A model and experimental study of fiber orientation effects on shear wave propagation through composite laminates

The strong elastic anisotropy of the discrete unidirectional plies in a composite laminate interacts sensitively with the polarization direction of a shear ultrasonic wave propagating in the thickness direction. The transmitted shear wave can therefore be used to detect errors in the ply orientation and stacking sequence of a laminate. The sensitivity is particularly high when the polarization directions of the shear wave transmitter and receiver are orthogonal to each other. To understand the interaction between normal-incident shear waves and ply orientations in a laminate, a complete analytical model was developed using local and global transfer matrices. The model predicted the transmitted signal amplitude as a function of polarization angle of the transmitter and time (or frequency) for a given laminate and input signal. To alleviate the experimental problems associated with shear wave coupling, electromagnetic acoustic transducers (EMATs) and metal delay lines were used in the angular scan of the transmitted signal. The EMAT system had the added advantage of being applicable to uncured composite laminates. Experiments were performed on both cured and uncured laminates with common layups for model verification. The sensitivity of the measured shear wave signals to fiber misorientation and stacking sequence errors was also demonstrated.     

Effect of interfacial bonding on impact properties of chopped glass fiber polymer nanocomposites

This paper aims to presents the investigations made on the effect of impact response of chopped glass fiber–epoxy nanocomposite laminates subjected to low velocity impact using instrumented falling weight impact tests. The laminates were prepared using six layers of chopped strand mat with density of 610 gsm with epoxy resin and nanoclay content varied from 1, 3, and 5 wt%, by hand lay-up method. The nanoclay was dispersed into the epoxy by high shear mixing process in order to obtained uniform distribution of individual nanoclay. Laminates were impacted at constant mass with different impact energies. During these low velocity impact tests, the maximum load, absorbed energy, and deflection at peak load were recorded. It was observed that by dispersion of nanoclay as reinforcement, there was significant improvement in load carrying capacity and energy absorption. When a small amount of nanoclay (1 wt%) was added into the epoxy, the maximum load was enhanced by 20%. The presence of stiffer nanoclay significantly reduced the surface cracks propagation and controlled delamination area. Scanning electron microscopy was performed to characterize the damage progression.     

A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach

Large-amplitude (geometrically non-linear) vibrations of circular cylindrical shells subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated. The Lagrange equations of motion are obtained by an energy approach, retaining damping through Rayleigh's dissipation function. Four different non-linear thin shell theories, namely Donnell's, Sanders-Koiter, Flügge-Lur’e-Byrne and Novozhilov's theories, which neglect rotary inertia and shear deformation, are used to calculate the elastic strain energy. The formulation is also valid for orthotropic and symmetric cross-ply laminated composite shells. The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of the lowest natural frequency is computed for all these shell theories. Numerical responses obtained by using these four non-linear shell theories are also compared to results obtained by using the Donnell's non-linear shallow-shell equation of motion. A validation of calculations by comparison with experimental results is also performed. Both empty and fluid-filled shells are investigated by using a potential fluid model. The effects of radial pressure and axial load are also studied. Boundary conditions for simply supported shells are exactly satisfied. Different expansions involving from 14 to 48 generalized co-ordinates, associated with natural modes of simply supported shells, are used. The non-linear equations of motion are studied by using a code based on an arclength continuation method allowing bifurcation analysis.     

Diffraction grating interferometers for mechanical characterisations of advanced fabric laminates

It is demonstrated that two grating interferometers with high spatial resolutions can successfully be applied for the mechanical characterisation of the advanced fabric composite materials. Based on these two techniques, the mechanical properties of two kinds of fabric laminates are obtained without assumption of uniform strain fields to be used in the characterisation approaches using the local strain sensors. The degree of the yarn crimp effects of the two laminates is compared in terms of the out-of-plane displacement derivatives. Especially, it is shown that the grating shearing interferometer is appropriate for the crimped fabric structure requiring a three-dimensional analysis. The modification from moiré interferometer to grating shearing interferometer is performed by introducing a Michelson interferometer modified for image shearing.     

Application of pulse acoustic microscopy technique for 3D imaging bulk microstructure of carbon fiber-reinforced composites

Impulse acoustic microscopy technique is applied for 3D imaging of bulk microstructure of composite materials. Short pulses of focused high-frequency ultrasound have been employed for layer-by-layer imaging of internal microstructure of carbon fiber-reinforced composite (CFRC) laminates. The method provides spatial resolution of 60 microm and in-depth resolution of 80 microm, approximately. Echo signals reflected from structural units--plies, fiber bundles; and microflaws form acoustic images of microstructure at different depth inside samples. The images make it possible to see ply arrays, packing of bundles in plies; binding material distribution over the specimen body. They reveal failure of interply adhesion, buckling of single plies and fiber bundles, internal defoliations and disbonds, voids in the specimen body. The series of successive images offer outstanding possibilities to reconstruct the bulk structure, to estimate local variations of properties, topological and geometrical characteristics of structural components. The imaging technique has been applied to study different types of fiber packing--unidirectional, cross-ply and woven laminates. Mechanisms of ultrasonic contrast for diverse elements in acoustic images of CFRC laminate bulk microstructure and structural defects are discussed.     

