Bend End-notched Flexure Test Research Articles

Mode II critical stress intensity factor of solid wood obtained from the asymmetric four-point bend fracture test using groove-free and side-grooved samples

Asymmetric four-point bend fracture (AFPBF) tests and three-point bend end-notched flexure (3ENF) tests were performed on groove-free and side-grooved samples of western hemlock, and the Mode II fracture critical stress intensity factor (KIIc) was obtained. Differences in the KIIc values obtained from the AFPBF and 3ENF tests were significant. However, these differences were effectively reduced when the additional crack length Δ was introduced into the data reduction process. These results indicate that the KIIc value can be determined by considering the Δ value and the results obtained from previous Mode II fracture mechanics tests.

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.

Mode II fracture behavior of parallel strand bamboo measured by 3-point end-notched flexure tests

Parallel strand bamboo (PSB) is a new type of bio-composite. In the present study, three-point bend end-notched flexure (3ENF) tests of PSB were conducted to analyze the fracture behavior including fracture process, resistant curves, and critical energy release rate in the longitudinal (L) system. The results show that transverse-longitudinal (TL) and thickness-longitudinal (ZL) specimens had the same fracture process including the stages of fracture process zone (FPZ) development and opening crack propagation but different mode II critical energy release rate (GIIc), and they indicate that the fiber bridging had a significant influence. The fracture processes suggest the PSB specimens of which the initial crack length was 0.5 times the half span had a stable crack propagating process, and the crack propagation length was wide enough to evaluate GIIc, which was 5.02 N∙mm-1 of TL specimens and 2.71 N∙mm-1 of ZL specimens. Besides, there was no obvious influence of span/depth ratio on the fracture resistance of both ZL and TL specimens when the ratio was larger than 15.

Real-time damage monitoring in trailing edge bondlines of wind turbine blades with triboluminescent sensors

Adhesively bonded joints in wind turbine blades, particularly trailing edge joints, are prone to damage due to high-intensity stress concentrations, missing adhesive, or deficient bonds at the bonding surfaces. If not detected early, cracks or disbonds in the trailing edge might propagate rapidly resulting in catastrophic failure of the whole blade. No dedicated in situ sensor system is, as of now, available for real-time damage monitoring in the critical adhesively bonded joints. This article discusses the use of in situ triboluminescent optical fiber sensors for damage monitoring in adhesively bonded composite joints. Double cantilever beam and three-point bend end-notched flexure samples were fabricated from a thick glass fiber/vinyl ester composite and glued with a two-part methacrylate-based structural adhesive. The in situ triboluminescent optical fiber sensors were embedded into the adhesive layer. Double cantilever beam and three-point bend end-notched flexure tests were performed to determine the mode I and mode II fracture toughness of the adhesive joints, respectively. The results show that the triboluminescent emissions occur at the onset of damage when performing double cantilever beam and three-point bend end-notched flexure fracture tests on adhesively bonded composite panels of different adhesive thicknesses. The triboluminescent response increases with the fracture toughness of adhesive joints. The double cantilever beam and three-point bend end-notched flexure specimens undergo cohesive failure in the adherend thickness. Optical microscopy was utilized to obtain better insights of fracture lines. Results indicate that in situ triboluminescent optical fiber sensors can monitor damage in adhesive in real-time without generating false alarms.

Mode II Critical Stress Intensity Factor of Medium-Density Fiberboard Measured by Asymmetric Four-Point Bending Tests and Analyses of Kink Crack Formation

Using medium-density fiberboard specimens, asymmetric four-point bending tests were conducted to obtain the Mode II critical stress intensity factor for this in-plane system. Because the medium-density fiberboard is in-plane quasi-isotropic about its board plane, the crack propagates obliquely with respect to the initial crack direction under the asymmetric four-point loading condition. A finite element analysis is required to obtain the Mode II stress intensity factor. The analysis herein was conducted to take into account the kink crack formation. In addition, a three-point bend end-notched flexure test was also conducted, and the results obtained by the experiments and numerical calculations were compared. When the initial crack’s length-to-specimen’s depth ratio ranged from 0.85 to 0.95 and when the additional crack length was taken into account, the Mode II critical stress intensity factor KIIc was appropriately obtained by the asymmetric four-point bending test.

