End-notched Flexure Specimens Research Articles

Characterization of Fiber Bridging in Mode II Fracture Growth of Laminated Composite Materials

The present study involves an experimental and analytical investigation of the Mode II delamination propagation and the fibre bridging effects incorporated in the Fracture Process Zone (FPZ). End Notch Flexure (ENF) specimens from a unidirectional glass/epoxy composite material have been fabricated and tested. In order to construct the fracture resistance curve (R-curve) of the ENF tests, three different data reduction schemes have been utilized. The fibre bridging effects in the FPZ have been addressed with the use of traction-separation laws, as extracted from the corresponding calculated R-curves. These laws can be used to describe the constitutive relationship in interface finite elements, for the numerical modelling of delamination growth in laminated composite structures.

Nonlinear interface shear fracture of end notched flexure specimens

The nonlinear analytical solutions of an end notched flexure adhesive joint or fracture test specimen with identical or dissimilar adherends are investigated. In the current study, a cohesive zone model (with arbitrary nonlinear cohesive laws) based analytical solution is obtained for the interface shear fracture of an end notched flexure (ENF) specimen with sufficiently long bond length. It is found that the scatter and inconsistency in calculating Mode II toughness may be significantly reduced by this model. The present work indicates that the Mode II toughness G IIc under pure shear cracking condition is indeed very weakly dependent on the initial crack length. And this conclusion is well supported by the experimental results found in the literature. The parametric studies show that the interface shear strength is the most dominant parameter on the critical load. It is also interesting to note that with very short initial crack length and identical interface shear strength, higher Mode II toughness indeed cannot increase the critical load. Unlike the high insensitivity of critical load to the detailed shape of the cohesive law for Mode I peel fracture, the shape of the cohesive law becomes relatively important for the critical load of joints under pure Mode II fracture conditions, especially for joints with short initial crack length. The current study may help researchers deepen the understanding of interface shear fracture and clarify some previous concepts on this fracture mode.

Influence of temperature and strain rate on cohesive properties of a structural epoxy adhesive

Effects of temperature and strain rate on the cohesive relation for an engineering epoxy adhesive are studied experimentally. Two parameters of the cohesive laws are given special attention: the fracture energy and the peak stress. Temperature experiments are performed in peel mode using the double cantilever beam specimen. The temperature varies from −40 to + 80°C. The temperature experiments show monotonically decreasing peak stress with increasing temperature from about 50 MPa at −40°C to about 10 MPa at + 80°C. The fracture energy is shown to be relatively insensitive to the variation in temperature. Strain rate experiments are performed in peel mode using the double cantilever beam specimen and in shear mode, using the end notch flexure specimen. The strain rates vary; for peel loading from about 10−4 to 10 s−1 and for shear loading from 10−3 to 1 s−1. In the peel mode, the fracture energy increases slightly with increasing strain rate; in shear mode, the fracture energy decreases. The peak stresses in the peel and shear mode both increase with increasing strain rate. In peel mode, only minor effects of plasticity are expected while in shear mode, the adhesive experiences large dissipation through plasticity. Rate dependent plasticity, may explain the differences in influence of strain rate on fracture energy between the peel mode and the shear mode.

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.

The strain energy release rates in adhesively bonded balanced and unbalanced specimens and lap joints

An analytical model is developed to determine the strain energy release rate in adhesive joints of various configurations such as the double-cantilever beam and single-lap joints. The model is based on asymptotic analysis of adhesive layer stresses and Irwin’s crack closure integral. Closed-form solutions are presented for balanced and unbalanced joints under mode I, II and mixed-mode I/II that take into account the influence of the shear force on the adhesive stresses, and its influence on the strain energy release rate. The accuracy of the model is tested against the classical beam theory expressions for double-cantilever beam and end-notch flexure specimens. In fact, classical beam theory’s expressions are found to be the lower bound of the proposed model solutions, and the two methods converge as the adhesive layer thickness decreases. Analysis of single-lap joints reveals the influence of edge shear forces on the total strain energy release rate, and more importantly on the ratio between modes I and II. Results from the proposed analytical model are in good agreement with finite element results and with analytical models found in the literature.

