功能梯度形状记忆合金复合梁的力学行为

功能梯度形状记忆合金（Functionally graded shape memory alloy,FGSMA）兼具功能梯度材料和形状记忆合金材料的双重特性,广泛应用于微机电、航空航天等工程领域。为研究FGSMA复合梁的弯曲行为,本文对形状记忆合金（SMA）力学本构方程进行简化处理,并根据复合材料层合板理论建立了FGSMA复合梁的力学模型,据此研究了SMA体积分数沿厚度方向呈线性变化的FGSMA悬臂梁内SMA纤维铺设角度对悬臂梁横截面应变、中面轴向位移、中性面高度和相变层高度的影响以及悬臂梁中面应变、曲率、SMA马氏体相变临界层高度和中性面高度随弯矩载荷的变化规律。研究结果表明:在弯矩载荷作用下,悬臂梁中性面位置与中面位置不重合,且悬臂梁上下层SMA马氏体相变临界层位置不对称;截面轴向应变绝对值随铺设角度增大而增大,截面纵向应变绝对值随铺设角度增大先增大后减小,中面轴向位移随铺设角度增大先增大后减小;随着铺设角度增大,悬臂梁中性面高度逐渐增大,拉伸状态下相变结束临界层高度先减小后增大,压缩状态的趋势相反;随着弯矩载荷绝对值逐渐增大,中性面位置高度表现出先稳定后减小然后逐渐增大的趋势,相变临界层逐渐向中性面位置靠拢;中面正应变和挠曲率随着弯矩载荷绝对值逐渐增大而发生变化,且变化率先增大后减缓。      

The effect of fibre aspect ratio on the stiffness of discontinuous fibre-reinforced composites

The mechanics underlying the stiffness of discontinuous fibre-reinforced composites are well understood. In particular the critical fibre aspect ratio is known to affect the resultant deformation of the composite. This paper will explain how the Cox theory can be used to determine the critical aspect ratio for a given fibre/matrix combination at a given volume fraction. Supporting experimental evidence for the key dependencies influencing the critical aspect ratio are shown at the microscopic level (by a Raman spectroscopic approach) and at the macroscopic level (by a tensile creep approach) for a series of different composite materials.     

Experimental measurement and predictive modelling of bending behaviour for viscous unidirectional composite materials

It is widely accepted that the key deformation mechanisms during forming of viscous textile composite (prepreg) sheets are in-plane shear and out-of-plane bending. This paper focuses on the bending deformation mechanism, including experimental characterisation and theoretical modelling of bending behaviour during viscous composite forming. Experimental measurements are obtained by means of a large-displacement buckling test at a variety of displacement rates and temperatures. Some important aspects, such as viscoelastic behaviour, are also investigated. A bending model based on elastic theory combined with uniaxial continuum theory for ideal fibre-reinforced fluids for viscous shear deformation has been developed, using material parameters obtained from industrial manufacturers as input data, such as composite geometry, fibre properties, fibre volume fraction and matrix rheology. Model predictions demonstrate that the model can capture the main characteristics of material properties, such as rate dependence. This bending model can be used in formability analysis for viscous unidirectional composite materials, and might be applied in a finite element forming simulation to account for the bending stiffness.     

Second-gradient plane deformations of ideal fibre-reinforced materials II: forming flows of fibre–resin systems when fibres resist bending

