压电复合材料正交层板的精确理论

基于一个六自由度的位移场和电势场, 建立了压电复合材料层板的控制方程。在简支边界条件下, 得到了正交矩形压电复合材料层板的解析解。该理论是一个等效单层理论, 控制方程的变量仅六个, 且不随层数变化, 使解的数学过程简洁。在该理论中, 决定精度的位移分布函数和电势分布函数由三维应力和静电平衡方程的特解来确定, 使之满足压电层板界面连续条件与板面力及电条件。算例验证了本文中等效单层理论的高精度。     

Simulation of fatigue performance of cross-ply composite laminates

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

Analysis of stiffness loss in cross-ply composite laminates

The behaviour of laminated composite plates beyond first-ply failure has been the subject of much research work. It is well known that generally, the load-bearing capability of laminated composite plates can remain significant despite the presence of some damage in the plies. Traditionally, the ply-discount method has been used among analysts and designers, although the approach is generally regarded as too conservative. It is therefore desirable to develop models for the prediction of the mechanical properties of damaged composite laminates at various applied loads, and to be able to correlate the changes in properties with the amount of damage and cracking within each constituent ply. Generally, if the models are to be useful as predictive tools, they must be capable of not only sufficiently describing the damage state but also the nature of the damage evolution with loading. This ‘evolution law’ is often obtained through fracture analysis, although it should be noted that the diffused nature of cracks and the multiplicity of failure modes in composites in general greatly complicates the analysis. The problem of transverse matrix cracking in cross-ply laminates under uniaxial tension is considerably simpler because it is essentially dominated by mode I fracture. Thus it is necessarily the first step for any model aiming to predict stiffness losses in composite laminates. In this paper, a constitutive model of the damage state for composite laminates, first proposed by Allen et al., is used with a damage evolution criterion based on strain energy to predict the stiffness loss due to matrix cracking in cross-ply laminated composite plates. Although the constitutive model does not require the determination of many constants, the state of damage is described by a vector of internal state variables (ISV), which contains information on the crack geometry and fracture modes. A series of parametric finite element analyses was performed to determine the effects of relative ply thicknesses, crack density and crack opening profile on the vector of ISVs. A computer algorithm was written for the analysis of cross-ply laminates based on the damage evolution criterion proposed in this work. The results of the analysis compare favourably with experimental measurements of progressive stiffness loss in damaged cross-ply graphite-epoxy laminates obtained from other researchers.     

复合材料非对称正交薄层板的固化变形

利用Rayleigh-Ritz 法研究了复合材料非对称正交薄层板的固化变形。建立了考虑几何非线性的固化变形分析模型, 预报了其固化后的变形形状及变形量。利用热压釜工艺进行了实验研究。实验发现, 方板边缘发生了较大的向内卷曲变形, 板边缘附近理论预报值与实验结果差别较大, 在距板边缘一定距离内理论预报值和实验结果吻合较好, 矩形板实验结果与理论预报值吻合良好。      

Edge effects of uniformly loaded cross-ply composite laminates

Interlaminar stresses resulting from bending of rectangular cross-ply composite laminates are determined using a layer wise laminate theory. Two types of laminates are considered. First a fully simply supported laminate subjected to bi-directional bending is analyzed. The results obtained from this theory are compared with those of the published three-dimensional elasticity solutions to verify the validity and accuracy of the present theory. Then laminates with two edges simply supported and the other two edges free are examined. The results indicate the presence of significant interlaminar stresses near the free edges.     

双稳定矩形非对称复合材料层板的跳变研究

对双稳定矩形非对称复合材料层合板两种稳定构型的跳变行为进行了实验和数值研究。通过实验测得中心加载下层合板两种稳定构型跳变的临界载荷, 建立了两种稳定构型的非线性有限元分析模型, 成功预报了层合板固化后的两种稳定构型, 并进一步预报了两种稳定构型的跳变临界载荷, 预报结果与实验结果吻合良好。实验和有限元模拟结果表明, 中心加载下矩形非对称层合板两种构型的临界载荷相差较大, 并且跳变的过程有所差异。      

Damage response of stitched cross-ply laminates under impact loadings

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

Analysis of the transverse cracking in hybrid cross-ply composite laminates

A modified shear-lag analysis, taking into account the concept of interlaminar shear stress, is employed to evaluate the effect of transverse cracks on the stiffness reductions in different glass/epoxy and graphite/epoxy hybrid cross-ply laminates. The modified shear-lag model is proposed that assumes interlaminar adhesive layer between two neighbouring layers transferring not only interlaminar shear stress but also normal stress. The stress distribution is solved by the used model which rigorously satisfies the stress equilibrium equations, boundary conditions and the traction continuity at interfaces between layers.     