Mode II Fracture Characterization of <i>Pinus Pinaster</i> Wood

This paper describes experimental and numerical studies on the application of the End Notched Flexure (ENF) and End Loaded Split (ELS) tests to mode II wood fracture characterization. In this context, ENF and ELS specimens were used to determine GIIc of a clear Pinus pinaster wood in the RL system, which is the most relevant for structural design. In mode II fracture tests the crack faces are in contact, thus hindering a rigorous visualization of the crack tip. This makes classic methodologies based on crack length measurement during experimental tests inadequate, since they induce significant errors on the mode II fracture properties. To overcome this experimental problem a Compliance Based Beam Method (CBBM) is used. This new data reduction scheme does not require crack length monitoring and includes the effect of the Fracture Process Zone (FPZ) ahead of crack tip. Furthermore, the clamped cross-section rotation of the ELS specimen is also taken into account. In the present work a numerical analysis considering a cohesive damage model was performed with a cohesive damage model in order to validate the application of the CBBM to the experimental results. The results confirmed the adequacy of the CBBM and the applicability of the ENF and ELS tests for mode II wood fracture characterization.

Comparison of failure mechanisms between rubber-modified and unmodified epoxy adhesives under mode II loading condition

The effect of rubber modification on fracture toughness of adhesive joints under mode II loading condition was investigated in comparison with that under mode I loading, wherein the two adhesives rubber-modified and unmodified were used. To evaluate the fracture toughness on the basis of R-curve characteristics under mode II loading condition, four-point bend tests had been conducted for the adhesively bonded end-notched flexure (ENF) specimens. Thus obtained R-curves revealed the following trend: its behavior did not appear for the unmodified adhesive, whereas the rubber-modified adhesive exhibited a typical behavior. In the initial stage of crack propagation, GIIC of the rubber-modified adhesive is lower than that of the unmodified adhesive, but becomes greater in the range of Δa > 25 mm. Nevertheless, the significant improvement of the fracture toughness with the rubber modification under mode I loading condition was not observed under mode II loading. Moreover, FEM analysis was made to elucidate the relation between the above fracture behavior and stress distributions near the crack tip. The results gave the reasonable relationship between evolution of plastic zone and the area with high void-fraction as well as the R-curves behavior. In addition, macroscopic and SEM observations for the fracture surfaces were also conducted.

Analysis of composite ENF specimen using higher order beam theories

Mathematical modelling, for the stress analysis of symmetric composite end notch flexure (ENF) specimen, has been presented using classical beam theory, first, second, and third order shear deformation beam theories to determine the strain energy release rate (SERR) for symmetric composites under mode II interlaminar fracture. In the present formulation, appropriate matching conditions have been applied at the crack tip and these matching conditions at the crack tip have been derived by enforcing the displacement continuity at the crack tip in conjunction with the variational equation. Compliance method has been used to calculate the SERR. Beam models under plane stress and plane strain conditions agree with each other with good performance to analyze the unidirectional and cross-ply composite ENF specimens, whereas for multidirectional composite ENF specimen, only the beam model under plane strain condition appears to be applicable with moderate performance. Third order shear deformation beam model of ENF specimen has been found to be better than other beam models in determining the SERR for unidirectional, cross-ply and multidirectional composites under mode II interlaminar fracture.

The Relation of the Interlaminar Fracture Toughness and the Acoustic Emission (Ae) under the Enf Test

Recently, composite materials are used in many fields because their properties are high strength, high stiffness, and they have light weight, good corrosion resistance and good thermal conductivity. However, composite materials have relatively a lot of problems, especially delamination, compared with common materials such as a steel and aluminum, etc. Therefore, having the interlaminar fracture toughness for a laminate composite is important. In this study, the end notched flexure (ENF) specimens are employed in order to evaluate modeⅡ interlaminar fracture toughness for CFRP laminate composites. Three kinds of a/L ratio were applied to these specimens under the different pressure level. Also, we discuss the relation of crack growth and the interlaminar fracture toughness in terms of AE characteristics using ENF test.

Correction method for evaluation of interfacial fracture toughness of DCB, ENF and MMB specimens with residual thermal stresses

The energy release rates associated with crack growth in multilayered double cantilever beam (DCB), three-point end notched flexure (ENF), and mixed-mode bending (MMB) specimens, including the effects of residual thermal stresses, are derived as special cases of Nairn’s formulation [Nairn JA. On the calculation of energy release rates for cracked laminates with residual stresses. Int J Fract 2006;139:267–93]. The difference between the true toughness and apparent toughness attributable to the consequence of ignoring residual stresses can be calculated for a given specimen geometry and mechanical properties based on classical lamination theory. The true fracture toughness is obtainable using the apparent fracture toughness and the present correction method. Numerical examples of DCB, ENF, and MMB tests are presented, and the calculated difference in the energy release rates based on the present correction method is compared to those obtained using FEM to verify the correction method.

