Anisotropic Composite Materials Research Articles

Limited samples wavelet network and its application for damage detection composites

A new data processing method is proposed for the damage detection of anisotropic composite materials. The wavelet transform and its phase space property are discussed to illustrate how the signal features are represented in the time-frequency plane. The terms in the expansion of the wavelet series that have the same time-frequency property as the original signal are then obtained by comparing the time- frequency space of the signal with the phase space of the wavelet transform. For wavelet neural networks, the training process can be very slow because the number of terms in the wavelet series is often too large for a reasonable search. Here we apply the Gram-Schmidt orthogonal- ization to remove the redundant wavelets in the series using the characteristics of sampled data. Moreover, the values of the features corresponding to different damage types are obtained by linear equations. Experiments on the damage detection of composites with various size cracks and delamination are conducted to demonstrate the feasibility of the proposed method. They show that the reconstructed curves obtained by the proposed approach can well approximate the original sampled curves and that the features corresponding to different damage types are identified.

Interaction between an interface crack and a parallel subinterface crack in dissimilar anisotropic composite materials

In this paper, the pseudo-traction method is combined with the edge-dislocation method (i.e. PTDM) to solve the interaction problem between an interface crack and a parallel subinterface crack in dissimilar anisotropic materials. After deriving the fundamental solutions for an interface crack loaded by normal or tangential tractions on both crack surfaces and the fundamental solutions for an edge dislocation beneath the interface in the lower anisotropic material, the interaction problem is reduced to a system of a singular integral equations by adopting the well-known superposition technique. The equations are then solved numerically with the aid of the Chebyshev numerical integration and the Chebyshev polynomial expansion technique. Several typical examples are calculated and numerical results are shown in figures and tables from which a series of valuable conclusions is obtained. Since the present results should be verified and since no previous results exist to compare them with a consistency check in introduced which starts from the conservation law of the J-integral in anisotropic cases. It is shown that the check provides a powerful tool to examine the results, although it really presents a necessary condition rather than a sufficient way to the crack-tip parameters of the interface crack and the subinterface crack in the dissimilar anisotropic materials.

Strength/size effect for anisotropic brittle materials under a random stress state

A simple analytical method for predicting the strength/size effect is proposed for anisotropic brittle materials under 2- or 3-D random stress states. Statistical characteristics of the stress state (mean values and all possible correlations) along with statistical characteristics of random strength properties are assumed to be known and are used as initial data. The anisotropy of the random strength response is also taken into account. The method is a generalization of a previously proposed approach allowing one to predict the probability of failure or reliability by means of an exact analytical solution. The new method is developed for ideally brittle materials and accounts for the size effect and non-uniformity of the random stress state, when all statistical parameters of loading are functions of the coordinates. Examples are provided to illustrate the use of the method and to show effects of size, variability of strength properties, and variability of loading for typical composites. Although the method is proposed for anisotropic composite materials, it may also be used for brittle isotropic materials (glass, ceramic, etc.).

Stress analysis of notched anisotropic finite plates under mechanical and hygrothermal loads

Notch-induced stress concentrations in anisotropic composite materials depend on their directional material properties, especially for uniaxially reinforced composites with high-modulus fibres. The design of notched high-performance composites requires therefore a special proof of their notched strength, which includes the structural parameters of the fibre/matrix combination, fibre orientation and layer arrangement. The assessment of the effects of the finite outer boundary is of practical importance when dimensioning critical notched regions. An anisotropic plate with finite dimensions and a hole in its center will be used here to model stress concentrations. The calculation is based on conformal mappings combined with complex-valued stress functions. The outer boundary is described using point-matching and the least-squares method. The solutions are conducive to the assessment of the essential influencing factors of material properties, geometry and loads. Notched finite plates made of fibre/matrix composites, mainly carbon-fibre reinforced polymers, will be presented as illustrations.