Mode I and mode II initiation fracture toughness and resistance curve of medium density fiberboard measured by double cantilever beam and three-point bend end-notched flexure tests

Using specimens of medium density fiberboard, double cantilever beam and three-point bend end-notched flexure tests were conducted to obtain the mode I and mode II initiation fracture toughness and resistance curve for in-plane and through-the-thickness systems. The mode I initiation fracture toughness was smaller than that of mode II for the in-plane crack systems, but this tendency was inverse for the through-the-thickness systems. The fracture toughness increased during the crack propagation because of the significant fiber bridgings induced between the crack surfaces, but the increase of the mode I propagation fracture toughness was moderated after the crack reached a certain length. In contrast, the mode II propagation fracture toughness continuously increased during the crack propagation.

Delamination growth mechanisms in woven glass fiber reinforced polymer composites under Mode II fatigue loading at cryogenic temperatures

The purpose of this research is to characterize the cryogenic delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates subjected to Mode II fatigue loading. Mode II fatigue delamination tests were performed at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K) using the four-point bend end-notched flexure (4ENF) test method, and the delamination growth rate data for the woven GFRP laminates were obtained. The energy release rate range was determined by the finite element method. Microscopic examinations of the specimen sections and fracture surfaces were also carried out. The present results are discussed to obtain an understanding of the fatigue delamination growth mechanisms in the woven GFRP laminates under Mode II loading at cryogenic temperatures.

OS0417 極低温における織物ガラス繊維強化ポリマーコンポジットのモードII疲労はく離進展メカニズム(先端材料システムの力学とメゾスケールモデリング,オーガナイズドセッション)

The purpose of this research is to characterize the cryogenic delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates subjected to Mode II fatigue loading. Mode II fatigue delamination tests were performed at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K) using the four-point bend end-notched flexure (4ENF) test method, and the delamination growth rate data for the woven GFRP laminates were obtained. The energy release rate range was determined by the finite element method. Microscopic examinations of the specimen sections and fracture surfaces were also carried out The present results are discussed to obtain an understanding of the fatigue delamination growth mechanisms in the woven GFRP laminates under Mode II loading at cryogenic temperatures.

Shear and crack tip deformation correction for the double cantilever beam and three-point end-notched flexure specimens for mode I and mode II fracture toughness measurement of wood

Using specimens of western hemlock with various depths, double cantilever beam and three-point bend end-notched flexure tests were conducted to obtain the mode I and mode II fracture toughness. To correct the deflection caused by shearing and crack tip deformation, four conventional data reduction methods were examined as well as the compliance combination method, which was proposed by the author. In addition to the actual fracture tests, finite element analyses were conducted and the validity of the data reduction methods were also examined. The compliance combination method was more suitable for the data reduction than the others examined here because the fracture toughness was determined simply and appropriately while correcting the deflection caused by shearing as well as the crack tip deformation.

Mode II fracture mechanics properties of wood measured by the asymmetric four-point bending test using a single-edge-notched specimen

Using a single-edge-notched specimen of spruce, an asymmetric four-point bending test was conducted to obtain the mode II fracture toughness G IIc and critical stress intensity factor K IIc, and the test method was numerically and experimentally analyzed. A three-point bend end-notched flexure test was also conducted and the results were compared with those of the asymmetric four-point bending tests. The crack length had a small influence on the load/loading-line displacement relationship in the asymmetric four-point bending test, so it was difficult to determine the value of G IIc, which requires the measurement of loading-line displacement. In contrast, the value of K IIc obtained by two tests was similar when the initial crack length ranged from 0.7 to 0.85 times the depth of the specimen. These results show that the asymmetric four-point bending test is a promising means of determining K IIc.

Influence of bending rotations on three and four-point bend end notched flexure tests

It has been experimentally observed that mode II critical energy release rate ( G IIC) values determined by four-point end notched flexure test and three-point end notched flexure test are different for the same material. At the present work correction factors related to bending rotations are introduced to explain the differences between values of G IIC obtained by three point and four point end notched flexure tests. The bending angle leads to the contact zones between specimen and supports and specimen and load rollers changing in both test configurations. The present analysis has been carried out by the classical beam theory, neglecting shear effects and assuming the hypothesis of small rotated angles. Results show that the relative differences between corrected and uncorrected values of G IIC are greater in the case of four-point end notched flexure than in the case of three-point end notched flexure test.

