Dynamic delamination fracture toughness in unidirectional polymeric composites

A modified end-notched flexure (ENF) specimen was used to determine Mode-II-dominated dynamic delamination fracture toughness of fiber composites at high crack propagation speeds. A strip of FM-73 adhesive film was placed at the tip of the interlaminar crack created during laminate lay-up. This adhesive film with its greater toughness delayed the onset of crack extension and produced crack propagation at high speeds. Dynamic delamination experiments were performed on these ENF specimens made of unidirectional S2/8553 glass/epoxy and AS4/3501-6 carbon/epoxy composites. Crack speed was measured by means of conductive aluminum lines created by the vapor deposition technique. A finite-element numerical simulation based on the measured crack speed history was performed and the dynamic energy release rate calculated. The results showed that the dynamic fracture toughness is basically equal to the static fracture toughness and is not significantly affected by crack speeds up to 1100 m/s.     

Dynamic delamination growth in laminated composite structures

The dynamic growth of a thin strip delamination in a thick base laminate under in-plane loadings has been analysed. A variational principle, coupled with a Griffith-type fracture criterion, is used to formulate the delamination growth problem. Two approximate solutions, including one mode and two modes, respectively, are calculated in this paper. The resulting equations of motion and the dynamic local growth condition at the crack tip turn out to be two and three coupled ordinary differential equations for one-mode and two-mode solutions. A fourth-order Runge-Kutta method is then used to obtain the numerical solutions. The results show that delamination growth will approach a state of arrest for materials with high fracture toughness, and continue all the way without a limit for low fracture toughness materials. The inertial effect is important and should not be ignored in calculation of the arrested delamination length for high fracture toughness materials. For materials with low fracture toughness, the inertial effect is significant and high admissible modes are noticeable. A comparison between the present results and the previously known quasi-dynamic solution is also given.     

Influence of adsorption behaviour of a silane coupling agent on interlaminar fracture in glass fibre fabric-reinforced unsaturated polyester laminates

The relationship between the interphase consisting of physisorbed and chemisorbed silane on glass fibres and the resultant composite Mode I delamination fracture toughness in glass fibre fabric laminate, was studied. The Mode I interlaminar fracture toughness of the laminate specimen was obtained by using a double cantilever beam (DCB) specimen. The delamination resistance of the laminate specimen finished with two silane concentrations and washed in methanol solvent, is discussed on the basis of the interlaminar fracture toughness. In order to determine the amount of physisorbed and chemisorbed silane on the glass fibre, the amount of total carbon was determined using an analysis instrument. The physisorbed silane migrated into the resin matrix and influenced the mechanical properties and interlaminar fracture of the laminate specimen. The amount of unsaturated polyester resin blended with a silane coupling agent was measured using dynamic mechanical spectroscopy, and a DCB specimen for mechanical properties and fracture toughness.     

Fracture Parameters for Natural Rubber Under Dynamic Loading

Abstract: An experimental study was conducted to evaluate the tear energy of unfilled and 25 phr carbon black‐filled natural rubber with varying loading rates. The variation of the tear energy with far‐field sample strain rate between 0.01 to 10 s^?1 was found to be different from tensile strip and pure shear specimens. Above a sample strain rate of 10 s^?1, the tear energy calculated from either specimen was comparable. The differences in the tear energy derived from the tensile strip and pure shear specimens were attributed to differences in the local crack tip stress state and strengthening of the material due to strain‐induced crystallisation. Both of these factors resulted in crack speeds 3–4 times higher in the pure shear specimen as compared to the tensile strip specimen. Finite element analysis (FEA) indicated that fracture would initiate at the crack tip either when the strain energy density approached the material toughness or when the maximum principal stress and strain approached the material tensile strength and fracture strain, respectively. It was concluded that these parameters would be better than the tear energy in predicting fracture of natural rubber under dynamic loading.     

Prediction of initiation and growth of single level delaminations in a transversely loaded composite specimen using fracture mechanics

The behaviour of a composite test specimen with an embedded delamination subjected to transverse tension has been investigated through experimental testing and finite element (FE) analyses. The testing program consisted of specimens in two geometrical configurations; square and rectangular delamination. The initiation and growth of the delamination was numerically predicted by fracture mechanics. FE models were analysed with both MSC.Nastran and Abaqus FE codes. The MSC.Nastran model was used to calculate strain energy release rates employing a crack tip element methodology. The Abaqus model was evaluated using the virtual crack closure technique. Both approaches accurately predicted failure initiation locations as observed in the test specimens. Failure loads were also well predicted. The mode mix at the crack tip in the proposed specimen was found to be similar to the mode mix expected in a conventional in-plane compression specimen.     