Analysis of Nonlinear Multibody Systems with Elastic Couplings

This paper is concerned with the dynamic analysis of nonlinear multi-body systems involving elastic members made of laminated, anisotropic composite materials. The analysis methodology can be viewed as a three-step procedure. First, the sectional properties of beams made of composite materials are determined based on an asymptotic procedure that involves a two-dimensional flnite element analysis of the cross-section. Second, the dynamic response of nonlinear, ∞exible multi-body systems is simulated within the framework of energy-preserving and energy-decaying time integration schemes that provide unconditional stability for nonlinear systems. Finally, local three-dimensional stresses in the beams are recovered, based on the stress resultants predicted in the previous step. Numerical examples are presented and focus on the behavior of multi-body systems involving members with elastic couplings.

Structure of Nd2Fel4B / Fe Resulting from Reaction of Nd2Fe17 and B

A novel method to prepare anisotropic composite magnetic material was described. A block of Nd2Fe17 compound was heated with the surrounding B (or B2O3) powder and the reaction accelerator Ca. In the reaction region, rod-shaped Fe precipitates were formed inside Nd2Fe14B matrix grains. The longitudinal directions of those are parallel to the B diffusion path, while perpendicular to the c-axis of Nd2Fe14B crystals. The Fe diameter depends on the heating temperature, below 100nm at 1123K. This structure is regarded as eutectic, and differ from that formed by peritectic solidification. The similar reaction product was formed in the powder form by using Nd2Fe17 powder instead of the bulk material. That product has larger magnetization than Nd2Fe14B, but has no coercivity and the small anisotropy field about 1.6MA/m.

Mixed layer-wise models for multilayered plates analysis

This paper addresses the problem of the fulfillment of a number of requirements which are essential towards the reliable modeling of multilayered thick plates made of anisotropic composite materials. Among them, the fulfillment of both the continuity of displacements and transverse shear and normals stresses at the interfaces between two consecutive layers are such necessary requirements. Two independent fields are assumed in the thickness direction for the transverse stress and displacement unknowns in each layer. Linear, parabolic as well as the case of AT-order expansion are treated. Legendre polynomials are employed as base functions and top/bottom values of displacement and stress components are introduced as unknown variables. Displacement and mixed governing equations are derived by referring to the equation of virtual displacements and to a Reissner mixed variational equation, respectively. The interface continuity conditions, referred to as C z 0-requirements, have been fulfilled a priori by writing the governing equations at the multilayered level. Displacements and mixed formulations have yielded partial and complete fulfillments of such requirements, respectively. A few closed form solutions related to the bending problem of cross-ply laminated, thick plates and comparison with exact, elasticity results show the accuracy of the proposed models.

Optimal Hole Profile In A Composite MaterialPlate Under Biaxial Tension By Finite ElementSimulation

For an infinite plate made of anisotropic composite material under biaxial tensile stress, the theoretical solution for the optimum hole profile has not been available. By using finite element simulation (FES) of Professor Durelli's method of Photoelastic Stress Minimization (PSM) to remove material that has low Tsai-Wu index, an algorithm can be found to get the profile converge towards the optimum. A smoothing algorithm is used to smooth the nibbled boundary after each step of iteration. The results showed that FES can be viably used to solve optimization problems of composite material structures.

A Sample Preparation Method for Paper Cross-Sections using a Focused Ion Beam.

A new preparation technique of cross-section for examining the fine structure of fiber and paper was investigated. A critical point in the structural characterization study of paper is to prepare cross-sections in a way the structure remains unchanged. However, the destruction of internal structure or creation of artifact in the thin sections during their preparation process even in a epoxy resin embedded sample is not avoidable. A focused ion beam (FIB) technique was applied as an improved method for a variety of papers. This technique has specially been used for fine processing of semiconductor or metals. Advantageous points of this method are as follows; (1) Sample temperature during the beam cutting is kept lower than 40°C, (2) Any optional area can be selected for sectioning, (3) A two step irradiation method is applicable for anisotropic composite materials. As a result, smooth cross-sections of a woodfree compressible paper and a double coated paper composed of materials with different hardness were successfully prepared and the micrographs with no structural change or artifact was satisfactory obtained. Further, a clear observation of printed ink transferred to paper was realized for the first time by this method.

