Simulation of fatigue performance of cross-ply composite laminates

The fatigue life of cross-ply composite laminates was evaluated using a statistical model. A modified shear-lag analysis was applied to describe the cycle-number-dependent stiffness reduction and consequent stress redistribution processes in the laminates resulted from both progressive transverse matrix cracking in transverse plies and local delamination at tips of transverse cracks. From the strength degradation behaviour and the static strength distribution of 0° plies as well as the fatigue behaviour of 90° plies, the fatigue life of cross-ply laminates with various types of lay-up can be simulated from the model. Predictions of fatigue performance are compared with experimental data for [0/90₂] _s , [02/90₂] _s and [0₂/90₄] _s graphite/epoxy cross-ply laminates: good agreements are obtained.     

Damage Assessment of CFRP [90/±45/0] Composite Laminates over Fatigue Cycles

The present paper develops a stiffness-based model to characterize the progressive fatigue damage in quasi-isotropic carbon fiber reinforced polymer (CFRP) [90/±45/0] composite laminates with various stacking sequences. The damage model is constructed based on (i) cracking mechanism and damage progress in matrix (Region I), matrix-fiber interface (Region II) and fiber (Region III) and (ii) corresponding stiffness reduction of unidirectional plies of 90°, 0° and angle-ply laminates of ±45° as the number of cycles progresses. The proposed model accumulates damages of constituent plies constructing [90/±45/0] laminates by means of weighting factor η ₉₀, η ₀ and η ₄₅. These weighting factors were defined based on the damage progress over fatigue cycles within the plies 90°, 0° and ±45° of the composite laminates. Damage model has been verified using CFRP [90/±45/0] laminates samples made of graphite/epoxy 3501-6/AS4. Experimental fatigue damage data of [90/±45/0] composite laminates have fell between the predicted damage curves of 0°, 90° plies and ±45°, 0/±45° laminates over life cycles at various stress levels. Predicted damage results for CFRP [90/±45/0] laminates showed good agreement with experimental data. Effect of stacking sequence on the model of stiffness reduction has been assessed and it showed that proposed fatigue damage model successfully recognizes the changes in mechanism of fatigue damage development in quasi-isotropic composite laminates.     

Damage Modeling of Notched Graphite/Epoxy Sandwich Panels in Compression

Open-hole honeycomb sandwich panels with woven graphite/epoxy facesheets and Nomex cores were tested uniaxially in compression to characterize their damage tolerance. A plain weave T-300 graphite fiber fabric was used for the facesheets in two stacking sequences: [45/0₂] and [0₃]. Observations of macroscopic sub-critical damage behavior were different in the two material systems. Linear damage zones (LDZ), consisting of fiber micro-buckles and extensive delamination, were typically observed in the [0₃] material. The [45/0₂] material exhibited a delamination/bulge zone (DBZ), which consisted of an out-of-plane curved deformation of the outer 45° ply accompanied by a delamination from the interior 0° plies. Modeling of these apparently distinct failure modes, and comparison to experimental data, revealed that the only mode representative of damage tolerant behavior is linear damage zone formation and propagation for both material systems, and that the delamination/bulge behavior is a secondary phenomenon.     

Mechanical properties of cross-ply and quasi-isotropic composite laminates processed using aligned multi-walled carbon nanotube/epoxy prepreg

This study examined the processing and mechanical properties of cross-ply and quasi-isotropic composite laminates processed using aligned multi-walled carbon nanotube/epoxy prepreg sheets. Three kinds of CNT/epoxy laminates, ([0°/90°]s, [60°/0°/?60°]s, [0°/45°/90°/?45°]s) were successfully fabricated using aligned CNT/epoxy prepreg sheets. The CNT volume fraction was approximately 10%. No visible void or delamination was observed in composite laminates, and the thickness of each layer was almost equal to that of the prepreg. To evaluate the elastic moduli, E₁₁, E₂₂, and G₁₂, of each ply in the laminates, on-axis and off-axis tensile tests (0°, 45°, 90°) were conducted of aligned CNT/epoxy lamina specimens. The Young’s modulus of CNT/epoxy cross-ply and quasi-isotropic laminates agreed with the theoretical values, which were calculated using classical laminate theory and elastic moduli of CNT/epoxy lamina. The respective failure strains of [0°/90°]s, [60°/0°/?60°]s, and [0°/45°/90°/?45°]s laminates are 0.65, 0.92, 0.63%, which are higher than that of 0° composite lamina (0.5%). Results suggest that the failure strain of 0° layer in composite laminates is improved because of the other layers.     

