Composite Double Cantilever Beam Specimens Research Articles

Evaluation of mode-I delamination toughness of composites for automotive applications

Abstract With the increasing need for energy efficiency, fiber-reinforced composites are being widely used in the automotive industry. This study investigates the inter-laminar fracture behavior of fiber-reinforced composite double cantilever beam specimens considering a non-zero slope at the root. Experiments were conducted on unidirectional and cross-ply glass fiber reinforced epoxy composite specimens and the critical delamination toughness G I C has been evaluated by the proposed weighted residual equation. The proposed mathematical model requires crack length and the load versus displacement data to evaluate delamination fracture energy. This method accounts the measurement scatter and the rotation at the crack tip. For a particular specimen, the proposed model gives a unique value of critical delamination toughness value. The critical interface failure load estimates utilizing the evaluated delamination toughness agrees well with literature and in-house test results of double cantilever beam specimens.

Analysis of the adhesively bonded composite double cantilever beam specimen with emphasis on bondline constraint, adherend through-thickness flexibility and fracture process zone relative size

ABSTRACT The double cantilever beam (DCB) specimen is widely used to characterise the mode I fracture of adhesive joints. This paper analyses some particular characteristics of adhesively bonded composite DCB specimens which could affect test results. Three-dimensional (3D) and two-dimensional (2D) finite element analyses (FEA) were conducted in order to evaluate the effects bondline constraint and adherend through-thickness flexibility on the specimen response. Since beam theory-based data reduction schemes are widespread, beam models were also employed to analyze the effects of adherend through-thickness flexibility and fracture process zone relative size. It is shown that, although composite adherends are usually thinner and have much lower transverse moduli than metal adherends, the level of bondline constraint is similarly high. This may: limit the level of adhesive plastic deformations in the fracture process zone; generate high bondline tractions that increase the likelihood of interface failure and interlaminar damage in the composite adherends. The present analyses also show relevant effects of adherend through-thickness flexibility in the adhesive elastic loading stage. Finally, smaller fracture process zones relative to metal adherend DCB specimens were predicted by a beam cohesive zone model. This may explain lower fracture energy values reported with composite adherends in some studies.

Delamination resistance of GFRP‐epoxy rods with nanoparticle‐ and microparticle‐modified matrix and its correlation with the fracture properties of epoxy nanocomposites

AbstractPultruded glass fiber–reinforced plastic (GFRP) rods are industrially produced for various applications. The mechanical properties of GFRP rods can be tailored, eg, with modified epoxy matrix by adding microsized and nanosized fillers. In this work, we investigated the transferability of the fracture properties of epoxy nanocomposites to GFRP epoxy rods. For this purpose, nanosilica particles, micron‐sized rubber, and micron‐sized calcium carbonate were used as fillers. Firstly, epoxy plates with different combinations of nanosized and micron‐sized fillers were produced and their fracture toughness evaluated. Secondly, using binary and ternary epoxy filler systems as matrices, GFRP rods were produced, and their fracture toughness was determined using a modified testing procedure derived from standard composite double cantilever beam specimens. Lastly, the correlation between fracture properties of epoxy nanocomposites and GFRP rods was analysed. Besides that, the fractographic investigations of both epoxy nanocomposites and GFRP rods were carried out and discussed.

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.

Fracture analysis of finite length angle-ply composite double cantilever beam specimens

The double cantilever beam specimen is assumed as two finite length beams, connected together, except at the initial delamination length. The energy release rate ( GI) is evaluated analytically by considering a Timoshenko beam on Winkler and Pasternak elastic foundations. The current data reduction methods have a blind spot in calculating GI when crack approaches the end of the ligament, which is considered in this study and, therefore, the simplifying assumption of infinite ligament length is not assumed here. GI will be strongly dependent on the ligament length if it is less than twice the thickness. Furthermore, the R-curves of different layups including their first points (fracture toughness) are drawn using Ρ–δ curves reported in the literature and they are compared to the experimental results. These comparisons show that Timoshenko beam on Winkler foundation gives the best results in comparison with experimental results for unidirectional and angle-ply laminates.

