Modelling off-axis ply matrix cracking in continuous fibre-reinforced polymer matrix composite laminates

The fracture process of composite laminates subjected to static or fatigue tensile loading involves sequential accumulation of intra- and interlaminar damage, in the form of transverse cracking, splitting and delamination, prior to catastrophic failure. Matrix cracking parallel to the fibres in the off-axis plies is the first damage mode observed. Since a damaged lamina within the laminate retains certain amount of its load-carrying capacity, it is important to predict accurately the stiffness properties of the laminate as a function of damage as well as progression of damage with the strain state. In this paper, theoretical modelling of matrix cracking in the off-axis plies of unbalanced symmetric composite laminates subjected to in-plane tensile loading is presented and discussed. A 2-D shear-lag analysis is used to determine ply stresses in a representative segment and the equivalent laminate concept is applied to derive expressions for Mode I, Mode II and the total strain energy release rate associated with off-axis ply cracking. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

The behaviour of cross-ply hybrid matrix composite laminates: Part 1: Experimental results

Two types of cross-ply laminate have been made from prepreg: (a) hybrid matrix laminates consisting of longitudinal plies of glass fibres in epoxy resin and transverse plies of glass fibres in epoxy resin/urethane elastomer blend; and (b) uniform matrix laminates with the same resin in both the longitudinal and transverse plies. The presence of the urethane in the transverse plies increases the applied strains necessary for the initiation and development of transverse cracking during the extension of both hybrid matrix and uniform matrix laminates. The effect is greater with increasing amounts of urethane. The cracking data, stress/strain behaviour, acoustic emission response and ply thickness effects on crack development are discussed in the light of existing theories concerning transverse cracking.     

Behaviour of unidirectional and crossply ceramic matrix composites under quasi-static tensile loading

Experimental results are presented for the quasi-static tensile behaviour of unidirectional, (0/90)_s, (0₂/90₄)_s and (0/90)_3s silicon carbide fibre (Nicalon) reinforced calcium aluminosilicate glass-ceramic matrix laminates. The stress-strain behaviour and associated damage development is described in detail for each laminate. The damage development is quantified by counts of crack density (in both the longitudinal and transverse plies) and stiffness reduction as functions of applied strain. The damage initiation and growth (and its effect on residual properties) are discussed with reference to the Aveston-Cooper-Kelly (ACK) theory for unidirectional ply cracking and crossply laminate shear-lag (originally developed for polymer matrix composites) to describe the transverse ply cracking behaviour.     

Impact damage characterisation of carbon fibre/epoxy composites with multi-layer reinforcement

Low-velocity impact tests were performed to investigate the impact behaviour of carbon fibre/epoxy composite laminates reinforced by short fibres and other interleaving materials. Characterisation techniques, such as cross-sectional fractography and scanning acoustic microscopy, were employed quantitatively to assess the internal damage of some composite laminates at the sub-surface under impact. Scanning electron microscopy was used to observe impact fractures and damage modes at the fracture surfaces of the laminate specimens. The results show that composite laminates experience various types of fracture; delamination, intra-ply cracking, matrix cracking, fibre breakage and damage depending on the interlayer materials. The trade-off between impact resistance and residual strength is minimised for composites reinforced by Zylon fibres, while that for composites interleaved by poly(ethylene-co-acrylic acid) (PEEA) film is substantial because of deteriorating residual strength, even though the damaged area is significantly reduced. Damages produced on the front and back surfaces of impact were also observed and compared for some laminates.     

Quantification of flexural fatigue life and 3D damage in carbon fibre reinforced polymer laminates

Carbon fibre reinforced polymer (CFRP) laminated composites have become attractive in the application of wind turbine blade structures. The cyclic load in the blades necessitates the investigation on the flexural fatigue behaviour of CFRP laminates. In this study, the flexural fatigue life of the [+45/−45/0]_2s CFRP laminates was determined and then analysed statistically. X-ray microtomography was conducted to quantitatively characterise the 3D fatigue damage. It was found that the fatigue life data can be well represented by the two-parameter Weibull distribution; the life can be reliably predicted as a function of applied deflections by the combined Weibull and Sigmodal models. The delamination at the interfaces in the 1st ply group is the major failure mode for the flexural fatigue damage in the CFRP laminate. The calculated delamination area is larger at the interfaces adjacent to the 0 ply. The delamination propagation mechanism is primarily matrix/fibre debonding and secondarily matrix cracking.     