Damage evolution of angle-ply SCS-6/Ti composites under static and fatigue loading

The effect of fibre orientation and laminate stacking sequence on the tensile and fatigue behaviour of SCS-6/Ti 15-3 composites were investigated. The laminates used in this study were: (90)₆, (0/ ± 45)_s, (0/90)_s, and (90/ +-45)_s. The initiation and progression of microstructural damage at various stress levels was thoroughly characterized. It was found that fatigue life at high applied stresses were controlled by fibre fracture; progressive damage involving fibre fracture, interfacial debonding and matrix cracking became dominant at low applied stresses. Observation of the damage mechanisms in the angle-ply laminates under cyclic loading suggests that increasing the fibre-matrix bonding strength may improve the load carrying capability and fatigue life of laminates containing off-axis plies.     

Damage response of stitched cross-ply laminates under impact loadings

The impact response of stitched graphite/epoxy laminates was examined with the aim of evaluating the efficiency of stitching as a reinforcing mechanism able to improve the delamination resistance of laminates. The investigation, which focussed on two classes of cross-ply stacking sequences ([0₃/90₃]_s and [0/90]_3s), showed that the role of stitches in controlling damage progression of laminates and their capability to reduce the impact sensitivity of specimens are greatly dependent on the impact behaviour of base (unstitched) laminates. In [0₃/90₃]_s laminates, in particular, stitching is able to reduce damage area, on condition that the impact energy is higher than a threshold level and delaminations are sufficiently developed. In [0/90]_3s laminates, on the other hand, stress concentration regions generated by the stitching process appear to promote the initiation and propagation of fibre fractures, thereby inducing a decrease in the penetration resistance of the laminate.     

The effect of edge stresses on the failure of (0°, 45°, 90°) CFRP laminates

Four (0°, 45°, 90°) CF RP laminates with different stacking sequences of plies were tested in tension, and the development of damage and failure processes was monitored by visual observation and acoustic emission. All four developed cracks across the 90° layers before final failure, the thicker 90° layers cracking at lower applied loads. Cracks also formed parallel to the plies at the edges of three of the four laminates and grew, with increasing load, towards the middle. A theoretical model was developed to calculate the normal stresses perpendicular to the plane of a laminate at its edges. Effects were included for the residual stresses caused by cooling from the moulding temperature and by moisture absorption by the epoxy resin. The theoretical predictions agreed well with the observed differences in longitudinal edge cracking and delamination tendency of the four laminates.     

Fiber direction and stacking sequence design for bicycle frame made of carbon/epoxy composite laminate

According to the maximum stress theory and the results of strength-to-stress ratios, the fiber direction and stacking sequence design for the bicycle frame made of the carbon/epoxy composite laminates have been discussed in this paper. Three testing methods for the bicycle frame, i.e. torsional, frontal, and vertical loadings, are adopted in the analysis. From the finite element results, the stacking sequences [0/90/90/0]_s and [0/90/45/−45]_s are the good designs for the composite bicycle frames. On the contrary, the uni-directional laminates, i.e. [0/0/0/0]_s, [90/90/90/90]_s, [45/45/45/45]_s and [−45/−45/−45/−45]_s, are the bad designs. In addition, weak regions of failure occur at the fillets and connections of the frame, i.e. the stress concentration regions. All weak points occur at the inner or outer layer of the laminated composite tube. The 0°-ply and 90°-ply located on the inner and outer layer of the tube can effectively resist the higher stress at its location.     

