Multidirectional Composite Laminates Research Articles

Effects of fiber orientation of adjacent plies on the mode I crack propagation in a carbon-epoxy laminates

The influence of ply orientation on the resistance to mode I delamination of multidirectional composite laminates can be assessed by Double Cantilever Beam (DCB) tests. However, one of the difficulties associated with such a study is the change in overall elastic parameters occurring when modifying local ply orientations. The present work uses laminates with special stacking sequences allowing for isolating the orientation parameter. Multidirectional DCB specimens were designed so as to obtain an uncoupled quasi isotropic and quasi-homogeneous elastic behavior, with the same properties for the entire laminate and the two sub laminates separated by the pre crack at mid-plane. The results show that the toughness in term of GIC is slightly affected by the variation of ply orientations at the crack interface. The differences are more pronounced in the crack propagation behavior after the initiation point. Even with the same orientation at the crack interface, different subsequent ply orientations can also lead to different crack resistance behavior.

Simulation and experimental validation of mixed mode delamination in multidirectional CF/PEEK laminates under fatigue loading

Cyclic mixed mode delamination in multidirectional composite laminates subjected to high cycle fatigue loading has been investigated by numerical simulations and cyclic mixed mode bending experiments. The numerical model includes lamina and interface elements. The description of the delamination crack growth rate is based on the cyclic degradation of bilinear interface elements linking the evolution of the damage variable with the delamination crack growth rate. The constitutive cyclic damage model is calibrated by means of mixed mode fatigue experiments and reproduces the experimental results successfully and with minor error. It is concluded that only with implementing a cyclic damage variable in the cohesive interface element the experimentally observed crack growth and stiffness degradation can be captured properly. Scanning electron microscopy of fracture surfaces after cyclic loading revealed that abrasion of crack bridging surface roughness is the main microscopical cause of weakening and degradation of the interface.

The response of a multi-directional composite laminate to through-thickness loading

The through-thickness mechanical response of a carbon fibre/epoxy laminated composite of lay-up [0/45/−45]ns is measured at low rates of strain. Uniaxial tension and compression experiments are carried out on dogbone specimens cut from a thick laminate along different directions, and failure mechanisms are observed via optical and electron microscopy. The effect of direct and shear stresses at the ply interfaces on the onset of failure is measured, and a failure envelope is constructed. The compressive response of specimens of different shape is investigated. Composite beams of different volume and aspect ratios are tested to failure in three-point bending and these tests reveal a strong dependence of the apparent out-of-plane tensile strength of the composite on the beam volume; this effect is modelled by Weibull theory.

Evolution of ply cracks in multidirectional composite laminates

This paper treats evolution of ply cracks in multidirectional composite laminates subjected to a quasi-static tensile load in the longitudinal direction. Starting with pre-existing ply cracks in off-axis plies, the formation of additional cracks is analyzed by an energy-based approach. A critical laminate energy parameter associated with formation of these cracks is defined and is evaluated using experimental data for a reference cross-ply laminate. The modeling approach requires crack surface displacements, which are calculated by a three-dimensional finite element (3-D FE) analysis performed on a suitable representative volume of the given cracked laminate. The model predictions agree well with experimental data for [ 0 / ± θ 4 / 0 1 / 2 ] s and [ 0 / 90 / ∓ 45 ] s laminates. A parametric study is conducted to evaluate effects of ply thickness and ply stacking sequence on damage evolution in [ 0 m / 90 n / ∓ θ p ] s laminates.

Fracture simulation of CFRP laminates in mixed mode bending

This paper analyses the progressive mixed mode delamination failure in unidirectional and multidirectional composite laminates using fracture experiments, finite element (FE) simulations and an analytical solution. The numerical model of the laminate is described as an assembly of damageable layers and bilinear interface elements subjected to mixed mode bending. The analytical approach is used to estimate the total mixed mode and decomposed fracture energies for laminates with different stacking sequences, which is also validated through experiments. It is concluded that the interlaminar fracture toughness of multidirectional laminates is considerably higher than that of the unidirectional ones. The effect of initial interfacial stiffness and element size is studied and it is also shown that their value must not exceed a definite limit for the numerical simulations to converge. The model can also be further extended to simulate the mixed mode fracture in hybrid fiber metal laminates.

