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.     

The characterization of Mode I delamination failure in non-woven,multidirectional laminates

The Mode I delamination failure of fibre-reinforced epoxy laminates was characterized using the uniform double cantilever beam test specimen and scanning electron microscopy. Generally, this failure appeared in a variety of forms, depending on ply orientation, test-specimen geometry and matrix toughness. The calculated fracture energy heavily depended on the fracture surface morphology. By defining interlaminar fracture strictly as an interlaminar separation including no fibre breakage, pull-out, etc, a material property independent of test-specimen geometry and orientation of the plies constituting the delaminating interface was elucidated. Since this quantity dissipated the least amount of energy possible during crack growth, it is the controlling factor for laminate toughness.     

Micromechanisms of compressive failure in a glass fibre-reinforced amorphous thermoplastic

Compressive failure of a 0°/90° glass fibre-reinforced amorphous thermoplastic has been characterized. It was found that the critical event is the nucleation within 90° laminates of multiple shear crazes, which become shear microcracks, transition to axial cracks, and permit the specimen to fail by the flexure of 0° elements. It is shown that the apparent kinetics of this process provide a rationale for the dramatic strain-rate strengthening of these composites at high loading rate.     

On the relation between the mode I fracture toughness of a composite laminate and that of a 0° ply: Analytical model and experimental validation

This paper proposes a simple model to predict the fracture toughness of multidirectional carbon–epoxy composite laminates using the fracture toughness of the 0° ply. The model is based on a combination of Linear-Elastic Fracture Mechanics and lamination theory, and uses as material properties the ply elastic properties and the fracture toughness of the 0° ply measured in compact tension test specimens. A good correlation is obtained by comparing the model predictions and experimental data obtained in center-cracked specimens manufactured using different lay-ups and materials.     

Effect of ply angle misalignment on out-of-plane deformation of symmetrical cross-ply CFRP laminates: Accuracy of the ply angle alignment

This paper discusses the accuracy of ply angle alignment and how it relates to out-of-plane deformation in carbon fiber reinforced plastics (CFRP) laminates. We investigated the deformation of symmetrical cross-ply laminates under hot and humid conditions. In spite of the symmetrically stacked laminates, unpredictable out-of-plane deformation occurred over time due to ply angle misalignment. The deformation was unstable and disproportionate to the absorbed moisture. A Monte Carlo simulation based on laminate theory was performed to quantify the deformation induced by the ply angle misalignment. Symmetrical cross-ply laminates were found to twist as they absorbed water when they underwent ply angle misalignments. By comparing the analytical results with experimental results, we concluded that a standard deviation of approximately 0.4° exists as ply angle misalignment in the laminates used in this study and that this slight ply angle misalignment can be a significant factor in out-of-plane deformation of cross-ply laminates.     

The interlaminar fracture behaviour and toughening mechanisms of new carbon fibre-reinforced bismaleimide composites

The interlaminar fracture behaviour of carbon fibre-reinforced bismaleimide (BMI) composites prepared by using a new modified BMI matrix has been investigated by various methods. Laminates of three typical stacking sequences were evaluated. Double cantilever beam, end-notch flexure and edge-delamination tension tests were conducted under conventional conditions and in a scanning electron microscope. The strain energy release rates in Mode I and Mode II, G_Ic and G_IIc, as well as the total strain energy release rate, G_mc, have been determined and found to be higher than those for laminates with an epoxy matrix. Dynamic delamination propagation was also studied. The toughening mechanisms are discussed.     

Fracture of glass/polypropylene laminates: influence of cooling rate after moulding

This paper presents results from mechanical tests on glass fibre-reinforced polypropylene laminates. Materials were manufactured in a press and the average rate of cooling from the forming temperature after pressing was varied from 0.23 to 55°C min⁻¹. The cooling rate was found to affect the matrix structure and to strongly influence fracture behaviour. Faster cooling resulted in improved Mode I and Mode II fracture energies, and smaller delaminated areas after impact. Results are compared with those obtained on a glass fibre-reinforced thermoset polyester composite.     

