Numerical investigation to prevent crack jumping in Double Cantilever Beam tests of multidirectional composite laminates

During the experimental characterization of the mode I interlaminar fracture toughness of multidirectional composite laminates, the crack tends to migrate from the propagation plane (crack jumping) or to grow asymmetrically, invalidating the tests.The aim of this study is to check the feasibility of defining the stacking sequence of Double Cantilever Beam (DCB) specimens so that these undesired effects do not occur, leading to meaningful onset and propagation data from the tests. Accordingly, a finite element model using cohesive elements for interlaminar delamination and an intralaminar ply failure criterion are exploited here to thoroughly investigate the effect of specimen stiffness and thermal residual stresses on crack jumping and asymmetric crack growth occurring in multidirectional DCB specimens.The results show that the higher the arm bending stiffness, the lower the tendency to crack jumping and the better the crack front symmetry. This analysis raises the prospect of defining a test campaign leading to meaningful fracture toughness results (onset and propagation data) in multidirectional laminates.     

Composite toughness enhancement with interlaminar reinforcement

An experimental investigation of a newly proposed through-thickness reinforcement approach aimed to increase interlaminar toughness of laminated composites is presented. The approach alters conventional methods of creating three-dimensional fiber-reinforced polymer composites in that the reinforcing element is embedded into the host laminate after it has been cured. The resulting composite is shown to possess the benefits of a uniform surface quality and consolidation of the original unreinforced laminate. This technique was found to be highly effective in suppressing the damage propagation in delamination double-cantilever beam (DCB) test samples under mode I loading conditions. Pullout testing of a single reinforcing element was carried out to understand the bridging mechanics responsible for the improved interlaminar strength of reinforced laminate and stabilization and/or arrest of delamination crack propagation. The mode I interlaminar fracture of reinforced DCB samples was modeled using two-dimensional cohesive finite-element scheme to support interpretation of the experiments.     

Studies of mode I delamination in monotonic and fatigue loading using FBG wavelength multiplexing and numerical analysis

Bridging by intact fibers in composite materials is one of the most important toughening mechanisms. However, a direct experimental assessment of its contribution is not easy to achieve. In this work a semi-experimental method is proposed to quantify its contribution to fracture of unidirectional carbon fiber/epoxy double cantilever beam (DCB) specimens in mode I delamination under monotonic and 1 Hz fatigue loads. In each specimen, an embedded optical fiber with an array of eight wavelength-multiplexed fiber Bragg gratings is used to measure local strains close to the crack plane. The measured strain distribution serves in an inverse identification procedure to determine the tractions in the bridging zone in monotonic and fatigue loads. These tractions are used to calculate the energy release rate (ERR) associated with bridging fibers. The results indicate that the ERR due to bridging is about 40% higher in fatigue. The bridging tractions are further included in a cohesive element model which allows to predict precisely the complete load displacement curve of monotonic DCB tests. Using the principle of superposition and the identified tractions, the total stress intensity factor (SIF) is calculated. The results show that the SIF, at initiation, is very close to the one calculated at crack propagation and bridging by intact fibers is responsible for the entire increase in toughness seen in the DCB specimens used herein.     

DCB test simulation of stitched CFRP laminates using interlaminar tension test results

A simulation model for the delamination extension of stitched CFRP laminates and 3-D orthogonal interlocked fabric composites (3-D OIFC) has been developed using a 2-D finite element method incorporating interlaminar tension test results to simulate the experimental results of their DCB tests. The mechanical properties of through-the-thickness fiber were determined from the results of interlaminar tension tests in which the specimen included only one through-the-thickness yarn. The fracture phenomena around the through-the-thickness thread, such as debonding from the in-plane layer, slack absorption, fiber bridging, and the pull-out of broken threads from the in-plane layers, are also introduced into the FEM model. The present FEM simulation results were compared to DCB test results for certain stitched laminates and a 3-D OIFC, and the simulation results showed good agreement with the experimental results of DCB tests, including the load–displacement curve and Mode I strain energy release rate (GI). While it was difficult to estimate GI accurately when the DCB test specimen included different types of z-fiber fracture modes, the present model of FEM analysis can simulate the experimental results of DCB tests of stitched laminates and 3-D OIFC. It is suggested that the GI of CFRP with arbitrary z-fiber densities can be predicted by using this FEM analysis model together with interlaminar tension test results.     

