Graphite-epoxy Composite Plate Research Articles

Stochastic dynamic analysis of composite plate with random temperature increment

During the service life, laminated composites may be subject to some random thermal environment. Quantification of the uncertainty in static and dynamic response of the composites under such condition is still a challenging issue. This work presents a stochastic dynamic response analysis of a graphite-epoxy composite plate using generalized polynomial chaos (gPC) expansion due to random mean temperature increment. A stochastic finite element method (SFEM) based on the first-order shear deformation theory (FSDT) is used to describe the free and forced vibration response of the graphite-epoxy composite plate under a uniform distribution of the temperature throughout the plate. Newmark’s time integration scheme is used to predict the time-dependent displacement response under dynamic loading. The collocation-based non-intrusive gPC expansion method is used for stochastic dynamic analysis of the graphite-epoxy composite plate. The increment in the temperature is considered as an uncertain parameter and presented by the truncated gPC expansion. The stochastic system response of the plate is projected to the deterministic solver by using the stochastic Galerkin method. The statistical response of eigen frequencies and dynamic displacements of the composite plate at incremental random mean temperature are investigated, and are compared with the results of the Monte Carlo simulation. The numerical studies show a reduction in amplitude of the dynamic mean displacements with the increment in the time and it increases with the increment in the random mean temperature. The characteristics of loading have also significantly influenced the uncertainty in the time-dependent displacement response.

Deformation control method of composite structural elements by fiber-optic acoustic emission sensor

Subject of Research.The paper presents the study of a graphite-epoxy composite plate strain detection possibility by the fiber-optic acoustic emission sensor mounted on its surface. Method. The proposed method consisted in additional low-frequency phase-generated carrier implementation in the impulse Fabry-Perot interferometer and its amplitude evaluation. The phase-generated carrier amplitude depends on the interferometer optical path difference, therefore, its value change can be used for the studied composite strain estimation. VCSEL with a wavelength of 1550 nm was used as a light source. The phase carrier was generated by current modulation of the light source that caused center wavelength shift of the VCSEL. Main Results. The low-frequency phase-generated carrier signal amplitude dependence on the interferometer optical path difference and wavelength shift of the light source were obtained. According to simulation results the sensitivity of the proposed method is 1.6 urad×ppm, 5.3 urad×ppm and 13.3 urad×ppm at different values of the coefficient Kd 30, 100 and 250 pm, respectively. Experimental study of the proposed method and results analysis were performed. According to experimental results, the accuracy of the proposed method was about 1´10–3% that corresponds to the sensor relative stretch of 10 me, while the accuracy of the market available fiber optic systems based on fiber Bragg grating sensors equals to 4 ppm. Practical Relevance.The proposed method can be used for strain detection of the graphite-epoxy composite constructions along with its acoustic emission control by one fiber-optic sensor.

Dynamic Response of Composite Plate Subjected to Sudden Heat Flux

Composite plates’ subjected to sudden surface heating is investigated. Simply supported boundary conditions along the four sides of the plat are considered. The effect of plate thickness and stacking sequence on the maximum deflection that is induced by the thermal heat flux for a graphite-epoxy composite plate is studied using finite element analysis. Symmetric angle ply laminates plate shows least deformation compared the other stacks of the same thickness.

System probability of failure and sensitivity analyses of composite plates under low velocity impact

Probabilistic response of graphite epoxy composite plates under low velocity impact is studied modeling matrix cracking and delamination damage. Probabilistic design methodology of composite material based on progressive damage model is developed and implemented in a user defined subroutine to consider the scatter in material properties (Young’s moduli, Poisson’s ratio, ultimate strength, and fracture energy) and in initial velocity. Damage initiation and propagation failure due to matrix cracking and delamination are investigated for limiting criteria for the low velocity impact. The Gaussian process response surface method, is adopted to determine the system probability of failure and sensitivity analyses of the composite plates. The scatter in random parameters shows significant influence on the contact force and displacement histories. There is a probability of underestimation of the peak contact force and displacement by 28% and 44% respectively, if the scatter in the properties is not considered. The target reliability of the plate is achieved for an optimal combination of impactor masses and velocities. The sensitivity based probabilistic design optimization procedure is investigated to achieve better strength and lighter weight of composite for body armors.

Error Suppression via Tension for Flexible Square Antenna Panels and Panel Arrays

The concept of passive surface error control via tension is explored for flexible square panels and for a rectangular array of such panels suspended with four catenaries. The panels are 1 mm thick 1 m square graphite-epoxy composite plates with a four-ply symmetric layup. Individual panel response to a uniform through-thickness temperature gradient field both alone and combined with in-plane tension (stretch) are examined. When integrated into a grid (a simple phased array configuration), the effects of a transient slew are considered. Characteristic responses are identified and studied symbolically as well as numerically. The results demonstrate the feasibility of combined global and component-level error suppression for the considered structure, exercised singularly by global prestress that also maintains the integrity of the tension structure. Limited attention is paid to mission-specific issues such as stowage and deployment. Assuming an X-band radar context, surface errors are related to a 1 mm limit. Out-of-flatness is evaluated with three metrics relevant to different aspects of signal processing: the maximum depth of the deformed surface, its maximum lateral deviation from the best-fit plane, and the phased-array radiometric rms surface error.