Mixed Bending-Tension (MBT) test for mode I interlaminar and intralaminar fracture

A new Mixed Bending-Tension (MBT) test is proposed for mode I fracture of laminated composites. The MBT specimen consists of a relatively small pre-cracked laminate adhesively bonded to pin-loaded steel beams. This design reduces significantly the bending stresses that prevent successful application of DCB tests to certain laminates. The MBT was here applied to carbon/epoxy unidirectional [0°]₂₆ and [90°]₂₆ laminates with starter delaminations. Interlaminar initiation G_IC values of [0°]₂₆ laminates agreed well with previous DCB test results, while [90°]₂₆ laminates exhibited 50% higher values. Significant lengths of fairly planar intralaminar crack propagation were seen in the latter laminates. The results showed a fibre bridging related R-curve, which was more pronounced in [0°]₂₆ laminates. The consistency of the present results indicates that the MBT opens new possibilities for the interlaminar and intralaminar mode I fracture.     

Experimental characterization of the tensile behaviour of Nicalon fibre-reinforced calcium aluminosilicate composites

Mechanical behaviour studies were conducted on Nicalon SiC/calcium aluminosilicate (CAS) composites. Tensile tests were carried out to study the stress-strain behaviour, as well as to identify the failure mechanisms, of unidirectional and cross-ply SiC/CAS composites. The evolution of the various damage modes and the synergistic effects among them were investigated. The effect of the 90° ply thickness on the damage modes was also determined. The composite stiffness reduction during damage evolution was evaluated. A tensile test specimen was designed for glass and glass-ceramic composites to avoid end-tab shear failure and expensive machining as well as to reduce the effect of bending due to misalignment. The results of this work provide insight into the stress-strain behaviour and damage mechanisms of continuous fibre-reinforced ceramic composites which can be very valuable in design with these materials.     

An investigation on the bearing test procedure for fibre-reinforced aluminium laminates

Excellent fatigue, static strength and damage tolerance characteristics together with low density make fibre-reinforced aluminium laminates a prime candidate sheet material for application in fatigue- and fracture-critical aircraft structures. Their use requires that mechanical property design allowables be established for incorporation in design handbooks (e.g. MIL-HDBK-5). An experimental programme based on statistical design was conducted to establish a meaningful test procedure for determination of fibre-metal laminate bearing strength design allowables. The test procedures investigated are the pin-type bearing test method (ASTM E-238) and the bolt-type bearing test method, a modified method based on the procedure for bearing strength determinations in plastics (ASTM D-953). Results are presented from an experimental programme which measured the bearing strengths of two grades of S-2 glass-based and one grade of aramid-based aluminium laminates. The influences of lateral constraint and ply orientation on bearing strength and failure mode are shown. The bolt-type bearing test method, which combines the attributes of the two aforementioned methods, is recommended. The study also showed that the bearing properties for edge distance ratio e/D = 2 can be predicted by correlation with the aluminium volume fraction in fibre-reinforced aluminium laminates. In addition, diagrams of joint structural efficiency, shown to be comparable to those of aluminium alloy sheets, have been established.     

High-temperature tensile load-bearing capacity of unidirectional continuous-fibre composites: significance of a specimen-end effect

A specimen-end effect which is of significance for the determination of high-temperature tensile load-bearing capacity of metal-matrix composites reinforced with continuous metal fibres has been indicated. The effect arises from the fact that differential axial straining of the fibre and matrix can occur at high temperatures due to viscous sliding at the fibre-matrix interface. A model-system study has been carried out using a tungsten fibre-copper composite, whose ultimate tensile stress (UTS) at temperatures up to 1000° C is determined indirectly from four-point bending data as well as directly from tensile test results. It is found that at temperatures above 0.6 of the matrix homologous temperature the UTS thus determined has much smaller values than those estimated on the basis of a simple rule-of-mixtures equation. Significance of the result is discussed in terms of potential turbine-blade applications of heat-resistant metal-matrix composites, such as tungsten fibre-reinforced superalloys.     