The continuum theory of ideal fibre-reinforced fluids, namely incompressible viscous fluids exhibiting some direction of inextensibility is extended to account for the fibre bending stiffness; namely a property that prevents discontinuity of the fibre slope under normal loading conditions. The principal kinematics of this new theoretical development is consistent with three-dimensional forming flows of fibre–resin systems though, for simplicity, formulation of relevant constitutive equations is confined within the framework of relevant plane flows. The theory adopts the macroscopic view that the resin matrix behaves as a viscous fluid but the resin and fibres form a homogeneous composite material. Consideration of the fibre bending resistance requires the inclusion of couple-stress and, hence, non-symmetric stress. The outlined theoretical developments are therefore relevant to polar-media behaviour; in this context, the anisotropic viscous fluids of interest become part of the material class of the so-called polar fluids. For plane flows of this type of fluids, a manner is also outlined in which the non-symmetric stress distributions sought can be determined by solving two simultaneous, first-order linear differential equations. Moreover, a relevant stress-resultants technique is adopted and extended appropriately to make possible complete determination of the kinematics dictating the creeping forming plane flow of the composite fluids of interest. Details of the mechanisms that capture fibre bending resistance are revealed and illustrated through a relatively simple example application. This considers and resolves the forming flow process of an ideal fibre-reinforced composite, moulded into a sharp corner under the action of an external line force.     

基于弯曲刚度最大分层临界载荷的层压板局部屈曲预测

提出了一种预测含特定分层损伤层压板发生局部屈曲时整体应变的方法。认为含分层子板的局部屈曲载荷由其弯曲刚度最大的分层决定, 因而含有相同最大弯曲刚度分层的不同子板具有相同的屈曲载荷。在已知弯曲刚度最大分层的屈曲载荷的情况下, 根据层压板的轴向刚度公式, 计算出发生局部屈曲时弯曲刚度最大的分层与完好的基板分别承受的载荷, 即得到总载荷, 进而得到层压板的整体应变。用ABAQUS有限元分析软件建立含分层损伤的层压板模型, 使用准静态加载进行了多种分层深度和分层位置下的局部屈曲仿真, 所得局部屈曲载荷符合上述推论。用所提方法预测发生局部屈曲时的整体应变, 结果与有限元结果吻合较好, 此方法可用于建立分层参数识别的参照样本库。     

The influence of mechanical couplings on the compressive stability of anti-symmetric angle-ply laminates

The compressive stability of anti-symmetric angle-ply laminated plates with particular reference to the degrading influence of membrane–flexural coupling is reported in this paper. The degree of membrane–flexural coupling in the laminated composite plates is varied, essentially, by altering the ply-angle and the number of plies in the laminated stack for a given composite material system. The coupled compressive buckling solutions are determined in the paper using the finite strip method of analysis and the buckling displacement fields of the strip formulation are those which are able to provide zero in-plane normal movement at the edge boundaries of the laminated plates.

Results are given for anti-symmetric angle-ply laminated plates subjected to uniaxial compression and these have been obtained from fully converged finite strip structural models. Validation of the finite strip formulation is indicated in the paper through comparisons with exact solutions where appropriate. Increasing the number of plies in the laminated system is seen to reduce the degree of coupling and the critical stress levels are noted to tend towards the plate orthotropic solutions. The ply-angle corresponding to the optimised buckling stress for any particular laminate is noted in the paper to be influenced by the support boundary conditions at the plates unloaded edges. For any particular laminate the minimum critical buckling stress and corresponding natural half-wavelength of the buckling mode are shown to be highly sensitive to ply-angle variation.

Some post-buckling results are presented in the paper and these have been determined using the finite element method of analysis. The influence of membrane–flexural coupling is shown to be significant throughout the compressive post-buckling history of the laminated plates. The optimised ply-angle with regard to the critical compressive buckling stress of square simply supported anti-symmetric angle-ply laminates is shown to be less effective in the post-buckling range with regard to post-buckled compressional stiffness.     

RTM Hemp Fibre-Reinforced Polyester Composites

Hemp fibre-reinforced polyester composites were prepared using a Resin Transfer Moulding (RTM) technique and the flexural and impact behaviour investigated. Flexural stress at break and flexural modulus showed an increasing trend with fibre content. Impact strength was found to decrease at low fibre content, then gradually increase with further addition of fibres.A strong interfacial adhesion between hemp and polyester was obtained using chemically modified hemp. This modification consisted in introducing reactive vinylic groups at the surface of the fibres, via esterification of hemp hydroxyl groups, using methacrylic anhydride. Increased bonding between fibres and matrix did not affect the flexural stress at break of the composite but was detrimental to toughness. This behaviour was ascribed to a change in the mode of failure, from fibre pull-out to fibre fracture, resulting in a marked reduction in the energy involved in the failure of the composite, leading to a more brittle material.     

