Characterization and analysis of carbon fibre-reinforced polymer composite laminates with embedded circular vasculature

A study of the influence of embedded circular hollow vascules on structural performance of a fibre-reinforced polymer (FRP) composite laminate is presented. Incorporating such vascules will lead to multi-functional composites by bestowing functions such as self-healing and active thermal management. However, the presence of off-axis vascules leads to localized disruption to the fibre architecture, i.e. resin-rich pockets, which are regarded as internal defects and may cause stress concentrations within the structure. Engineering approaches for creating these simple vascule geometries in conventional FRP laminates are proposed and demonstrated. This study includes development of a manufacturing method for forming vascules, microscopic characterization of their effect on the laminate, finite element (FE) analysis of crack initiation and failure under load, and validation of the FE results via mechanical testing observed using high-speed photography. The failure behaviour predicted by FE modelling is in good agreement with experimental results. The reduction in compressive strength owing to the embedding of circular vascules ranges from 13 to 70 per cent, which correlates with vascule dimension.     

Stiffness and fracture analysis of laminated composites with off-axis ply matrix cracking

Matrix cracks parallel to the fibres in the off-axis plies is the first intralaminar damage mode observed in laminated composites subjected to static or fatigue in-plane tensile loading. They reduce laminate stiffness and strength and trigger development of other damage modes, such as delaminations. This paper is concerned with theoretical modelling of unbalanced symmetric laminates with off-axis ply cracks. Closed-form analytical expressions are derived for Mode I, Mode II and the total strain energy release rates associated with off-axis ply cracking in [0/θ]_s laminates. Stiffness reduction due to matrix cracking is also predicted analytically using the Equivalent Constraint Model (ECM) of the damaged laminate. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy and carbon/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

Finite element analysis of the end notched flexure specimen for measuring mode II fracture toughness

This paper presents a finite element analysis of the End Notched Flexure (ENF) test specimen for Mode II interlaminar fracture testing of composite materials. Virtual crack closure and compliance techniques employed to calculate strain energy release rates from linear elastic two-dimensional analysis indicate that the ENF specimen is a pure Mode II fracture test within the constraints of small deflection theory. Furthermore, the ENF fracture specimen is shown to be relatively insensitive to process induced cracks offset from the laminate midplane. Frictional effects are investigated by including the contact problem in the finite element model. A parametric study investigating the influence of delamination length, span, thickness and material properties is presented to assess the accuracy of beam theory expressions for compliance and strain energy release rate, G_II. Finite element results indicate that data reduction schemes based upon beam theory underestimate G_II by approximately 20–40% for typical unidirectional graphite fiber composite test specimen geometries. Consequently, an improved data reduction scheme which retains the simplicity of beam theory but also includes the accuracy of the finite element method is proposed.     

Interaction between tensile strength failure and mixed mode crack propagation in concrete

Crack size and structure size transitions are illustrated which connect the two limit-cases of ultimate tensile strength failure (small cracks and small structures) and mixed-mode crack propagation (large cracks and large structures). The problem of mixed-mode crack propagation in concrete is then faced. By increasing the size-scale of the element the influences of heterogeneity and cohesive crack tip forces disappear and crack branching is governed only by the linear elastic stress-singularity in the crack tip region. It is proved in this way that the fracture toughness of the material is measured by a unique parameter (G_IF, G_IC or K_IC) even for the mixed-mode condition. The ratio of the sliding or Mode II fracture toughness (G_IIF, G_IIC or K_IIC) to the opening or Mode I fracture toughness depends only on the crack branching criterion adopted and not on the material features. Eventually, very controversial experimental results recently obtained on the shear fracture of concrete are explained on the basis of the above-mentioned size-scale transition.     