Influence of carbon fiber’s surface state on interlaminar shear properties of CFRP laminate

In order to investigate the influence of carbon fiber’s surface state on the interlaminar shear properties of carbon fiber-reinforced plastic (CFRP) laminate, the carbon fiber’s surface state was modified by thermal treatment at elevated temperatures. The interlaminar shear strength (ILSS) of CFRP laminates reinforced with treated fibers was measured by means of short-beam shear test, and the surface state of fiber was characterized by Electron Spectroscopy for Chemical Analysis (ESCA) analysis to reveal the dominate factor for controlling the ILSS. Combining the ILSS measurement with the ESCA analysis, the results indicated that: (1) the ILSS is strongly dependent on the oxygen-containing functional groups on the surface of carbon fiber; (2) the fiber treated at 600?°C has the highest oxygen-containing functional groups that lead to the highest ILSS of CFRP; and (3) at temperatures beyond 600?°C, the oxygen-containing functional groups decrease with increasing the heat treatment temperature, resulting in a low ILSS of CFRP laminates. Furthermore, from the microstructure observation, it was found that the CFRP mainly failed in the mode of multi-interlaminar shear. The multi-interlaminar shear failure in the CFRP laminates with low ILSS is more severe due to a weak fiber-matrix interface.     

激光辐照下预加载CFRC层合板断裂行为实验研究

针对激光与机械载荷联合作用下碳纤维/环氧树脂增强复合材料（CFRC）层合板失效时间的预测需求,实验研究了不同激光功率密度（70～210 W/cm2）、不同预应力水平（拉伸强度的50%和70%）、不同光斑尺寸（拉伸试件宽度的70%和100%）下2 mm厚层合板的失效机理,获取了不同影响因素对断裂时间的影响规律。结果表明:预加载层合板失效机制为迎光面环氧树脂基底材料热解、纤维氧化断裂,背光面剩余结构偏脆性断裂;在预应力一定条件下,试件断裂时间与辐照激光功率密度成指数规律;预应力水平对断裂时间影响显著。     

Mechanics and finite elements for the damped dynamic characteristics of curvilinear laminates and composite shell structures

Integrated mechanics and a finite element method are presented for predicting the damping of doubly curved laminates and laminated shell composite structures. Damping mechanics are formulated in curvilinear co-ordinates from ply to structural level and the structural modal loss factors are calculated using the energy dissipation method. The modelling of damping at the laminate level is based on first order shear shell theory. An eight-node shell damping finite element is developed. Comparisons of the present model with classical and discrete layer laminate damping theory predictions are shown. Modal damping and natural frequencies of composite plates and open cylindrical shells were measured and correlated with predicted results. Parametric studies illustrate the effect of curvature and lamination on modal damping and natural frequency.     

Use of principle velocity patterns in the analysis of structural acoustic optimization

This work presents an application of principle velocity patterns in the analysis of the structural acoustic design optimization of an eight ply composite cylindrical shell. The approach consists of performing structural acoustic optimizations of a composite cylindrical shell subject to external harmonic monopole excitation. The ply angles are used as the design variables in the optimization. The results of the ply angle design variable formulation are interpreted using the singular value decomposition of the interior acoustic potential energy. The decomposition of the acoustic potential energy provides surface velocity patterns associated with lower levels of interior noise. These surface velocity patterns are shown to correspond to those from the structural acoustic optimization results. Thus, it is demonstrated that the capacity to design multi-ply composite cylinders for quiet interiors is determined by how well the cylinder be can designed to exhibit particular surface velocity patterns associated with lower noise levels.     

Rotor drop and following thermal growth simulations using detailed auxiliary bearing and damper models

Catcher bearings (CBs) or auxiliary bearings provide mechanical backup protection in the events of magnetic bearing failure. This paper presents numerical analysis for a rotor drop on CBs and following thermal growths due to their mechanical rub using detailed CB and damper models. The detailed CB model is determined based on its material, geometry, speed and preload using the nonlinear Hertzian load–deflection formula, and the thermal growths of bearing components during the rotor drop are estimated using a 1D thermal model. A finite-element squeeze film damper provides the pressure profile of an annular oil film and the resulting viscous damping force. Numerical simulations of an energy storage flywheel with magnetic suspensions failed reveal that an optimal CB design using the detailed simulation models stabilizes the rotor drop dynamics and lowers the thermal growths while preventing the high-speed backward whirl. Furthermore, CB design guides based on the simulation results are presented.     