Experimental evidence of crack tip shielding mechanisms in quasi-brittle materials

To gain insight into the shielding processes in quasi-brittle materials, in situ crack propagation and crack profile measurements were performed inside the scanning electron microscope (SEM). Crack tip shielding phenomena were studied in monolithic alumina and in SiC fibre-reinforced alumina matrix composites as a function of fibre coatings. The crack in the fibre-reinforced composite samples is bridged by a row of fibres which contains a fibre area fraction of 10%. The applied stress intensity factor necessary to extend the crack in the composite materials increased 25% for the gold coated fibre-reinforced alumina matrix composites and 13% for the polymer-coated fibre-reinforced composites, compared to the monolithic samples. Crack extension in the monolithic samples and in the fibre-reinforced composites occurred after the crack opening displacements close to the crack tip approached the critical crack tip profile corresponding to the intrinsic toughness of alumina. A hypothesis on the effect of closure stresses on crack profile shape and net toughness has been developed. Furthermore, crack profiles revealed that grain bridging in the vicinity of the fibres was operative in the fibre-reinforced composites at stress intensity factors far exceeding the critical stress intensity factor of the monolithic matrix material. The additional grain bridging in the vicinity of the fibres has never been reported and can only be revealed through crack profile measurements. This revised version was published online in November 2006 with corrections to the Cover Date.     

Fracture behaviour of 2D-weaved, silica–silica continuous fibre-reinforced, ceramic–matrix composites (CFCCs)

Significantly improved fracture resistance (in terms of fracture toughness and fracture energy) can be imparted to monolithic ceramics by adopting composite design methodology based on fibre reinforcement technology. The present paper describes the fracture behaviour of one such fibre-reinforced material, namely the silica–silica based continuous fibre-reinforced, ceramic–matrix composite (CFCC) in two orthogonal notch orientations of crack divider and crack arrester orientations. Different fracture resistance parameters have been evaluated to provide a quantitative treatment of the observed fracture behaviour. From this study, it has been concluded that the overall fracture resistance of the CFCC is best reflected by total fracture energy release rate (J_c), which parameter encompasses most of the fracture events/processes. The J_c values of the composite are found to be more than an order of magnitude higher than the energy values corresponding to the plane strain fracture toughness (J_KQ, derived from K_Ic, the plane strain fracture toughness) and >200% higher than elastic–plastic fracture toughness (J_Ic). Apart from this, the composite is found to exhibit high degree of anisotropy in the fracture resistance and also, a significant variation in the relative degree of shear component with crack extension.     

Enhancing the Deformation of Shape Memory Sandwich Panels

Abstract: Composite sandwich panels fabricated using a thermosetting shape memory polymer matrix material and a corresponding thermoset shape memory polymer foam core offer the potential to demonstrate large, recoverable, deformations in otherwise stiff structures, under flexural loading. However, as with flexure of thin, fibre‐reinforced shape memory matrix laminates, deflection is limited by fibre compression buckling because of the reduced shape memory matrix stiffness at elevated temperature. A hybrid matrix concept has been developed for sandwich panels loaded in flexure in a single direction. This concept uses a non‐shape memory resin as the matrix for a fraction of the plies on the surface of the facesheet loaded in compression. It is predicted that, at the elevated temperatures required for the generation of deformation in the shape memory structural sandwich panel, the shape memory matrix and foam moduli will be substantially reduced, while the modulus of the non‐shape memory resin will not. Thus, at elevated temperature this effectively leads to a shift of the neutral axis towards the non‐shape memory surface, keeping the low stiffness shape memory matrix material in tension and extending the range of deformation prior to onset of fibre buckling. The experiments performed demonstrate that this hybrid matrix approach enables a three‐fold increase in mid‐span deformation prior to buckling of fibres in the compression surface plies. Furthermore, the force measured to attain the deformed geometry, at elevated temperature, only increases approximately 10–15%, while the magnitude of the force required remains very low. Thus, the hybrid matrix approach functions as predicted and enables the development of sandwich panel structural elements which can undergo large, recoverable deformations.     

