Double Cantilever Beam Specimens Research Articles

Delamination R-curve behavior of curved composite laminates

The effect of curvature on the delamination R-curve behavior of composite unidirectional laminates is investigated in both the experimental and numerical manners. The flat and curved double cantilever beam specimens with different radii of curvatures are manufactured and tested subjected to mode I loading. A new data reduction method is developed for the curved specimens by adopting the Timoshenko curved beam theory. Experimental R-curves indicate that curvature has no effect on the initiation toughness, while it significantly affects the steady-state toughness and fiber bridging length. Variation of the steady-state toughness and fiber bridging length vs. The different curvatures is formulated for the curved specimens with R/h > 25 (R/h: the ratio of the radius of curvature to thickness). Finally, delamination propagation is simulated in the curved double cantilever beam specimens in commercial finite element software, ABAQUS, by applying both the virtual crack closure technique and cohesive zone model.

Finite Element Simulation of Delamination in Carbon Fiber/Epoxy Laminate Using Cohesive Zone Model: Effect of Meshing Variation

Delamination or interlaminar fracture often occurs in composite laminate due to several factors such as high interlaminar stress, stress concentration, impact stress as well as imperfections in manufacturing processes. In this study, finite element (FE) simulation of mode I delamination in double cantilever beam (DCB) specimen of carbon fiber/epoxy laminate HTA/6376C is investigated using cohesive zone model (CZM). 3D geometry of DCB specimen is developed in ANSYS Mechanical software and 8-node interface elements with bi-linear formulation are employed to connect the upper and lower parts of DCB. Effect of variation of number of elements on the laminate critical force is particularly examined. The mesh variation includes coarse, fine, and finest mesh. Simulation results show that the finest mesh needs to be employed to produce an accurate assessment of laminate critical force, which is compared with the one obtained from exact solution. This study hence addresses suitable number of elements as a reference to be used for 3D simulation of delamination progress in the composite laminate, which is less explored in existing studies of delamination of composites so far.

Finite element analysis of mode-I interlaminar fracture of lignocellulosic laminate specimens by virtual crack closure technique

The paper aims to study the interlaminar fracture of lignocellulosic laminate specimens made of beech veneer with urea formaldehyde resin and rye flour under pure mode-I loading. In order to determine the critical value of strain energy release rate GIc, representing one of the material input parameters for a finite element analysis involving the interlaminar fracture behaviour of a laminate structure under complex loading conditions, a lot of double cantilever beam (DCB) specimens processed from a lignocellulosic laminate beech veneer plate were tested by applying the specific standard procedures in conjunction with the modified beam theory method for data reduction. The propagation of interlaminar fracture under pure mode-I was then simulated by finite element analysis using layered conventional shell elements, based on the Virtual Crack Closure Technique (VCCT) in Abaqus/Explicit. Good agreements between the load-displacement curves obtained through the use of finite element analyses and the experimental testing results were obtained.

Mode I and II Interlaminar Fracture in Laminated Composites: A Size Effect Study

This work investigates the mode I and II interlaminar fracturing behavior of laminated composites and the related size effects. Fracture tests on geometrically scaled double cantilever beam (DCB) and end notch flexure (ENF) specimens were conducted. The results show a significant difference between the mode I and mode II fracturing behaviors. The strength of the DCB specimens scales according to the linear elastic fracture mechanics (LEFM), whereas ENF specimens show a different behavior. For ENF tests, small specimens exhibit a pronounced pseudoductility. In contrast, larger specimens behave in a more brittle way, with the size effect on nominal strength closer to that predicted by LEFM. This transition from quasi-ductile to brittle behavior is associated with the size of the fracture process zone (FPZ), which is not negligible compared with the specimen size. For the size range investigated in this study, the nonlinear effects of the FPZ can lead to an underestimation of the fracture energy by as much as 55%. Both the mode I and II test data can be captured very accurately by the Bažant’s type II size effect law (SEL).

