Identification of Fracture Toughness for Discrete Damage Mechanics Analysis of Glass-Epoxy Laminates

A methodology for determination of the intralaminar fracture toughness is presented, based on fitting discrete damage mechanics (DDM) model predictions to available experimental data. DDM is constitutive model that, when incorporated into commercial finite element software via user material subroutines, is able to predict intralaminar transverse and shear damage initiation and evolution in terms of the fracture toughness of the composite. The applicability of the DDM model is studied by comparison to available experimental data for Glass-Epoxy laminates. Sensitivity of the DDM model to h- and p-refinement is studied. Also, the effect of in-situ correction of strength is highlighted.     

Strength prediction in CFRP woven laminate bolted double-lap joints under quasi-static loading using XFEM

The current paper is concerned with modelling damage and fracture in woven fabric composite double-lap bolted joints that fail by net-tension. A 3-D finite element model is used, which incorporates bolt clamp-up, to model a range of CFRP bolted joints, which were also tested experimentally. The effects of laminate lay-up, joint geometry, hole size and bolt clamp-up torque were considered. An Extended Finite Element (XFEM) approach is used to simulate damage growth, with traction–separation parameters that are based on previously reported, independent experimental measurements for the strength and toughness of the woven fabric materials under investigation. Good agreement between the predicted and measured bearing stress at failure was obtained.     

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.     

Characterising fibre compression fracture toughness of composites using bearing tests

In this paper we propose the use of a bearing test with a coupled experimental–numerical approach to characterise the critical strain energy release rate, or “fracture toughness”, for fibre compression failure in bearing. This property is used in continuum damage mechanics (CDM) approaches for progressive failure analysis of composite laminates. In the proposed approach, experimental results for a standard bearing test are used to calibrate the fracture toughness with a progressive failure analysis using a CDM damage model. The approach is demonstrated for a plain weave carbon/epoxy material using the CDM damage model available in a commercial finite element package (Abaqus). The results indicate that the bearing test method provides a simple and convenient means of quantifying fibre compression fracture toughness. Analysis results applying the characterised value show good comparison with experimental results, and confirm the value of the bearing test as part of a novel material characterisation technique.     

Real-time inference of stochastic damage in composite materials

This study describes a control system designed for real-time monitoring of damage in materials that employs methods and models that account for uncertainties in experimental data and parameters in continuum damage mechanics models. The methodology involves (1) developing an experimental set-up for direct and indirect measurements of damage in materials; (2) modeling damage mechanics based constitutive equations for continuum models; and (3) implementation of a Bayesian framework for statistical calibration of model with quantification of uncertainties. To provide information for real-time monitoring of damage, indirect measurement of damage is made feasible using an embedded carbon nanotube (CNT) network to perform as sensor for detecting the local damage. A software infrastructure is developed and implemented in order to integrate the various constituents, such as finite element approximation of the continuum damage models, generated experimental data, and Bayesian-based methods for model calibration and validation. The outcomes of the statistical calibration and dynamic validation of damage models are presented. The experimental program designed to provide observational data is discussed.     

Modelling complex progressive failure in notched composite laminates with varying sizes and stacking sequences

The emergence of advanced computational methods and theoretical models for damage progression in composites has heralded the promise of virtual testing of composite structures with orthotropic lay-ups, complex geometries and multiple material systems. Recent studies have revealed that specimen size and material orthotropy has a major effect on the open hole tension (OHT) strength of composite laminates. The aim of this investigation is develop a progressive failure model for orthotropic composite laminates, employing stepwise discretization of the traction–separation relationship, to predict the effect of specimen size and laminate orthotropy on the OHT strength. The results show that a significant interaction exists between delamination and in-plane damage, so that models without considering delamination would over-predict strength. Furthermore, it is found that the increase in fracture toughness of blocked plies must be incorporated in the model to achieve good correlation with experimental results.     

Mode-I,mode-II and mixed-mode I+II fracture behavior of composite bonded joints: Experimental characterization and numerical simulation

The fracture behavior of composite bonded joints subjected to mode-I, mode-II and mixed-mode I + II loading conditions was characterized by mechanical testing and numerical simulation. The composite adherents were bonded using two different epoxy adhesives; namely, the EA 9695 film adhesive and the mixed EA 9395-EA 9396 paste adhesive. The fracture toughness of the joints was evaluated in terms of the critical energy release rate. Mode-I tests were conducted using the double-cantilever beam specimen, mode-II tests using the end-notch flexure specimen and mixed-mode tests (three mixity ratios) using a combination of the two aforementioned specimens. The fracture behavior of the bonded joints was also simulated using the cohesive zone modeling method aiming to evaluate the method and point out its strengths and weaknesses. The simulations were performed using the explicit FE code LS-DYNA. The experimental results show a considerable scatter which is common for fracture toughness tests. The joints attained with the film adhesive have much larger fracture toughness (by 30–60%) than the joints with the paste adhesive, which exhibited a rather brittle behavior. The simulation results revealed that the cohesive zone modeling method performs well for mode-I load-cases while for mode-II and mixed-mode load-cases, modifications of the input parameters and the traction-separation law are needed in order for the method to effectively simulate the fracture behavior of the joints.     