DYNAMIC STABILITY OF CURVED PANELS WITH CUTOUTS

The parametric instability behaviour of curved panels with cutouts subjected to in-plane static and periodic compressive edge loadings are studied using finite element analysis. The first order shear deformation theory is used to model the curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to Sanders' first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. The effects of static and dynamic load factors, geometry, boundary conditions and the cutout parameters on the principal instability regions of curved panels with cutouts are studied in detail using Bolotin's method. Quantitative results are presented to show the effects of shell geometry and load parameters on the stability boundaries. Results for plates are also presented as special cases and are compared with those available in the literature.     

EVALUATION OF THE ADHESION QUALITY BETWEEN DIFFERENTLY TREATED CARBON FIBERS AND AN IN-SITU POLYMERIZED POLYAMIDE 12 SYSTEM

The aim of this study was to investigate interfacial effects on differently treated carbon fibers and a new in-situ PA12 polymerized matrix system. The surface free energies of the single filaments and the influence of the sizing were determined with regard to their compatibility with the semicrystalline thermoplastic PA12. The polyamide 12 matrix was in-situ polymerized in the presence of the fibers in an internal mixer, and afterwards the compounds were tensile and impact loaded at room and cryogenic temperature, respectively. The failure mechanisms were evaluated by examination of the fracture surfaces by scanning electron microscopy. Further, the residual monomer content and the degree of crystallinity were measured by thermogravimetric analysis and differential scanning calorimetry, respectively. In addition, the dynamic mechanical analysis and macromechanical properties determination of the fiber reinforced laminates were performed.     

A computational analysis of the ballistic performance of light-weight hybrid composite armors

The ability of hybrid light-weight fiber-reinforced polymer-matrix composite laminate armor to withstand the impact of a fragment simulating projectile (FSP) is investigated using a non-linear dynamics transient computational analysis. The hybrid armor is constructed using various combinations and stacking sequences of a high-strength/high-stiffness carbon fiber-reinforced epoxy (CFRE) and a high-ductility/high-toughness Kevlar fiber-reinforced epoxy (KFRE) composite laminates of different thicknesses. The results obtained indicate that at a fixed thickness of the armor both the stacking sequence and the number of CFRE/KFRE laminates substantially affect the ballistic performance of the armor. Specifically, it is found that the armor consisting of one layer of KFRE and one layer of CFRE, with KFRE laminate constituting the outer surface of the armor, possesses the maximum resistance towards the projectile-induced damage and failure. The results obtained are rationalized using an analysis of the elastic wave reflection and transmission behavior at the inter-laminate and laminate/air interfaces.     

Exact vibration solutions for cross-ply laminated plates with two opposite edges simply supported using refined theories of variable order

This paper presents exact solutions for free vibration of rectangular cross-ply laminated plates with at least one pair of opposite edges simply supported using refined kinematic theories of variable order. Exact natural frequencies are obtained using an efficient and unified formulation where the solving set of second-order differential equations of motion and related boundary conditions are expressed at layer level in terms of so-called fundamental nuclei having invariant properties with respect to the order of the plate theory. The nuclei are then appropriately expanded according to the number of layers and the order of the theory and the resulting equations are transformed into a first-order model whose solution is obtained by using the state space concept. In this way, the mathematical effort needed to derive analytical solutions is highly reduced. Both higher-order equivalent single-layer and layer-wise theories are considered in this study. Comparisons with other exact solutions are presented and useful benchmark frequency results for symmetric and un-symmetric cross-ply laminates are provided.     

Mechanical behavior and health monitoring by Acoustic Emission of unidirectional and cross-ply laminates integrated by piezoelectric implant

Recent progress in sensor technologies, signal processing and electronics has made it possible to fulfill the need for the development of in-service structural health monitoring (SHM) systems. This study presents a health monitoring of composite materials integrated by piezoelectric sensor using Acoustic Emission (AE) technique. A series of specimens of composite laminates with and without piezoelectric implant were subject to three-point bending in static and creep tests while continuously monitoring the response by the AE technique. The analysis and observation of AE signals lead to the identification of the acoustic signatures of damage mechanisms in composite laminates. The mechanical behavior of composites with and without integrated sensor shows no difference in the form. The incorporation of piezoelectric sensor influences specially the fracture load and causes low degradation of mechanical properties of materials. One of the major differences between the two types of materials (with and without embedded sensor) is the intense acoustic activity in the integrated material.     