Influences of Friction, Geometric Nonlinearities, and Fixture Compliance on Experimentally Observed Toughnesses from Three and Four-point Bend End-notched Flexure Tests

Three and four-point bend end-notched flexure tests, comprising a number of different test geometries, are performed on two different graphite/epoxy composites, and the toughnesses are obtained by a compliance calibration method of data reduction. The coefficient of friction along the crack plane and the flexural modulus of each material are then determined experimentally and used with nonlinear finite-element analyses to simulate these same test configurations. By using the mean experimentally observed critical load, these simulations are used to obtain the materials' toughnesses by three different methods. The first uses a previously developed `direct energy balance approach,' which is assumed to produce the `true' toughness. The second is by a simulated compliance calibration procedure, which is used to obtain the perceived toughness for an infinitely stiff fixture. In the third approach, experimentally determined fixture compliances, as a function of the test geometry, specimen, and crack length, are used along with the simulated compliance calibration procedure to obtain a perceived toughness that accurately accounts for the effects of friction, geometric nonlinearities, and fixture compliance. The perceived toughnesses as obtained by these simulations are shown to accurately recreate the perceived values of toughness that are obtained from the physical tests. Moreover, the finite-element simulations indicate that the true toughness values are essentially constant for a given material, and that the three-point bend end-notched flexure test will provide perceived toughnesses that correspond quite closely to the true value, whereas the four-point bend test often will not. For these reasons, the three-point bend configuration was found to be the more preferable of the two tests.

Theoretical analysis of 4-ENF tests for mode II fracturing in wood by finite element method

In this note, the four-point bend end notched flexure tests of wood of the specimen with an I-shaped cross-section were simulated by the finite element method. It was suggested that the relation between the mode II energy release rate and crack length was appropriately obtained by the data reduction method proposed in a previous work [Yoshihara H. Mode II R-curve of wood measured by 4-ENF test. Engng Fract Mech 2004;71:2065–77].

Numerical evaluation of the effects of friction and geometric nonlinearities on the energy release rate in three- and four-point bend end-notched flexure tests

Nonlinear finite element analyses are used to examine the effects of friction and geometric nonlinearities on the energy release rate in three- and four-point bend end-notched flexure tests. Energy release rates are first determined by a recently developed direct energy balance approach. It is shown that the finite diameter loading rollers that are typically used in practical test set-ups cause both tests to be inherently nonlinear. The effect of these nonlinearities on the energy release rate is shown to be larger in the four point than the three point test and to increase with increasing roller diameter, increasing coefficient of friction along the crack plane, and decreasing supporting span length. For the four point test, the effect of these nonlinearities is also shown to increase with increasing ratio of inner to outer span length. Next, energy release rates at the onset of crack advance are determined by a simulated compliance calibration technique. This “perceived toughness” is compared with predictions of the “true toughness” given by the direct energy balance approach at the same load. It is shown that perceived toughnesses from this simulated compliance calibration procedure are larger than previously reported results that were obtained in a similar fashion using linear theory. In addition, the perceived toughness is shown to strongly depend upon the range used for fitting the load versus deflection data to obtain compliance. These findings are used to make some general recommendations regarding use of the two test methods and their associated data reduction techniques.

Influence of Crack Length on the Measurement of Mode II Initiation Fracture Toughness of Wood by Three-Point Bend End-Notched Flexure (3ENF) Test

Influence of Crack Length on the Measurement of Mode II Initiation Fracture Toughness of Wood by Three-Point Bend End-Notched Flexure (3ENF) Test

Examination of the 4-ENF test for measuring the mode III R-curve of wood

The four-point bend end-notched flexure (4-ENF) test, which was originally developed for measuring the mode II R-curve, is thought to be applicable for measuring the mode III R-curve. In this study, a 4-ENF fracture test of spruce was conducted for obtaining the mode III R-curve, and the test method was numerically and experimentally analyzed. In the numerical analysis, three-dimensional finite element calculations were conducted to determine the distribution of the strain energy release rate along the delamination front by the virtual crack closure technique (VCCT). In the experimental analysis, the mode III R-curve was examined by the modified beam theory and compliance calibration methods of data reduction, which have been conventionally used for analyzing the mode I or mode II R-curve. In addition to these conventional data reduction methods, the strain at each loading point was measured, as was the loading-line displacement and critical load for crack propagation, and the R-curve was obtained by the combination of loading-line compliance, load–longitudinal strain compliance, and critical load for crack propagation, which is named the “compliance combination method”. The finite element analyses suggested that the pure mode III fracture state existed in the mid-section of the specimen in spite of the existence of a small mode II component at the free edges of the delamination front, and the mode III strain energy release rate component calculated by the VCCT coincided well with those obtained by the data reduction methods examined here. The actual R-curve obtained by the compliance combination method coincided well with those by the modified beam theory and compliance calibration methods when the strain was appropriately measured. From these results, therefore, the 4-ENF fracture test is a promising means for obtaining the mode III R-curve of wood.