Prediction of stitch crack evolution and gas permeability in multidirectional composite laminates

Stitch cracks in multidirectional laminates were observed by many researchers in the literature. In the present work, the damage evolution in multidirectional laminates is investigated using the strain energy release rate concept. Two methods are used to compute the strain energy release rate. The effects of ply angle and ply thickness on stitch crack evolution are investigated. Then, a model based on Darcy’s law for porous materials is developed for predicting gas permeability in composite laminates containing microcracks and delaminations. Gas permeability is presented as a function of crack density and crack intersection area. Then the intersection areas formed by crack opening displacements are computed using 3D finite element analysis. The progressive gas permeability in multidirectional laminates is predicted and compared with the gas permeability predicted in the cross-ply laminates in our previous work.

Adaptive neuro-fuzzy inference system in modelling fatigue life of multidirectional composite laminates

Adaptive neuro-fuzzy inference system (ANFIS) has been successfully used for the modelling of fatigue behaviour of a multidirectional composite laminate. The evaluation of the neuro-fuzzy model has been performed using a data base containing 257 valid fatigue data points. Coupons were cut at 0° on-axis and 15°, 30°, 45°, 60°, 75°, and 90° off-axis directions from an E-glass/polyester multidirectional laminate with a stacking sequence of [0/(±45)2/0]T. Constant amplitude fatigue tests at different tensile and compressive conditions were conducted for the determination of the 17 S–N curves. The modelling accuracy of this novel, in this field, computational technique is very high. For all cases studied, it has been proved that a portion of around 50% of the available data are adequate for accurate modelling of the fatigue behaviour of the material under consideration. The new technique is a stochastic process which leads to the derivation of a multi-slope S–N curve based on the available experimental data without the need for any assumptions. Employment of this technique can lead to a substantial decrease of the experimental cost for the determination of reliable fatigue design allowables.

Generalized Technique for Cumulative Damage Modeling of Composite Laminates

This article introduces an iterative model to predict the fatigue behavior of fiber reinforced laminated composites under general loading conditions. The model simulates the damage progress and subsequent material property degradation of composite laminates and predicts their fatigue life by using a three-stage procedure. In the first stage, state of stresses in the whole component is specified. Then, multi-axial stresses of each element are utilized to damage assessment by using a newly developed damage estimation technique. Considering each element as an orthotropic material, stiffness degradation due to the induced damage is calculated based on two sets of material property degradation rules. For this aim, a generalized approach is used for gradual and sudden material property degradation. In order to evaluate the model, a macro program is developed that simulates the fatigue behavior of unidirectional and multidirectional composite laminates. The results of the model are consistent with available experimental data. Using this program, some fatigue life predictions are also accomplished for laminates with arbitrary stacking sequences.

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.

A unified multiaxial fatigue damage model for isotropic and anisotropic materials

A unified multiaxial fatigue damage model based on a characteristic plane approach is proposed in this paper, integrating both isotropic and anisotropic materials into one framework. Compared with most available critical plane-based models for multiaxial fatigue problem, the physical basis of the characteristic plane does not rely on the observations of the fatigue crack in the proposed model. The cracking information is not required for multiaxial fatigue analysis and the proposed model can automatically adapt for very different materials experiencing different failure modes. The effect of the mean normal stress is also included in the proposed model. The results of the proposed fatigue life prediction model are validated using experimental results of metals as well as unidirectional and multidirectional composite laminates.

Artificial neural networks in spectrum fatigue life prediction of composite materials

An artificial neural network has been proved to be a sufficient tool for modelling fatigue life of multidirectional composite laminates made of GFRP composite materials and tested under constant amplitude loading patterns. Modelling efficiency of the network was satisfactory for both on- and off-axis coupons’ life, irrespective of the test conditions, i.e., R-ratio that defines the developed stress state on the coupon. Tension–Tension, Compression–Compression and even Tension–Compression loading patterns were investigated and modelling accuracy of the proposed ANN model was validated. The main benefit of this new modelling tool is that only a small portion, in the range of 40–50%, of the experimental data is needed for the whole analysis. Thus, expensive and time consuming tests required by the conventional way for the establishment of S– N curves could be significantly reduced without significant loss of accuracy. We applied the neural network method using experimental data from two different (in nature) material systems and proved that constant life diagrams (CLDs), which are very useful for the design of structures loaded under variable amplitude loading spectra, can be efficiently modelled using a much smaller set of experimental data compared to that needed for the development of CLDs by the conventional way.

Modelling Fatigue Life of Multidirectional GFRP Laminates under Constant Amplitude Loading with Artificial Neural Networks

An artificial neural network has proven to be a sufficient tool for modelling fatigue life of multidirectional composite laminates made of Glass Fibre Reinforced Plastic (GFRP) composite materials and tested under constant amplitude loading patterns. Modelling efficiency of the network was satisfactory for both on- and off-axis coupons life, irrespective of test conditions, i.e., R-ratio that defines the developed stress state on the coupon. Tension-Tension, Compression-Compression and even Tension-Compression loading patterns were investigated and modelling accuracy of the proposed ANN model was validated. The main benefit that this new modelling tool brings is that only a small portion, in the order of 40%-50%, of the experimental data is needed for the whole analysis and thus, expensive and time consuming tests needed for the establishment of S-N curves could be eliminated without any significant loss of accuracy.

