Predicting mode-II delamination suppression in z-pinned laminates

A finite element model for predicting delamination resistance of z-pin reinforced laminates under the mode-II load condition is presented. End notched flexure specimen is simulated using a cohesive zone model. The main difference of this approach to previously published cohesive zone models is that the individual bridging force exerted by z-pin is governed by a specific traction-separation law derived from a unit-cell model of single pin failure process, which is independent of the fracture toughness of the unreinforced laminate. Therefore, two separate traction-separation laws are employed; one represents unreinforced laminate properties and the other for the enhanced delamination toughness owing to the pin bridging action. This approach can account for the so-called large scale bridging effect and avoid using concentrated pin forces in numerical models, thus removing the mesh-size dependency and permitting more accurate and reliable computational solutions.     

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.     

Effect of z-pin surface treatment on delamination and debonding properties of z-pinned composite laminates

The effect of z-pin surface treatment on the delamination fracture properties of z-pinned unidirectional carbon fibre/epoxy prepreg laminate is presented in this paper. Cryogenic and plasma treatments were used to increase the pin/composite interface properties. Z-pin pullout tests were carried out to study the relations between the bridging force and the displacement. Mode-I double-cantilever beam tests were used to characterize the improvements in delamination toughness. It was pointed out that appropriate treatments could effectively increase the delamination fracture properties. Oxygen-containing functional groups could be induced on the pin surface through cold plasma treatment. An increasing surface energy is improving the wettability so that more chemical reactions can be generated between the epoxy group and z-pin surface. Furthermore, the surface roughness of z-pins can be extended with a plasma or cryogenic treatment. The pins obtained a larger surface area, which could wet by the epoxy matrix during the z-pin-insertion and curing process.     

Finite element model for compression after impact behaviour of stitched composites

A finite element (FE) model using coupling continuum shell elements and cohesive elements is proposed to simulate the compression after impact (CAI) behaviour and predict the CAI strength of stitched composites. Continuum shell elements with Hashin failure criterion exhibit the composite laminate damage behaviour; whilst cohesive elements using traction-separation law characterise the laminate interfaces. Impact-induced delamination is explicitly modelled by reducing material properties of damaged cohesive elements. Computational results have demonstrated the trend of increasing CAI strength with decreasing impact-induced delamination area. Spring elements are introduced into the model to represent through-thickness stitch thread in the composite laminates. Results in this study validate experimental finding that CAI strength is improved when stitching is incorporated into the composite structure. The proposed FE model reveals good CAI strength predictions and indicates good agreement with experimental results, making it a valuable tool for CAI strength prediction of stitched composites.     

Influence of z-pin length on the delamination fracture toughness and fatigue resistance of pinned composites

The effect of z-pin length on the mode I and mode II delamination toughness and fatigue resistance of z-pinned carbon-epoxy composites is investigated. Experimental testing and mechanical modelling reveals that both the mode I fracture toughness and fatigue resistance increase with the z-pin length due to increased bridging traction loads generated by elastic stretching and pull-out of the pins. The opposite trend occurs for mode II toughness, which decreases with increasing z-pin length due to lower traction loads arising from restrictions on the shear-induced rotation and pull-out of the pins. The mode II fatigue resistance is increased by z-pinning, although it is not dependent on the z-pin length. Increasing the z-pin length beyond a critical size also changes the mode I and mode II delamination fracture and fatigue processes from single to multiple cracking. The effect of z-pin length on the delamination toughening and fatigue strengthening mechanisms is determined.     

Modelling delamination onset and growth in pin loaded composite laminates

A three-dimensional (3D) finite element (FE) model is created with cohesive zone elements (CZE) to simulate a mechanically fastened [0°/90°]_s pin-loaded joint in a composite laminate. The model incorporates fully integrated solid elements in the pin-loaded area to accurately capture the high stress gradients. Contact based cohesive elements with a bilinear traction–separation law are inserted between the layers to capture the onset and growth of delamination. The stress distribution around the pin-loaded hole was verified with the widely used cosine stress distribution model. Results from the FE model show that delamination damage initiated at the point of maximum average shear stress at the 0°/90° interface. The delaminated area develops an elliptical shape which grows in a non-self similar manner with increasing pin displacement. It is concluded that a progressive damage model should be included to provide a full understanding of the failure sequence, work that the authors are currently engaged with.     