Rate-dependent traction-separation relations for a silicon/epoxy interface informed by experiments and bond rupture kinetics

In this work, double cantilever beam specimens were used to investigate the rate-dependent fracture of a silicon/epoxy interface. Fracture experiments were conducted at 5 different separation rates, ranging from 0.042 to 8.5 mm/s. For each separation rate, the interfacial properties were extracted by a beam on elastic foundation model and an iterative method, assuming a bilinear traction-separation relation. Rate dependence is observed for the silicon/epoxy interface as both the interfacial toughness and strength increased with the separation rates, which is opposite to the rate dependent fracture behavior of the bulk epoxy in its glassy state. Motivated by this observation, a rate-dependent cohesive zone model is proposed based on a thermally activated bond rupture mechanism. This model relates the interfacial fracture to the breakage of molecular bonds at the interface, and the rate effect develops naturally from the kinetics of damage evolution via the statistical concept of bond survival probability. The double cantilever beam problem with the interfacial bond rupture kinetics was then solved numerically, and the model parameters were extracted by fitting the numerical results to the experimental data. Ideally, this model should be able to explain and predict the rate-dependent fracture of a specific interface (e.g., silicon/epoxy interface) with four parameters, including the bond energy, the critical stress, the initial stiffness and a time scale. However, in order to fit the experimental data, the critical stress had to be adjusted in the present study. Nevertheless, this mechanism-based cohesive zone model offers a promising approach for modeling the rate-dependent fracture, which may also incorporate other mechanisms in future studies.

Mode I interlaminar fracture toughness of woven glass/epoxy composites with mat layers at delamination interface

Abstract In this study, double cantilever beam (DCB) specimen was employed to take into account the effects of mat layer at delamination interface on mode I fracture toughness of woven glass/epoxy laminated composites. DCB specimens were made using hand lay-up method assisted by the vacuum bagging technique. The experiments revealed that the mat-interlayer changed crack propagation mechanism, reducing the initiation and propagation fracture toughness during mode I interlaminar tests, by 80 and 69%, respectively. Also, the results show that fiber bridging is not the main mechanism for increasing fracture toughness in DCB samples without mat interlayer. Moreover, for numerical simulation of delamination propagation in DCB samples, the cohesive traction was measured in tests using J-integral approach. Comparing load-displacement response curves of numerical and experimental results, proved that the proposed cohesive zone model capable of precisely predicting the experimental load-displacement curve.

An experimental study of the translaminar fracture toughnesses in composites for different crack growth directions, parallel and transverse to the fiber direction

This work studies how the direction of crack propagation affects the translaminar fracture toughness in composites. In particular, this work focuses on propagation mode-I toughness. The two extreme cases are analyzed: crack propagating in the direction either parallel or perpendicular to the fibers (always without breaking fibers). To evaluate the effect of the direction of crack propagation, an experimental campaign was carried out by two new cracked Three Point Bending (TPB) specimens specially developed for this purpose. Using these specimens, the fracture toughness was measured for different directions of the crack propagation. In addition, a set of standard Double Cantilever Beam (DCB) specimens (corresponding to the longitudinal interlaminar fracture toughness) were tested for the sake of comparison. The results show that the translaminar fracture toughness is higher when the crack grows parallel to the fiber direction than when it grows perpendicular. In both cases, the fracture toughness is higher than that measured for the longitudinal interlaminar growth using DCB specimens. The physical reasons for these experimental results are discussed.

Inverse parameter identification of n-segmented multilinear cohesive laws using parametric finite element modeling

Delamination in laminated composites are efficiently modelled with the cohesive zone model (CZM). The shape of the cohesive law becomes important when simulating delamination in material systems experiencing large scale fiber bridging, as several competing damage mechanisms occurs in the fracture process zone at multiple length scales. For this purpose a multilinear cohesive law has recently been developed in [1], which readily can be adapted to a variety of shapes. However, a key challenge in applying such cohesive laws is their model calibration, i.e. identification of parameters that define the shape of the cohesive law. In this work, a new methodology for experimental characterization of multilinear cohesive laws is proposed. The methodology is an inverse approach, which identifies cohesive laws by iteratively varying cohesive zone parameters using a gradient-based optimization scheme to minimize the error in structural response between a fracture mechanical experiment and a parametric finite element model. The method is demonstrated on a moment loaded double cantilever beam (DCB) specimen made of unidirectional glass-epoxy showing large-scale fiber bridging. Multilinear cohesive laws are characterized which result in an excellent agreement between the finite element simulation and the experiment. The results and sensitivity studies demonstrate the accuracy and robustness of the proposed methodology, even for a large number of design variables in the optimization problem.