Finite element modelling of delamination growth in the DCB and edge delaminated DCB specimens

This paper presents the results of a finite element investigation of delamination growth in a conventional Mode I double cantilever beam (DCB) specimen and in an edge-delaminated version of this specimen. The investigation was performed using a recently developed FE model for delamination growth prediction to which an approximate contact area detection method has been added. The results of the FE analyses are used to evaluate the existing data reduction techniques for calculation of interlaminar fracture toughness. It is shown that the conventional DCB data reduction schemes can be applied to the edge delaminated specimen but the results are dependent upon the difference between the measured apparent delamination length and the actual length being constant. An alternative data reduction method is presented in which the critical energy release rate is determined by comparison of the experimental data with finite element results and does not require measurement of the delamination length.     

A cohesive zone model for predicting delamination suppression in z-pinned laminates

This paper presents a cohesive zone model based finite element analysis of delamination resistance of z-pin reinforced double cantilever beam (DCB). The main difference between this and existing cohesive zone models is that each z-pin bridging force is governed by a traction-separation law derived from a meso-mechanical model of the pin pullout process, which is independent of the fracture toughness of unreinforced laminate. Therefore, two different traction-separation laws are used: one representing the toughness of unreinforced laminate and the other the enhanced delamination toughness owing to the pin bridging action. This approach can account for the large scale bridging effect and avoid using concentrated pin forces, thus removing the mesh dependency and permitting more accurate analysis solution. Computations were performed using a simplified unit strip model. Predicted delamination growth and load vs. displacement relation are in excellent agreement with the prediction by a complete model, and both models are in good agreement with test measured load vs. displacement relation. For a pinned DCB specimen, the unit strip model can reduce the computing time by 85%.     

Application of a dynamic numerical solution to high speed fracture experiments—I. analysis of experimental geometries

The application of a dynamic, generation mode, finite element program to the analysis of experimental geometries is reported. Particular attention is given to the DCB specimen, which is widely used in high speed fracture studies despite strong inertia effects, which are described. Finite strip and infinite plate results are also considered. Here, idealised cases are discussed, while in Part II the application of the analysis to experimental measurements, to derive propagating crack fracture resistance data, is reported.     

Delamination of multidirectional composite laminates at 0°/θ° ply interfaces

The main objective of this study is to develop a methodology for establishing mixed-mode delamination propagation criteria of non-unidirectional laminates. The crack interface was chosen to be 0°/45° and the effort was mainly focused on obtaining the mode I fracture toughness (G_IC). The widely used DCB test was avoided due to anticipated problems with intralaminar damage developing at the ply interface of interest. The ADCB and AMMF methods were used to determine the mixed-mode fracture toughness with the largest amount of mode I. The selected stacking sequence resulted in desirable crack propagation behavior; there was no change of delamination plane, an acceptable crack front profile, no initial specimen curvature, and no energy dissipation through global specimen damage. Finite element simulation was found to be the only tool capable of analyzing the experimental data.     

Analysis of fracture and delamination in laminates using 3D numerical modelling

The static failure behaviour of the fibre-metal laminate GLARE is examined using 3D finite element simulations. The configuration analysed is a centre-cracked tensile specimen composed of two aluminium layers sandwiching a cross-plied, fibre-epoxy layer. The crack and delamination growths are simulated by means of interface elements equipped with a mixed-mode damage model. The mode-mixity is derived from an energy criterion typically used in linear elastic fracture mechanics studies. The damage kinetic law is rate-dependent, in order to simulate rate effects during interfacial delamination and to avoid numerical convergence problems due to crack bifurcations. The numerical implementation of the interface damage model is based on a backward Euler approach. In the boundary value problem studied, the failure responses of GLARE specimens containing elastic aluminium layers and elasto-plastic aluminium layers are compared. The development of plastic deformations in the aluminium layers stabilizes the effective failure response, and increases the residual strength of the laminate. For a ‘quasi-brittle’ GLARE specimen with elastic aluminium layers, the residual strength is governed by the toughness for interfacial delamination, and is in close correspondence with the residual strength obtained from a closed-form expression derived from energy considerations. Conversely, for a ‘ductile’ GLARE specimen with elasto-plastic aluminium layers, the residual strength is also determined by the relation between the fracture strength and the yield strength of the aluminium. The amount of constraint by the horizontal displacements at the vertical specimen edges has a moderate to small influence on the residual strength. Furthermore, the ultimate laminate strength is lower for a larger initial crack length, and shows to be in good correspondence with experimental values.     