A New ENF Test Specimen for the Mode II Delamination Toughness Testing of Stitched Woven CFRP Laminates

This paper presents an experimental and numerical investigation on the effects of stitching distribution on the interlaminar fracture toughness of carbon fiber reinforced polymers (CFRPs) using an end notch flexure (ENF) specimen. To avoid premature failure in bending, reinforcing tabs were bonded to either side of the ENF specimens to create a tabbed ENF (TENF) specimen. The effect of stitch distribution on mode II delamination toughness is investigated by considering several stitch distribution patterns. The experimental results indicate that the mode II delamination toughness of stitched TENF specimens can be effectively measured and that stitch distribution does not play a significant role in improving the steady-state mode II delamination toughness of stitched CFRPs. Numerical results are also obtained using both MSC/NASTRAN and an in-house software for the tested specimens. A reasonable correlation exists between the numerical and experimental results.

Application of prestressed transparent composite beams in fracture mechanics

This work presents the mixed-mode I/II/III version of the prestressed end-notched flexure system for the general delamination characterization of composite materials. The novel fracture mechanical configuration combines the traditional mode-I double-cantilever beam and the mode-II end-notched flexure specimens with the mode-III modified split-cantilever beam. First, a steel roller with a given diameter - which should not exceed the critical crack opening - is inserted to the delamination front, this fixes the mode-I part of the total energy release rate. Second, the prestressed specimen is put into the special rig of the MSCB specimen, and with the help of a prestressing screw the mode-III part of the total energy release rate is also fixed. Third, the prestressed specimen is put into a simple three-point bending setup and the mode-II part of the total energy release rate is increased up to fracture initiation. Using this method, i.e. varying the crack opening displacement by the steel roller and the crack te aring displacement by the MSCB rig the fracture surface in the GI-GII-GIII space can be obtained. To demonstrate the applicability and limitations of the novel system experiments on glass-fiber reinforced polyester specimens were performed including separated mode-I, mode-II, mode-III, mixed-mode I/II, II/III, I/III and I/II/III fracture tests. To reduce the measured data a previously validated improved beam theory scheme is applied. Finally, the surface of the fracture criterion is constructed by the generalization of the traditional criterion by Williams.

Monitoring mode II fracture behaviour of composite laminates using embedded fiber-optic sensors

Utilization of embedded Fiber Bragg Grating (FBG) sensors for monitoring mode II fracture behaviour of composite laminate beams containing different delaminations along the thickness-wise direction, by virtue of End-Notch Flexure (ENF) tests, is presented. Non-uniform strain distribution due to the stress concentration at the delamination tip was examined by the way of observing the reflection spectrum from the FBG sensor. The stress concentration in ENF specimens, which are subjected to various applied loads, was analyzed in terms of the shift, shape, bandwidth and intensity of the reflection spectrum. Relationships between the load–displacement graphs and the corresponding reflection spectra under ENF tests were established. In addition, the feasibility and reliability of using the embedded FBG sensors for mode II fracture behaviour monitoring in the composite laminates is discussed.

Application of the effective crack method to mode I and mode II interlaminar fracture of carbon/epoxy unidirectional laminates

This paper describes an experimental study involving double cantilever beam (DCB), end-notched flexure (ENF) and four-point end-notched flexure (4ENF) tests on carbon/epoxy unidirectional specimens. The main purpose was to evaluate the so-called effective crack method (ECM), which avoids operator crack position monitoring. Extensive fibre bridging in DCB tests made the ECM inappropriate, as shown in subsequent finite element analyses. On the other hand, the ECM gave very consistent results from ENF tests, despite the usually unstable initiation. The present results confirmed some dependence of perceived initiation toughness values on ENF specimen geometry predicted in recent numerical studies. Differences between results of ENF and 4ENF tests could be explained by friction effects in the latter.

Prediction of energy release rates for crack growth using FEM-based energy derivative technique

This paper presents a new method, named energy derivative technique, to calculate energy release rate for a variety of crack growth scenarios. The new method is based on energy conservation principle for crack growth, and is applicable to crack development in any quasi-static condition in which dynamic energy for crack growth is negligible. The method has the advantage over existing finite element-based methods in that the former does not require an elaborate fine mesh in the vicinity of a crack tip, and is not limited to linear deformation behaviour. Several case studies are presented to demonstrate validity of the method, which are (i) growth of penny-shaped crack for linear elastic fracture behaviour, (ii) crack growth in rubber sheet under tension for nonlinear elastic fracture behaviour, (iii) delamination in end-notched flexure specimen with friction, and (iv) crack growth with plastic deformation in double-edge-notched plate under tension. Results from these case studies show excellent agreement with data available in the literature, which were determined using either analytical or other FEM-based techniques.