Numerical simulation of the damage behavior of bidirectionally reinforced ceramic cross-ply laminates

The behavior of bidirectionally reinforced SiC/SiC cross-ply laminates is studied with the help of numerical simulations based on the finite element method (FEM). Within the presented model the composite is regarded on the layer scale considering each layer as homogeneous with `layer properties'. Brittle cracking as well as damage effects can appear within each layer, which is why both a damage and a fracture model for the plies is derived. The damage model is based on damage variables depending on the strain state. Fracture is checked using a fracture criterion, a crack and a post-failure model. In this way fracture can be considered for multiaxial stress states and the statistical distribution of strength values as well as load transfer effects after crack initiation can be taken into account. By subjecting the structure to a cooling down process before mechanical loading in one of the fiber directions the residual thermal stresses within the layers can also be regarded. The purpose of the simulations is to indicate the influence of important parameters on the composite behavior.     

Stress distributions in bluntly-notched ceramic composite laminates

We present a methodology for determining stress distributions ahead of blunt notches in plates of fiber-reinforced ceramic–matrix composites subject to uniaxial tensile loading, accounting for the effects of inelastic straining due to matrix cracking. The methodology is based on linear transformations of the corresponding elastic distributions. The transformations are derived from adaptations of Neuber’s law for stress concentrations in inelastic materials. Comparisons are made with results computed by finite element analysis using an idealized (bilinear) form of the Genin–Hutchinson constitutive law for ceramic composite laminates. Effects of notch size and shape as well as the post-cracking tangent modulus are examined. The comparisons show that, for realistic composite properties, the analytical solutions are remarkably accurate in their prediction of stress concentrations and stress distributions, even in cases of large-scale and net-section inelasticity. Preliminary assessments also demonstrate the utility of the solution method in predicting the fields under multiaxial stressing conditions.     

The behaviour of cross-ply hybrid matrix composite laminates: Part 2: Modelling

In Part 1 of this work experimental data were presented for the initiation and propagation of damage in hybrid matrix and uniform matrix laminates. The data showed that during the extension of cross-ply laminates, either constrained (stable) matrix cracking or brittle (unstable) matrix cracking occurs in the transverse plies, with the transverse ply thickness and level of urethane in the transverse ply determining which type of cracking is observed. In the present paper the stable cracking behaviour is modelled using a shear-lag stress analysis combined with an energy balance and the unstable cracking behaviour is discussed in terms of a statistical distribution of transverse ply strengths.     

Damage characterisation of fibre metal laminates under interlaminar shear load

Transverse composite plies are part of the fibre metal laminate Glare^®4B and were investigated under interlaminar shear load. Double-notched shear (DNS) tests were performed and deformation and damage were in situ observed by Scanning Electron Microscopy (SEM) equipped with a loading apparatus. Interlaminar shear strength as well as shear stress values corresponding to the onset of the fibre/matrix-debonding were determined.Although a cross-ply lay-up within the laminate has been interlaminar shear loaded, damage and failure could only be found within the transverse plies. Over their thickness, fibre/matrix-debonding proved to be pronounced near the ply boundaries of the transverse plies, where exceptionally high shear strains could be found. Nevertheless, single fibre/matrix-debonding phenomena were also observed within the centre area of these transverse plies. Although interlaminar shear strain within latter regions is reduced, single events of fibre/matrix-debonding could be attributed to local high stress concentrations due to the fibre arrangement and to small inter fibre distances.     

Environmental effects on thermally induced multistability in unsymmetric composite laminates

The principles involved in the generation of thermal induced multistability in carbon fibre epoxy laminates have received much interest in the published literature. This work examines the effects of moisture absorption on the mechanical properties of these plates focussing on geometry and ‘snap-through’ loadings. Samples were monitored from a dry state until moisture equilibrium was achieved. It was observed that substantial changes in geometry and snap-through performance occurred as moisture content increased. As part of this work, a first order strain energy analysis was modified to incorporate a hygrothermal strain term to enable prediction of the laminate shape due to moisture content.     

