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.     

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.     

Interlaminar fracture toughness and associated fracture behaviour of bead-filled epoxy/glass fibre hybrid composites

To investigate enhancement of matrix-dominated properties (such as interlaminar fracture toughness) of a composite laminate, two different bead-filled epoxies were used as matrices for the bead-filled epoxy/glass fibre hybrid composites. The plane strain fracture toughness of two different bead-filled epoxies have been measured using compact tension specimens. Significant increases in toughness were observed. Based on these results the interlaminar fracture toughness and fracture behaviour of hybrid composites, fabricated using bead-filled epoxy matrices, have been investigated using double cantilever beam and end notch flexure specimens for Mode I and Mode II tests, respectively. The hybrid composites based on carbon bead-filled matrix shows an increase in both G _IC initiation and G _IIC values as compared to a glass fibre reinforced plastic laminate with unmodified epoxy matrix. The optimum bead volume fraction for the hybrid composite is between 15% and 20%. However, the unmodified epoxy glass-fibre composite shows a higher G _IC propagation value than that of hybrid composites, due to fibre bridging, which is less pronounced in the hybrids as the presence of the beads results in a matrix-rich interply region.     

Mixed-mode fracture toughness testing of concrete beams in three-point bending

Results obtained for mixed-mode fracture toughness parameters K _c , G _c , J _c , G _F (plane strain mixed-mode stress-intensity factor, energy release rate, J-integral and fracture energy, respectively) for small notched concrete beams in bending indicate that all these parameters decrease with x/S (x is the distance from support, S is the span) in general to values near midspan consistent with Mode I results. All the parameters except J _c vary with notch depth in a similar manner for each notch location.     

Rubber-crumb modified polystyrene

The strain energy release rate,G _c, of polystyrene (PS) containing rubber crumb has been examined. It was found that for unmodified crumb, addition of small amounts (5%) leads to 100% increase inG _c. This is attributed to crazing in the PS. However, further addition of crumb leads to reductions inG _c, as the crumb-PS adhesion is low and interfacial failure results. If the crumb is modified with PS its adhesion to the matrix PS increases and internal rupture of the rubber occurs.G _c for these composites increases linearly with crumb loading, and is due to matrix crazing as well as rupture of the rubber phase.     

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.     

Delamination characterization of laminates under tension,bending and torsion loads

A two-dimensional finite-element model has been developed to calculate interlaminar stresses and strain energy release rates for the study of delamination in composite laminates subjected to tension, bending and torsion loads. This paper addresses the formulation, implementation, and verification of this element to investigate the variation of the interlaminar stresses and strain energy release rates for composite laminates. The study concentrates on establishing relationships of G_I, G_II, and G_III as functions of crack length and stacking sequence in laminates due to beding and torsion.     

Compressive fatigue limit of impact damaged composite laminates

A new analytical model for predicting the compressive fatigue limit strain of composite laminates which contain barely visible impact damage (BVID) is presented. The model represents the complex damage morphology as a single, circular delamination, and calculates the strain at which thin-film buckling of the circular region of delaminated plies occurs. The fatigue limit strain is defined as the strain at which the strain energy release rate for a thin post-buckled strip of the delaminated plies is equal to the critical Mode I value (G_1C) for the resin. The model predicts a “critical” depth at which propagation of damage during fatigue is likely to occur. Results obtained using the model are compared with two sets of experimental results, and show agreement of fatigue limit strain to within 4% of the experimental value.     

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.     

Fracture and fatigue study of unidirectional glass/epoxy laminate under different mode of loading

Interlaminar fracture is the dominant failure mechanism in most advanced composite materials. The delaminating behaviour of materials is quantified in terms of the strain energy release rate G. In this paper, the experimental measurements of the fatigue delaminating growth for some combinations of energy release rate mode ratio have been carried out on unidirectional glass/epoxy laminates. On this base the constants in the Paris equation have been determined for each G_II/G_T considered modal ratio. The fatigue threshold strain energy release rate Δ G_Tth , below which delaminating doesn't occur, were measured. Three type specimens were tested, namely: double cantilever beam (DCB), end‐loaded split (ELS) and mixed‐mode bending (MMB) under mode I, mode II and mixed‐mode (I + II) loading, respectively. Scanning electron microscopy techniques were used to identify the fatigue delamination growth mechanisms and to define the differences between the various modes of fracture.     

