness to accurately predict the response of notched specimens. The thorough characterisation of fracture toughness presented in this paper can contribute to design safer and more efficient damage-tolerant IM-SFRP components.

Compliance Methods For Bonded Joints: Part I - Investigation Of The Standardized Methods To Obtain The Strain Energy Release Rate For Mode I

ABSTRACT The double cantilever beam (DCB) is the most acceptable geometry to obtain the critical strain energy release rate (GIc ) of adhesive joints under Mode I. However, there are still some areas of uncertainty in the standardized compliance methods recommended by the ISO and ASTM standards in terms of accuracy in estimating the compliance of a bonded double cantilever beam and, consequently, GIc . In this work, an investigation of the standardized compliance methods for fracture characterization of bonded joints under Mode I is conducted, employing a finite element model to obtain the compliance of a double cantilever beam, considering different crack lengths. The compliance values determined from the finite element model are compared with those recommended by the standards. It is concluded that the standardized compliance methods are very sensitive to issues derived from crack length measurements. The crack length correction methodology proposed by the corrected beam theory is inadequate, which can lead to a wrong interpretation of the structure’s behavior and the structural integrity assessment. The best approach to obtain the compliance of a double cantilever beam in respect of crack length is to use a compliance calibration method, fitting an expression for the experimental curve.

Experimental and Numerical Research of Delamination Process in CFRP Laminates with Bending-Twisting Elastic Couplings.

This paper aims at experimental and numerical research of delamination process in carbon/epoxy composite laminates with different fiber orientation angles in stacking sequence exhibiting the bending-twisting elastic couplings. Experimental specimens were subjected to the double cantilever beam (DCB) tests according to the ASTM D5528 regulations. Values of the mode I strain energy release rates were calculated by using three different data reduction schemes: the modified beam theory, the compliance calibration method and the modified compliance calibration. Determination of delamination initiation point was conducted in twofold way: by visual observation of crack tip using high resolution camera and by utilization of the acoustic emission technique. Numerical analyss were prepared in Abaqus/CAE Software environment by using the virtual crack closure technique (VCCT). The numerical beam model consisted of SC8R continuum shell elements. Obtained outcomes revealed that extensive fiber bridging phenomenon occurring during delamination process pronouncedly affected propagation values of strain energy release rate (GIprop) and numerically obtained load-displacement curves. Nevertheless, in initial stage of delamination, results obtained by using the VCCT were in agreement with experimental data. The greatest value of the mode I fracture toughness equal 0.56 N/mm was obtained for the BT45 laminate.

Mode I tensile fracture behavior of adhesively-bonded metal–metal, metal–CFRP, and CFRP–CFRP bi-material combinations analyzed by size effect method

Understanding the adhesive and interfacial fracture is important for developing better adhesive performance in bi-material joints, i.e. adhesive joint between dissimilar materials. However, to characterize the fracturing behavior of various adhesively-bonded materials, it was shown in this work that the Mode I fracture energies estimated from conventional methods (e.g., work-of-fracture, (modified) compliance calibration method, (modified) beam theory, etc.) can be strongly affected by adherend thickness, adhesive bond length, and adherend material type. Consequently, the proper understanding of fracturing in bi-material joints has been hindered since the estimated fracture energies can exhibit unreasonable difference among various material combinations depending on the method of fracture energy calculation. This has led to confusion in the literature due to the unfair comparison of these non-objective results estimated by leveraging conventional methods on the specimens with different geometries or dissimilar adherend materials.This work introduced the size effect method to adhesively-bonded joints and compared the results with conventional methods of calculating the Mode I fracture energies of metal–metal, metal–CFRP, and CFRP–CFRP material combinations via Double Cantilever Beam (DCB) tests. The results showed that the estimated fracture energies obtained using the size effect method were not dependent on the specimen geometries, whereas conventional methods were strongly dependent on specimen geometry for most material combinations. The size effect method allowed objective comparison particularly on the interfacial fracturing between metal/adhesive and CFRP/adhesive combinations. The difference was further explained by and correlated with the damage morphology on the material surface after failure, which was quantified by three-dimensional profilometer.