Experimental and numerical analysis of size effects on stress intensity in anisotropic porous materials

A prominent size effect has previously been reported for the fracture behaviour of brittle porous materials, with smaller specimens behaving quite differently to their larger counterparts. In such materials, the size of the K-dominant zone has been numerically found to be greatly affected by the presence of voids in the near-tip area, thus putting the assumption of a single fracture parameter under question. In order to address this, in this study mode I tests are conducted on porous double cantilever beam specimens, while the stress distribution in the near-tip area is being observed by means of photoelasticity. Results validate the predicted size effect and suggest that the voids can indeed alter the size and shape of the stress pattern in the specimens. A parametric study is then conducted to investigate the influence of void shape variations that can be caused by manufacturing inaccuracies on the stress concentration at the crack tip. It is found that although the stress intensity at the crack tip can be greatly affected by such factors, the size of the K-dominant zone remains unaffected.

Dynamic behaviour in mode I fracture toughness of CFRP as a function of temperature

The aim of this work is to assess the influence of high strain rates and testing temperature on the fracture energy in mode I, GIC, of carbon fibre reinforced plastic (CFRP) plates. Double cantilever beam (DCB) specimens were tested to determine GIC as a function of temperature (24 and 80 °C) under an impact load of 4.7 m/s (using a falling-wedge impact test machine), with the results being compared with the values previously determined by the authors under quasi-static loads. This work has demonstrated a significant influence of the testing temperature on the GIC of composite materials, as this value greatly increased for higher temperatures. On the other hand, a less significant influence of the strain rate on GIC was found, which slightly decreased by increasing the strain rate.

Modeling of delamination in fiber-reinforced composite using high-dimensional model representation-based cohesive zone model

Prediction of delamination failure is challenging when the researchers try to achieve the task without overburdening the available computational resources. One of the most powerful computational models to predict the crack initiation and propagation is cohesive zone model (CZM), which has become prominent in the crack propagation studies. This paper proposes a novel CZM using high-dimensional model representation (HDMR) to capture the steady-state energy release rate (ERR) of a double-cantilever beam (DCB) under mode I loading. The finite element models are created using HDMR-based load and crack length response functions. Initially, the model is developed for 51-mm crack size DCB specimens, and the developed HDMR-based CZM is then used to predict the ERR variations of 76.2-mm crack size DCB model. Comparisons have been made between the available unidirectional composite (IM7/977-3) experimental data and the numerical results obtained from the 51-mm and 76.2-mm initial crack size DCB specimens. In order to demonstrate the efficiency of the proposed model, the results of the second-order nonlinear regression model using RSM are used for the comparison study. The results show that the proposed method is computationally efficient in capturing the delamination strength.

Effect of pre-crack length on Mode I fracture toughness of 3-D angle-interlock woven composites from finite element analyses

Fracture toughness is a key factor to design impact behaviors of composite materials. This paper reports the influence of pre-crack length on Mode I fracture toughness of 3-D angle-interlock woven composites. Double cantilever beam specimens with different pre-crack lengths were tested to obtain load-displacement curves and strain energy release rates. A finite element analysis model at microstructure level was established to reveal the fracture damage development and stress distribution in the specimens. We found that the fracture toughness decreases with increase in pre-crack length. The higher pre-crack length resulted in increased stress concentration at crack tip position and the enhanced crack propagation. The higher strength through-thickness yarns are recommended for improving fracture toughness.

Finite element modeling strategies for 2D and 3D delamination propagation in composite DCB specimens using VCCT, CZM and XFEM approaches

Virtual crack closure technique (VCCT), cohesive zone modeling (CZM) and extended finite element method (XFEM) are three well-known numerical methods frequently used for crack propagation modeling. It is often questioned by new researchers and engineers: which method is more appropriate for modeling of delamination propagation in composites? In this study, advantages, limitations, and challenges of each method are discussed with the goal of finding a suitable and cost-effective solution for modeling of delamination propagation in laminated composites. To this end, a composite double cantilever beam (DCB) specimen as a benchmark example is modeled in ABAQUS and delamination propagation is simulated using three above methods and the combination of XFEM with VCCT and CZM. Two-dimensional plain strain and three-dimensional DCB models are both considered. Finite element results are compared with experimental results available in the literature for unidirectional DCB specimens. Finally, the accuracy, convergence speed, run-time and mesh dependency of each method are discussed. The XFEM-CZM was found as a suitable method for simulation of delamination growth.