Fixtureless superlayer-driven delamination test for nanoscale thin-film interfaces

A fixtureless delamination test has been developed to measure the interfacial fracture toughness of patterned nanoscale thin films on a substrate. The driving energy for delamination propagation is supplied by a highly stressed superlayer deposited on top of the nanoscale thin film. The amount of energy available for delamination propagation is changed by depositing an etchable thin release layer with varying width between the nanoscale thin-film strip and the substrate. By designing a decreasing area of the release layer, it is possible to arrest the delamination at a given location, and the interfacial fracture toughness or critical energy release rate can be found at the location where the delamination ceases to propagate. For titanium film with a thickness of 90 nm, the results show that the interfacial fracture toughness of titanium/silicon ranges from 3.45 J/m² to 5.70 J/m² when the mode mixity increases from 6.8° to 38.4°. The methodology presented in this paper is generic in nature, and can be used to measure the process-dependent interfacial fracture toughness of various micro and nanoscale thin films on a substrate.     

Comparative study of dynamic and static delamination behaviour of carbon fibre/epoxy composite laminates

Dynamic and static delamination characteristics of two unidirectional carbon fibre-reinforced epoxy composite laminates (Hercules MI 1610 and Torayca T300) have been studied under impact and low-speed (2 mm min¹) test conditions. The influence of interlaminar reinforcement with chopped Kevlar fibres on toughness has also been examined. The quasi-static or low-speed delamination tests were conducted with the usual double cantilever beam, end-notched flexure and mixed-mode flexure specimens. To determine the corresponding mode I, mode II and mixed-mode toughnesses under the impact condition, a special specimen design has been adopted and tests were performed with a Charpy impact machine. The novel aspect of the test scheme in the present study is that a single-plane delamination surface with a well-defined fracture mode has been obtained. The dynamic and static delamination characteristics of the same fracture mode were then studied by scanning electron microscopy, and special features were compared. While interlaminar reinforcement with a small amount of chopped Kevlar fibres resulted in an appreciable increase in the quasi-static delamination toughness, it was less effective under the impact condition.     

Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues

The finite element analysis of delamination in laminated composites is addressed using interface elements and an interface damage law. The principles of linear elastic fracture mechanics are indirectly used by equating, in the case of single‐mode delamination, the area underneath the traction/relative displacement curve to the critical energy release rate of the mode under examination. For mixed‐mode delamination an interaction model is used which can fulfil various fracture criteria proposed in the literature. It is then shown that the model can be recast in the framework of a more general damage mechanics theory. Numerical results are presented for the analyses of a double cantilever beam specimen and for a problem involving multiple delamination for which comparisons are made with experimental results. Issues related with the numerical solution of the non‐linear problem of the delamination are discussed, such as the influence of the interface strength on the convergence properties and the final results, the optimal choice of the iterative matrix in the predictor and the number of integration points in the interface elements. Copyright © 2001 John Wiley & Sons, Ltd.     

Fracture surface evolution and apparent delamination toughness in split composite beam specimens subjected to mixed mode I–III loading

The influence of specimen twisting during global anti-plane shear loading in composite split beam specimens is studied. Tests were conducted on specimens with different thicknesses and delamination lengths to produce different amounts of specimen twisting prior to fracture. It is shown that specimen twisting causes mode I stresses to develop, thereby producing mixed mode I–III conditions along the delamination front. This causes near-tip transverse cracks to initiate, prior to delamination advance, at an orientation related to the mode mix. Unlike in homogeneous materials, transverse crack extension is accompanied by planar delamination advance, and transverse crack rotation during extension is restricted by the laminate’s fibers. The overall fracture surface evolution is therefore strongly controlled by specimen geometry. The influence of these findings on the apparent delamination toughness as obtained from composite split beam and other types of mode III tests is discussed.     