Bearing damage evolution of a pinned joint in CFRP laminates under repeated tensile loading

A mechanical pinned joint in the CFRP laminates such as [0/±45/90]_3S, [90/±45/0]_3S, [0/±45/90]_2S and [90/±45/0]_2s is loaded statically and cyclically to finally obtain the critical condition for fatigue. It is derived that in the static loading, the critical damage that yields shear matrix crack is kink and the critical condition to the final failure is the appearance of kink in every inner 0° layer and that in the fatigue loading within the moderate load, the critical damage that yields shear matrix crack is almost always kink-like damage along the collapse front and at high load it is rather kink. Next, the non-elastic elongation of a joint at the maximum load subtracted by the one at 10th cycle is focused on and its capability is figured out for various stacking sequences. The critical value U_NE,F^* for the elongation rate change to the final fatigue failure is around 50–65 μm in the present material. The critical condition to the final fatigue failure and corresponding to U_NE,F^* is roughly the appearance of mostly kink-like damage in every inner 0° layer.     

Low velocity impact behaviour of a hybrid carbon‐epoxy/cork laminate

This work addresses low velocity impact behaviour of monolithic cross‐ply carbon‐epoxy and hybrid carbon‐epoxy/cork laminates. The [0₄, 90₄]_s layup was selected due to its high mismatch bending between different oriented layers, which is a critical aspect concerning large delamination development at these critical interfaces. The effect of a cork layer inserted at the most critical interface on low velocity impact behaviour of the carbon‐epoxy laminate is discussed. Impact response and resulting damage profiles of monolithic and hybrid laminates are compared, and advantages of the hybrid solution are underlined. A numerical analysis including cohesive zone modelling was also performed to assess the damage profiles obtained for the two laminates analysed. The model revealed to be effective for a better comprehension of damage mechanism for both studied cases.     

A generalized micromechanical approach for the analysis of transverse crack and induced delamination in composite laminates

The previously developed micromechanical approaches for the analysis of transverse cracking and induced delamination are limited for laminates with specific lay-ups such as cross-ply and specific loading conditions. In this paper a new micromechanical approach is developed to overcome such shortcomings. For this purpose, a unit cell in the ply level of composite laminate including transverse cracking and delamination is considered. Then, the governing equations for the stress and displacement fields of the unit cell are derived. The obtained approximate stress field is used to calculate the energy release rate for the propagation of transverse cracking and induced delamination. To show the capability of the new method, it is employed for the analyses of general laminates with [0/90]_s, [45/−45]_s, [30/−30]_s and [90/45/0/−45]_s lay-ups under combined loadings to calculate the energy release rate due to the transverse cracking and induced delamination. It is shown that the obtained energy release rates for transverse cracking and delamination initiation are in good agreement with the available results in the literature and finite element method. Furthermore, the occurrence priority of further transverse cracks and/or delamination at each damage state of the laminates will be discussed.     

Effect of off-axis ply orientation on 0°-fibre microbuckling

The aim of the present work is to study both experimentally and theoretically the compression failure mechanisms in multi-directional composite laminates, and especially the effect of the off-axis ply orientation on fibre microbuckling in the 0°-plies. The critical mechanism in the compressive fracture of unidirectional polymer matrix composites is plastic microbuckling/kinking. In multi-directional composites with internal 0°-plies, catastrophic failure also initiates by kinking of 0°-plies at the free-edges or manufacturing defects, followed by delamination. When 0°-plies are located at the outside, or in the case of cross-ply laminates, failure rather tends to occur by out-of-plane buckling of the 0°-plies. T800/924C carbon-fibre–epoxy laminates with a [(±θ/0₂)₂]_s lay-up are used here to study the effect of the supporting ply angle θ on the stress initiation of 0°-fibre microbuckling. Experimental data on the compressive strength of laminates with θ equal to 30, 45, 60 or 75° are compared to theoretical predictions obtained from a fibre kinking model that incorporates interlaminar shear stresses developed at the free edges at (0/θ) interfaces. Initial misalignment of the fibres and non-linear shear behaviour of the matrix are also included in the analysis.     

