Stability and failure of composite laminates with various shaped cutouts under combined in-plane loads

The objective of this paper is to study stability and failure of a composite laminate with a centrally placed cutout of various shapes (i.e., circular, square, diamond, elliptical-vertical and elliptical-horizontal) under combined action of uni-axial compression and in-plane shear loads. The FEM formulation based on the first order shear deformation theory and von Karman’s assumptions has been utilized. Newton–Raphson method is used to solve nonlinear algebraic equations. Failure of a lamina is predicted by the 3-D Tsai–Hill criterion whereas the onset of delamination is predicted by the interlaminar failure criterion. The effects of cutout shape, direction of shear load and composite lay-up on buckling and postbuckling responses, failure loads and failure characteristics of the laminate has been discussed. An efficient utilization of material strength is observed in the case of laminate with circular cutout as compared to the laminate with other shaped cutouts. In addition, it is also concluded that although the buckling strength of the (0/90)_4s laminate is lower than that of the (+45/?45/0/90)_2s and (45/?45)_4s laminates, but its strength is increased in the advanced stage of postbuckling deformation.     

Effects of boundary conditions on buckling and postbuckling responses of composite laminate with various shaped cutouts

The objective of the present work is to study the effects of flexural boundary conditions on buckling and postbuckling behavior of axially compressed quasi-isotropic laminate, (+45/−45/0/90)_2s with various shaped cutouts (i.e., circular, square, diamond, elliptical–vertical and elliptical–horizontal) of various sizes using the finite element method. The FEM formulation is based on first order shear deformation theory and von Karman’s assumptions are used to incorporate geometric nonlinearity. 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. It is observed that the laminates clamped and simply supported on all edges have the highest and lowest buckling and postbuckling strength, respectively, irrespective of cutouts shape and size. It is also noted that a fully clamped laminate with large size elliptical–vertical cutout can take higher compressive buckling load than the laminate without cutout for same boundary condition.     

Buckling analysis of rectangular composite plates with rectangular cutout subjected to linearly varying in-plane loading using fem

A numerical study is carried out using finite element method, to examine the effects of square and rectangular cutout on the buckling behavior of a sixteen ply quasi-isotropic graphite/epoxy symmetrically laminated rectangular composite plate [0°/+45°/-45°/90°]_2s, subjected to various linearly varying in-plane compressive loads. Further, this paper addresses the effects of size of square/rectangular cutout, orientation of square/rectangular cutout, plate aspect ratio(a/b), plate length/thickness ratio(a/t), boundary conditions on the buckling bahaviour of symmetrically laminated rectangular composite plates subjected to various linearly varying in-plane compressive loading. It is observed that the various linearly varying in-plane loads and boundary conditions have a substantial influence on buckling strength of rectangular composite plate with square/rectangular cutout.     

Buckling Characteristics of Symmetrically and Antisymmetrically Laminated Composite Plates with Central Cutout

A numerical and experimental study was carried out to determine the effects of anti-symmetric laminate configuration, cutout and length/thickness ratio on the buckling behavior of E/glass-epoxy composite plates. The buckling loads were presented for symmetrically and anti-symmetrically laminated plates subjected to axial compression load. The study included two different laminate configurations ([90/45/−45/0]_as and [90/45/−45/0]_s), two different cutout shapes (circular and semi-circular), two different length/thickness ratios (L/t = 75 and 37.5) and three boundary conditions (clamped–clamped [CC], clamped–pinned [CP] and pinned–pinned [PP]). Firstly, the buckling loads of eight-ply E/glass-epoxy rectangular plates were determined experimentally. Then, the buckling loads of the laminated composites were calculated by ANSYS finite-element computer code. The changing in buckling load of the composites due to the presence of cutout and changing of length/thickness ratio was calculated. Finally, the experimental test results were compared to the buckling loads of plates obtained from the finite element analysis.     

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.     