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.     

Finite element simulation of delamination growth in composite materials using LS-DYNA

In this paper, a modified adaptive cohesive element is presented. The new elements are developed and implemented in LS-DYNA, as a user defined material subroutine (UMAT), to stabilize the finite element simulations of delamination propagation in composite laminates under transverse loads. In this model, a pre-softening zone is proposed ahead of the existing softening zone. In this pre-softening zone, the initial stiffness and the interface strength are gradually decreased. The onset displacement corresponding to the onset damage is not changed in the proposed model. In addition, the critical energy release rate of the materials is kept constant. Moreover, the constitutive equation of the new cohesive model is developed to be dependent on the opening velocity of the displacement jump. The traction based model includes a cohesive zone viscosity parameter (η) to vary the degree of rate dependence and to adjust the maximum traction. The numerical simulation results of DCB in Mode-I is presented to illustrate the validity of the new model. It is shown that the proposed model brings stable simulations, overcoming the numerical instability and can be widely used in quasi-static, dynamic and impact problems.     

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.     

A study on the influence of cohesive zone interface element strength parameters on mixed mode behaviour

This paper presents a detailed study of the influence of maximum interfacial stress on interface element analyses for composites delamination. The development of the non-linear cohesive zone ahead of a crack tip is analysed with respect to length, stress distribution and mode ratio. The energy absorbed by interface elements is compared with the crack tip strain energy release rate from fracture mechanics analyses. These studies are performed initially on standard fracture toughness specimens, where mode-ratio is fixed by the applied displacement constraints. Results show close agreement with linear elastic fracture mechanics solutions. A simple ply drop specimen is then modelled, where the mode ratio is not constrained by the boundary conditions, and results are compared with the Virtual Crack Closure Technique. In this case maximum interfacial stress has a far greater influence on the numerical results, due to its significant influence on cohesive zone length, mode ratio and energy absorbed.     

A Stochastic XFEM Model to Study Delamination in PPS/Glass UD Composites: Effect of Uncertain Fracture Properties

A nonlinear extended finite element (XFEM) modeling framework under a stochastic cohesive zone is presented for realistic prediction of delamination in polyphenylene sulfide (PPS)/glass composites in mode I of fracture. The cohesive zone model adopts damage evolution of the material based on a bilinear traction-separation law, the critical energy release rate and the J-integral method to formulate the delamination interface under stochastic fracture properties. To demonstrate the application of the approach, numerical predictions are compared to experimental data using Double Cantilever Beam (DCB) tests. In particular, it is shown how the XFEM model can be used to capture test non-repeatability due to uncertain fracture properties, which is often the case during the characterization of composites using standard fracture tests.     

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.     

Experimental investigation and finite element modeling of mixed-mode delamination in a moisture-exposed carbon/epoxy composite

An investigation of the effects of moisture on mixed-mode I/II delamination growth in a carbon/epoxy composite is presented. Experimental quasi-static and fatigue delamination tests were carried out on composite specimens. The quasi-static fracture test results showed that exposure to moisture led to a decrease in mode II and mixed-mode delamination toughness while mode I toughness was enhanced. The fatigue tests revealed an adverse effect of moisture on delamination growth under mixed-mode loadings. Existing delamination criteria and growth rate models were evaluated to determine which ones best predict delamination toughness and growth, respectively, at any given mixed-mode ratio. Quasi-static and fatigue simulations with a cohesive zone-based finite element model that incorporated the selected mixed-mode delamination models were performed and good agreement between experimental and numerical data was shown for dry and moisture-exposed specimens.     

Mode II fracture characterization of a hybrid cork/carbon-epoxy laminate

Fracture characterization under mode II loading of a hybrid laminate composed by a unidirectional carbon fiber-epoxy composite and cork was performed using the End Notched Flexure test. A data reduction scheme based on equivalent crack length concept, specimen compliance and Timoshenko beam theory was applied to evaluate fracture toughness under mode II loading of a composed beam (cork and carbon-epoxy composite). The adopted procedure depends exclusively on the data issuing from load–displacement (P–δ) curve and does not require crack length monitoring during the test which is a difficult task to be accomplished with the necessary accuracy in the ENF test. A numerical analysis using cohesive zone modeling and an inverse procedure was performed to assess the mode II cohesive law that simulates the material fracture under shear loading. It was concluded that hybridization is advantageous relative to monolithic carbon-epoxy laminate in which concerns the observed failure mode, which altered from typically brittle to very ductile thus contributing to avoid sudden shear failures in real applications.     