Matrix crack-induced delamination in composite laminates under transverse loading

Fibre-reinforced multidirectional composite laminates are observed in experiments under transverse static or low-velocity impact loading to suffer considerable delamination damage. The intensity of this damage depends on the difference in the ply angles above and below the interface. In this paper a fracture mechanics model is presented for investigating the role of matrix cracks in triggering delaminations and the influence of ply angles in adjacent plies on delamination cracking. The fracture mechanics analysis shows that for a graphite fibre-reinforced composite laminate containing a transverse intraply crack, the crack-induced largest interfacial principal tensile stress is a maximum when the difference between the ply angles across the interface is 90 °, and it attains a minimum when the difference is 40 °. When the crack tips touch the interfaces, the minimum mode II stress singularity, which is weaker than the usual square-root type, appears when the difference between the ply angles is about 45 ° for one glass fibre-reinforced laminate and three graphite fibre-reinforced laminates. These results are in agreement with the experimental observation that the largest delaminations appear at the interface across which the difference between the ply angles is the largest i.e. 90 °.     

A criterion for modelling initiation and propagation of matrix cracking and delamination in cross-ply laminates

A variational approach is used to model the behaviour of composite cross-ply laminates damaged by transverse, longitudinal cracking and delamination. An energetic criterion is proposed. It is based on the strain energy release rate associated with each of the three damage modes. The first part of this paper is concerned with the modelling of the transverse and longitudinal cracking. In the second part, a model for studying delamination damage is presented. The numerical results show that these models provide a consistent level of accuracy for a variety of thin laminate material systems and configurations, with various combinations of delaminations and matrix cracks. In this paper several numerical simulations meant to describe initiation for each damage mode are proposed. The estimation of damage modes contributions is achieved for two thin laminates in order to predict the evolution of damage mode transition.     

Prediction for progression of transverse cracking in CFRP cross-ply laminates using Monte Carlo method

This study predicted transverse cracking progression in laminates including 90° plies. The refined stress field (RSF) model, which takes into account thermal residual strain for plies including transverse cracks is formulated, and the energy release rate associated with transverse cracking is calculated using this model. For comparison, the energy release rate based on the continuum damage mechanics (CDM) model is formulated. Next, transverse cracking progression in CFRP cross-ply laminates including 90° plies is predicted based on both stress and energy criteria using the Monte Carlo method. The results indicated that the RSF model and the CDM model proposed in this study can predict the experiment results for the relationship between transverse crack density and ply strain in 90° ply. The models presented in this paper can be applied to an arbitrary laminate including 90° plies.     

Interaction between matrix cracking and edge delamination in composite laminates

Matrix cracking and edge delamination are two main damage modes in continuous-fibre composite laminates. They are often investigated separately, and so the interaction between two damage modes has not yet been revealed. In this paper, a simple parallel-spring model is introduced to model the longitudinal stiffness reduction due to matrix cracking and edge delamination together. The energy release rate of edge delamination eliminating the matrix crack effect and the energy release rate of matrix cracking in the presence of edge delamination are then obtained. Experimental materials include carbon- and glass-fibre-reinforced bismaleimide composite laminates under static tension. The growth of matrix cracks and edge delaminations was recorded by means of NDT techniques. Results show that matrix cracks may initiate before or after edge lamination. This depends on the laminate layup, and especially on the thickness of the 90° plies. Edge delamination may also induce matrix cracking. Matrix cracking has a significant effect on the stiffness reduction in GRP laminates. The present model can predict the stiffness reduction in a laminate containing both matrix cracks and edge delaminations. The mixed-mode delamination fracture toughness obtained from the present model shows up to 50% differences compared with O'Brien's model for GRP laminates. However, matrix cracking has a small effect on the mixed-mode interlaminar fracture toughness of the CFRP laminates.     

Matrix cracking and delamination in laminated composites. Part II: Evolution of crack density and delamination

This paper presents a model to predict the propagation of transverse cracks in polymer matrix composite laminates. Different possibilities for the crack pattern are analyzed and the different stress-strain response are compared. Taking into account that matrix cracking promotes delamination between the plies, the propagation of delamination is also simulated. The model predictions are compared with experimental data obtained in composite laminates that accumulate transverse cracks and delaminations before failing catastrophically. The possibility and limitations of a general constitutive law applied at ply level, as a mesomodel, is analyzed and the bounds of applicability of the model are explained.     

Ultrasonic birefringence as a measure of mechanically induced fatigue damage in laminated composites

A non-destructive testing method based on polarization effects of ultrasonic transverse waves is suggested to monitor fatigue damage in polymer matrix composites. Using a transverse wave probe in reflection mode, phase and amplitude of its output signal are measured as a function of the polarization angle. From the material properties of a single ply and the proposed calculation approach, the birefringence response of carbon fibre reinforced polymers composed of many plies with different fibre orientations is predicted. The effect of ply sequence is investigated using two types of quasi-isotropic specimens with different layups. Cyclic tensile loading of composites results in fatigue damage that is characterised by matrix cracking along the fibre direction through the thickness of each ply. These myriads of transverse cracks affect the ultrasonic attenuation and degrade the homogenised stiffness of single plies. In the experiments, stepwise increase of fatigue damage is alternated with ultrasonic measurements, which show the effect of ply-dependent crack densities on the birefringence behaviour. Simulated and measured transverse wave response are matched by variation of the input parameters shear moduli and attenuations, which are therefore the final results. The obtained data from the investigated composite specimens is proposed to characterise the distinct fatigue state for each ply orientation.     