Deformation micromechanics in high-modulus fibres and composites

It is demonstrated that Raman spectroscopy can be used to study the deformation micromechanics of aramid fibres and of the fibres in a model single-fibre composite with an epoxy resin matrix. It is shown that the peak position of the 1610cm⁻¹ aramid Raman band shifts to lower frequency under the action of stress or strain as a result of the macroscopic deformation leading to direct stretching of the aramid molecules. The strain-induced band shifts can be used to follow the deformation of the aramid fibres in a composite matrix. This allows the distribution of strain to be mapped along a fibre, and it is shown that the behaviour is consistent with that predicted by the classical shear-lag analysis. It is also demonstrated that the interfacial shear stress can be calculated from the distribution of strain along the fibre. Finally, the technique is extended to measure the strain in fibres in a single-fibre composite which are aligned at an angle to the tensile axis. In this case it is shown that the strain in the centre of the fibres is identical to that predicted by classical elasticity theory.     

Processing,structure and flexural strength of CNT and carbon fibre reinforced,epoxy-matrix hybrid composite

Advanced materials such as continuous fibre-reinforced polymer matrix composites offer significant enhancements in variety of properties, as compared to their bulk, monolithic counterparts. These properties include primarily the tensile stress, flexural stress and fracture parameters. However, till date, there are hardly any scientific studies reported on carbon fibre (C_f) and carbon nanotube (CNT) reinforced hybrid epoxy matrix composites (unidirectional). The present work is an attempt to bring out the flexural strength properties along with a detailed investigation in the synthesis of reinforced hybrid composite. In this present study, the importance of alignment of fibre is comprehensively evaluated and reported. The results obtained are discussed in terms of material characteristics, microstructure and mode of failure under flexural (3-point bend) loading. The study reveals the material exhibiting exceptionally high strength values and declaring itself as a material with high strength to weight ratio when compared to other competing polymer matrix composites (PMCs); as a novel structural material for aeronautical and aerospace applications.     

On steady-state fibre pull-outII Computer simulation

On the basis of Part I of this paper (Zhang X, Liu, H-Y, Mai Y-W, Diaox X. On steady-state fibre pull-out Part I: stress field. Composites Science and Technology, 1999;59:2179–89) we present an extended analysis for the single-fibre pull-out process. The solutions of fibre axial stress, fibre displacement, and applied pull-out stress versus fibre displacement are obtained for the whole pull-out process. As distinct from previous work (Gao Y-C, Mai Y-W, Cottrell B. Fracture of fibre-reinforced materials. ZAMP 1988;39:550–72; Hutchinson JW, Jensen HN. Model of fibre debonding and pull-out in brittle composites with friction. Mechanics of Materials 1990;9:139–63; Hsueh C-H. Interfacial debonding and fibre pull-out stresses of fibre-reinforced composites. Materials Science and Engineering 1990;A123:1–11), a local shear strain criterion, in which the critical shear strain depends on the pull-out rate, is adopted as a more realistic interface debonding criterion. Load/displacement curves of the fibre pull-out process, which includes elastic deformation with a fully bonded interface, elastic deformation with a partially debonded interface and elastic deformation plus frictional sliding with a fully debonded interface, are obtained by computer simulations. The effects of fibre pull-out rate, thermal residual stress, friction coefficient and fibre volume fraction are also discussed.     

Mikromechanisches stochastisches Versagensmodell uniaxial faserverstärkter Verbundwerkstoffe

Micromechanical stochastic failure model of uniaxial fibre-reinforced composites A theoretical model of stress transfer between a transversal isotropic fibre and the surrounding matrix material in a uniaxially fibre-reinforced composite near a single matrix flaw is discussed including friction controlled fibre-matrix interface debonding. The rise of fracture toughness due to frictional fibre sliding is studied accounting for Weibull strength distribution of fibres. The total dissipative work may be used as figure of merit regarding the damage tolerance. A critical evaluation is presented concerning some previous models of local failure probabilities. Numerical results are demonstrated. Conditions for an optimized C/Al-composite are presented.     