Damage mechanics characterization of transverse cracking behavior in quasi-isotropic CFRP laminates with interlaminar-toughened layers

Microscopic damage behavior in quasi-isotropic CFRP laminates with interlaminar-toughened layers under tensile fatigue loading is investigated. Damage observation is conducted using an optical microscope and soft X-ray radiography. The material used is CFRP with interlaminar-toughened layers, T800H/3900-2. The laminate configurations are quasi-isotropic [45/0/−45/90]_s, [0/45/−45/90]_s and [45/−45/0/90]_s to discuss the effect of stacking sequence on microscopic fatigue damages. A damage mechanics analysis is used to obtain the energy release rate for transverse cracking which is correlated to the transverse crack density growth rate. The modified Paris-law analysis proves to be valid for characterization of transverse crack multiplication when the effect of other damage is small.     

复合材料双曲率壳屈曲和后屈曲的非线性有限元研究

基于 ABAQUS软件分析平台 , 采用非线性有限元法研究了横向载荷作用下复合材料双曲率壳的屈曲和后屈曲行为。通过在有限元模型中引入 Tsai2Wu失效准则 , 预测了复合材料双曲率壳的初始失效及渐进破坏过程 , 数值结果和试验数据吻合较好 , 表明了该模型的合理有效性 , 并详细讨论了各种参数对屈曲和后屈曲行为的影响。经分析复合材料双曲率加筋壳在均布压载和剪力联合作用下的屈曲和后屈曲行为 , 得到了屈曲载荷的拟合曲线 , 研究表明顺剪力的存在有利于提高屈曲载荷。     

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.     

剪切载荷下含椭圆形大开口层合板的试验研究

在面内纯剪切载荷作用下, 采用试验与有限元模拟方法研究了结构中心设置椭圆形大开口的正方形复合材料层合板的应力/应变集中现象及屈曲、 后屈曲行为, 通过测试结果对试验件失效模式进行了评估。研究结果表明: 层合板开口附近应力/应变集中程度很高; 大尺寸开口使结构稳定性显著降低, 且开口层合板具有较好的后屈曲承载能力; 由于弯曲产生高水平的层间应力, 导致局部分层损伤并伴有基纤剪切破坏; 随着横向挠度的增加, 各应力集中区域的纤维发生拉伸断裂, 导致整体结构瞬间发生脆性失效。有限元模拟结果与试验结果符合较好。     

Shear buckling of corrugated composite panels

Corrugated composite panels are used in aerospace vehicles primarily because of their ability to withstand higher loads before buckling compared to plain sheets. Shear buckling is one of the important modes of failure. In this paper are presented details of prediction of the shear buckling loads of composite panels having sinusoidal or hat type corrugation. The given panel is idealised as an homogeneous orthotropic plate whose equivalent properties are determined based on the given parameters of the panel. In the analysis Kirchhoff-Love assumptions are used. Two opposite edges of the panel in one direction are assumed to be simply supported and the panel is assumed to be very long in the other direction. Critical buckling loads are obtained using conventional orthotropic plate theory. A large class of 0°/90°/45°-45° lamination schemes leading to quadridirectional, tridirectional and bidirectional T300/N5208 corrugated panels is examined and ranked based on buckling loads. Results indicate that by proper choice of lamination scheme, very significant increases in buckling load compared to the quasi-isotropic case can be obtained. Having the corrugation plane normal to the shorter side is significantly better than having the corrugation plane normal to the longer side. Optimum layup schemes are found for 8, 6, 4 and 2 ply cases.     