Mode I delamination propagation and R-ratio effects in woven composite DCB specimens for a multi-directional layup

In this paper, a method is proposed for evaluating the delamination growth rate da/dN for any given R-ratio (load or displacement ratio) using data from a relatively small number of tests. To this end, double cantilever beam (DCB) specimens fabricated from a plain woven prepreg (G0814/913) arranged in a multi-directional (MD) layup were tested. First, quasi-static tests were carried out to obtain the resistance GIR-curve. Then, constant amplitude fatigue tests were preformed to determine the delamination growth rate da/dN. In both tests, displacement control was imposed. Four different cyclic displacement ratios Rd, namely 0.1, 0.33, 0.5 and 0.75, were used for the fatigue tests. When the delamination growth rate da/dN, calculated from the experimental data, was plotted with respect to GImax and ΔGIeff=(GImax-GImin)2, different behavior of the da/dN curves was observed. In addition, modification of the Hartman-Schijve representation was made. When the da/dN data was plotted with respect to the new modified representation which was denoted here as ΔK‾I, all of the data obtained for different displacement ratios collapsed into one master curve. From this master curve, da/dN values may be calculated for any given R-ratio.

In-situ measurements of fracture toughness properties in composite laminates

Prediction of matrix failure in composite laminates can be accomplished using computational methods based on material strength and fracture toughness. Engineering theories and failure criteria, which use such material properties generated by current standard experimental methods, may result in poor accuracy of predicting structural strength and fatigue characteristics due to complexity of deformation and failure mechanisms in composites. In this work the applicability of fracture toughness properties measured using standard test methods is investigated. A customized X-ray Computed Tomography system with a 50kN axial force capacity integrated load frame, enabling full scanning under load, is utilized for accurate 3D in-situ measurements of crack geometry in composite Double Cantilever Beam specimens and Open Hole Tension specimens. These experiments are used to determine Mode I and Mode II fracture toughness based on finite element analysis of models transferred from the tomographic measurements. While measured interlaminar Mode I fracture toughness is in good agreement with standard tests, intralaminar Mode II fracture toughness is shown to depend on crack length.

Multiscale finite element analysis of mode I delamination growth in a fabric composite

Mode I delamination of a five harness satin weave carbon fibre composite and the corresponding toughening mechanisms are studied using a multiscale finite element model of delamination growth in a double cantilever beam (DCB) specimen. The toughening mechanisms related to the fabric structure are studied by embedding a meso-scale model of the fibre architecture in the delamination zone into a macro-scale model of a DCB specimen. The R-curves and the load–displacement curves obtained from this analysis agree with the lower bound of the experimental results. The analysis identified two major toughening mechanisms: the inter-yarn locking ahead of the delamination front causing stress relaxation and the formation of sub-surfaces. Contribution of each toughening mechanism towards total delamination toughness is quantitatively evaluated, identifying the inter-yarn locking as the main source of toughening in mode I delamination of fabric composites. Video abstractMultimedia 1 shows the different stages of the mode I delamination growth in a 5HS composite DCB specimen and its corresponding load–displacement curve.

Delamination propagation in a multi-directional woven composite DCB specimen subjected to fatigue loading

Double cantilever beam (DCB) specimens fabricated from a graphite/epoxy (G0814/913) woven prepreg containing a straight through notch were tested by means of constant amplitude fatigue. The specimen was composed of 15 layers with fibers alternating between the weft and warp in the 0°/90° and the +45°/−45° directions. Eight fatigue tests were carried out to determine the delamination growth rate da/dN vs the nearly mode I cyclic energy release rate ΔGI. Comparison of the delamination growth rate was made to the crack propagation rate of an aluminum alloy. It was found that a crack in the aluminum will grow faster but will be less sensitive to uncertainties or changes in load level.