A numerical investigation on the interlaminar strength of nanomodified composite interfaces

The effect of Nylon 6,6 electrospun nanofibers interleaved in composite laminate material is simulated numerically to investigate the differences in the fracture strength between a nanomodified laminate interface and the corresponding non-modified material. DCB and ENF mechanical test results from a previous work of some of the authors are used as reference for the identification of cohesive zone model by numerical simulations with the finite element software Abaqus using implicit time integration. A bilinear damage law came out to be necessary to match the experimental behavior of the nanomodified interface, while the virgin material can be represented through a simple linear damage law. The necessity of using a bilinear damage law has been related to the crack bridging and to the obstacle to crack growth caused by nanofibers.     

Dynamic crack propagation and arrest in orthotropic DCB fiber composite specimens

An orthotropic double cantilever beam (DCB) model is used to study dynamic crack propagation and arrest in 90° unidirectional Hercules AS/3501-6 graphite fiber epoxy composites. The dynamic fracture toughness of the composite is determined from tests performed on the long-strip specimen and DCB crack arrest experiments are conducted. By using the dynamic fracture toughness in a finite-difference solution of the DCB governing partial differential equations, a numerical solution of the crack propagation and arrest events is computed. Excellent agreement between the experimental and numerical crack arrest results are obtained.     

A dynamic analysis of unstable crack propagation and arrest in the DCB test specimen

A simple analytical model is developed to accompany experimental work on rapid crack propagation and arrest in the DCB test specimen. The present work extends the beam-on-elastic foundation model used previously by taking account of shear deformation and of both translational and rotary inertia. Crack speeds predicted with the model are found to be in good agreement with the constant-speed behavior observed experimentally. It is demonstrated that kinetic energy makes an important contribution to maintaining unstable crack propagation and to crack arrest.     

Fracture characterization of sandwich structures interfaces under mode I loading

The accurate prediction of failure of sandwich structures using cohesive mixed-mode damage models depends on the accurate characterization of the cohesive laws under pure mode loading. In this work, a numerical and experimental study on the asymmetric double cantilever beam (DCB) sandwich specimen is presented with the objective to characterize the debonding fracture between the face sheet and the core under pure mode I. A data reduction method based on beam theory was formulated in such a way to incorporate the complex damaging phenomena of the debonding due to the material and geometric asymmetry of the specimen, via the consideration of an equivalent crack length (a_e). Experimental DCB tests were performed and the proposed methodology was followed to obtain the debonding fracture energy (G_Ic). The experimental tests were numerically simulated and a cohesive damage model was employed to reproduce crack propagation. An inverse method was followed to obtain the local cohesive strength (σ_u,I) based on the fitting of the numerical and experimental load–displacement curves. With the value of fracture energy and cohesive strength defined, the cohesive law for interface mode I fracture is characterized. Good agreement between the numerical and the experimental R-curves validates the accuracy of the proposed data reduction procedure.     

Delamination modelling of GLARE using the extended finite element method

In this paper, an application of the Extended Finite Element Method (XFEM) for simulation of delamination in fibre metal laminates is presented. The study consider a double cantilever beam made of fibre metal laminate in which crack opening in mode I and crack propagation were studied. Comparison with the solution by standard Finite Element Method (FEM) as well as with experimental tests is provided. To the authors’ knowledge, this is the first time that XFEM is used in the fracture analysis of fibre metal laminates such as GLARE. The results indicated that XFEM could be a promising technique for the failure analysis of composite structures.     

Effect of the crack length on the piezoelectric damage monitoring of glass fiber epoxy composite DCB specimens

A new nondestructive method using the piezoelectric characteristics of polymer matrix was suggested for the damage monitoring of glass fiber polymer composites, and the feasibility of the use of the method was proven through basic experiments. Heretofore, most studies have focused on basic material properties such as the piezoelectric properties of unidirectional glass fiber epoxy composites with respect to the fiber orientation or the loading speed. In this study, the effect of the crack length on the piezoelectric damage monitoring of glass fiber polymer composites was experimentally investigated. Dynamic tests of mode I were performed using double-cantilever-beam (DCB) specimens, and the relationship between the crack length and the electric-charge signals measured from the electrodes on the DCB specimens was analyzed. The experiment results showed that the magnitude of the electric-charge signals increased very slowly as the crack tip approached the electrodes, rose sharply when the crack tip was passing through the electrodes, and then decreased fast and maintained relatively very low values when the crack tip had completely passed through the electrodes. The investigation of the mechanical behaviors via finite-element analyses during the dynamic tests revealed that the tendency of electric-charge signals is quite similar to that of the strain changes in glass fiber epoxy composites near electrodes. Based on the results of the experiments and finite-element analyses conducted in this study, it was concluded that piezoelectric damage monitoring can detect crack propagation.     