Effect of geometry on compressive failure of notched composites

The compressive failure of carbon fibre-epoxy laminates is investigated theoretically and experimentally. Panels with a single edge notch, a central notch or a central hole are considered. The failure mechanism is by microbuckling in the 0° plies and is accompanied by delamination and plastic deformation in the off-axis plies [1]. To predict the critical length of the microbuckle and the failure load, the microbuckle is modelled as a cohesive zone. The magnitude of the normal compressive traction across the microbuckle is assumed to decrease linearly with increasing overlap of material on either side of the microbuckle. The relative effect of the specimen size and a bridging length scale is investigated to illustrate the transition between small-scale and large-scale bridging. If the bridging length scale is small compared with the specimen dimensions, the specimen fails when the stress intensity at the notch tip equals a critical compressive stress intensity factorK _IC . When the bridging length scale is not small compared with either the initial defect size or the unnotched ligament length then it is necessary to include the details of the traction across the microbuckle to predict the failure load accurately.     

Mechanical properties and failure mechanisms of composite laminates with classical fabric stacking patterns

In the design of composite materials, the properties and failure modes/mechanisms are always of the main concern. In this work, the mechanical properties and failure mechanisms of composite laminates with classical fabric stacking patterns ([(0, 90)]₈ and [(0, 90)/(±?45)]₄) were systematically investigated through mechanical experiments and FEM (finite element method) numerical simulations. The results show that the tensile modulus and bending modulus of the laminates were reduced by 22.2% and 37% after partially changing the stacking angle to?±?45°, but corresponding elongation and bending displacement were increased by 8.8% and 11.7%, respectively. Bending failure mode changes from complete fracture to partial fracture. Meanwhile, the delamination damage and tow peeling from the matrix increase significantly. FEM simulations on tensile and bending processes of the composites indicate that the?±?45° stacking angle leads to the change of the axial stress direction from S_X (0°) to S_Y (±?45°), which is difficult to be observed from mechanical experiments. The FEM simulation provides a cost effective and efficient way for the structural visual optimization design and failure prediction of the actual composite materials.

     

Stability analysis of delaminated composite beams

This study describes the dynamic stability of composite cantilever beams subjected to periodic axial loading with delaminations at pre-set locations. A computer code based on the finite element method is developed to calculate the natural frequencies, critical buckling loads and dynamic instability regions of the woven and laminated composite beams with different stacking sequences ([0]₄, [0/90]_s and [90]₄), corresponding to this peculiar delamination case. The results of the developed code for the natural frequencies are compared with the natural frequencies obtained experimentally and numerically with commercial FEA (ANSYS). The critical buckling loads are also compared with the ones obtained from ANSYS simulations.     

An investigation into the damage development and residual strengths of open-hole specimens in fatigue

An extensive experimental program was carried out to investigate and understand the sequence of damage development throughout the life of open-hole composite laminates loaded in tension–tension fatigue. Quasi-isotropic carbon/epoxy laminates, with stacking sequence [45₂/90₂/−45₂/0₂]_S, [45/90/−45/0]_2S and [45/90/−45/0]_4S were examined. These were selected on the basis that under quasi-static loading the [45₂/90₂/−45₂/0₂]_S configuration exhibited a delamination dominated mode of failure whilst the [45/90/−45/0]_2S and [45/90/−45/0]_4S configurations showed a fibre dominated failure mode, previously described as “pull-out” and “brittle” respectively. Specimens were fatigue loaded to 1 × 10⁶ cycles or catastrophic failure, which ever occurred first. A number of tests were interrupted at various points as the stiffness dropped with increasing cycles, which were inspected using X-ray computed tomography (CT) scanning. A static residual strength program was carried out for run-out specimens of each configuration.     