Influence of overloads and block loading sequences on Mode III fatigue crack propagation in A469 rotor steel

A study has been made of the influence of variable amplitude loading on Mode III (anti-plane shear) fatigue crack propagation in circumferentially-notched cylindrical specimens of ASTM A469 rotor steel (yield strength 621 MN/m²), subjected to cyclic torsional loading. Specifically, transient crack growth behavior has been examined following spike and fully-reversed single overloads and for low-high and high-low block loading sequences, and the results compared to equivalent tests for Mode I (tensile opening) fatigue crack growth. It is found that the transient growth rate response following such loading histories is markedly different for the Mode III and Mode I cracks. Whereas Mode I cracks show a pronounced transient retardation following single overloads (in excess of 50% of the baseline stress intensity), Mode III cracks show a corresponding acceleration. Furthermore, following high-low block loading sequences, the transient velocity of Mode I cracks is found to be less than the steady-state velocity corresponding to the lower (current) load level, whereas for Mode III cracks this transient velocity is higher. Such differences are attributed to the fact that during variable amplitude loading histories. Mode III cracks are not subjected to mechanisms such as crack tip blunting/branching and fatigue crack closure, which markedly influence the behavior of Mode I cracks. The effect of arbitrary loading sequences on anti-plane shear crack extension can thus be analyzed simply in terms of the damage accumulated within the reversed plastic zones for each individual load reversal. Based on a micro-mechanical model for cyclic Mode III crack advance, where the crack is considered to propagate via a mechanism of Mode II shear (along the main crack front) of voids initiated at inclusion close to the crack tip, models relying on Coffin-Manson damage accumulation are developed which permit estimation of the cumulative damage, and hence the crack growth rates, for arbitrary loading histories. Such models are found to closely predict the experimental post-overload behavior of Mode III cracks, provided that the damage is confined to the immediate vicinity of the crack tip, a notion which is consistent with fractographic analysis of Mode III fracture surfaces.     

The correlation of interfacial and macroscopic toughness in SiC laminates

Specimens have been manufactured by viscous processing of SiC powder into sheets, which were then laminated with thin carbon interlayers and sintered without pressure to give a > 98% dense product. These have been tested both in four-point bend delamination' of single interlayer sandwich specimens, to give interfacial critical strain energy release rate. G_IC data, and in three-point bending of multi-layer laminates. The value of G_ic was found to be ∼7.5 J m⁻², which compares with about 28 J m⁻² for G_bc of the bulk SiC itself produced by this route. During three-point bending of the laminates, crack deflection was consistently observed at the interfaces between laminae. This led to energy dissipation during the process, such that the apparent G_c value of the laminate was around 6 kJ m⁻². A numerical model was set up to describe the crack advance sequence. This is based on through-thickness cracks propagating when a critical stress is reached (using a Monte Carlo method to determine the strength of successive laminae, for a given Weibull modulus) and interfacial cracks then advancing a distance dictated by the available energy. This model allowed accurate prediction of both load/displacement curves and the absorption of energy within the specimen (by interfacial cracking). A distinction is drawn between the area under the load/displacement curve and the energy absorbed in the specimen. These differ if the energy available to drive the interfacial cracks is more than sufficient for them to reach the ends of the specimen. It is shown that there is scope for maximization of the energy absorbed in the specimen (i.e., for optimization of the toughness of the laminate when loaded in bending) by control over the G_ic value and the thickness of individual laminae.     

Mode II interlaminar fracture properties of Moso bamboo

Bamboo is a kind of biological composites reinforced by unidirectional long fiber. Once there exists crack, the propagation of delamination is controlled by the interlaminar fracture toughness instead of by strength. In this paper, the end notched flexure (ENF) beam specimen was used to test the Mode II interlaminar fracture toughness G_IIC along grain of Moso bamboo internode and the fracture surface was analyzed. The results were obtained that the Mode II interlaminar fracture toughness G_IIC calculated by the experiment parameter substitution method was more accurate and the value was 1303.18 J/m² (coefficient of variation = 8.96%) which was about three times higher than the value of Mode I interlaminar fracture toughness; the crack propagation of Mode II interlaminar fracture was mainly self-similar cracking, but the fracture surface was rougher. Ground tissue in the zone of Mode II crack propagation was characterized by hackle shearing deformation. The SEM photos showed that ground tissue separated from fiber along middle lamella under shear stress and as the increasing of the dislocation of upper and lower layer, the thin-walled ground tissue would fracture transversely by tension, while to thick-walled fiber cell, only middle lamella and primary wall were torn then debonded, fragments remained.     