A Direct Energy Balance Approach for Determining Energy Release Rates in Three and Four Point Bend End Notched Flexure Tests

A direct energy balance approach has been developed and used to determine energy release rates in three and four point bend end notched flexure tests. This study was performed in the context of the larger goal of understanding the wide variation in mode II toughnesses that have been obtained by the two tests when used on the same material. The primary motivation for developing the direct energy balance approach was to fully account for the effects of friction, large deformations, and other geometric nonlinearities that occur during these tests. The direct energy balance approach simulates crack advance as it occurs in physical testing. Most significantly, this approach accounts for frictional dissipation that occurs during crack advance, which is an effect that has been neglected in previous analyses of these tests. The direct energy balance approach is used to show that, for most cases of practical interest, the virtual crack closure technique is quite accurate, and predictions by this latter approach are only in error when moderately large geometric nonlinearities occur prior to crack advance. Based on these results, a “cut-off value,” expressed in terms of the maximum slope in the specimen as predicted by classical beam theory, is suggested for the upper limit of applicability of the virtual crack closure technique.

Mode II Delamination of a Unidirectional Carbon Fiber/Epoxy Composite in Four-Point Bend End-Notched Flexure Tests

Results from an experimental study on the delamination of a unidirectional carbon fiber/epoxy composite by using the four-point bend end-notched flexure (4ENF) test are presented. It was found that the compliance data obtained in load-unload-reload and continuous loading tests were very similar. The R-curves for specimens of different thickness were also found experimentally. These curves showed an appreciable toughening with crack advance, which can be explained by the presence of fiber bridging. The finite-element method with cohesive elements allowing us to model the progressive delamination was used to analyze the 4ENF test.

Effects of Friction, Geometry, and Fixture Compliance on the Perceived Toughness from Three-and Four-Point Bend End-Notched Flexure Tests

Linear and nonlinear finite element analyses are used to examine the effects of friction, test geometry, and fixture compliance on the perceived toughness as obtained from threeand four-point bend end-notched flexure tests. To this end, a newly developed ‘direct energy balance approach’ is used to obtain the ‘true’ energy release rate for any given specimen, test geometry, and coefficient of friction. Finite element analyses are also used in a simulated compliance calibration technique, which is combined with experimental results from fixture compliance tests to obtain a perceived toughness, i.e., the value that would be obtained by experiment. By varying the different parameters, the individual and combined effects of friction, test geometry, and fixture compliance on the ratio of the perceived to true toughness is obtained. The approach is applied to two graphite/epoxy materials for which toughnesses by the three(3ENF) and four-point bend end-notched flexure (4ENF) tests are obtained experimentally for a range of geometries. These experiments produced larger perceived mode II toughnesses, GIIc, by the 4ENF than the 3ENF test, and GIIc values from the 4ENF test were observed to decrease with increasing outer span length. The finite element simulations were shown to accurately recreate the perceived values of GIIc obtained from these tests. Moreover, the finite element simulations indicate that the true toughness values are essentially constant for a given material. These findings are used to make some general recommendations for choosing 3ENF and 4ENF specimen and test geometries, as well as to discuss the relative advantages and disadvantages of the 3ENF and 4ENF test methods.

Effect of Crack Length Measurement Technique and Data Reduction Procedures on the Perceived Toughness from Four-Point Bend End-Notched Flexure Tests

Results are presented from a study to determine the most appropriate crack length measurement and data reduction techniques for use with the four-point bend end-notched flexure test. Using two different graphite/epoxy materials, the variability in crack length measurements due to different observers and/or measurement techniques, including visual observation and ultrasonic inspection, and their effects on the perceived values of the mode II delamination toughness, GIIc, were evaluated for two different data reduction techniques. It was found that a technique using pretest compliance calibrations is the only approach that will produce accurate non-precracked and precracked values of GIIc regardless of the material being tested or the nature of crack advance. For those materials where GIIc values, as obtained by the more common approach that utilizes compliance values obtained during the test, agree with those obtained by compliance calibration, the results from the more common approach may be applied to obtain resistance curve toughnesses.