The dynamic crack propagation behavior of mode I interlaminar crack in unidirectional carbon/epoxy composites

The dynamic propagation behavior of the mode I interlaminar crack in unidirectional carbon/epoxy composites was investigated by using double cantilever beam (DCB) specimens. The dynamic interlaminar propagation toughness was obtained using a hybrid experimental-numerical method. Using a novel electromagnetic Hopkinson bar system, pure mode I fracture was guaranteed by symmetrical opening displacement rates in the range of 10 – 30 m/s. The crack velocities before crack arrest were between 100 and 250 m/s, which was monitored by crack-propagation gauges and high-speed photography. To model the interlaminar crack, a user-defined cohesive element was developed, which integrated the experimentally measured crack propagation history. The propagation toughness was calculated by the energy balance method and the dynamic J-integral technique. Results from extensive studies indicate that the dynamic propagation toughness is not a single-valued function of the crack velocity for mode I interlaminar crack. Both the external dynamic loads and the interaction with the bending waves emanating from the moving crack tip affect the behavior of the crack propagation.

R-curve behaviour of the mixed-mode I/II delamination in carbon/epoxy laminates with unidirectional and multidirectional interfaces

To successfully predict the delamination behaviour of the laminated composite structures with fibre bridging, the R-curve has to be studied. This work experimentally investigates the complete R-curve behaviour of the unidirectional and multidirectional carbon/epoxy composite laminates. The delamination tests use the double cantilever beam (DCB), mixed-mode bending (MMB) and end-notched flexure (ENF) specimens for mode I, mixed-mode I/II and mode II loading, respectively. The test results show that the interfacial ply and mode mixity (φ-ratio) have significant influences on the initial fracture toughness, steady-state fracture toughness and fibre bridging length. The ratio between the steady-state fracture toughness and its initial value is approximately same for both interfaces, which indicates a similar enhanced effect of the fibre bridging on the fracture toughness. The Benzeggagh-Kenane (B-K) criterion is capable of representing the relation between the fracture toughness and the φ-ratio. Based on the DCB and MMB test results, the predicted values of the mode II fracture toughness via the B-K criterion are very close to the experimental ones, which illustrates the possibility of determining the mode II fracture toughness without executing the mode II delamination tests. Furthermore, a semi-empirical expression is proposed, which can well predict the mixed-mode I/II delamination behaviour.

Calibration of nasgro equation for mixed-mode loading using experimental and numerical data

A procedure to calibrate the NASGRO equation in a high yield-strength steel under mixed-mode loading (I + II) is presented. The calibration consists in obtaining the material parameters known as C, m, p and q. The procedure is based on experimental and numerical results. The experimental tests were used to characterize the material and obtain fatigue crack growth data. For the fatigue tests, tapered double cantilever beam (TDCB) specimens with different maximum load and load ratio values were used. Through the numerical analysis, the stress intensity factors, the crack growth direction and the crack path coordinates were calculated. The numerical analysis was performed using XFEM and the maximum energy release rate criterion. The calibrated model allows predicting the number of load cycles with an RMS value of less than 5%, compared with the experimental results.

Influence of ply-angle on fracture in antisymmetric interfaces of CFRP laminates

Laminated composites are prone to fracture at layer interfaces. Such damage impairs their structural response and engenders important constraints in design. In this work, the influence of ply orientation on crack growth resistance was studied for three different antisymmetric interfaces and compared to a unidirectional reference one, using double cantilever beam specimens with equivalent stiffness, loaded under mode I conditions. Fracture toughness at initiation was found interface-independent. In all angle-ply specimens, distinct slow and fast phases of crack propagation were observed. Crack increments due to fast growth, were characterized using experimental energy release rates and verified from fracture surface analysis. The slow propagation phases were accompanied by large scale bridging involving intra-ply growth in the adjacent plies, with toughness increasing inversely with the angle. Mechanistic investigations suggest a consistent fracture pattern in terms of the interface angle. For each interface angle, a single traction-separation relation, obtained from the experimental energy release rate and crack opening displacements, was sufficient to model two consecutive slow propagation phases. These relations were used in 2D cohesive element models to predict very well the loading history.