Retardation and repair of fatigue cracks in a microcapsule toughened epoxy composite—Part II: In situ self-healing

Successful arrest and retardation of fatigue cracks is achieved with an in situ self-healing epoxy matrix composite that incorporates microencapsulated dicyclopentadiene (DCPD) healing agent and Grubbs’ first generation Ru catalyst. Healing agent is released into the crack plane by the propagating crack, where it polymerizes to form a polymer wedge, generating a crack tip shielding mechanism. Due to the complex kinetics of healing a growing crack, the resulting in situ retardation and arrest of fatigue cracks exhibit a strong dependence on the applied range of cyclic stress intensity ΔK_I. Significant crack arrest and life-extension result when the in situ healing rate is faster than the crack growth rate. In loading cases where the crack grows too rapidly (maximum applied stress intensity factor is a significant percentage of the mode-I fracture toughness value), a carefully timed rest period can be used to prolong fatigue life up to 118%. At moderate ΔK_I, in situ healing extends fatigue life by as much as 213%. Further improvements in fatigue life-extension are achieved by employing a rest period, which leads to permanent arrest at this moderate ΔK_I. At lower values of applied stress intensity factor, self-healing yields complete arrest of fatigue cracks providing infinite fatigue life-extension.     

The relationship between pure delamination modes I and II on the crack growth rate process in cracked lap shear specimen (CLS) of 5 harness satin composites

Carbon fiber reinforced polymers (CFRP) structure can include dropping-off plies in order to comply with design requirements aiming at significant weight savings. However this type of discontinuity represents a potential source of delamination initiation and propagation which requires assessment of the mechanisms acting at the crack tip. This research investigates the influence of delamination modes I and II on the overall damage process observed in CLS specimen subjected to cyclic loads. The main contribution of this work focuses on the identification and physical interpretation of complex failure mechanisms in harness satin fabric. For this purpose a detailed fractographic analysis was carried out to qualitatively assess the surface fractures in these type of laminates. Results obtained for cyclic loaded CLS specimens were compared to analytical closed form solutions available in the literature. Results indicated that delamination front exhibited distinguishable delamination modes I and II propagating at constant mixed mode ratio (G_I/G_T).     

Influence of electrospun Nylon 6,6 nanofibrous mats on the interlaminar properties of Gr-epoxy composite laminates

The present work aims at investigating the influence of electrospun Nylon 6,6 nanofibrous mat to interlaminar strength. Mode I and the Mode II fracture mechanics of virgin and nanomodified laminates are investigated. Nanomodified laminates are fabricated by interleaving an electrospun nanofibrous mats in laminate mid-plane. Double Cantilever Beam (DCB) and End Notched Flexure (ENF) tests are performed on both virgin and nanomodified configuration. Results show that electrospun nanofibrous mat is able to increase by 23.2% the mechanical energy absorbing capability and by about 5% the G_IC. ENF tests reveal that the nanofibrous mats contribute to improve the maximum stress before the material crisis (6.5% of increment) and a measurable increment of (8.1%) the maximum mechanical energy that can be absorbed by the material during the crack propagation is registered. The acoustic emission (AE) technique is used to monitor both DCB and ENF tests. The AE information highlight that the nanofibrous mats mitigate the interlaminar matrix failure on both the fracture modes.     

Elastodynamic forms of caustics for running cracks under constant velocity

For the study of elastodynamic problems of propagating cracks it is necessary to evaluate the dynamic stress intensity factor K^d_I, which depends on the form of expressions for the stress components existing at the running crack tip at any instant of the propagation of the crack and the corresponding dynamic mechanical and optical properties of the material of the specimen under identical loading conditions. In this paper the distortion of the form of the corresponding reflected caustic from the lateral faces of a dynamically loaded transparent and optically inert specimen containing a transverse crack running under constant velocity was studied on the basis of complex potential elasticity theory and the influence of this form on the value of the dynamic stress intensity factor was given. The method was applied to the study of a propagating under Mode I crack in a PMMA specimen under various propagation velocities and the corresponding dynamic stress intensity factor K^d_I, evaluated.     