A Discrete Model for Simulation of Composites Plate Impact Including Coupled Intra- and Inter-ply Failure

Laminated composites can undergo complex damage mechanisms when subjected to transverse impact. For unidirectional laminates it is well recognized that delamination failure usually initiates via intra-ply shear cracks that run parallel to the fibres. These cracks extend to the interface of adjacent orthogonal plies, where they are either stopped, or propagate further as inter-ply delamination cracks. These mechanisms largely determine impact energy absorption and post-delamination bending stiffness of the laminate. Important load transfer mechanisms will occur that may lead to fibre failure and ultimate rupture of the laminate. In recent years most Finite Element (FE) models to predict delamination usually stack layers of ply elements with interface elements to represent inter-ply stiffness and treat possible delamination. The approach is computationally efficient and does give some estimate of delamination zones and damaged laminate bending stiffness. However, these models do not properly account for coupled intra-ply shear failure and delamination crack growth, and therefore cannot provide accurate results on crack initiation and propagation. An alternative discrete meso-scale FE model is presented that accounts for this coupling, which is validated against common delamination tests and impact delamination from the Compression After Impact (CAI) test. Ongoing research is using damage prediction from the CAI simulation as a basis for residual strength analysis, which will be the published in future work.     

Acoustic Emission as a Tool for Damage Identification and Characterization in Glass Reinforced Cross Ply Laminates

Loading of cross-ply laminates leads to the activation of distinct damage mechanisms, such as matrix cracking, delaminations between successive plies and fibre rupture at the final stage of loading. This study deals with the investigation of the failure of cross ply composites by acoustic emission (AE). Broadband AE sensors monitor the elastic waves originating from different sources of failure in coupons of this material during a tensile loading-unloading test. The cumulative number of AE activity, and other qualitative indices based on the waveforms shape, were well correlated to the sustained load and mechanical degradation as expressed by the gradual decrease of elastic modulus. AE parameters indicate the succession of failure mechanisms within the composite as the load increases. The proposed methodology based on Acoustic Emission for the identification of the damage stage of glass reinforced cross ply laminates is an initial step which may provide insight for the study of more complex laminations.     

Post-impact compressive strength of curved GFRP laminates

Low velocity impacts to fibre reinforced plastic composites cause a pattern of damage consisting in general of delamination, fibre breakage and matrix cracking. Such damage is accidental and may go unnoticed; therefore composite structures must be designed assuming impact damage exists. Previous work on flat composite laminates has resulted in a reasonable understanding of the mechanisms of compressive strength reduction. There are, however, many instances where curved laminates are used in structures where impact is likely. Furthermore, due to the mechanisms of strength reduction, it may be expected that curvature would have a significant effect on the behaviour of the laminates.The work described here consists of experimental measurement of the post-impact compressive strength of curved GFRP laminates. The laminates were of 8 plies of 0.3 mm thick pre-impregnated glass fibre/epoxy tape in a (0, ±45, 0°)_s lay-up. Each laminate was 200 mm in length by 50 mm wide with the plane of curvature normal to the length. Laminates were impacted on the convex surface of the laminate by dropping a steel mass from 1 m vertically above it.Impacted laminates were loaded in compression and the out-of-plane displacements of the top and bottom surfaces were recorded. Final failure was typically due to fibre breakage occurring through the centre of the impacted area of the laminate. Possible differences in the impact response, and measurable differences in the sizes of the impact damage area, were found to arise from these curvatures, and differences were observed in their post-impact buckling behaviour. However, perhaps unexpectedly, the post-impact compressive strength for a curved laminate was found to be similar to that for a flat laminate. The failure loads for the impact damage laminates are shown to be comparable with those for laminates containing artificial delaminations.     

The behaviour of cross-ply hybrid matrix composite laminates: Part 2: Modelling

In Part 1 of this work experimental data were presented for the initiation and propagation of damage in hybrid matrix and uniform matrix laminates. The data showed that during the extension of cross-ply laminates, either constrained (stable) matrix cracking or brittle (unstable) matrix cracking occurs in the transverse plies, with the transverse ply thickness and level of urethane in the transverse ply determining which type of cracking is observed. In the present paper the stable cracking behaviour is modelled using a shear-lag stress analysis combined with an energy balance and the unstable cracking behaviour is discussed in terms of a statistical distribution of transverse ply strengths.     

