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.     

Three-dimensional simulations of impact induced damage in composite structures using the parallelized SPH method

To address the strain-rate dependent behavior of unidirectional composites in Air Force and Navy military systems subjected to impact loading, a one-parameter visco-plasticity composite material model was developed and incorporated into the MAGI code which was parallelized for this study. This code is based on the smoothed particle hydrodynamics method. The strain-rate dependent composite model is applied here to investigate the high-velocity impact induced damage of armored composite plates which consisted of eight graphite/epoxy (Gr/Ep) layers with a lay-up of [±45/0/90]_s. The face sheets consisted of two different materials (either aluminum or boron carbide) of variable thickness. The effects of face sheet position, face sheet material types, and impact velocity on the detailed damage of the laminate are presented.     

Hygroscopic aspects of epoxy/carbon fiber composite laminates in aircraft environments

In this study, various hygroscopic effects of such parameters as hygrothermal temperature, matrix volume ratio (V_m), void volume ratio (V_v), specimen thickness, lay-up sequence and internal stress were investigated for epoxy/carbon fiber composite laminates. The specimen thickness and lay-up sequence had little effect on the through-the-thickness water absorption behavior of composite laminates, but the other parameters affected the moisture absorption rate and equilibrium water uptake in different ways and intensities. The glass transition temperature of composite laminates was strongly affected and linearly decreased by the quantity of equilibrium water uptake. A characteristic length of moisture migration through the unidirectional laminates was proposed as a function of fiber angle to the exposed laminate surface. In this approach, the fibers imbedded in the matrix were assumed to act as a barrier to the penetrating water molecules, and the developed model was well compared with the experimental results.     

Statistical model of the transverse ply cracking in cross-ply laminates by strength and fracture toughness based failure criteria

Cross-ply laminate subjected to tensile loading provides a relatively well understood and widely used model system for studying progressive cracking of the transverse ply. This test allows to identify material strength and/or toughness characteristics as well as to establish relation between damage level and the composite stiffness reduction. The transverse ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. The variability affects both crack initiation (governed by the local strength) and propagation (governed by the local fracture toughness). The primary aim of the present study is elucidation of the relative importance of these phenomena in the fragmentation process at different transverse and longitudinal ply thickness ratios. The effect of the random crack distribution on the mechanical properties reduction of the laminate is also considered. Transverse ply cracking in glass fiber/epoxy cross-ply laminates of the lay-ups [0₂/90₂]_s, [0/90₂]_s, and [0/90₄]_s is studied. Several specimens of each lay-up were subjected to uniaxial quasistatic tension to obtain crack density as a function of applied strain. Crack spacing distributions at the edge of the specimen also were determined at a predefined applied strain. Statistical model of the cracking process is derived, calibrated using crack density vs. strain data, and verified against the measured crack spacing distributions.     

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.     

Selection of an in-plane shear test method based on the shear sensitivity of laminate tensile modulus

The sensitivity of the tensile modulus for a number of Hercules AS4/3501-6 laminates to changes in the values of in-plane shear modulus was used to select the fibre orientations for four highly shear-sensitive laminates of the form [±θ₁,±θ₂]_3s. The in-plane shear moduli for the Hercules AS4/3501-6 composite material were then determined for 90° Iosipescu, 10° off-axis tensile and ±45° tensile specimens. These values were used with classical laminate plate theory to predict laminate tensile moduli. The best agreement between these predicted values and those which were experimentally measured was obtained when the ± 45° tensile test method was used to determine the in-plane shear modulus.     

Numerical and Experimental Study on the Effect of Lay-Up Type and Structural Elements on Thickness Uniformity of L-Shaped Laminates