Optimum design of laminates with natural frequency constraints

A method of optimally designing symmetric fibre reinforced composite laminates subject to constraints on natural frequencies is presented. The problem is cast as a non-linear mathematical programming problem in which the thickenesses of material placed at preassigned orientation angles are treated as the design variables. The resulting optimization problem is solved by using an interior penalty function algorithm. Several non-linear programming problems are solved by taking minimization of weight or maximization of fundamental frequency/buckling load/maximum transverse deflection under the stated loading condition as the behaviour constraints. The numerical results are presented in the form of design studies which reveal the influence of different design constraints on the optimum design. These design studies illustrate that the method presented offers an efficient and practical optimum design procedure for composite laminates.     

Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory

Higher order shear deformation theory (HSDT) is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived. The developed equations of motion have been applied to study buckling characteristics of nanoplates such as graphene sheets. Navier's approach has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions for critical buckling loads of the graphene sheets are presented. Nonlocal elasticity theories are employed to bring out the small scale effect on the critical buckling load of graphene sheets. Effects of (i) nonlocal parameter, (ii) length, (iii) thickness of the graphene sheets and (iv) higher order shear deformation theory on the critical buckling load have been investigated. The theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories as applied to the stability analysis of nanoplates and nanoshells.     

Micro-crack detection of nonlinear Lamb wave propagation in three-dimensional plates with mixed-frequency excitation

We propose a nonlinear ultrasonic technique by using the mixed-frequency signals excited Lamb waves to conduct micro-crack detection in thin plate structures. Simulation models of three-dimensional(3D) aluminum plates and composite laminates are established by ABAQUS software, where the aluminum plate contains buried crack and composite laminates comprises cohesive element whose thickness is zero to simulate delamination damage. The interactions between the S_0 mode Lamb wave and the buried micro-cracks of various dimensions are simulated by using the finite element method.Fourier frequency spectrum analysis is applied to the received time domain signal and fundamental frequency amplitudes,and sum and difference frequencies are extracted and simulated. Simulation results indicate that nonlinear Lamb waves have different sensitivities to various crack sizes. There is a positive correlation among crack length, height, and sum and difference frequency amplitudes for an aluminum plate, with both amplitudes decreasing as crack thickness increased, i.e.,nonlinear effect weakens as the micro-crack becomes thicker. The amplitudes of sum and difference frequency are positively correlated with the length and width of the zero-thickness cohesive element in the composite laminates. Furthermore,amplitude ratio change is investigated and it can be used as an effective tool to detect inner defects in thin 3D plates.     

Natural vibration of unsymmetric cross-ply laminates

This study considers the linear vibration characteristics of square [0_n/90_n]_T laminates relative to their room-temperature static equilibrium configurations. A Rayleigh-Ritz approach combined with Hamilton's principle is used to provide approximate solutions to this vibration problem. The vibration mode shapes are assumed to have the same spatial dependence as used in past investigations to study the room-temperature configurations of these laminates, and are thus assumed to be perturbations on the static equilibrium configurations. Hamilton's principle then results in the so-called zero- and first-order equations. The zero-order equations lead to the classic static equilibrium results of past investigations, presented here in nondimensional form with analytical solutions at the bifurcation point. The first-order equations, combined with zero-order results, lead to the vibration characteristics for each zero-order static configuration. Interest centers on the lowest natural frequency and the associated mode shape for laminates clamped at their midpoints, with special attention as to how these vibration characteristics depend on the laminate side-length-to-thickness ratio. With an imaginary-valued frequency, the static saddle configuration for side-length-to-thickness ratios larger than the critical value is correctly assessed as unstable. A finite element model is also used to study the vibration characteristics and to compare with the findings for the developed analysis. The qualitative comparisons between the developed analysis and the finite element model are generally good, and the quantitative comparisons are also satisfactory.     

碳纤维-泡沫铝夹芯板低速冲击响应

为研究夹芯结构的低速冲击响应,以碳纤维(T700)/环氧树脂复合材料层合板为上下面板,以闭孔泡沫铝为芯层,模拟夹芯板落锤冲击时的损伤演化过程。复合材料层合板采用三维实体单元建模,基于有限元软件ABAQUS中的用户子程序VUMAT,引入三维Hashin失效准则模拟复合材料的损伤破坏;采用二次应力准则,Cohesive单元模拟黏结层的层间失效;闭孔泡沫铝芯层采用3D Voronoi细观模型建模。分析复合材料夹芯结构在落锤冲击下的损伤起始、损伤扩展和最终破坏模式,通过锤头的接触力、位移、夹芯板的内能、后面板的最大位移研究夹层结构的能量吸收情况及抗冲击特性,得出了在质量保持不变的情况下,5种芯层相对密度和厚度的耦合关系中的最优设计是芯层相对密度15.0%,厚度为10 mm,为满足实际工程中的需求提供了设计依据。