Micromechanics characterization of sublaminate damage

A micromechanics analytical model is developed for characterizing the fracture behaviour of a fibre reinforced composite laminate containing a transverse matrix crack and longitudinal debonding along 0/90 interface. Both the matrix and the fibres are considered as linear elastic. A consistent shear lag theory is used to represent the stress-displacement relations. The governing equations, a set of differential-difference equations, are solved satisfying the boundary conditions appropriate to the damage configuration by making use of an eigenvalue technique. The properties of the constituents appear in the model explicitly. Displacements and stresses in the fibres and the matrix are obtained, and the growth of damage is investigated by using the point stress criterion. The investigation includes fibre stress distribution in zero degree plies, transverse crack and debonding intitiation as functions of laminate geometry, and the effect of fibre breaks in the zero degree ply on damage growth. The predicted damage growth patterns and the corresponding critical strains agree with the finite element and experimental results.     

Model for prediction of simultaneous time-dependent damage evolution in multiple plies of multidirectional polymer composite laminates and its influence on creep

A model to predict time-dependent evolution of simultaneous transverse cracking developed in multiple plies during creep loading and its effects on creep of multidirectional polymer matrix composite laminates is presented. The stress states in the intact regions of the plies are determined using the lamination theory during an incremental change in time. The stored elastic energy, determined using this stress state, is compared with a critical stored elastic energy value for damage to determine if a ply would fracture after the increment. If fracture is predicted, variational analysis is used to determine the perturbation in ply stresses due to cracking. This procedure is repeated to determine the crack evolution and creep strain. Model predictions compared well with experimental results for a [±θ_m/90_n]_s laminate.     

Behaviour of woven hybrid basalt-carbon/epoxy composites subjected to laser shock wave testing: Preliminary results

This study addresses the effect of basalt fibre hybridization on the damage tolerance of carbon/epoxy laminates subjected to laser shock wave tests. Interply hybrid specimens with two different stacking sequences (sandwich-like and intercalated) were tested at different laser intensities and residual post-shock properties of the different configurations have been characterized by quasi-static three point bending tests monitored by acoustic emission. Results indicate that the best compromise in terms of both quasi-static properties (2% reduction in flexural strength compared to all carbon laminates) and damage tolerance appears to be the sandwich-like structure with basalt fibre skins. In particular, this configuration exhibited the highest damage tolerance among the hybrids, with a percent decrease in flexural strength of about 5% compared to 15% in the case of all carbon laminates. Damage induced by laser shock testing in carbon-basalt woven fabric/epoxy composites is mainly inter-ply delamination. This study also highlights the tougher behaviour of basalt plies in response to a sudden application of load compared to carbon layers with a favourable hybridization effect.     

Statistical model of the transverse ply cracking in cross-ply laminates by strength and fracture toughness based failure criteria

Cross-ply laminate subjected to tensile loading provides a relatively well understood and widely used model system for studying progressive cracking of the transverse ply. This test allows to identify material strength and/or toughness characteristics as well as to establish relation between damage level and the composite stiffness reduction. The transverse ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. The variability affects both crack initiation (governed by the local strength) and propagation (governed by the local fracture toughness). The primary aim of the present study is elucidation of the relative importance of these phenomena in the fragmentation process at different transverse and longitudinal ply thickness ratios. The effect of the random crack distribution on the mechanical properties reduction of the laminate is also considered. Transverse ply cracking in glass fiber/epoxy cross-ply laminates of the lay-ups [0₂/90₂]_s, [0/90₂]_s, and [0/90₄]_s is studied. Several specimens of each lay-up were subjected to uniaxial quasistatic tension to obtain crack density as a function of applied strain. Crack spacing distributions at the edge of the specimen also were determined at a predefined applied strain. Statistical model of the cracking process is derived, calibrated using crack density vs. strain data, and verified against the measured crack spacing distributions.     

Energy-based prediction of failure in general symmetric laminates

This paper describes a new homogenisation technique for general symmetric laminates that enables progressive ply crack formation to be predicted in any number of plies having a variety of orientations. The approach involves (i) the analysis of non-uniformly spaced discrete ply cracks having a single orientation, (ii) a novel technique to homogenise the properties of the cracked ply so that discrete ply cracking can be analysed in plies having a different orientation, and (iii) the use of energy based methods to predict the progressive formation of ply cracks in any number of plies during loading. The analysis takes full account of the effects of thermally induced residual stresses. A key feature of the approach is the inclusion of a shear coupling term in the stress-strain relations for homogenised plies that ensures that the homogenised laminate has exactly the same effective properties as the laminate having a ply with discrete cracks in place of one of the homogenised plies. The model is applied to the prediction of the significant dependence of ply thickness and ply lay-up on laminate strength, and results for carbon fibre reinforced plastic laminates are compared favourably with published experimental results.