A mesoscale in situ method for assessing fracture toughness of intra-yarn and interface in 3D woven composites

Accurate acquisition of mesoscale in situ properties of 3D woven composites (3DWC) is necessary for characterizing damage behavior and strength. However, it is difficult and very limited studies have been conducted. In this paper, a mesoscale in situ (MIS) method is proposed to assess fracture toughness of intra-yarn and interface in 3DWC. Two types of specimens, interface specimens and intra-yarn specimens, are designed and cut on 3DWC plates, so that they contain typical in situ interface and yarn structures. The thickness, cutting surface, cutting position and notch tip position of both types of specimens, are particularly designed to ensure that the cracks occur in the area of interest. Compact tension experiments are performed to obtain fracture toughness. For intra-yarn specimens, the crack grows inside the weft yarn as expected. The results calculated by the area method and the compliance calibration method show a consistent trend. For interface specimens, the crack passes through the matrix, weft yarn and interface. A modified area method is proposed to remove the energy consumed by the crack segments passing through the matrix and weft yarn. Finally, the possible influence of matrix plasticity is discussed.

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.

Steel plate cold commercial - carbon fiber reinforced plastics hybrid laminates for automotive applications: curing perspective with thermal residual effect

The curing effect on hybrid materials consisting of steel plate cold commercial - carbon fiber reinforced plastics (SPCC-CFRP) hybrid laminates that have potential applications in automobile structures were evaluated in the present study. Specimens with stacking sequences consists of one SPCC plate and six layers of CFRP ([SPCC/[0] 6 ]) under a double cantilever beam (DCB) test were investigated experimentally and analytically. The characterization was performed using a differential scanning calorimetry (DSC) and fourier transform infrared (FTIR) analysis. The specimens were exposed to two different curing times to observe the different strain energy release rates. The results show specimens with a curing time of three hours have stability in strain energy release rate value compared to one-hour curing time. However, in the early stage of fracture, the fracture toughness of 1-hour has a higher value than 3-hour. The critical crack length in this study occurred between 40 and 70 mm. Furthermore, the average strain energy release rate value of G I in 1-hour and 3-hour curing time from the crack length between 98 and 104 mm was 116.6687 J/m 2 based on compliance calibration (CC) method, 113.3966 J/m 2 based on correction factor, and 116.3831 J/m 2 from considering temperature effect theory compared to 1-hour curing time with 81.3232; 79.1026; and 81.0376 J/m 2 , respectively. Based on this study, the fracture toughness and energy release rate of hybrid laminate significantly affected by the curing conditions during the manufacturing process.

Effect of material nonlinearity on the toughness evaluation in quasi-static mode II interlaminar fracture toughness tests of composite laminates

In mode II interlaminar fracture toughness tests of composite laminates, the fracture toughness evaluated based on linear elastic fracture mechanics deviates from the true toughness due to the material nonlinearity of the matrix. In this study, an elastoplastic finite-element analysis was performed on a new quasi-static mode II interlaminar fracture toughness test, i.e., the doubly end-notched tension (DENT) test, to investigate the difference between the perceived energy release rate and the J-integral. The effect of material nonlinearity was compared with other quasi-static mode II interlaminar fracture toughness tests: three- and four-point bend end-notched flexure tests. Analysis of the DENT showed that for a given J-integral loading, the size of the plastic zone at the delamination crack tip was the same regardless of the crack length. The difference between the perceived energy release rate and J-integral in the DENT test with respect to the plastic zone size was independent of the crack length, and was smaller compared with that of flexure-type tests. Furthermore, the compliance calibration method was applied to the elastoplastic analysis results of the DENT test to reduce the evaluation difference of the energy release rate.

Challenges in the fatigue crack growth characterization of metal/composite joints: A compliance-based investigation of a Ti/CFRP joint

The challenges and issues that arise in the fatigue crack growth characterization of dissimilar joints due to multiple crack formation, suitable compliance and strain energy release rate definitions are thoroughly investigated in the present work. The framework is set by the need to characterize the fatigue behavior of a new Ti/CFRP adhesive joint. A new method for measuring the experimental compliance is proposed and critically compared to the dynamic compliance concept. The compliance calibration method while taking into account secondary cracking is addressed. The fatigue crack growth curves are extracted and discussed under the prism of the aforementioned challenges.

Parametric and non-parametric tests for the evaluation of interlaminar fracture toughness of polymer composites

This study is based on the statistical analysis of interlaminar fracture toughness of various laminated polymer composites used in aerospace applications through parametric and non-parametric tests. Tukey’s, Dunkan’s, two-sample t-test, and Kolmogorov–Smirnov tests are used to analyze tensile mode interlaminar fracture toughness of various fiber-reinforced polymer composites obtained by beam theory, modified beam theory, and modified compliance calibration method. Among the studied composite samples, modified compliance calibration method provided the highest average interlaminar fracture toughness, whereas the modified beam theory showed the lowest one. Room temperature cured carbon fiber-reinforced composite samples exhibited higher interlaminar fracture toughness than the autoclave cured samples. Two-sample t-test show that all methods are found coherent with each other in terms of being significantly different. On the contrary, Kolmogorov–Smirnov test revealed no significant difference. Besides, Tukey’s and Duncan’s tests exhibited almost the same results in regard to significant differences except those obtained by the modified compliance calibration method. Two-sample t-test method should have to be performed in order to observe significant relations rather than Kolmogorov–Smirnov test, since the results of Tukey’s and Duncan’s tests are only consistent with each other for the beam theory and modified beam theory method.