Compressive strength of composite laminates with interlaminar defects

The compressive strength of composite laminates is greatly reduced by the local instabilities initiated by interlaminar defects. In the present study, the reduction in compressive strength of a (0/±45₂/0)s AS/3501-6 graphite-epoxy laminate containing implanted interlaminar defects is examined. The experimental study consisted of the four-point static loading of sandwich beams with graphite-epoxy face sheets having through-width delaminations of 0·5 in. (12·7 mm), 0·75 in. (19·1 mm), 1·0 in. (25·4 mm) and 1·5 in. (38·1 mm) in length. Failure consisted of the unstable interlaminar crack growth within the compressive face of the sandwich. Reduction in flexure strength was found to be directly proportional to debond length and varied from 41 to 87% of the pristine value. Combined stability and finite element analysis showed that the initial out-of-plane deformations of the sublaminate induced by residual stresses decreased axial stiffness of the buckled sublaminate and resulted in both Mode I and Mode II propagation at the interlaminar crack tip. An approximate strain energy release rate formulation for Mode I fracture is correlated with the experimental data, where a value of the strain energy release rate G_IC = 1·4 lb/in. (250 N/m) yields accurate predictions of the compressive strength for all defect geometries considered.     

Piezoelectric sensor for stress intensity factor measurement of two dimensional cracks

A piezoelectric sensor for the measurement of stress intensity factors (SIFs) of two dimensional cracks induced in a structure is developed. Two small pieces of piezoelectric elements are adhered near the crack tip so that the piezoelectric elements are placed close to each other and the crack tip’s position is between them. The electric currents from the piezoelectric elements are integrated by integration circuits and the output voltages which are proportional to the electric charge induced in the piezoelectric elements are measured. The SIFs of Mode I (K_I) as well as of Mode II (K_II) based on the piezoelectric constitutive law and fracture mechanics are calculated.     

Mixed Mode I/II fatigue crack growth in adhesive joints

Fatigue crack growth (FCG) tests have been carried out on adhesively bonded compact tension-shear (CTS) specimens to assess the behaviour of a structural adhesive under Mixed Mode I/II conditions. The fractographic analysis revealed that energy dissipation mechanisms due to inelastic phenomena like bulk plastic deformation and crazing are more pronounced in Mode I than in Mixed Mode and Mode II. This is reflected by a FCG rate that increases going from Mode I to Mode II for a given value of the range of strain energy release rate, ΔG.     

Dynamic mixed-mode I/II delamination fracture and energy release rate of unidirectional graphite/epoxy composites

Mixed-mode open-notch flexure (MONF), anti-symmetric loaded end-notched flexure (MENF) and center-notched flexure (MCNF) specimens were used to investigate dynamic mixed I/II mode delamination fracture using a fracturing split Hopkinson pressure bar (F-SHPB). An expression for dynamic energy release rate G_d is formulated and evaluated. The experimental results show that dynamic delamination increases linearly with mode mixing. At low input energy E_i ? 4.0 J, the dynamic (G_d) and total (G_T) energy rates are independent of mixed-mode ratio. At higher impact energy of 4.0 ? E_i ? 9.3 J, G_d decreases slowly with mixed I/II mode ratio while G_T is observed to increase more rapidly. In general, G_d increases more rapidly with increasing delamination than with increasing energy absorbed. The results show that for the impact energy of 9.3 J before fragmentation of the plate, the effect of kinetic energy is not significant and should be neglected. For the same energy-absorption level, the delamination is greatest at low mixed-mode ratios corresponding to highest Mode II contribution. The results of energy release rates from MONF were compared with mixed-mode bending (MMB) formulation and show some agreement in Mode II but differences in prediction for Mode I. Hackle (Mode II) features on SEM photographs decrease as the impact energy is increased but increase as the Mode I/II ratio decreases. For the same loading conditions, more pure Mode II features are generated on the MCNF specimen fractured surfaces than the MENF and MONF specimens.     

The effect of steady torsion on fatigue crack growth in shafts

Most of catastrophic mechanical failures in power rotor shafts occur under cyclic bending combined with steady torsion: Mode I (ΔK_I) combined with Mode III (K_III). An analysis of the influence of steady torsion loading on fatigue crack growth rates in shafts is presented for short as well as long cracks. Long cracks growth tests have been carried out on cylindrical specimens in DIN Ck45k steel for two types of testing: rotary or alternating bending combined with steady torsion in order to simulate real conditions on power rotor shafts. The growth and shape evolution of semi-elliptical surface cracks, starting from the cylindrical specimen surface, has been measured for several loading conditions and both testing types. Short crack growth tests have been carried out on specimens of the same material DIN Ck45k, under alternating bending combined with steady torsion. The short crack growth rates obtained are compared with long crack growth rates. Results have shown a significant reduction of the crack growth rates when a steady torsion Mode III is superimposed to cyclic Mode I. A 3D Finite Element analysis has also shown that Stress Intensity Factor values at the corner crack surface depend on the steady torsion value and the direction of the applied torque.     