Based on the two-dimensional resin flow and fiber compaction model developed by our group, we studied the cured laminate thickness uniformity of the L-shaped CF/BMI resin laminates and the effects of lay-up type and structural elements on it. Both the simulated and experimental data showed that the quasi-isotropic laminate thickness was more uniform than that of the [90°]_n laminates and the cured thickness of laminates molded by rigid convex tool was more uniform than that molded by the rigid concave tool. Lay-up type has a great influence on the cured laminate thickness uniformity. For the quasi-isotropic laminates, the structural elements, such as curvature radius, flat part length, and the number of plies, did not have much influence on the cured laminate thickness uniformity in the studied scope. For the [90°]_n laminates, the corner radius has a larger effect on the corner consolidation in comparison with the flat part length and the number of plies. According to the simulated results, resin pressure and consolidation time were largely affected by the lay-up type, due to the different permeability and compressibility. The rich resin defect was observed in the metallographic photos of the corner region of the [90°]_n laminates fabricated with the rigid concave tool, which demonstrated that the resin flow in the laminates played an important rule and validated the numerical prediction. Good agreement between the simulated results and experimental data demonstrated the reliability and universality of the numerical simulation method. These results are greatly helpful for the control of defects in angle-bended laminates and the optimization of cure cycle in autoclave process.     

A three-segment anisomorphic constant life diagram for the fatigue of symmetric angle-ply carbon/epoxy laminates at room temperature

The anisomorphic constant fatigue life (CFL) diagram approach that was developed in an earlier study is further tested for applicability to the matrix-dominated fatigue failure in symmetric angle-ply carbon/epoxy laminates. An extension of the CFL diagram approach is also attempted to improve the accuracy of fatigue life prediction. The original anisomorphic CFL diagram approach can be used for approximately predicting the CFL diagrams for the [±30]_3S and [±45]_3S laminates, while it fails to accurately predict the CFL diagram for the [±60]_3S laminate due to its significant local distortion. For accommodating the anisomorphic CFL diagram approach to the local distortion in CFL curves due to a significant change in mean stress sensitivity in fatigue, a transitional segment is inserted between the tension–tension and compression–compression dominated segments. It is demonstrated that the three-segment anisomorphic CFL diagram approach allows improved predictions of the CFL diagrams and S–N relationships for the angle-ply laminates.     

An empirical fatigue-life model for high-performance fibre composites with and without impact damage

This article follows earlier work on the development of a life-prediction method for carbon-fibre/epoxy laminates. For comparison with the behaviour of a number of different CFRP laminates already studied, further constant-life fatigue data have now been obtained for a further CFRP composite and a GRP laminate of similar construction – a 16-ply [(±45,0₂)₂]_S lay-up. Fatigue tests have been carried out on these materials in both the virgin condition and after damage by low-velocity impacts. Following analysis of these new data and a re-examination of the older data base, the constant-life model has been appropriately modified. It now offers a prediction procedure for the fatigue response of composite materials in the virgin and impact-damaged conditions which requires, in the first instance, only the tensile and compressive strengths of the composite in question. The model is equally applicable to both GRP and CFRP, despite the fact that the fatigue response of a GRP laminate is different from that of an equivalent CFRP material.     

In-plane shear properties of unidirectional glass fiber (U)/random glass fiber (R)/epoxy hybrid and non-hybrid composites

The in-plane shear properties (shear strength τ_xy and shear modulus G_xy) of unidirectional glass fiber (U)/random glass fiber (R)/epoxy hybrid and non-hybrid composites have been investigated experimentally and theoretically. The effect of stacking sequence and random fiber relative volume fraction (V_fR/V_fT) in hybrid composites were reported. Laminates were fabricated by hand lay-up technique with a total of 5 plies, by varying the number and position of random glass layers so as to obtain four different hybrid laminates; i.e. [0.5R/U/U]_S, [U/0.5R/U]_S, [U/U/0.5R]_S, and [U/R/U/R/U]. All unidirectional fiber laminate [U]₅ and another of all random fiber laminate [R]₅ were also fabricated for comparison purpose. The average thickness of the manufactured laminates is 5.5 ± 0.2 mm and the total fiber volume fraction (V_fT) is 37%. Failure modes of all specimens were investigated. Results indicated that the in-plane shear properties (shear strength τ_xy and shear modulus G_xy) of unidirectional fiber composite can be considerably improved by incorporation of random glass fiber and forming hybrid composites.     