Stochastic modeling of delamination growth in unidirectional composite DCB specimens using cohesive zone models

Delamination between plies is the most common failure mode in composite laminates that can cause fiber breakage and reduction in life of the composite. Currently Mode-I interlaminar fracture toughness or critical energy release rate of a composite is measured using double cantilever beam (DCB) with unidirectional composites (ASTM D5528). Unlike metals, the energy plot of a DCB specimen shows increase in energy release rate with increase in crack length. Also during testing the steady state energy release rate from each of the samples of the same batch shows a lot of variation due to fiber cross-over bridging that occurs only in unidirectional composites. In this study, a probabilistic Cohesive Zone Model (CZM) is developed to capture steady state energy release rate variations of 51mm crack size DCB specimens based on unidirectional composite (IM7/977-3) test data. Then using the probabilistic CZM, the energy release rate variations of 76.2mm crack size DCB model are predicted and compared to the test results. The predictions showed good agreement with the experiments suggesting a probabilistic CZM is capable of simulating the delamination process in unidirectional composites.

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.

Fracture Behavior of Multidirectional DCB Specimen: Higher-Order Beam Theories

Mathematical models, for the stress analysis of symmetric multidirectional double cantilever beam (DCB) specimen using classical beam theory, first and higher-order shear deformation beam theories, have been developed to determine the Mode I strain energy release rate (SERR) for symmetric multidirectional composites. The SERR has been calculated using the compliance approach. In the present study, both variationally and nonvariationally derived matching conditions have been applied at the crack tip of DCB specimen. For the unidirectional and cross-ply composite DCB specimens, beam models under both plane stress and plane strain conditions in the width direction are applicable with good performance where as for the multidirectional composite DCB specimen, only the beam model under plane strain condition in the width direction appears to be applicable with moderate performance. Among the shear deformation beam theories considered, the performance of higher-order shear deformation beam theory, having quadratic variation for transverse displacement over the thickness, is superior in determining the SERR for multidirectional DCB specimen.

Analysis of unidirectional (0°) fiber-reinforced laminated composite double cantilever beam specimen using higher order beam theories

Mathematical models, for the stress analysis of unidirectional (0°) fiber-reinforced laminated composite double cantilever beam (DCB) specimen using classical beam theory, first and higher order shear deformation beam theories, have been developed to determine the mode I strain energy release rate (SERR) for unidirectional composites. In the present study, appropriate matching conditions at the crack tip of the DCB specimen have been derived by using variational principles. SERR has been calculated using compliance method. In general, the performance of shear deformation beam models of DCB specimen with variationally derived matching conditions at the crack tip is good in determining the SERR for medium to long crack lengths. Performance of higher order shear deformation beam model (having quadratically varying transverse displacement over the thickness) of DCB specimen, with non-variationally derived matching conditions at the crack tip, is good in determining the SERR for all the crack lengths in comparison with the available theoretical and finite element solutions in the literature. Higher order shear deformation beam theories having varying transverse displacement over the thickness are more appropriate to analyze DCB specimen as they predict the appropriate nature of the interlaminar normal stress at the crack tip and its distribution ahead of the crack tip.

Experimental studies of Mode I energy release rate in adhesively bonded width tapered composite DCB specimens

The Mode I energy release rate, G I, derived from conventional uniform width double cantilever beam (DCB) test data depends on crack length. Data acquisition and analysis from such experiments can be simplified if G I is independent of crack length, particularly at high loading rates. Previous research by others has shown that width tapered double cantilever beam (WTDCB) specimens made from aerospace grade carbon/epoxy composite laminates without adhesive layers exhibit critical energy release rates which are independent of crack length. The purpose of the present investigation was to determine whether or not adhesively bonded WTDCB specimens of automotive type sheet molding compound (SMC) composites show similar behavior. It was observed that the critical energy release rate was practically independent of crack length for unidirectional carbon/epoxy WTDCB specimens without adhesive layers but not for unidirectional carbon/epoxy, unidirectional E-glass/epoxy or automotive SMC WTDCB specimens with adhesive layers, and that self-similar crack growth only occurred in unidirectional carbon/epoxy WTDCB specimens without adhesive layers.