Comparison of Interlaminar Fracture Toughness in Unidirectional and Woven Roving Marine Composites

This paper investigates the effect of fibre lay-up and matrix toughness on mode I and mode II interlaminar fracture toughness (G_Ic and G_IIc) of marine composites. Unidirectional and woven roving fibres were used as reinforcements. Two vinyl ester resins with different toughness were used as matrices. Results from both modes showed toughness variation that is consistent with matrix toughness. Values of G_Ic were not significantly influenced by fibre lay-up except at peak load points in the woven roving/brittle-matrix composite. Each peak load point, caused by interlocked bridging fibres, signified the onset of unstable crack growth. For unidirectional specimens, crack growth was stable and G_Ic statistically more reliable than woven roving specimens, which gave fewer G_Ic values due to frequent unstable crack growth. Mode II tests revealed that, except for crack initiation, G_IIc was higher in woven roving composites. This was due to fibre bridging, perpendicular to the crack growth direction, which encouraged stable crack growth and increased energy absorption. Mode II R-curves were obtained for the woven roving specimens. These R-curves provide additional information useful for characterising delamination resistance. The paper concludes that composites with woven roving fibres show similar mode I delamination characteristics to the unidirectional composites; but their mode II delamination characteristics, after crack initiation, are quite different.     

Fatigue crack growth acceleration due to intermittent overstressing in adhesively bonded CFRP joints

Double cantilever beam joints were used to investigate cohesive and interlaminar crack growth in bonded composite joints under constant and variable amplitude (VA) loading. Numerical crack growth integration was used to predict the VA fatigue life using constant amplitude data. This underestimated the fatigue crack growth rate for interlaminar cracks, indicating crack growth acceleration due to load interactions. This was also the case for cohesive cracks subjected to a moderate initial strain energy release rate (G_max). An unstable crack growth regime was also identified for the case of high initial G_max cohesive crack propagation. This behaviour is attributed to the development of a damage zone ahead of the crack tip.     

FINITE ELEMENT ANALYSIS OF DELAMINATION CRACKS IN BENDING OF CROSS-PLY LAMINATES

SUMMARY

A study of delamination crack growth due to bending in cross-ply laminates is presented. For the understanding of interlaminar fracture behaviour of laminated composites the modelling of delamination crack growth induced by bending and shear cracks in three point bending specimens is carried out. A plane strain two-dimensional (2-D) finite element analysis is used to determine the strain energy release rates during delamination of the laminated beam. Contact elements were used to prevent the material interpenetration on the crack surfaces. The solution of the contact problem taking into account friction along crack surfaces is obtained. Energy release rates G_I and G_II for Mode I and Mode II fracture are calculated by virtual crack closure integral (VCCI) methods. Comparison of total energy release rates, obtained by local energy methods, with an analytical solution based on the beam theory and a global energy method have been carried out. Good agreement of the results obtained by various methods have been observed. Comparison of the results obtained by the solution of the contact problem and without contact elements have been performed. Significant differences between the values of energy release rates obtained with and without using contact elements have been observed. The influence of the coefficient of friction on the energy release rates is insignificant.     

Non-propagating cracks and high-cycle fatigue failures in sharply notched specimens under in-phase Mode I and II loading

Sharply notched specimens were tested under in-phase Mode I and II loading to study the non-propagating crack behaviour in the presence of complex stress states. The material employed in the present investigation was a commercial low carbon steel. Non-propagating cracks were generated under different ratios between Mode I and Mode II stress components. The direct inspection of the cracked samples showed that the early stage of the crack propagation was mixed Mode governed (Stage 1-like process), whereas the subsequent propagation was seen to be mainly Mode I dominated (Stage 2-like process). Moreover, it was observed that non-propagating crack length tended to increase as the Mode II contribution to fatigue damage increased. In any case, independently of the degree of multiaxiality, their average length was of the order of 2L, where L was the material characteristic length calculated according to the theory of critical distances. Finally, the detected crack paths were used to form some hypotheses on the reason why two methods previously formulated by the authors are successful in predicting the multiaxial high-cycle fatigue strength, even though they make quite different assumptions on the physical mechanisms damaging metallic materials in the high-cycle fatigue regime.