Control of Cantilever Vibration via Structural Tailoring and Adaptive Materials

A dual approach integrating structural tailoring and adaptive materials technology and designed to control the dynamic response of cantilever beams subjected to external excitations is presented. Whereas structural tailor- ing uses the anisotropy properties of advanced composite materials, adaptive materials technology exploits the actuating capabilities of piezoelectric materials bonded or embedded into the host structure. A control law relat- ing the piezoelectrically induced boundary bending moment with the velocity at given points of the structure is implemented and its effect on the closed-loop frequencies and dynamic response to harmonic excitations is inves- tigated. The combination of structural tailoring and control by means of adaptive materials proves very effective in damping out vibration. I. Introduction A Sthe requirements for higherexibility on high-speed aircraft increase, so do the challenges of developing innovative de- sign solutions. Whereas the increasedexibility is likely to provide enhanced aerodynamic performance, the aircraft also must be able to ful® ll a multitude of missions in complex environmental condi- tions and to feature an expanded operational envelope and longer operational life. To achieve such ambitious goals- advanced con- cepts resulting in the enhancement of static and dynamic response of the multimission- highlyexible aircraft must be developed and implemented. One way of achieving such goals consists of the in- tegration of advanced composite materials in the aircraft structure. 1 In this regard, the directionality property featured by anisotropic composite materials is capable of providing the desired elastic cou- plings through the proper selection of the ply angle. However, such a technique is passive in nature in the sense that, once the design is in place, the structure cannot respond to the variety of conditions in which it must operate. The situation can be mitigated by incorporating into the host structure adaptive materials able to respond actively to changing conditions. In a structure with adaptive capabilities, the natural fre- quencies, damping, and mode shapes can be tuned to reduce the vibration so as to avoid structural resonance andutter instability, and in general toenhance the dynamic response characteristics.The adaptivecapabilityisachievedthroughtheconversepiezoelectricef- fect,whichconsistsofthegenerationoflocalized strainsinresponse to an applied voltage. This induced strain ® eld produces, in turn, a change in the dynamic response characteristics of the structure. It is proposedheretoenhancethefreevibrationanddynamicresponseto externalexcitationsofwing structures by incorporating theadaptive capabilityreferredtoasinduced strain actuationinconjunctionwith structural tailoring. Under consideration is a cantilevered aircraft wing, modeled as a thin/thick-walled closed cross-section beam of anisotropic material. Implementation of a control law relating the applied electric ® eld to one of the mechanical quantities charac- terizing the response of the wing according to a prescribed func- tional relationship results in eigenvalue/boundary-value problems. The solution consists of closed-loop eigenvalues/dynamic response characteristics, which are functions of the applied voltage, i.e., of the feedback control gain. Investigation of static and dynamic control of aircraft wing structures via the simultaneous implementation of induced strain

STRAINS AND STRESSES OF THREE—LAYER COMPOSITE BARS AND BEAMS/TRISLUOKSNIŲ KOMPOZITINIŲ STRYPŲ IR SIJŲ DEFORMACIJOS BEI ĮTEMPIMAI

New composite anisotropic materials (CM) glass, carbon and boric plastics are more and more frequently used in engineering construction. By tuning strength and stiffness characteristics of CM under tension or bending with their density or price it is possible to get laminated construction of maximum strength and stiffness and minimum mass or price. The purpose of this work is to analyse regularity of distribution of stiffness or strains and stresses in three-layer bars, subjected to tension or bending by changing geometric characteristics of layer, materials and their position in cross-section of bars. The bar layers were formed of carbon plastic (A), hot (Sk) and cold hardening (Sc) glass plastics and epoxy resin (D). Equations were obtained describing the alteration of bar and beam stiffness and the alteration of normal stresses, all depending on relative thichness Ψ of bar or beam. The relative thickness Ψ is the ratio of middle layer height to the whole height. It has been shown that maximum stresses in exterior and middle layers (with elasticity modules E1 and E2accordingly) become equal when Ψ = E1 /E2 . The intensity of stiffness alteration depends on the magnitude of | E2 —E1 |. In the case of positive magnitude, the bar or beam stiffness increases while increasing Ψ. In the opposite case the stiffness decreases with decrease of Ψ. For the example of structure A-Sk—A and Ψ = 0,5, the price economy for 42% and mass reduction for 4% have been shown and compared with carbon plastic beam.