Ultrasonic wave interaction with multidirectional composites: modeling and experiment.

Phenomena of wave transmission through a multidirectional composite laminate immersed in a fluid have been investigated. Based on a recently-developed recursive stiffness matrix method time-domain beam models have been developed to simulate the problem. Experimental and theoretical results at frequency 2.25 MHz show that the transmission amplitude is highly dependent on lamina orientation and angle of incidence. Large transmission amplitude appears at small (<10 degrees) and large incident angles (45 degrees-60 degrees). At intermediate incident angles (16 degrees-40 degrees) the transmission amplitude is almost zero. At high frequency, the residue epoxy layers between each lamina become important and corresponding resonances may be observed. These transmission phenomena have been interpreted in terms of Floquet waves. It shows that the pass and stop bands of the three Floquet waves obtained from the unit cell stiffness matrix determine the transmission amplitude distribution in frequency, incident angle and rotation angle domains. The effect of random deviation of the laminated structure periodicity has also been assessed. At normal incidence, the variation of the thickness of the epoxy residual layer between composite lamina has little effect on the overall stop and pass band structures but introduces random reverberation and scattering in the pass bands. It is shown that for oblique incidence the transmittivity spectrum of a composite with random lamina lay-up converges with increase of randomness to that of a [0/-45/90/45]2s quasi-isotropic composite. Randomization of lamina lay-up produces a small effect in the transmittivity spectrum for a quasi-isotropic composite.

Lifetime Prediction for Fatigue Damage in Bonded Joints

A procedure is outlined and programmed in software in order to predict the fatigue threshold in composite adhesively bonded joints. Two different joint configurations are considered in this study, namely, Double Lap (DL) and Lap Strap (LS). The substrates are made of either uni-directional (UD) or multi-directional (MD) composite laminates and bonded together using an epoxy film adhesive. The theory of continuum damage mechanics has been used to develop damage evolution laws for UD/DL joints at different temperatures. The number of cycles to failure was then expressed in terms of the stresses in the adhesive layer and material constants (damage parameters). The stresses were calculated from non-linear finite element analyses. In order to calculate the damage parameters, a system of equations, in which the number of unknowns is less than the number of equations, has been derived using a combination of experimental data, finite element results and the damage law. The system of equations has been solved using the concept of pseudo-inverse by solving a singular value decomposition problem. Software has been developed to automatically calculate the damage parameters and produce the required load-number of cycle to failure curves. From those curves, the fatigue crack initiation thresholds were predicted for several joints, e.g. MD/DL, UD/LS and MD/LS joints. Good predictions were found.

Stiffened composite panels with a stress concentrator under in-plane compression

The in-plane compressive strength of a stiffened thin-skinned composite panel with a stress concentrator is examined. Two possible in-plane failure mechanisms are investigated. The first one is near-surface instability at the edge of the cutout, where high stress gradients are expected because of the stress concentration and the thickness heterogeneity of the laminated skin. Analytical 3D formulas allowing simple parametrical investigation of the phenomenon under consideration are derived. The second failure mechanism is fiber microbuckling in 0°-plies. An equivalent crack model is used to predict the compressive strength of a multidirectional composite laminate. How a stiffener affects the compressive strength of the thin-skinned panel with a hole is studied for both mechanisms. Experimental and predicted values of the critical load are in good agreement.

Modeling Strength of Multidirectional Laminates under Thermo-Mechanical Loads

This paper investigates the progressive failure process in a multidirectional composite laminate subjected to an arbitrary thermo-mechanical load condition. A micromechanics modeling approach is employed to predict each-ply failure strength of the laminate and to identify the corresponding failure mode. The analysis has incorporated both material non-linearity and stiffness reduction. The load shared by each lamina in the laminate is determined based on the classical laminate theory, whereas the internal stresses in the constituent fibers and matrix of the lamina are explicitly related to this load by making use of combining the bridging model and the Benveniste and Dvorak’s formula. The lamina failure is assumed whenever any constituent material attains its ultimate stress state. A generalized maximum normal stress criterion is employed to detect the constituent failure. In this approach, all the simulation equations are given explicitly, no iteration is involved, and a minimum number of input data are required. Comparison of the predicted thermo-mechanical strengths of several laminates with available experimental data is favorable.