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.     

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.     

Fracture toughness of the fibre-matrix interface in glass-epoxy composites

The failure process arising at a broken fibre end in polymer matrix composite materials has been studied experimentally and analytically using the finite element method. A series of experiments were carried out using S-glass and E-glass single filaments, with different sizings and/or coupling agents, embedded in epoxy matrices with different moduli. A finite element analysis was used to simulate the experiments and calculate the change in strain energy accompanying the observed fracture mode. The strain energy release rate upon arrest of the crack, G _arrest, was then calculated. The measured interface debonding energies varied from G _arrest=57–342 J m^–2, depending primarily on the nature of the fibre sizing and the ratio of moduli of the fibre and matrix. Transverse and shear matrix cracks were characterized by G _arrest values of 58–103 J m^–2. Subtle changes in the constituent properties or fibre surface treatment resulted in a change in the fracture mode. This measurement and analysis technique may suggest reasons for the variability of previous measurements of interfacial adhesion, and provide a standard method for characterizing fracture modes at broken fibre ends.     

Fatigue behaviour characterization of the fibre-matrix interface

The fracture behaviour of FRP composite materials is significantly influenced by the behaviour of the fibre-matrix interfacial bond. Thus far interfacial bond mechanical characterization has been based upon the critical strength and critical fracture energy of debonding. Characterization of the fatigue behaviour of the interfacial debonding process, however, may be more valuable for composite design and fibre-matrix selection. A fracture mechanics model of interfacial bond fatigue based on the mode II strain energy release rate (G _II) is presented. An expression forG _II is derived for a single fibre in matrix cylinder model. By fitting the model to single fibre pull-out fatigue test data, fatigue crack propagation plots for specific fibre-matrix combinations can be drawn. These should prove useful for the development of fatigue resistant FRP composite materials.     

Mode I fracture resistance of glass fiber mat-reinforced polypropylene composites at various degree of consolidation

The energy release rate at steady-state fracture of glass fiber mat-reinforced polypropylene (GMT-PP) composites of different degree of consolidation was determined by various methods considering the mechanical energy (G_ss), acoustic emission energy (G_AE) and heat (G_h) release rates. All these energy release rates showed the same tendency, namely increase with increasing surface weight (consolidation degree) of the GMT-PP sheets. To determine the initiation fracture toughness (K_IC) the resistance curve concept was adopted. K_IC increased whereas the related strain energy release rate (G_IC) did not change with the consolidation degree.     

Effect of rubber interlayers on the fracture of glass bead/epoxy composites

The effectiveness of rubber interlayers between inorganic particles and polymer matrix for toughening has been a controversial subject. In this research, a series of rubber-encapsulated glass beads and its epoxy composites were prepared, and underlying mechanisms which can connect material parameters related with rubber interlayers with energy dissipation mechanisms, were investigated. The critical stress intensity factor (K _IC) and critical strain energy release rate (G _IC) of rubber-encapsulated glass bead filled epoxies were found to insignificantly depend on the existence and thickness of rubber interlayers. Microscopy studies on fracture process identified four different micro-mechanical deformations which can dissipate fracture energy: step formation, micro-shear banding, debonding of glass beads, and diffuse matrix shear yielding. It was found that the first two became less extensive and the others became more extensive as the thickness of rubber interlayers increases. This offsetting effect of micro-mechanical deformations seems to be the reason for the absence of significant toughening effect of rubber interlayers.     