Compressive failure of fibre-reinforced composites: buckling,kinking, and the role of the interphase

Recent experimental studies of compressive failure in fibre-reinforced polymeric composites have been analysed. It is shown that the parametric basis for most compressive strength models, i.e. pure plastic buckling controlled by matrix shear strength and initial fibre misorientation, is probably incomplete. It is argued that, instead, failure is triggered by the initiation of an unstable kink band prior to buckling instability, and that additional parameters (interfacial shear stress/strain; fibre strength) are responsible for this transition in mechanisms.     

Flexural behaviour of structural fibre composite sandwich beams in flatwise and edgewise positions

The flexural behaviour of a new generation composite sandwich beams made up of glass fibre-reinforced polymer skins and modified phenolic core material was investigated. The composite sandwich beams were subjected to 4-point static bending test to determine their strength and failure mechanisms in the flatwise and the edgewise positions. The results of the experimental investigation showed that the composite sandwich beams tested in the edgewise position failed at a higher load with less deflection compared to specimens tested in the flatwise position. Under flexural loading, the composite sandwich beams in the edgewise position failed due to progressive failure of the skin while failure in the flatwise position is in a brittle manner due to either shear failure of the core or compressive failure of the skin followed by debonding between the skin and the core. The results of the analytical predictions and numerical simulations are in good agreement with the experimental results.     

Plane Problem for Layered Composites with Periodic Array of Interfacial Cracks Under Compressive Static Loading

The current paper addresses the problem of 2-D modelling of the onset of failure process in a layered composite with periodic array of interfacial cracks under static compression along layers. The statement of the problem is based on the most accurate approach, the model of piecewise-homogenous medium. The condition of plane strain state is considered. The shear and the extensional buckling modes are examined. The laminae are modelled by transversally isotropic material (a matrix reinforced by continuous parallel fibres). The complex non-classical failure mechanics problem is solved utilizing finite element analysis. It is found that the 0°-plies volume fraction, the crack length and the mutual position of cracks influence the critical strain in the composite.     

Direct measurements of non-linear stress-strain curves and elastic properties of metal matrix composite sandwich beams with any core material

A theory for measuring non-linear stress-strain curves and elastic properties of metal matrix composite (MMC) sandwich beams subjected to pure bending loads is discussed. The beam is made from any core material sandwiched between an upper facing of unreinforced metal and a lower facing of MMC with unidirectional fibre reinforcement or vice versa. The model developed shows that the determination of the position of the neutral axis is critical to the measurements discussed in this paper. The analysis removes the restriction of the effects of the core. With the aid of this model, we show that the position of the neutral axis can be determined directly from surface strain measurements. Measurements of neutral axis position lead directly to the determination of the beam elastic properties and, thus, directly obtained from surface strain measurements. It is shown that the model predicts longitudinal stresses and strains within any layer of the beam. The analysis includes the limiting case of a very weak core material. A consequence of this model is the determination of the MMC facing fibre volume fraction. A detailed error analysis predicts that the longitudinal elastic modulus of an MMC material facing can be obtained with an uncertainty between 4 and 6% if the surface strain measurements and beam dimensions can be obtained with an uncertainty of 1%. The volume fraction can be obtained within 10% uncertainty, although better methods are available for that measurement.     

The strength of the fibre-polymer interface in short glass fibre-reinforced polypropylene

A method for the determination of the interfacial bond strength in well-aligned short glass fibre-reinforced polypropylene samples is discussed. The method takes into account the variation of the interfacial shear stress during the deformation process; consequently, it yields very consistent results at all values of the composite strain. The influence of the fibre orientation with respect to the load axis is appropriately considered using macro-mechanical analyses for stiffness and strength of the composite. The method is compared with two other methods reported in the literature.