Improvement of the dynamic properties of a steel-composite hybrid flexspline of a harmonic drive

The harmonic drive is a special gear-drive speed reduction system whose operation principle is based on elastic deformation rather than rigid-body motion of the general gearing system. From the components of the harmonic drive, the flexspline is the key element for the transmission of motion. It must be flexible in the radial direction, but must be stiff in the torsional direction to accurately transmit rotational motion. Because the contradictory dual role of the flexspline cannot be satisfied effectively with conventional isotropic materials, but can be achieved with anisotropic composite materials, in this paper the cup section of the flexspline was hybridly manufactured by laying-up composite material on the inside surface of the steel cup section. The static and dynamic characteristics of the hybrid flexspline were investigated with respect to the fibre volume fraction, stacking sequence and the mass ratio of the composite to steel.

STRAINS AND STRESSES OF THREE—LAYER COMPOSITE BARS AND BEAMS

Summary New composite anisotropic materials (CM) glass, carbon and boric plastics are more and more frequently used in engineering construction. By tuning strength and stiffness characteristics of CM under tension or bending with their density or price it is possible to get laminated construction of maximum strength and stiffness and minimum mass or price. The purpose of this work is to analyse regularity of distribution of stiffness or strains and stresses in three-layer bars, subjected to tension or bending by changing geometric characteristics of layer, materials and their position in cross-section of bars. The bar layers were formed of carbon plastic (A), hot (Sk) and cold hardening (Sc) glass plastics and epoxy resin (D). Equations were obtained describing the alteration of bar and beam stiffness and the alteration of normal stresses, all depending on relative thichness Ψ of bar or beam. The relative thickness Ψ is the ratio of middle layer height to the whole height. It has been shown that maximum s...

Non-linear current-voltage characteristics in anisotropic epoxy resin-graphite flake composites

The conductivity of anisotropic composite materials constituted of single-crystal graphite flakes in an epoxy resin and subjected to a variable d.c. electric field has been studied. Non-linearities in the current-voltage characteristics have been found and are discussed within the framework of two theoretical models, the non-linear random resistor network and the dynamic random resistor network. We show that our materials can be modelled by the non-linear random resistor network, which, to our knowledge, is the first time that the predictions of this model seem so well supported in a real, three-dimensional composite.

Effective permittivity of anisotropic composite material of dense nonspherical particles and conductivity transition

Effective permittivity of anisotropic composite material of dense nonspherical particles and conductivity transition

Effective permittivity of anisotropic composite material of dense nonspherical particles and conductivity transition

Employing the strong fluctuation theory for random media, this article presents numerical results for the effective permittivity and conductivity transition for composite material of dense, nonspherical particles. It shows the functional dependence of anisotropic properties of composite material upon the particle shape and fraction. © 1996 John Wiley & Sons, Inc.

Playing with the Anisotropy of the Matrix and Fiber for the Improvement of the Strength of Composites