Size effect on the contact state between fracture specimen and supports in Hopkinson bar loaded fracture test

To thoroughly understand the dynamic behavior of a fracture specimen under stress wave loading, dynamic fracture test with various three-point bend (3PB) specimens are performed on the Hopkinson bar loaded experimental apparatus. The contact state between the fracture specimen and supports during the loading process is examined via stress wave propagation analysis. The experimental results show that the fracture specimen with usual dimensions does not keep contact with supports in the initial loading stage, i.e. a loss of contact phenomenon occurred. The specimen dimensions and the span of the loading apparatus are important factors affecting specimen’s contact state. The loss of contact is more obvious with increasing span under the same specimen dimensions. Conversely, the loss of contact gradually disappears with increasing specimen length or increasing width under a fixed span. Based on experimental investigations, a criterion is established to ensure the fracture specimen keep in contact with supports during dynamic fracture test.     

Development of a simple dynamic model for fast fracture research

The aim of this study was to devise a simple fracture model, which could be hosted on a personal computer (PC), to assist in researching the dynamic behaviour of materials during fast crack propagation. A model was required which could be easily reconfigured to represent different materials, provide good visibility of the dynamic fracture processes being simulated and generate information to complement the results of experimental research. A version of the devised PC model and its use with a recently developed experimental technique to achieve rapid crack propagation in a small specimen, is presented.     

Numerical Analysis of the Three Point Bend Impact Test for Polymers

The three point bend impact test is analysed by employing the finite volume method. Numerical modelling was necessary to enhance understanding of the test and to obtain dynamic correction functions, which are convenient to calculate K and G from measured time to fracture. A simple model of the three point bend test and a more sophisticated model, which included contact effects, were analysed. A good fit with experiments was found when using the contact model. The anvils were found to be important only at a late stage in the test. Several test parameters were varied to investigate their influence on the dynamic correction function. The contact stiffness was found to have an important influence on the shape of the dynamic correction function. Due to the nonlinear contact stiffness the impact velocity also affects the dynamic correction function. For a polymer specimen and a steel striker the specimen width and the specimen material were found to have only a small influence on the dynamic correction function. The dynamic correction function for G was found to exhibit higher oscillations than the dynamic correction function for Kas expected, and hence the former is a more sensitive parameter.     

Constraint Loss under Dynamic Loading in Rate Independent Plastic Solids

The objectives of this paper are to examine the loss of crack tip constraint in dynamically loaded fracture specimens and to assess whether it can lead to enhancement in the fracture toughness at high loading rates which has been observed in several experimental studies. To this end, 2-D plane strain finite element analyses of single edge notched (tension) specimen and three point bend specimen subjected to time varying loads are performed. The material is assumed to obey the small strain J ₂ flow theory of plasticity with rate independent behaviour. The results demonstrate that a valid J–Q field exists under dynamic loading irrespective of the crack length and specimen geometry. Further, the constraint parameter Q becomes strongly negative at high loading rates, particularly in deeply cracked specimens. The variation of dynamic fracture toughness K _dc with stress intensity rate K for cleavage cracking is predicted using a simple critical stress criterion. It is found that inertia-driven constraint loss can substantially enhance K _dc for .     

Dynamic delamination fracture toughness of a graphite/epoxy laminate under impact

Dynamic delamination fracture toughness in a [90/0]_5s T300/934 graphite/epoxy laminate was investigated using impact loading. Delamination cracks of three different sizes were embedded at the mid-plane of the composite specimen. The threshold impact velocity that causes propagation of the delamination crack was used in the dynamic analysis with the finite element method. From the finite element solution, the time-history of the strain energy release rate was calculated. The critical strain energy release rate was taken to equal the maximum value of the response history.     

An investigation into the mixed-mode delamination growth in unidirectional T800/924C laminates

This study presents the results of experimental investigations and numerical simulation on mixed-mode I/II delamination growth initiated from an artificial transverse notch. Specimens made of unidirectional carbon fiber epoxy (T800/924C) composite have been tested under three-point-bend condition. A finite element procedure has been introduced to model 3-D stable delamination growth in the specimen to generate numerical growth data including loads, displacements, delamination lengths, and the growing crack front shapes. The simulation method uses strain energy release rate criterion in conjunction with a moving mesh facility. It is shown that very good compatibility exists between experimental and numerical results. A finite element-based data reduction method is then described as an application of the simulation procedure. Based on the obtained results, it is stated that this bending specimen can effectively be used in practice to study the mixed-mode crack growth and to measure interlaminar fracture toughness of unidirectional laminates.