Monte-Carlo simulation of multiple fracture in the transverse ply of cross-ply graphite-epoxy laminates

Graphite-epoxy cross-ply laminates generally show multiple fracture of the transverse ply at higher applied stress. This phenomenon is described by means of a Monte Carlo simulation method based on the assumption that the strength of the transverse ply obeys a two-parameter Weibull distribution function. The main results show that the smaller the scatter of strength of the 90°-ply (i.e. the larger the shape parameter at a constant mean strength of the Weibull distribution), the higher becomes the threshold for the multiple fracture to occur, and the more rapidly the length of 90°-ply segments decreases with increasing applied stress once multiple fracture takes place. The methods to determine the shape and scale parameters of the Weibull distribution for the strength of the 90°-ply proposed by Manderset al. and Peters are proved to be useful even for a small number of test specimens. When the interfacial bond strength between 0°- and 90°-plies is low, saturation of 90°-ply cracking occurs at higher applied stress. The stress-carrying capacity and stiffness of the composites as a whole are reduced by multiple fracture of the 90°-ply. This reduction is more pronounced at increasing applied stress or at a larger number of transverse cracks, especially when the interfacial bond strength is low.     

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 °.     

Transverse ply cracking strains in (0°/90°) and (±θ°/90°) laminates

Comparisons have been made between experimental data on transverse ply cracking in various types of (0°/90°) and (°/90°) laminates and the predictions of the constrained cracking and strain field theory. Generally it is observed that the predictions of the strain field theory are in closer agreement with the experimental data over a wider range of experimental conditions than those of the constrained cracking model. It is shown that reasonable agreement with the observed transverse ply cracking strains of various laminates produced from similar material can be obtained through the use of a standard set of material property values.     

Effect of polymeric precursors on properties of semiconducting carbon/carbon composites

Microstructure, oxidation behaviour, and electrical and mechanical properties of quasi-carbon fibre-reinforced quasi-carbon matrix (QC/QC) composites were investigated. The composite was prepared by heat treating a QC fibre or OXPAN fibre-reinforced polymer matrix composite at a temperature of 500 °C. Different polymer precursors have resulted in the QC/QC composites with varying thermal behaviour. The phenolic matrix derived QC/QC composites followed a self-acceleration mechanism and had better oxidation resistance than the polyacrylonitrile (PAN) matrix-derived QC/QC composites. Because of fewer chemical reactions involved in the pyrolysis process, the QC/QC composites obtained from QC fibre-reinforced composite precursors exhibited higher flexural modulus and strength and were superior to those derived from oxidized PAN (OXPAN) fibre-reinforced composite precursors. Unique semiconducting and switching characteristics have been observed in the QC/QC composites, which would make them promising for electronic device applications. © 1998 Chapman & Hall     

Effect of curing stresses on the behaviour of fibre reinforced plastic composites under biaxial loading

Residual stresses are induced in fibre reinforced plastic (FRP) composites during fabrication and environmental exposure. The curing residual stresses induced during fabrication are mainly due to the thermal expansion mismatch of the constituents. The residual stresses can be either microresidual or macroresidual stresses. Macroresidual stresses in 0° plies and 90° plies of [90/0]_s symmetric cross-ply laminates are calculated starting with ply elastic and thermal properties for different material systems. The calculated curing stresses in Kevlar49/Epoxy unidirectional tape plies in the transverse direction are more than the transverse strength of the corresponding ply. First ply failure (FPF) envelopes are plotted using classical lamination theory and Tsai-Wu quadratic failure theory with and without considering the curing residual stresses. There is a significant effect of residual stresses on the FPF envelopes.     