Quasi-static penetration and ballistic properties of kenaf–aramid hybrid composites

In this research, quasi-static penetration and ballistic properties of non-woven kenaf fibres/Kevlar epoxy hybrid laminates with thicknesses ranging from 3.1 mm to 10.8 mm by hard projectile at normal incidence have been experimentally investigated. Hybrid composites were fabricated by hand lay-up technique in a mould and cured at room temperature for 24 h by static load. Hybrid composites consist of Kevlar layers and non-woven kenaf layers at three different configurations, i.e. kenaf at the innermost layers, outermost layers and at the alternating layers. Kevlar/epoxy and kenaf/epoxy composites were also fabricated for comparison purpose. Quasi-static experiments were conducted using a tensile testing machine at the speed of 1.27 mm/min and 2.54 mm/min. Ballistic tests were conducted using 9 mm full metal jacket bullet using a powder gun at speeds varying from 172 to 339 m/s, with the initial and a residual velocity of the projectiles is measured. The tested sample was carefully examined with respect to failure modes. Results showed the effect of hybridization in term of force–displacement curves, energy dissipation and damage mechanisms for quasi-static test. Maximum force to initiate penetration is higher in hybrid composites compared to kenaf/epoxy and Kevlar/epoxy composites. Hybridization of kenaf–Kevlar resulted in a positive effect in terms of energy absorbed (penetration) and maximum load. In the case of ballistic tests, hybrid composites recorded lower ballistic limit (V₅₀) and energy absorption than the Kevlar/epoxy composite. The V₅₀ of hybrid composites with kenaf at the outermost layers is superior to other hybrid composites. These finding inspired further exploration of hybrid composite for ballistic armour spall-liner application.     

Interlaminar stresses in composite laminates: Thermoelastic deformation

An approximate elasticity solution for prediction of the displacement, stress and strain fields within the m-layer, symmetric and balanced angle-ply composite laminate of finite-width and subjected to uniform axial extension was developed earlier [4]. In the present paper, the authors have extended that solution to treat thermal stresses and deformations induced by a uniform change in laminate temperature. The results have revealed not only the complex fields within the laminate, but also inter-relationships between the lamina axial and shearing coefficients of thermal expansion and the effective laminate coefficients of thermal expansion. Further, the solution is shown to recover laminated plate theory predictions for thermally induced fields at interior regions of the laminate, thereby confirming the boundary layer nature of the interlaminar phenomena for the thermoelastic case. Finally, the results exhibit the anticipated response in congruence with the mechanical solution of Ref. [4] and the thermoelastic results satisfy the conditions of self-equilibration necessary for the finite-width laminate subjected to free thermal deformation. Integration of the stress σ_x over the laminate cross-section in the y–z plane is shown to converge to zero as the number of Fourier terms is increased. While the exact solution for mechanical loading is known to exhibit singular behavior, non-convergence of the interlaminar shearing strain is also seen to occur at the intersection of the free edge and planes between lamina of +θ and −θ orientation under thermal loading. The analytical results show excellent agreement with the finite-element predictions for the same boundary-value problem.     

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.     

Experimental determination of residual stresses in composite laminates [02/θ2]s

The present work aims to determine the residual stresses in carbon fiber/epoxy composite laminates, by means of the incremental hole-drilling method. Based on mechanical theories of composite laminates and an elastic plate with a circular hole, the relationship between the relaxed strains on the surface of laminates and the residual stresses in laminates was established. This newly deduced theoretical formula was adapted into the incremental hole-drilling method and allowed us to further study the residual stresses in the through-thickness direction for various composite laminates. Related numerical modeling of composite laminate with a hole was built to calibrate the coefficients within the formula. Experiments were conducted and the residual stresses in composite laminates [0₂/θ₂]_s are presented. The proposed approach was validated with the consistence between our results for cross-ply laminates and those in literature.     

High‐order layerwise finite element for the damped free‐vibration response of thick composite and sandwich composite plates

A high‐order layerwise finite element methodology is presented, which enables prediction of the damped dynamic characteristics of thick composite and sandwich composite plates. The through‐thickness displacement field in each discrete layer of the laminate includes quadratic and cubic polynomial distributions of the in‐plane displacements, in addition to the linear approximations assumed by linear layerwise theories. Stiffness, mass and damping matrices are formulated from ply to structural level. Interlaminar shear stress compatibility conditions are imposed on the discrete layer matrices, leading to both size reduction and prediction of interlaminar shear stresses at the laminate interfaces. The C¹ continuous finite element implemented yields an element damping matrix in addition to element stiffness and mass matrices. Application cases include thick [0/90/0], [±θ]_S and [±θ] composite plates with interlaminar damping layers and sandwich plates with composite faces and foam core. In the latter case, modal frequencies and damping were also experimentally determined and compared with the finite element predictions. Copyright © 2008 John Wiley & Sons, Ltd.     