Deformation limits for corrugated cross-ply laminates

This work determines the maximal possible deformations of a corrugated sheet where the corrugation pattern consists of two circular segments. The influence of the lay-up of cross-ply laminates and the influence of the geometry is investigated. The calculations are based on considerations of layerwise strains that are calculated with the help of an analytical singly-curved shell model. For the evaluation of the influence of geometric nonlinearities according finite element simulations are performed and compared to the linear strain limit calculations. The influence of scalable geometry parameters is also investigated.     

The behaviour of cross-ply hybrid matrix composite laminates: Part 1: Experimental results

Two types of cross-ply laminate have been made from prepreg: (a) hybrid matrix laminates consisting of longitudinal plies of glass fibres in epoxy resin and transverse plies of glass fibres in epoxy resin/urethane elastomer blend; and (b) uniform matrix laminates with the same resin in both the longitudinal and transverse plies. The presence of the urethane in the transverse plies increases the applied strains necessary for the initiation and development of transverse cracking during the extension of both hybrid matrix and uniform matrix laminates. The effect is greater with increasing amounts of urethane. The cracking data, stress/strain behaviour, acoustic emission response and ply thickness effects on crack development are discussed in the light of existing theories concerning transverse cracking.     

Impact damage characterisation of composite laminates using a statistical approach

Detecting impact damage is an important factor in maintaining the structural integrity of aerospace composite structures. Since impacts can cause severe reductions in stiffness and strength of composite structures, there is a need to investigate the material’s stiffness and strength after an impact event. The work discussed in this paper is concerned with one overall goal, which is to determine if an impact has caused damage and then to determine the extent of that damage using only the structural responses that are acquired from low-profile surface-mounted transducers. The work presented in this paper demonstrates that responses recorded from these sensors can provide sufficient information to infer impact damage. Previous work by various authors has established that it is possible to distinguish between damaging and non-damaging impacts if the impact force time-history is available. Therefore, it is the requirement that only response data be used here that distinguishes this work from the previous studies. Following a systematic series of experiments, on the induction of impact damage in Carbon Fibre Reinforced Polymer (CFRP) laminates, a damage model was proposed from this work which can provide preliminary information on the type and extent of damages through observations made from Scanning Electron Microscopy (SEM) and X-ray radiography. The model can be used to provide a general understanding on the prediction of damage and failure progression in CFRP as a function of the number of layers and impact energies. To accommodate the results from SEM and X-ray, discussions on outlier analysis and visualisation, which emphasise the idea of discordancy from the discipline of statistics, are presented. Results from discordancy tests, for both univariate and multivariate data, can be used to clearly separate the data (non-damaging and damaging impacts as well as the separation of the type of failure modes) by a calculated threshold value. Both of these features (univariate and multivariate) can be used as damage indicators and proxies for determining the extent of damage.     

Damage in composite laminates: Effects of transverse cracks

Two different methods of solution are used to study the effects of transverse cracks in cross-ply composite laminates. The results of an approximate analytical solution are compared with those obtained using a finite element analysis in order to study the effects of transverse cracks on the degradation of elastic and thermal coefficients as well as stress distributions. In particular, it is shown that transverse cracks cause significant degradation of the Poisson's ratio and shear modulus of the laminates, and also affect some stress distributions in a peculiar manner. Theoretical results are compared with existing experimental results where appropriate.     

An experimental investigation of the sequence effect in block amplitude loading of cross-ply composite laminates

The Palmgren–Miner rule has been shown to be inexact in many cases for various composite materials. Several empirical models have been conceived to account for this discrepancy, as well as the effect of block sequence. The approach taken here is based on the underlying mechanisms. A cross-ply laminate was used as a model material. In general, composites show both initiatory and progressive mechanisms under fatigue loading. The former is active at high static stresses, whereas the latter predominates at lower stress amplitudes where they are given sufficient time to propagate. Initiatory mechanisms give rise to damage from which the progressive mechanisms can start, and conversely the progressive mechanisms continually alter the local stress state which results in further damage accumulation caused by the initiation controlled mechanisms. In a cross-ply laminate, the initiatory mechanism is the formation of transverse cracks, and the progressive mechanism is mainly delamination growth initiated from the transverse cracks. In an experimental investigation of carbon fiber/epoxy cross-ply laminates, the interaction of these mechanisms has shown why a sequence of high–low amplitude levels results in shorter lifetimes than a low–high order. Such a sequence effect seems to be a common behavior for many other composite materials, and can be mechanistically explained by a similar kind of interaction. Advantages and drawbacks of the mechanistic approach compared with empirical rules are also discussed.