Inluence of water up-take on interlaminar fracture properties of carbon fibre-reinforced polymer composites

Composite materials in practical use can be subjected to a wide variety of different loading conditions. The most important conditions are mechanical stresses and environmental attacks. An issue of major concern in the utilization of composites is associated with the occurrence of delaminations or interlaminar cracks, which may be related to manufacturing defects or are induced in service by low-velocity impacts. The main environmental attacks are temperature, humidity, radiation, and chemical exposure. Three materials were investigated; two thermosetting matrices (unmodified and toughness-modified epoxy, EP and EP_mod) and one thermoplastic matrix (semicrystalline polyetheretherketone, PEEK), all reinforced with unidirectional continuous carbon fibres. Samples of these materials were exposed to water in baths of different temperatures; they were taken for mechanical testing after various time periods. As a result of absorbed moisture, G _IC-values increased with moisture content of the samples, whereas G _IIC-values decreased. By means of scanning electron microscopy, fracture surfaces were examined. Evidence was found that the increase of G _IC-values was due to a greater ductility of the matrix (as a result of the moisture absorbed) and hence more energy-consumptive fibre-bridging. On the other hand, interface failure, as well as a loss of shear strength of the epoxy with increasing amount of moisture absorbed, were responsible for the decrease in the G _IIC-values. The thermoplastic matrix system (CF/PEEK) exhibited no influence of moisture on the Mode I property, but a decrease of the values for Mode II.     

Influence of electroless nickel-plating on fracture toughness of pitch-based carbon fibre reinforced composites

Nickel-Pitch-based carbon fibres (Ni-PFs) were prepared by electroless nickel-plating to enhance fracture toughness of Ni-PFs reinforced epoxy matrix composites (Ni-PFs/epoxy). The surface properties of Ni-PFs were determined by scanning electron microscopy (SEM), X-ray photoelectron spectrometry (XPS), and X-ray diffraction (XRD). The fracture toughness of the Ni-PFs/epoxy was assessed by critical stress intensity factor (K_IC) and critical strain energy release rate (G_IC). The fracture toughness of Ni-PFs/epoxy was enhanced compared to those of PFs/epoxy. These results were attributed to the increase of the degree of adhesion at interfaces between Ni-PFs and matrix resins in the composites.     

Calculation of transient strain energy release rates under impact loading based on the virtual crack closure technique

This paper describes an interface element to calculate the strain energy release rates based on the virtual crack closure technique (VCCT) in conjunction with finite element analysis (FEA). A very stiff spring is placed between the node pair at the crack tip to calculate the nodal forces. Dummy nodes are introduced to extract information for displacement openings behind the crack tip and the virtual crack jump ahead of the crack tip. This interface element leads to a direct calculation of the strain energy release rate (both components G_I and G_II) within a finite element analysis without extra post-processing. Several examples of stationary cracks under impact loading were examined. Dynamic stress intensity factors were converted from the calculated transient strain energy release rate for comparison with the available solutions by the others from numerical and experimental methods. The accuracy of the element is validated by the excellent agreement with these solutions. No convergence difficulty has been encountered for all the cases studied. Neither special singular elements nor the collapsed element technique is used at the crack tip. Therefore, the fracture interface element for VCCT is shown to be simple, efficient and robust in analyzing crack response to the dynamic loading. This element has been implemented into commercial FEA software ABAQUS^® with the user defined element (UEL) and should be very useful in performing fracture analysis at a structural level by engineers using ABAQUS^®.     

A discrete constitutive model for transverse and shear damage of symmetric laminates with arbitrary stacking sequence

A damage constitutive model in conjunction with a 2-D finite element discretization is presented for predicting onset and evolution of matrix cracking and subsequent stiffness reduction of symmetric composite laminates with arbitrary stacking sequence subjected to membrane loads. The formulation uses laminae crack densities as the only state variables, with crack growth driven by both mechanical stress and residual stress due to thermal expansion. The formulation is based on fracture mechanics in terms of basic materials properties, lamina moduli, and critical strain energy release rates G_IC and G_IIC, only. No additional adjustable parameters are needed to predict the damage evolution. Spurious strain localization and mesh size dependence are intrinsically absent in this formulation. Thus, there is no need to define a characteristic length. Comparison of model results to experimental data is presented for various laminate stacking sequences. Prediction of crack initiation, evolution, and stiffness degradation compare very well to experimental data.