Effect of the actuation phase on the SIF in delaminated composites withembedded piezoelectric layers

The effect of the phase of harmonic actuation on the stress intensity factor(SIF) for delaminated composites with embedded piezoelectric (PZT)layers is studied. A plane-stress finite-element model using a four-nodequadrilateral element having one active degree of freedom per node isdeveloped. A fracture mechanics-based approach, which uses a general purposecomputational scheme to obtain the strain energy release rate and the SIFdue to delamination in orthotropic laminated composite, is employed.The performance of the finite-element result is first validated using theresults reported in published literature. A composite double cantileverbeam specimen with three embedded PZT layers around the tip of thedelamination is considered for actuation. Numerical simulations on the effects ofactuation voltage and phase on mode-II SIF are carried out. The results showthat for a specified voltage amplitude to the embedded actuators, theactuation phase can have a significant influence on delamination growth.

Delamination Modeling of Composites for Improved Crash Analysis

Modeling of crashworthy composite structures is limited by the inability of current generations of finite element crash codes to effectively model certain critical failure modes, such as delamination. Previous efforts to model delamination and debonding failure modes using crash codes have typically relied on ad hoc failure criteria and quasistatic fracture data. Improvements to these modeling procedures can be made by using an approach based on fracture mechanics. Finite element predictions of delamination growth using the virtual crack closure technique are implemented using the finite element crash code MSC/DYTRAN and compared with other methods of modeling delamination in finite element crash analyses. Computational results for composite double cantilever beam specimens are compared with experimental results from the literature. This investigation demonstrates the potential for improving the crash modeling of composites through improved delamination modeling. Further developments to this approach may result in improved analytical tools that can be used to model delamination using current generation crash codes.

Determination of fracture parameters of laminated thermoplastic composite materials: a finite element approach

With the advent of new adhesives bonded joints are growing in use. These joints made up of different materials such as thermoset and thermoplastic-laminated composite materials are prone to peel off at their interface leading to failure. In the present work an improved locking-free four-node finite element is developed. Developed locking-free element is validated for a cantilever beam under flexural loading condition. In fact, the element is observed to be free from parasitic shear leading to more accurate results. Further, the developed element is being applied for the fracture study of laminated composite materials for the first time. Double-cantilever beam (DCB) specimens of isotropy material and laminated composite materials are modelled with locking free four-node plane strain elements to predict the fracture parameters. Crack growth along the interface of the joints are simulated by sequential opening of paired nodes. Finite element analyses are carried out and strain energy release rates are computed. Using the developed element accurate fracture parameters are obtained for isotropy and laminated composite DCB specimens. Simultaneously, experiments are conducted and strain energy release rates of the DCB specimens are determined. Computed strain energy release rates employing the developed element are in good agreement with those reported in literature and those obtained from the experiments.

An Analytical Investigation of Delamination Front Curvature in Double Cantilever Beam Specimens

An analytical investigation is conducted to determine the shape of a growing delamination and the distribution of the energy release rate along the delamination front in a laminated composite double cantilever beam specimen. Distributions of the energy release rate for specimens with straight delamination fronts and delamination front con tours for delaminations whose growth is governed by the fracture criterion that G = Gc at all points are predicted as a function of material properties and delamination length. The predicted delamination front contours are utilized to ascertain the effect of the chang ing shape of the delamination front on the value of the critical strain energy release rate as computed from double cantilever beam fracture toughness test data.

Three-dimensional elastic analysis of a composite double cantilever beam specimen

Attention is given to the stresses and the strain energy release rate along the delamination front in the present three-dimensional elastic analysis of a 24-ply, cocured double-cantilever beam specimen by means of 20-noded parabolic-isoparametric finite elements. At the free surface, the strain energy release rate was found to be substantially smaller than the plane strain value; this is suggested to be due to the free-surface effect that exists where the delamination meets the surface edge.