Optimization of Composite Material System and Lay-up to Achieve Minimum Weight Pressure Vessel

The use of composite pressure vessels particularly in the aerospace industry is escalating rapidly because of their superiority in directional strength and colossal weight advantage. The present work elucidates the procedure to optimize the lay-up for composite pressure vessel using finite element analysis and calculate the relative weight saving compared with the reference metallic pressure vessel. The determination of proper fiber orientation and laminate thickness is very important to decrease manufacturing difficulties and increase structural efficiency. In the present work different lay-up sequences for laminates including, cross-ply [0 _m /90 _n ] _s , angle-ply [±θ] _ns , [90/±θ] _ns and [0/±θ] _ns , are analyzed. The lay-up sequence, orientation and laminate thickness (number of layers) are optimized for three candidate composite materials S-glass/epoxy, Kevlar/epoxy and Carbon/epoxy. Finite element analysis of composite pressure vessel is performed by using commercial finite element code ANSYS and utilizing the capabilities of ANSYS Parametric Design Language and Design Optimization module to automate the process of optimization. For verification, a code is developed in MATLAB based on classical lamination theory; incorporating Tsai–Wu failure criterion for first-ply failure (FPF). The results of the MATLAB code shows its effectiveness in theoretical prediction of first-ply failure strengths of laminated composite pressure vessels and close agreement with the FEA results. The optimization results shows that for all the composite material systems considered, the angle-ply [±θ] _ns is the optimum lay-up. For given fixed ply thickness the total thickness of laminate is obtained resulting in factor of safety slightly higher than two. Both Carbon/epoxy and Kevlar/Epoxy resulted in approximately same laminate thickness and considerable percentage of weight saving, but S-glass/epoxy resulted in weight increment.     

Off-axis fatigue crack growth and the associated energy release rate in composite laminates

Stable matrix crack growth behaviour under mechanical fatigue loading has been studied in a quasi-isotropic (0/90/-45/+45)_s GFRP laminate. Detailed experimental observations were made on the accumulation of cracks and on the growth of individual cracks in +45° as well as 90° plies. A generalised plain strain finite element model of the damaged laminate has been constructed. This model has been used to relate the energy release rate of growing cracks to the crack growth rate via a Paris relation.     

Einfluß der Laminatkomponenten von CFK-Werkstoffen auf das statische und das dynamische Verhalten

Influence of Different Laminate Components on the Static and Dynamic Properties of CERP The static and the dynamic properties of a conventional and a modified, toughened matrix system reinforced with two high strength carbon fibres of a different strain to failure was investigated. Three different laminates were chosen, an unidirectional laminate [0₈], a cross ply laminate [0₂, 90₂, 0₂, 90₂]_s, and a nearly quasi-isotropic laminate [0₂, ±45, 90 ]_s. It is shown, that the damage development under static as well as dynamic loading is delayed when using a toughened matrix system. This delay in damage development results in improved mechanical properties. However, when using a toughened matrix system together with fibres of a high strain to failure, the improvement of the static properties does not lead in the same extent to an improvement of the dynamic properties.     

Characterisation of Transverse Cracking in a Quasi-Isotropic GFRP Laminate under Flexural Loading

Transverse cracking behaviour in a quasi-isotropic glass/epoxy (GFRP) laminate loaded in flexure is studied experimentally and theoretically. A theory developed for cross-ply laminates is applied to a [0°/90°/–45°/45°] _S quasi-isotropic laminate. An equivalent laminate is introduced to derive the Young's modulus of a cracked transverse ply on the basis of a shear lag analysis. The model predicts the flexural stiffness, the neutral axis position and the residual curvature as a function of the transverse crack density and the in-situ ply stress at first ply failure. Experimental results are obtained with the use of the applied moment – strain data in four-point flexural tests and compared with predictions. Time-dependent behaviour of the residual curvature is also investigated.The theoretical predictions are in reasonably good agreement with the experimental results. It is found that the decrease in the residual curvature after unloading is mainly ascribed to viscoelasticity of the material.     

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.     