The paper deals with the theory of the coupling of strongly anisotropic fibers along their axis with anisotropic matrices along either the fiber direction or the transverse plane to the direction of the fibers. It is shown that the first arrangement deteriorates, whereas the second improves significantly the mechanical behavior of the composites. Indeed, it is shown that anisotropy of the matrix, increasing its mechanical properties on the transverse isotropic plane of the composite, increases also the transverse-transverse Poisson's ratio, v23, whereas decreases the longitudinal shear modulus, G,2. This results in values of the eigenangle wx approaching the corresponding value Wic for the equivalent isotropic material and caused a deterioration of the strength and toughness of the composite, since the material now has the tendency to develop higher stress concentrations for equivalent loadings [1,2]. On the contrary, a strong anisotropic matrix along the direction of the fibers yields the inverse results for the respective moduli of the anisotropic composite. Finally, the most important result is a perceptible decrease of the ratio E,1/2G,2 which yields values of the eigenangle wc tending to approach the critical value wi for the isotropic material. The decrease of wc indicates the improvement of the quality of the composite, since it develops relatively lower stress concentration factors, which approach their respective isotropic values [2]. Thus, the anisotropic composite material is approaching an equivalent state of quasi-isotropy and therefore improves its strength by reducing considerably the eventual anisotropic stress concentration factors of the respective structural elements [1]. Examples with T300/N5208 graphite-epoxy composites and Borsic-1100 aluminum metal-metal composites indicate clearly the beneficial effect of the anisotropy of their matrices.

Free vibration of laminated composite plates—a simple finite element based on higher order theory

A four-noded rectangular element with seven degrees of freedom at each node is developed for the vibration analysis of laminated composite plate structures having a constant thickness of any individual layer. The displacement model is so chosen that it can explain adequately the parabolic distribution of transverse shear stresses and the non-linearity of in-plane displacements across the thickness. The mass matrix is derived in a consistent manner. Rectangular plates of antisymmetric angle-ply laminates whose material properties are typical of highly anisotropic composite materials are considered. Two sets of material properties are used to show the parametric effects of plate aspect ratio, length-to-thickness ratio, number of layers and lamination angle. Results are compared with existing analytical and numerical solutions. The present element formulation confirms its applicability for a wide variety of laminated plates.

Comprehensive model of anisotropic composite aircraft wings suitable for aeroelastic analyses

A comprehensive plate-beam structural model suitable for aeroelastic analyses of aircraft wings made of anisotropic composite materials is developed. The equations governing the static and dynamic aeroelastic equilibrium of cantilevered swept-wing structures and the associated boundary conditions are derived by means of the Hamilton variational principle. These equations incorporate a number of effects: 1) anisotropy of the materials of constituent layers, 2) warping inhibition, 3) transverse shear flexibility, and 4) rotatory inertias. A uniform swept-wing model composed of a transversely isotropic material is considered to illustrate the coupled and separate effects of transverse shear deformation and warping restraint upon its divergence and static aeroelastic load distribution. An exact method based upon the Laplace integral transform technique is used to solve the above mentioned problems. The results displayed in this article reveal the importance of transverse shear and warping restraint effects in predicting more accurately the static aeroelastic response of swept-forward wings. However, for swept-back wings, these effects represent higher-order corrections to the classical theory.

Design and manufacture of the composite flexspline of a harmonic drive with adhesive joining

The harmonic drive, which is composed of a circular spline, a wave generator and a flexspline, is a compact, light-weight, and precise torque transmission mechanism with little backlash. From these components, the flexspline is the key element for motion transmission. It must be flexible in the radial direction but stiff in the tangential direction to accurately transmit rotational motion. In order to satisfy this dual role, the conventional steel flexspline is usually manufactured as a thin cup shape which requires a large amount of machining using special jigs. Because of the thin cup shape, the steel flexspline produces noise and vibration when operated at high speed. Since the dual role cannot be satisfied effectively with conventional isotropic materials, anisotropic composite materials have been considered. In this paper the cup section of the flexspline was manufactured with carbon-fiber epoxy composite material and the tooth section using steel. Then the two components were joined by adhesive bonding. Also, in order to make the manufacture of the steel flexspline easy and reduce the noise and vibration of the harmonic drive, the cup and tooth sections were manufactured separately and adhesively bonded. The static torque transmission capabilities and the vibration characteristics of the composite flexspline with adhesively bonded steel teeth and the steel flexspline with adhesively bonded steel teeth were experimentally tested. From these tests it was found that the flexspline manufactured with adhesive bonding had sufficient torque transmission capabilities and both the composite flexspline and the bonded steel flexspline had better dynamic characteristics than the conventional one-piece steel flexspline.