Mode I fracture modeling of elastomer-toughened polymers

Analytical models are developed to correlate the mode I fracture toughness of elastomer-toughened polymers with microstructural damage modes occurring around the crack-tip. The total energy dissipation caused by three dominant damage modes, namely, plastic shear band formation, plastic void growth, and plastic deformation of the entire matrix resin, is used as the basis to derive the analytical expression for the mode I fracture toughness of the toughened polymers. Numerical results are presented and compared with available experimental data for a typical toughened epoxy resin. Parametric results involving a number of material and microstructural variables indicate some very interesting trends, and provide some guidelines toward achieving optimum fracture toughness values for these types of material systems.     

Modelling of the carbon nanotube bridging effect on the toughening of polymers and experimental verification

The effect of aligned and randomly oriented carbon nanotube (CNT), with respect to the crack growth plane, on the fracture toughness of polymers is modelled in this paper using the Elastic Plastic Fracture Mechanics. According to a critical length, two dominant toughening mechanisms for CNT-modified polymers are presented, i.e. CNT pull-out and CNT rupture. The model is then used to identify the effect of CNTs geometrical and mechanical properties on the enhancement of fracture toughness in CNT-modified polymers. The key CNT properties are the CNT radius, average length, ultimate strength, elongation before failure, interfacial shear strength between CNTs and the polymer and nanotube volume fraction. Finally, experimental results are compared with the model predictions. The correlation shows that processing of long, aligned CNTs remains the main barrier in achieving major fracture toughness enhancement.     

Enhancement of delamination fatigue resistance in carbon nanotube reinforced glass fiber/polymer composites

We show that the addition of small volume fractions of multi-walled carbon nanotubes (CNTs) to the matrix of glass–fiber composites reduces cyclic delamination crack propagation rates significantly. In addition, both critical and sub-critical inter-laminar fracture toughness values are increased. These results corroborate recent experimental evidence that the incorporation of CNTs improve fatigue life by a factor of two to three in in-plane cyclic loading. We show that in both the critical and sub-critical cases, the degree of delamination suppression is most pronounced at lower levels of applied cyclic strain energy release rate, ΔG. High-resolution scanning electron microscopy of the fracture surfaces suggests that the presence of the CNTs at the delamination crack front slows the propagation of the crack due to crack bridging, nanotube fracture, and nanotube pull-out. Further examination of the sub-critical fracture surfaces shows that the relative proportion of CNT pull-out to CNT fracture is dependent on the applied cyclic strain energy, with pull-out dominating as ΔG is reduced. The conditions for crack propagation via matrix cracking and nanotube pull-out and fracture are studied analytically using fracture mechanics theory and the results compared with data from the experiments. It is believed that the shift in the fracture behavior of the CNTs is responsible for the associated increase in the inter-laminar fracture resistance that is observed at lower levels of ΔG relative to composites not containing CNTs.     

Toughening and self-healing of epoxy matrix laminates using mendable polymer stitching

This paper presents an experimental study into a new type of stitched fibre–polymer laminate that combines high interlaminar toughness with self-healing repair of delamination damage. Poly(ethylene-co-methacrylic acid) (EMAA) filaments were stitched into carbon fibre/epoxy laminate to create a three-dimensional self-healing fibre system that also provides high fracture toughness. Double cantilever beam testing revealed that the stitched EMAA fibres increased the mode I interlaminar fracture toughness (by ∼120%) of the laminate, and this reduced the amount of delamination damage that must subsequently be repaired by the self-healing stitches. The 3D stitched network was effective in delivering self-healing EMAA material extracted from the stitches into the damaged region, and this resulted in high recovery in the delamination fracture toughness (∼150% compared to the original material). The new self-healing stitching method provides high toughness which resists delamination growth while also having the functionality to repeatedly repair multiple layers of damage in epoxy matrix laminates.     

Experimental investigation on test methods for mode II interlaminar fracture testing of carbon fiber reinforced composites

In this paper, experimental investigation on the test methods for mode II interlaminar fracture testing of carbon fiber reinforced composites are carried out. Mode II interlaminar fracture testing of unidirectional composite of carbon fiber reinforced epoxy (T800/#3631) are conducted using four kinds of test methods, namely end notched flexure (ENF) test, end loaded split (ELS) test, four-point bend end notched flexure (4ENF) test, and over notched flexure (ONF) test. An analytical model based on a point-friction assumption and classical beam theory is proposed to evaluate the effect of friction between crack faces on the mode II interlaminar fracture toughness in the 4ENF and ONF tests. The analytical model is validated by the comparison of analytical results with previous ones obtained from finite element analysis. Experimental results show that the ENF test gives reliable initiation value of fracture toughness with a small scatter and that the average value of fracture toughness obtained from 4ENF test is about 2% higher than that obtained from the ENF test. The effect of friction in the 4ENF test is much lower than that in the ONF test in which the effect of friction increases with the crack growing. It is concluded that the 4ENF test method is an effective test method for the experimental evaluation of mode II propagation interlaminar fracture toughness of carbon fiber reinforced composites.     