Delamination fracture analysis in the GII– GIII plane using prestressed transparent composite beams

In this paper, the mixed-mode II/III version of the prestressed end-notched flexure fracture specimen is developed, which combines the well-known end-notched flexure and the modified split-cantilever beam specimens using a special rig. The new beam-like specimen is able to provide any combination of the mode-II and mode-III strain energy release rates. The mode-III part of the strain energy release rate is fixed by using the special rig, which loads the specimen in the plane of the delamination. The mode-II part of the strain energy release rate is provided by the external load using a three-point bending fixture. A simple closed-form solution using beam theory is developed for the strain energy release rates of the new configuration. The applicability and the limitations of the novel fracture mechanical test are demonstrated using unidirectional E-glass/polyester composite specimens. If only crack propagation onset is involved then the mixed-mode II/III prestressed end-notched flexure specimen can be used to obtain the fracture criterion of transparent composite materials in a relatively simple way.

Analysis of mode II interlaminar fracture and damage behavior in end notched flexure testing of GFRP woven laminates at cryogenic temperatures

Interlaminar fracture and damage behavior of glass fiber reinforced polymer (GFRP) woven laminates at cryogenic temperatures is investigated for end notched flexure (ENF) pure Mode II configuration. The corrected beam theory (CBT) and finite element analysis (FEA) are used to calculate the Mode II interlaminar fracture toughness of ENF specimen at room temperature (RT), liquid nitrogen temperature (77 K) and liquid helium temperature (4 K). A FEA coupled with damage is also employed to study the damage distributions within the specimen and to examine the effect of damage on the Mode II energy release rate. The numerical results show that damage occurs at the matrix and causes a decrease in the energy release rate. The technique presented can be efficiently used for the characterization of cryogenic Mode II interlaminar fracture and damage behavior of woven laminate ENF specimens.

Bending effect of through-thickness reinforcement rods on mode II delamination toughness of ENF specimen: Elastic and rigid–perfectly plastic analyses

Abstract In this paper, a new simple metallic z-rod model is proposed to study the bending effect of the metallic z-rods on mode II delamination toughness of laminated composites. A new transverse shear force–deformation relationship for a metallic z-rod is obtained by using the classical beam theory and modeling its surrounding matrix as linearly elastic, rigid–perfectly plastic or linearly elastic–perfectly plastic springs. The bridging traction provided by a metallic z-rod to the mode II delamination toughness is assumed to be only the shear force carried by a z-rod created by the relative slippage between two substrate beams in an end-notched flexure (ENF) specimen, whereas the longitudinal sliding friction is assumed to make negligible contribution to the bridging traction. Mode II strain energy release rate (SERR) is employed to evaluate the influence of the metallic z-rods on the interlaminar fracture toughness of end-notched flexure (ENF) specimens. A parametric study of ENF specimens reinforced with the z-rods is conducted to demonstrate the effect of the new bridging mechanism by the metallic z-rods on the mode II delamination toughness.

Shear behaviour of adhesive layers

An experimental method to determine the complete stress versus deformation relation for a thin adhesive layer loaded in shear is presented. The method is based on a classic specimen geometry; the end-notch flexure specimen. The experiments are evaluated using an inverse method. First, the variation of the energy release rate with respect to the shear deformation at the crack tip is measured during an experiment. Then the traction–deformation relation is derived using an inverse method. The theory is based on the path-independence of the J-integral and considers the effects of a flexible adhesive layer. Quasi-static experiments on three different specimen geometries are performed using a servo-hydraulic testing machine. The experiments give consistent results. This shows that the traction–deformation relation can be taken as independent of the dimensions of the adherends. Thus, the constitutive relation can be considered as a property of the adhesive layer. The deformation process at the crack tip is also monitored during the experiments by the use of a digital camera attached to a microscope.

Prestressed fracture specimen for delamination testing of composites

The prestressed end-notched flexure fracture specimen is developed in the present work, which combines the traditional double-cantilever beam and the end-notched flexure specimens in a very simple way. The most important features of the new beam-like specimen are that it is able to provide any combination of the modes I and II strain energy release rates and it may be performed by using a simple three-point bending fixture. The mode-I part of the strain energy release rate is fixed by inserting a steel roller, which causes a fixed crack opening displacement. The mode-II part of the energy release rate is provided by the external load. A simple closed-form solution using beam theory is developed for the energy release rates of the new configuration. The applicability and the limitations of the novel configuration are demonstrated using unidirectional glass/polyester composite specimens. If only propagation onset is involved then the prestressed end-notched flexure specimen can be used to obtain the fracture criterion of transparent composite materials in a very simple way.