A mechanical model for predicting critical thrust forces in drilling composite laminates

Among the various forms of material damage, delamination due to drilling is one of the major concerns in machining a composite laminate. The thrust force has been cited as the primary cause of the delamination. The analysis for multidirectional composite laminates is based on linear elastic fracture mechanics (LEFM), classical bending plate theory and the mechanics of composites. This paper presents a general closed-form mechanical model for predicting the critical thrust force at which delamination is initiated at different ply locations. Good correlation is observed between the model and the experimental results.

Prediction of fatigue thresholds in adhesively bonded joints using damage mechanics and fracture mechanics

The prediction of fatigue threshold in composite adhesively bonded joints using continuum damage mechanics (CDM) and fracture mechanics (FM) approaches has been investigated. Two joint types were considered in this study: double lap (DL) and lap strap (LS) joints. The substrates, which were made of uni-directional (UD) or multi-directional (MD) composite laminates, were bonded together using an epoxy film adhesive. The joints were tested under fatigue loading with a load amplitude ratio of 0.1 at various test temperatures. Damage evolution laws were derived using thermodynamics principles. The number of cycles to failure was then expressed in terms of the stresses in the adhesive layer and material constants. The stresses were calculated from non-linear finite element analyses, considering both geometrical and material non-linearities. The damage laws generated for the UD/DL joint data were then used to predict the fatigue crack initiation thresholds for the MD/DL, UD/LS, and MD/LS joints. The FM approach uses the crack closure integral method to compute the strain energy release rate at the threshold load (G th) from the results of geometrical non-linear finite element analysis. The G th value for an inherent crack size at the centre of the bondline in the UD/LS joint is used as the failure criterion in order to predict the fatigue threshold for the MD/LS, UD/DL, and MD/DL joints. It was found that the predictions using CDM were slightly more accurate than those obtained using the FM approach. In general, when predicting the fatigue thresholds of the LS joints using the DL joints data, or vice versa, good agreement was obtained between the measured and predicted thresholds at ambient and low temperatures, but poor agreement was seen at the high test temperature. This was attributed to the deleterious effect of creep, which was greater in the DL joints than in the LS joints.

The effect of environment on the fatigue of bonded composite joints. Part 2: fatigue threshold prediction

In Part 2 of this paper, the fatigue strength of adhesively bonded joints is analysed using stress analysis and fracture mechanics. Composite lap strap joints are considered for this study. Substrates made of unidirectional and multidirectional composite laminates are bonded together using epoxy film adhesive. Non-linear stress and fracture analyses are performed in order to predict the strength of the joints in different hostile environmental conditions. The use of several threshold criteria is investigated. Criteria based on the principal stress provide good threshold prediction for small plastic deformation. The maximum principal strain, von Mises strain, shear stress and von Mises stress predict with good accuracy the fatigue thresholds of the joints that undergo large plasticity. The plastic zone size does not show correlation at the fatigue threshold load in the different joint types. Furthermore, elastic and elasto-plastic fracture parameters are calculated for two different inherent cracks. The first one is initiated at the adhesive/adherend interface, while the second is in the centre of the adhesive layer. The J-integral that accounts for plasticity and the elastic strain energy release rate have been shown to correlate with the threshold load for the different joints.

Modelling stiffness degradation due to matrix cracking in angleply composite laminates

When a multidirectional composite laminate is subjected to in plane static or fatigue tensile loading, matrix cracks parallel to the fibres appear in the off axis plies long before catastrophic failure. Matrix cracking significantly reduces the laminate stiffness properties and triggers development of other harmful resin dominated damage modes such as delaminations. Concurrent matrix cracking in the adjacent off axis plies is an extremely complex problem to model analytically and has been analysed mostly using finite element methods.The present paper is concerned with the theoretical modelling of stiffness reduction in cracked angleply [θ1 /θ2 ]s laminates subjected to multiaxial in plane loading. A new approach based on the equivalent constraint model of the damaged ply and an improved two-dimensional shear lag method has been applied to model matrix cracking in angleply [θ1 /θ2 ]s laminates. Stresses in the cracked ply are determined from a system of two coupled ordinary differential equations and used to calculate the in situ damage effective functions, which describe the stiffness loss. For angleply [±θ ]s laminates with a cracked midlayer, it is found that the reduction due to matrix cracking of the laminate axial and transverse moduli is more significant than in crossply laminates, while for the shear modulus, the opposite is true. Matrix cracking in such laminates can result in an increase in the Poisson's ratio – a phenomenon not observed in crossply [0/90]s laminates. In addition, matrix cracking in angleply [±θ ]s laminates introduces coupling between extension and shear.