Off-axis Fatigue Crack Growth and the Associated Energy Release Rate in Composite Laminates

Stable matrix crack growth behaviour under mechanical fatigue loading hasbeen studied in a quasi-isotropic (0/90/-45/+45)_s GFRPlaminate. Detailed experimental observations were made on the accumulationof cracks and on the growth of individual cracks in +45° as well as 90° plies. A generalised plain strain finiteelement model of the damaged laminate has been constructed. This model hasbeen used to relate the energy release rate of growing cracks to the crackgrowth rate via a Paris relation.     

Post-impact compressive strength of curved GFRP laminates

Low velocity impacts to fibre reinforced plastic composites cause a pattern of damage consisting in general of delamination, fibre breakage and matrix cracking. Such damage is accidental and may go unnoticed; therefore composite structures must be designed assuming impact damage exists. Previous work on flat composite laminates has resulted in a reasonable understanding of the mechanisms of compressive strength reduction. There are, however, many instances where curved laminates are used in structures where impact is likely. Furthermore, due to the mechanisms of strength reduction, it may be expected that curvature would have a significant effect on the behaviour of the laminates.The work described here consists of experimental measurement of the post-impact compressive strength of curved GFRP laminates. The laminates were of 8 plies of 0.3 mm thick pre-impregnated glass fibre/epoxy tape in a (0, ±45, 0°)_s lay-up. Each laminate was 200 mm in length by 50 mm wide with the plane of curvature normal to the length. Laminates were impacted on the convex surface of the laminate by dropping a steel mass from 1 m vertically above it.Impacted laminates were loaded in compression and the out-of-plane displacements of the top and bottom surfaces were recorded. Final failure was typically due to fibre breakage occurring through the centre of the impacted area of the laminate. Possible differences in the impact response, and measurable differences in the sizes of the impact damage area, were found to arise from these curvatures, and differences were observed in their post-impact buckling behaviour. However, perhaps unexpectedly, the post-impact compressive strength for a curved laminate was found to be similar to that for a flat laminate. The failure loads for the impact damage laminates are shown to be comparable with those for laminates containing artificial delaminations.     

Failure behavior of quasi-isotropic carbon fiber-reinforced polyamide composites under tension

In this paper, the microscopic failure behavior of quasi-isotropic carbon fiber-reinforced polyamide-6 (CF/PA6) laminates under tension was investigated experimentally. Laminates of two layups, namely [45°/0°/?45°/ 90°]_s and [45°/0°/?45°/ 90°]_2s, were made from CF/PA6 tapes of two different manufacturers and then subjected to tensile testing. Crack initiation and progression on the polished free edge of specimens were examined using optical microscopy, under several load levels. Crack growth behavior through the specimen width was also traced by observing the crack configurations in different sections in the specimen width direction. The effects of the spatial distribution of fiber on the microscopic damage events were elucidated. The difference in failure behavior between the present CF/PA6 laminates and conventional thermosetting CF/Epoxy laminate is discussed.     

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.     

On the Through-the-Width Multiple Delamination, and Buckling and Postbuckling Behaviors of Symmetric and Unsymmetric Composite Laminates

Multiple delamination causes severe degradation of the stiffness and strength of composites. Interactions between multiple delamination, and buckling and postbuckling under compressive loads add the complexity of mechanical properties of composites. In this paper, the buckling, postbuckling and through-the-width multiple delamination of symmetric and unsymmetric composite laminates are studied using 3D FEA, and the virtual crack closure technique with two delamination failure criteria: B-K law and power law is used to predict the delamination growth and to calculate the mixed-mode energy release rate. The compressive load-strain curves, load-central deflection curves and multiple delamination process for eight composite specimens with different initial delamination sizes and their distributions as well as two angle-ply configurations 0₄//(±θ)₆//0₄ (θ?=?0° and 45°, and “//” denotes the delaminated interface) are comparatively studied. From numerical results, the unsymmetry decreases the local buckling load and initial delamination load, but does not affect the global buckling load compared with the symmetric laminates. Besides, the unsymmetry affects the unstable delamination and buckling behaviors of composite laminates largely when the initial multiple delamination sizes are relatively small.