Mode III interlaminar fracture characterization of composite materials

An experimental project was undertaken to develop two interlaminar Mode III tearing test methods. The first was a split cantilever beam test. A laminate, containing a starter crack, was bonded between aluminum bars. The ends of the bars were then loaded in opposite directions, parallel to the plane of the crack and normal to the beam length. Stable crack growth was achieved in carbon fiber material. Unidirectional carbon fiber composites showed Mode III critical strain energy release rates in the range 1·1–1·3 kJ/m². The effects of laminate thickness, beam depth, and data reduction method were investigated. In addition, testing was conducted on angle-ply laminates. Unsuccessful tests were conducted on a tougher matrix thermoplastic composite.An edge delamination specimen was also investigated. [15° _i/ – 15° _i]_S angle-ply laminates were fabricated with four implanted edge starter cracks. Both tension and compression tests were conducted. Difficulties in interpreting the results are discussed. The split cantilever beam and edge delamination results are compared.     

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.     

Postbuckling strengths of composite laminate with various shaped cutouts under in-plane shear

The aim of present investigation is to study the buckling and postbuckling response and strengths under positive and negative in-plane shear loads of simply-supported composite laminate with various shaped cutouts (i.e., circular, square, diamond, elliptical-vertical and elliptical-horizontal) of various sizes using finite-element method. The FEM formulation is based on the first order shear deformation theory which incorporates geometric nonlinearity using von Karman’s assumptions. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. The effect of cutout shape, size and direction of shear load on buckling and postbuckling responses, failure loads and failure characteristics of quasi-isotropic [i.e., (+45/−45/0/90)_2s] laminate has been discussed. In addition, the effect of composite lay-up [i.e., (+45/−45/0/90)_2s, (45/−45)_4s and (0/90)_4s] has also been reported. It is observed that the cutout shape has considerable effect on the buckling and postbucking behaviour of the quasi-isotropic laminate with large size cutout. It is also observed that the direction of shear load and composite lay-up have substantial influence on strength and failure characteristics of the laminate.     

Experimental and analytical assessment of axial crushing of circular hybrid tubes under quasi-static load

In the present article, axial crushing behavior of circular aluminum/glass–epoxy hybrid tubes is studied experimentally and analytically. 48 quasi-static axial crushing experiments are carried out on bare metal and hybrid tubes to evaluate the effect of different parameters such as metal and composite wall thicknesses and stacking sequence of composite layers on the crashworthiness characteristics. The specimens are made in two types of layups including angle ply pattern [±θ]_s and multi angle ply pattern (different ply angles). The experimental results reveal that stacking sequence has a considerable effect on crashworthiness characteristics, for example for layup [90/0/0/90], the absorbed energy is more than three times of aluminum tube with the same aluminum wall thickness. Also the aforementioned layup has better energy absorption compared to [90/90/90/90] which has been previously proposed as the best layup.     

Characteristics of aluminum/CFRP short square hollow section beam under transverse quasi-static loading

Energy absorption capability and bending collapse behavior of an aluminum (Al)/carbon fiber reinforced plastic (CFRP) short square hollow section (SHS) beam were investigated under transverse quasi-static loading. The Al SHS beam was reinforced by CFRP, and the specimen was co-cured via an autoclave curing process. Three-point bending test was performed with five different lay-up sequences and three different laminate thicknesses. Stable bending collapse accompanying plastic hinge was observed in all specimens. Individual bending collapse behaviors were different depending on the lay-up sequences. The specific energy absorbed (SEA) was improved by up to 29.6% in the Al/CFRP SHS beam specimen with a [0/+45°/90°/−45°]_n lay-up sequence and laminate thickness of 1.168 mm (thickness ratio of Al: CFRP = 1: 0.87, 8 plies of prepreg) compared to the Al SHS beam. The SEA was not related with damage area of the Al/CFRP SHS beam. Finite element analysis and theoretical analysis based on Kecman’s model were performed to investigate the effect of reinforcement by CFRP on the Al SHS beam.