Toughness,flexural, damping and interfacial properties of hybridized GFRE composites with MWCNTs

As the improved damping in fiber-reinforced composites can affect the other mechanical properties, therefore, the aim of this work is to investigate the effect of multiwall carbon nanotube (MWCNT) on the interfacial bond strength, flexural strength and stiffness, toughness and damping properties of hybridized glass-fiber reinforced epoxy (GFRE) composites. Nanophased epoxy resin was used to hybridize unidirectional and quasi-isotropic GFRE composites with [0/±45/90]_s and [90/±45/0]_s stacking sequences. Results from the interfacial characterizations of the hybridized composites showed improvement up to 30% compared to the control laminates. Hybridization of GFRE laminates with MWCNTs leads to decreasing the flexural and storage moduli, increasing flexural strength, toughness, natural frequencies and damping ratio. A high correlation coefficient of 0.9985 was obtained between static flexural and dynamic storage moduli. The highest flexural strength, flexural and storage moduli and natural frequency of quasi-isotropic laminate were observed for [0/±45/90]_s stacking sequence and vice versa for damping ratio.     

Damage tolerance of composite cylinders

The fracture of pressurized graphite/epoxy cylinders was investigated and their damage tolerance assessed. The cylinders were 610 mm long and 305 mm in diameter and were fabricated from Hercules A370-5H/3501-6 prepreg fabric in quasi-isotropic four-ply configurations: (0,45)_s and (45,0)_s. The cylinders were slit in the longitudinal direction and the critical notch sizes for three pressure levels were determined. Experiments on coupons of similar construction loaded in tension were previously conducted. The critical flaw sizes for the cylinders were well predicted from the flat coupon data corrected for the effects of curvature. In addition, circumferentially wrapped unidirectional plies of Hercules AS1/3501-6 tape of various stacking sequences were used as selective reinforcement on several (0,45)_s cylinders. These reinforcing plies did change the path of damage but did not prevent catastrophic failure.     

A critical evaluation of theories for predicting microcracking in composite laminates

We present experimental results on 21 different layups of Hercules AS4 carbon fibre/3501-6 epoxy laminates. All laminates had 90 ° plies; some had them in the middle ([(S)/90 _n ] _s ) while some had them on a free surface ([90 _n /(S)] _s ). The supporting sublaminates, (S), where [0 _n ], [±15], or [±30]. During tensile loading, the first form of damage in all laminates was microcracking of the 90 ° plies. For each laminate we recorded both the crack density and the complete distribution of crack spacings as a function of the applied load. By rearranging various microcracking theories we developed a master-curve approach that permitted plotting the results from all laminates on a single plot. By comparing master-curve plots for different theories it was possible to critically evaluate the quality of those theories. We found that a critical-energy-release-rate criterion calculated using a two-dimensional variational stress analysis gave the best results. All microcracking theories based on a strength-failure criteria gave poor results. All microcracking theories using one-dimensional stress analyses, regardless of the failure criterion, also gave poor results.     

Strength prediction in composites with stress concentrations: classical Weibull and critical failure volume methods with micromechanical considerations

Application of Weibull statistics to tensile strength prediction in laminated composites with open holes is revisited. Quasi-isotropic carbon fiber laminates with two stacking sequences [45/0/−45/90]_s and [0/45/90/−45]_s with three different hole sizes of 2.54, 6.35 and 12.7 mm were considered for analysis and experimental examination. The first laminate showed 20% lower strength for smaller and 10% for the larger hole sizes. A novel critical failure volume (CFV) method with minimum scaling length constraint as well as the traditional Weibull integral method were applied. The strength prediction was based on the state of stress in the 0^° ply by taking into account the redistribution of stress due to matrix damage in the form of splitting, delamination and matrix cracking of off axis plies. The state of matrix damage precipitating failure was recorded by using X-radiography and examined by a sectioning technique. The measured extent of damage was then included in a 3D stress analysis procedure by using a mesh independent crack modeling method to account for fiber direction stress redistribution. The CFV method gave results within one standard deviation from experimentally observed strength values for both laminates and all three hole sizes. The Weibull integral method underpredicted the strength in all cases from as much as 20–30% for smaller hole sizes to 8% for the large holes. The accuracy of failure predictions using CFV is attributed to the introduction of a minimum scaling length. This length has a physical meaning of the width of a process zone of formation of fiber macro-crack as a result of single fiber break interaction. Direct measurement or rigorous evaluation of this parameter is, however, difficult. Consistent with referenced micromechanical studies, its value was assigned equal to six times the Rosen’s ineffective length.