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.     

Prediction of Mode I interlaminar fracture toughness of stitched flax fiber composites

This paper aims to propose a simulation procedure to predict the interlaminar fracture toughness of stitched flax fiber composites through a virtual double cantilever beam test. The proposed procedure is constituted of two steps. First, the interlaminar failure of unstitched flax fiber laminate, as the parent laminate, is modeled using cohesive elements with a nonlinear softening law in order to model the large-scale fiber bridging occurred during delamination. The experimental results are used to calibrate the parameters of the cohesive law. Second, two-node beam elements are superposed onto the cohesive interface of the parent laminate at a prescribed stitch density and distribution to model the bridging stitches present in the validation samples. The stitch material behavior and properties are obtained from the tensile test of impregnated stitch fibers. The out-of-plane flax yarn stitching was found to generate a twofold increase in the delamination resistance of the composite laminate at a medium stitch density. The FE analysis results agreed well with the experimental results, where a good fit between the predicted and experimental R-curves was achieved.     

Monitoring of delamination onset and growth during Mode I and Mode II interlaminar fracture tests using guided waves

A delamination monitoring method was proposed to characterize Mode I and Mode II delamination onset in carbon fiber/epoxy (CF/EP) composite laminates through interrogation of guided waves activated and captured using piezoelectric actuators and sensors in a pitch–catch configuration. Mode I and Mode II interlaminar fracture tests were conducted using double cantilever beam (DCB) and end notch flexure (ENF) specimens to evaluate the proposed method. The changes in wave propagation velocity and wave magnitude (or attenuation), and the degree of waveform similarity between excitation and response signals, were calculated as delamination-sensitive wave parameters and plotted versus displacement recorded using a materials testing system. The kink points determined from wave parameter–displacement curves agreed well with the deviation from linearity (NL), visual observation (VIS) and maximum load (Max) points, which are often used in conventional methods for determining interlaminar fracture toughness. The propagation characteristics of the A₀ wave mode in a low frequency range were demonstrated to have high sensitivity to Mode I and in particular Mode II delamination onset in CF/EP composite laminates. It was concluded that the guided waves propagating in the DCB and ENF specimens were capable of determining Mode I and Mode II interlaminar fracture toughness, complementing current practices based on visual inspection or trivial interrogation using load–displacement curve alone.     

Numerical investigation on the loading-delamination-unloading behavior of adhesive joints

An elastic-plastic interface model at finite deformations is utilized to investigate the irreversible delamination behavior of adhesive joints subjected to loading-delamination-unloading. The interface model accounts for the irreversible delamination in the fracture process zone induced by the localized plastic deformation and damage. The interfacial parameters in the cohesive model are obtained by fitting the available experimental data. Results suggest that the cohesive model can capture the irreversible delamination failure behavior observed in adhesively bonded joints during a loading-unloading cycle. The overall nonlinear response is dominated by the cohesive strength and initial damage displacement jump. Further, we also investigate the effect of the ductile mechanisms for the bulk layer on the competition between the plastic deformation of the bulk layer and the delamination of the interface. It is observed that the degradation of unloading stiffness is attributed to the inelastic behavior of the interface.     

Environmental durability of z-pinned carbon fibre–epoxy laminate exposed to water

The influence of z-pins on the water absorption properties of a quasi-isotropic carbon fibre–epoxy laminate is assessed. Fibrous composite pins accelerate the moisture absorption rate and increase the total absorbed moisture concentration when the laminate is immersed in water. However, the moisture absorption properties of the laminate are not affected significantly by pins when exposed to hot and humid air. Water diffusion into the z-pinned laminate is aided by interfacial cracks between the pins and laminate. Also, the axial alignment of fibres within the composite pins in the through-thickness direction increases the water absorption rate. Pin pull-out tests reveal that water absorption reduces the mode I crack bridging traction load generated by pins by reducing the shear strength of the pin-laminate interface. This indicates that the mode I delamination toughness induced by pinning is weakened by moisture absorption.