Enhancement of mechanical performance of epoxy/carbon fiber laminate composites using single-walled carbon nanotubes

Carbon nanotubes (CNT) in their various forms have great potential for use in the development of multifunctional multiscale laminated composites due to their unique geometry and properties. Recent advancements in the development of CNT hierarchical composites have mostly focused on multi-walled carbon nanotubes (MWCNT). In this work, single-walled carbon nanotubes (SWCNT) were used to develop nano-modified carbon fiber/epoxy laminates. A functionalization technique based on reduced SWCNT was employed to improve dispersion and epoxy resin-nanotube interaction. A commercial prepregging unit was then used to impregnate unidirectional carbon fiber tape with a modified epoxy system containing 0.1 wt% functionalized SWCNT. Impact and compression-after-impact (CAI) tests, Mode I interlaminar fracture toughness and Mode II interlaminar fracture toughness tests were performed on laminates with and without SWCNT. It was found that incorporation of 0.1 wt% of SWCNT resulted in a 5% reduction of the area of impact damage, a 3.5% increase in CAI strength, a 13% increase in Mode I fracture toughness, and 28% increase in Mode II interlaminar fracture toughness. A comparison between the results of this work and literature results on MWCNT-modified laminated composites suggests that SWCNT, at similar loadings, are more effective in enhancing the mechanical performance of traditional laminated composites.     

Tensile Behaviour of Multilayer Knitted Fabric Composites with Different Stacking Configuration

In this paper, multilayer plain weft knitted glass fabric reinforced epoxy composite laminates with different stacking configurations, i.e., [0°]₄, [0°/±45°/0°], [0°/90°/90°/0°] and [90°]₄, were investigated experimentally. The laminates were uniaxially tensile loaded until final fractures occurred. The experimental results show that with the change in layer stacking structure, a corresponding variation in composite strength and stiffness was achieved. The tensile strength and modulus rank as follows: [0°]₄ > [0°/±45°/0°] > [0°/90°/90°/0°] > [90°]₄, which implicates a potential desiguability of Knitted Fabric Composites (KFC) for engineering applications. Failure behaviours of the fractured laminate specimens were examined using a matrix digestion and layer peeling method, based on which the behaviour of each lamina in the laminate can be clearly shown. It was found that an angle-plied lamina in the laminate when subjected to a uniaxial tensile load has a different fracture mode from that of a single ply composite under an off-axial tensile load. This means that the lamina in the laminate is subjected to a more complicated load combination. By comparing the fractured mode of the latter lamina with that of the single ply composite, the load direction sustained by the lamina in the laminate can be identified, which provides a qualitative benchmark for verifying a theoretical simulation.     

Delamination of multidirectional composite laminates at 0°/θ° ply interfaces

The main objective of this study is to develop a methodology for establishing mixed-mode delamination propagation criteria of non-unidirectional laminates. The crack interface was chosen to be 0°/45° and the effort was mainly focused on obtaining the mode I fracture toughness (G_IC). The widely used DCB test was avoided due to anticipated problems with intralaminar damage developing at the ply interface of interest. The ADCB and AMMF methods were used to determine the mixed-mode fracture toughness with the largest amount of mode I. The selected stacking sequence resulted in desirable crack propagation behavior; there was no change of delamination plane, an acceptable crack front profile, no initial specimen curvature, and no energy dissipation through global specimen damage. Finite element simulation was found to be the only tool capable of analyzing the experimental data.     

Fracture and fatigue performance of textile commingled yarn composites

The response to mechanical loads of unidirectional commingled warp knitted and woven glass fibre reinforced polyethylene terephthalate laminates has been characterized. The mechanical properties of the two materials were determined under tension, in-plane shear and flexure. The flexural fatigue properties were determined for the woven laminates by means of three-point bending tests with a loading ratio of R=0.1 at stress levels of 50–90% of the ultimate static strength. The Mode I, Mode II and mixed mode (Mode I : II ratios 4 : 1, 1 : 1 and 1 : 4) interlaminar fracture toughnesses of the laminates were determined by means of the double cantilever beam and mixed mode bending tests, respectively. The main fractographic features, as determined by a scanning electron microscopy examination, of the Mode I dominated failures were a brittle matrix failure and larger amounts of fibre pull-out. As the Mode II loading component increased, the amount of fibre pull-out was reduced and the features of the matrix appeared to be more sheared. Cusps were found on the fracture surfaces of specimens tested in pure Mode II and mixed mode I : II=1 : 4. Cusps are normally not found in thermoplastic matrix composites. © 1998 Kluwer Academic Publishers