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.     

Effects of void damage induced by warm prestressing (WPS) on cleavage fracture of notched steel specimens

The effects of void damage induced by warm prestressing (WPS) on cleavage fracture of notched steel specimens were studied by experiments and FEM calculations. The results show that the local stress concentration around the voids promotes the cleavage initiation and decreases the notch toughness and cleavage fracture stress. The fibrous cracks ahead of notch tips caused by the ductile tearing in the WPS obviously raise the normal stress in front of their tips and decrease fracture load and notch toughness. When the beneficial effects of WPS on improving apparent fracture toughness for specimens or structures are used, the loads in WPS need to be limited so that no obvious void damage and ductile tearing are produced in front of defects.     

Strength analysis of particulate polymers

Impregnating polymeric matrix with stiff particles may significantly improve structural response of a composite material. Such improvements have to be weighed against the effects of the stress concentration at the particle–matrix interface that influence local strength and toughness. In the present paper we elaborate on the issue of local stresses and strength in particulate polymer matrix composites considering polyurethane matrix impregnated with alumina particles in numerical examples. The parametric analysis presented in the paper is concerned with the effects of the particle volume fraction and the particle-to-matrix stiffness ratio on the local stresses and initial damage. We also discuss the resilience of the impregnated polyurethane, i.e. the density of energy necessary to produce initial damage. The approach to the analysis of fracture in the composite with initial damage is discussed accounting for available experimental observations. Three scales of fracture corresponding to different phases of the development and propagation of the crack are identified, including microfracture at the particle–matrix interface and mesofracture limited to the matrix surrounding the particle. While these scales of fracture should be analyzed by numerical methods, macrofracture that occurs after the crack “emerged” from the representative unit cell where it originated can be considered using available analytical techniques. The methodology of the stress analysis of a particulate material consisting of an incompressible hyperelastic matrix and much stiffer elastic particles is also proposed in the paper.     

The fracture energy of metal fibre reinforced ceramic composites (MFCs)

A model is presented for prediction of the fracture energy of ceramic-matrix composites containing dispersed metallic fibres. It is assumed that the work of fracture comes entirely from pull-out and/or plastic deformation of fibres bridging the crack plane. Comparisons are presented between these predictions and experimental measurements made on a commercially-available composite material of this type, containing stainless steel (304) fibres in a matrix predominantly comprising alumina and alumino-silicate phases. Good agreement is observed, and it’s noted that there is scope for the fracture energy levels to be high (∼20 kJ m⁻²). Higher toughness levels are both predicted and observed for coarser fibres, up to a practical limit for the fibre diameter of the order of 0.5 mm. Other deductions are also made concerning strategies for optimisation of the toughness of this type of material.     

Damage prediction in composite sandwich panels subjected to low-velocity impact

The paper illustrates the application of a finite element tool for simulating the structural and damage response of foam-based sandwich composites subjected to low-velocity impact. Onset and growth of typical damage modes occurring in the composite skins, such as fibre fracture, matrix cracking and delaminations, were simulated by the use of three-dimensional damage models (for intralaminar damage) and interfacial cohesive laws (for interlaminar damage). The nonlinear behaviour of the foam core was simulated by a crushable foam plasticity model. The FE results were compared with experimental data acquired by impact testing on sandwich panels consisting of carbon/epoxy facesheets bonded to a PVC foam. Good agreement was obtained between predictions and experiments in terms of force histories, force–displacement curves and dissipated energy. The proposed model was also capable of simulating correctly nature and size of impact damage, and of capturing the key features of individual delaminations at different depth locations.     

Fractographic observations on delamination growth and the subsequent migration through the laminate

This paper describes fractographic observations from the detailed examination of delamination fracture surfaces and offers an interpretation of the key growth mechanisms. Firstly, the relationship between toughness, delamination failure criteria and fracture morphology is presented and the influence of cusp formation and deformation on toughness is discussed. Observations regarding delaminations migrating through the lamina at multidirectional ply interfaces are then discussed. It is demonstrated how this migration process can be avoided in fracture toughness coupons and consequently the toughness of multidirectional ply interfaces can be characterised. The influence of migration on delamination growth from embedded defects in laminates under compression is presented, and these results are extended to demonstrate how migration influences damage growth in structures. The paper concludes by making recommendations for realistic modelling of migration, and suggests how it can be exploited in damage tolerant structural design.     

On experimental investigation of failure process of woven-fabric composites

In this paper an experimental investigation is performed to describe the fracture behavior and failure mechanisms of woven fabrics composites, under static loading, using a compact tension test (CT). We studied the development of the different damage phases using the digital image correlation and the compliance method. The crack length was estimated at in the front of the notch tip. The approach of the effective crack length via the compliance procedure was compared to the measures of the damage in the epoxy/glass fiber composite obtained by the digital image correlation (DIC).     

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.