Effect of initial crack length on the measured bridging law of unidirectional E-glass/epoxy double cantilever beam specimens

In this paper, the effect of initial delamination length is experimentally investigated on obtaining the mode I bridging law of unidirectional E-glass/epoxy double cantilever beam (DCB) specimens manufactured by hand layup method. To this end, an experimental test set-up is established for accurate measurement of crack tip opening displacement (CTOD) using digital image processing method. DCB tests are performed for three different delamination lengths and the corresponding bridging laws are calculated using J-integral approach. Results showed that the maximum bridging stress, the shape of bridging law and energy dissipation in bridging zone are slightly affected by changing initial crack length. In other words, the measured bridging law acts independent of initial delamination length. Therefore, the obtained bridging law can be used with the cohesive elements available in the commercial finite element software to simulate the delamination propagation behavior in unidirectional DCB specimens.     

Finite volume analysis of dynamic fracture phenomena – I. A node release methodology

A novel node release numerical methodology based on the Finite Volume discretisation (Ivankovic et al., 1994) has been developed and applied for the simulation of (non-linear) elastic fractures where crack propagation velocities are not a priori known. The analysis is performed in two-dimensions by means of an unconditionally stable implicit time-marching scheme and a second order accurate conservative spatial differencing scheme. Application to single crack propagation problems has demonstrated the validity and accuracy of the proposed formulation for dynamic crack propagation. The results obtained by two examples of crack propagation in single edge notch tensile (SENT) and double cantilever beam (DCB) specimens show good agreement with selected numerical, experimental and analytical results. Based on these results, the formulation appears to be well suited to the study of rapid crack propagation (RCP) phenomena in brittle materials. This, combined with the simplicity and accuracy of the formulation, may provide a solid foundation for more physically realistic RCP computational methodologies other than that of the single linear elastic crack representation considered here.     

Analytical modelling of dynamic fracture and crack arrest in DCB specimens under fixed displacement conditions

An analytical solution via the beam theory considering shear deformation effects is developed to solve the static and dynamic fracture problem in a bounded double cantilever beam (DCB) specimen. Fixed displacement condition is prescribed at the pin location under which crack arrest occurs. In the static case, at first, the compliance function of a DCB specimen is obtained and shows good agreement with the experimental results cited in the literature. Afterward, the stress intensity factor is determined at the crack tip via the energy release rate formula. In the dynamic case, the obtained governing equations for the model are solved supposing quasi‐static treatment for unstable crack propagation. Finally, a closed form expression for the crack propagation velocity versus beam parameters and crack growth resistance of the material is found. It is shown that the reacceleration of crack growth appears as the crack tip approaches the finite boundary. Also, the predicted maximum crack propagation velocity is significantly lower than that obtained via the Euler–Bernoulli theory found in the literature.     

Analysis of the sandwich DCB specimen for debond characterization

Analysis of the compliance and energy release rate of the sandwich double cantilever beam (DCB) specimen is presented. It is assumed that there is a starter crack at the upper face/core interface and that the crack remains at or near this interface during crack propagation. Beam, elastic foundation, and finite element analyses are presented and compared to experimentally measured compliance data, and compliance calibrated energy release rate over a range of crack lengths for foam cored sandwich DCB specimens. It is found that the beam analysis provides a conservative estimate on the compliance and energy release rate. The elastic foundation model is in agreement with finite element analysis and experimental compliance data. Recommendations for specimen design and an expression for an upper limiting crack length are provided.     

Fatigue crack growth in thin notched woven glass composites under tensile loading. Part I: Experimental

Helicopter blades are made of composite materials mainly loaded in fatigue and have normally relatively thin skins. A through-the-thickness crack could appear in these skins. The aim of this study is to characterize the through-the-thickness crack propagation due to fatigue in thin woven glass fabric laminates. A technological test specimen is developed to get closer to the real loading conditions acting on these structures. An experimental campaign is undertaken which allows evaluating crack growth rates in several laminates. The crack path is linked through microscopic investigations to specify damage in woven plies. Crack initiation duration influence on experimental results is also underlined.     