Nearly Mode I Fracture Toughness and Fatigue Delamination Propagation in a Multidirectional Laminate Fabricated by a Wet-Layup

Five double cantilever beam specimens were tested quasi-statically to obtain a GIR resistance curve. In addition, nine double cantilever beam specimens were tested in fatigue to obtain a Paris-type relation to describe the delamination propagation rate da/dN where a is delamination length and N is the cycle number. Displacement ratios of Rd = 0.10 and 0.48 were used for five and four specimens, respectively. The specimens were fabricated by means of a wet-layup process from carbon fiber reinforced polymer plies. The interface containing the delamination was between a unidirectional fabric and a woven ply. The fracture toughness and fatigue delamination propagation protocols are outlined. The mechanical and thermal residual stress intensity factors were obtained by means of finite element analyses and the conservative M-integral along the delamination front. They were superposed to determine the total stress intensity factors. It was found that the total mode I stress intensity factor dominates the other two stress intensity factors. Thus, nearly mode I deformation was achieved. Interpolation expressions for the mechanical and thermal residual stress intensity factors were determined using three and two-dimensional fittings, respectively. Results are presented with an expression for GIR determined. Moreover, the fatigue data is described including threshold values and master-curves. These results shed light on the behavior of delamination propagation in multidirectional laminate composites.

Studies on the influence of surface treatment type, in the effectiveness of structural adhesive bonding, for carbon fiber reinforced composites

Primary intent of the present paper is to correlate the effectiveness of surface preparation type (pre-bonding), such as solvent cleaning, sanding (mechanical abrade), chemical etching (alkaline and acid), and peeling of sacrificial surface layer (peel ply) of carbon fiber reinforced composite (CFRC) test specimens, with the corresponding effect to the final strength of adhesive bonding. The analysis was performed by means of several spectroscopic and microscopic techniques, such as XPS, SEM, AFM, and a contact angle measurement technique which provides a direct, fast and easy measurement of the surface energy of the fiber composites. The adhesively bonded carbon fiber composites based on the different surface treatments were mechanically tested by employing the ASTM D 5528-0 (reapproved 2007) standard. The double cantilever beam (DCB) specimen geometry was used to evaluate the value known as opening Mode I inter-laminar fracture toughness (GIC) in adhesive bonds of carbon fiber composite materials. The results were varying between 1 and 1.8 kJ/m2 for GIC analysis and around 50 mm for delamination lengths. The mechanics of the linear elastic fracture is considered a tool for the failure of the laminate in composite materials with cracks or cuts in the plane, due to the presence of damaged zones in the tip of the crack; which is therefore applied to the study of delamination or fracture toughness.

Experimental and numerical characterization of Mode I fracture in unidirectional CFRP laminated composite using XIGA-CZM approach

This article presents an effective study for characterization of interlaminar Mode I fracture process zone (FPZ) in unidirectional CFRP laminated composite structure. Mode I fracture toughness testing has been carried out on double cantilever beam (DCB) specimens. Experimental studies have been carried out on non-precraked DCB specimens in order to obtain the amount of energy released during crack initiation from the natural crack front. The energy release rate (ERR) is obtained from experimental data as a function of crack growth (Δa) and pre-crack tip opening displacement (δ∗) by utilizing five data reduction schemes. The analytical function between ERR and δ∗ is used to construct fibre bridging law using J-integral approach. The obtained traction separation laws from each data reduction scheme is implemented into cohesive zone modelling (CZM) for numerical simulation. Fractured surfaces have been examined by means of Scanning electron microscope (SEM). Numerical studies have been carried out for both non-precracked and precracked specimens using combined framework of fracture mechanics using extended isogeometric analysis (XIGA) and damage mechanics using CZM approach. It has been observed that crack travels catastrophically in non-precracked (NPC) specimens due to fast dissipation of excess energy. Introduction of fibre bridging law, obtained from experimental investigation, into CZM in combined framework of XIGA methodology shows a good agreement with experimental results.