Effect of short multi-walled carbon nanotubes on the mode I fracture toughness of woven carbon fiber reinforced polymer composites

The present study experimentally and theoretically investigated the effects of short multi-walled carbon nanotubes on the mode I fracture toughness of woven CFRP composites. COOH-functionalized short multi-walled carbon nanotubes (S-MWCNT-COOH) with three different amounts of 0.5, 1, and 1.5 wt% (by weight) of epoxy resin/hardener mixture were used. In total, 32 test specimens were fabricated and tested. The mode I fracture toughness was performed under double cantilever beam (DCB) test, and was evaluated using three different data reduction methods: modified beam theory method (MBT), compliance calibration method (CC), and modified compliance calibration method (MCC). The test results with the addition of 0.5, 1, and 1.5 wt% S-MWCNT-COOH showed 1.6, 31.0, and 31.7% increase on average, respectively, of the mode I fracture toughness of the CFRP composites. The mode I fracture toughness evaluated using the three data reduction methods of MBT, CC, and MCC was almost the same. Furthermore, an analytical model was constructed using the trilinear curves based on bridging law describing the pullout force–displacement response of short CNTs from an epoxy matrix, and the predicted results showed good agreement with the experimental results. Finally, idealized load–displacement curves of the CFRP composites were proposed based on the linear elastic fracture mechanics (LEFM) using initiation fracture toughness, and the predictions showed good agreement with the experimental curves.

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.

Delamination migration in CFRP laminates under mode I loading

This paper focuses on the effect of interfacial fibre orientation and interleaved veil on the delamination migration of carbon fibre reinforced polymer laminates under Mode I loading. Double cantilever beam specimens with midplane interfacial fibre orientations of 0/0, 90/90, 0/90, 0/45 and 90/45 were tested under two conditions: one with interleaved thermoplastic polyphenylene sulfide veil at the midplane and one without. Results show that, except for the 0/0 configuration, all other orientations exhibit varying levels of migration associated with the interfacial fibre orientation and veil interleaving. The apparent fracture toughness determined with the modified compliance calibration method is closely related to the delamination migration and hence a structural energy dissipation measure dependent on interfacial fibre orientation and the interleaved veil. Distributions of the fibre and matrix materials around the delamination front are found to be closely related to the delamination migration behaviour along its path. The experimental observation and rationalisation presented in this paper provide further knowledge regarding delamination migration and its correlation to the apparent fracture toughness, which is of direct relevance to the damage tolerance design of laminated composite components.

An experimental study on the influence of intralaminar damage on interlaminar delamination properties of laminated composites

Coupling between intralaminar and interlaminar damage plays a significant role in accurately predicting delamination and final failure. However, insufficient experimental data are available for models of this phenomenon. In this paper, we proposed a two-step experiment on cross-ply laminates to quantitatively study the influence of in-plane strain on the interlaminar fracture toughness. First, we performed a tensile test on the [02/902]s cross-ply laminates to introduce various extents of intralaminar damage. Next, we bonded a backing adherend of [06] plies to the cross-ply, so we could probe the delamination properties through a subsequent double cantilever beam (DCB) test. We identified the effective fracture toughness Gc,eff by the compliance calibration method. We found that intralaminar damage promotes fiber bridging in the transverse direction, which finally influence the out-of-plane properties significantly.

Experimental Investigation of Mode I Interlaminar Fracture Toughness in T300/914 Composite

Abstract An aerospace structural material T300/914 has been studied to understand the Mode I interlaminar fracture toughness. For experimental analysis a Double Cantilever Beam (DCB) test is conducted on the laminate to estimate the Mode I interlaminar fracture toughness of the sample. A 48-layer laminate was prepared by hand layup process and an insert included at the mid plane to produce the artificial initial crack required for the test. All the tests are conducted in accordance to the ASTM standards. Pulse-Echo test results and C-Scan images of the laminate were analyzed to find the defects in the laminate. The data from DCB test were analyzed by Modified Beam theory, Compliance calibration method and modified compliance calibration methods to find the interlaminar fracture toughness. A crack length correction method is implemented for data reduction. Numerical analysis of the data derives results in accordance with the experimental analysis.