Inverse End Loaded Split test configuration for stable mode II crack propagation in bonded joint: macroscopic analysis—effective crack length approach

Mode II crack propagation along a bonded joint is investigated using newly proposed Inverse-End Loaded Split experimental configurations. This test configuration allows stable crack propagation all along the crack propagation path. The specimen compliance and strain energy release rate for the new experimental arrangement are derived. An experimental data reduction procedure, based on the effective crack length approach, is also proposed. Two series of experiments are performed to assess the stable nature of the crack propagation and data reduction scheme associated to this new experimental arrangement. In addition to stable crack growth, the experiment may prove his worthiness in the study of crack onset under mode II loading.     

Mixed Bending-Tension (MBT) test for mode I interlaminar and intralaminar fracture

A new Mixed Bending-Tension (MBT) test is proposed for mode I fracture of laminated composites. The MBT specimen consists of a relatively small pre-cracked laminate adhesively bonded to pin-loaded steel beams. This design reduces significantly the bending stresses that prevent successful application of DCB tests to certain laminates. The MBT was here applied to carbon/epoxy unidirectional [0°]₂₆ and [90°]₂₆ laminates with starter delaminations. Interlaminar initiation G_IC values of [0°]₂₆ laminates agreed well with previous DCB test results, while [90°]₂₆ laminates exhibited 50% higher values. Significant lengths of fairly planar intralaminar crack propagation were seen in the latter laminates. The results showed a fibre bridging related R-curve, which was more pronounced in [0°]₂₆ laminates. The consistency of the present results indicates that the MBT opens new possibilities for the interlaminar and intralaminar mode I fracture.     

Application of bridging-law concepts to short-fibre composites 4. FEM analysis of notched tensile specimens

This is the fourth paper in a series of four where notch sensitivities, fracture energies and bridging laws in short-fibre polymer composites are investigated. In this paper finite-element modelling (FEM) of centre-hole-notched tensile specimens is performed, with different bridging laws governing crack growth. Crack lengths, crack profiles and stress distributions are predicted. The results are compared with experimentally determined crack shapes from an earlier investigation. Only with softening bridging laws can the experimental results be matched. The predicted crack lengths are sensitive to bridging-law parameters. When bridging laws determined by the double cantilever beam (DCB) method are applied, the predicted crack lengths and profiles show good correlation with the experimental results. The results support the validity of the DCB method to determine bridging laws in short-fibre composites.     

PBO纤维增强环氧树脂复合材料层间Ⅰ型断裂韧性的DIC技术测量

Ⅰ型双悬臂梁(DCB)试验通常用于单向复合材料的层间抗拉性能研究,目标是测量Ⅰ型层间断裂韧性,其可作为复合材料分层扩展及失效机制研究的重要输入参数。在DCB试验中必须经常暂停试验以实现多次测量裂纹长度,这不仅会对裂纹传播产生潜在影响,造成测量误差且多次反复试验的时效性较差。数字图像相关(DIC)测试技术应用于裂纹扩展长度测量具有实时跟踪、精确定位的优点,可有效提高Ⅰ型断裂韧性试验的测量效率,但应用于非连续变形行为仍存在局限性,且易受到图像噪声的干扰,产生测量误差。本文发展了一种基于DIC测试技术的实时获取裂纹长度的检测方法,通过图像匹配算法获取试件的非连续变形位移场,并提出一种根据全局横向位移离散程度的辨别方法,实现了裂纹尖端的实时捕捉。再通过DCB试验,与传统测量方式对比,裂纹长度的测量误差平均不超过2.76%,验证了该方法的准确性和高效性,同时也克服了聚对苯撑苯并双噁唑(PBO)/环氧树脂复合材料侧表面毛糙、散斑质量较差及纤维桥接对测量结果的干扰,最终获取了有效的Ⅰ型层间断裂韧性初始值及稳态扩展值。     

Delamination dynamics in through-thickness reinforced laminates with application to DCB specimen

Bridged crack models using beam theory formulations have proved to be effective in modeling quasi-static delamination crack growth under large scale bridging conditions in through-thickness reinforced structures. In this paper, beam theory is used to study dynamic mode I crack propagation in through-thickness reinforced laminar structures. In particular, steady state dynamic crack growth for a Double Cantilever Beam (DCB) loaded with a flying wedge is examined. The steady state crack propagation characteristics are mapped out in terms of controllable loading and material parameters including the crack velocity and the properties of the through-thickness reinforcement. For small crack velocities, the through-thickness reinforcement considerably enhances the delamination resistance of the structure. At higher velocities, the kinetic energy term dominates the overall energetics and the relative effect of the reinforcement on the delamination resistance is insignificant. The model suggests a simple fracture test for estimating the properties of the through-thickness reinforcement under dynamic loading conditions.