The Effect of Penetrator Geometry on the Dynamic Response of Woven Graphite/Epoxy Composites

The primary focus on this paper is to study the high energy penetration/perforation damage propagation of composite plates using the perforation split Hopkinson pressure bar. The objectives include: investigation of propagation of penetration and surface crack damage in the vicinity perforation threshold velocity; investigation of energy absorption and strain intensity profiling; and quantitative analysis of the interactive effects of penetrator geometry and sample thickness on the perforation damage of woven graphite-epoxy composite plates. The results show that strain rate increased with damage energy threshold levels and decreased with sample thickness from below to above the perforation limit velocity on the average. There was a significant difference between penetrator geometries on a specimen strain rate, and penetrator size other than shape was a more important factor. As the size of the penetrator increased, the perforation energy thresholds increased accordingly. Thus, for the same energy level, the larger penetrator delivered more energy to the target. The mode of perforation failure was localized with obliquely shaped cracks for the woven specimens. It was conceivable that the cracks first initiate at the point of intersections of the weave and move in both directions. These results would provide some instructions in building, designing, and evaluating protective structures that undergo any penetration type of impact.

The Symplectic Method for the Bending of Symmetrical Laminated Composite Plates with Clamped Boundary

The symplectic method is applied to study analytically the stress distributions of composite laminated plates in this paper applies. The dual equations were presented by variation principle and introducing separation of variables used. Then in the symplectic space which consists of the original variables and their dual variables, the problem can be solved via effective mathematical physics methods such as the method of separation of variables and Eigen function vector expansion. The equation and Eigen-vector are deduced. The results of cross-ply laminated graphite–epoxy composite plate with clamped boundary are shown, which is compared with established results. The parameters’ influences on mechanical property are also discussed.

Nonlinear Response of Graphite-Epoxy Composite Thin-Walled Structure under Elevated Thermal Environment

Composite materials thin-walled structures are widely used as skin panel in flight vehicles in recent years. These structures will encounter severe complex loading conditions, which may be a combination of mechanical, aerodynamic, thermal and acoustic loads. Thin-walled structures subjected to this kind of loadings will exhibit nonlinear response; as a result, fatigue failure will occur. High temperature may cause large thermal deflection and stress, for some special conditions, may cause thermal buckling. Once the thermal buckling appears, the stiffness will change correspondingly, it will cause significant influence on the dynamic response and fatigue failure. Accordingly, it is important to research the nonlinear response of this kind of structures under elevated thermal environment. Nonlinear response and thermal pre-buckling/post-buckling behavior of a Graphite-Epoxy composite plate subjected to server thermal loading is numerically investigated in this paper. A composite laminated plate with clamped-clamped boundary conditions is chosen as simulated body, nonlinear finite element model is developed using the first-order shear deformable plate theory, Von Karman strain-displacement relations, and the principle of virtual work. The thermal load is assumed to be a steady-state with different predefined temperature distribution. The thermal strain is stated as an integral quantity of the thermal expansion coefficient with respect to temperature. Then the modes of the plate are analyzed, the nature frequencies and modal shapes are obtained. The critical temperature of buckling is calculated. The static nonlinear equations of motions are solved by the Newton-Raphson iteration technique to obtain the thermal post-buckling deflection. The Riks method is used to analyze static post-buckling behavior. In the numerical examples, four types of situations are studied, which include i) the buckling behaviors for different initial imperfections, ii) the buckling behaviors for different thickness to width ratios, and iii) The buckling behaviors for different width to length ratios; The critical temperature, the static thermal post-buckling deflection and the load to displacement relation are presented respectively. The influences of different boundary conditions on the buckling behaviors of the plate are achieved as well. The simulation method and results presented in this paper can be valuable references for further analysis of the nonlinear responses of thin-walled structures under complex loading conditions.

The Bending of Symmetrical Laminated Composite Plate Based on Symplectic Method

This paper applies a symplectic method to study analytically the stress distributions of Composite laminated plates. Using variation principle and introducing separation of variables, dual equations were presented. Then in the symplectic space which consists of the original variables and their dual variables,the problem can be solved via effective mathematical physics methods such as the method of sepatation of variables and eigenfunction vector expansion. The transcendental equation and eigen-vector are deduced. The results of cross-ply and angle-ply laminated graphite–epoxy composite plate are shown, which is compared with established results. The parameters’ influences on mechanical property are also discussed.

Blind inversion method using Lamb waves for the complete elastic property characterization of anisotropic plates

A novel blind inversion method using Lamb wave S(0) and A(0) mode velocities is proposed for the complete determination of elastic moduli, material symmetries, as well as principal plane orientations of anisotropic plates. The approach takes advantage of genetic algorithm, introduces the notion of "statistically significant" elastic moduli, and utilizes their sensitivities to velocity data to reconstruct the elastic moduli. The unknown material symmetry and the principal planes are then evaluated using the method proposed by Cowin and Mehrabadi [Q. J. Mech. Appl. Math. 40, 451-476 (1987)]. The blind inversion procedure was verified using simulated ultrasonic velocity data sets on materials with transversely isotropic, orthotropic, and monoclinic symmetries. A modified double ring configuration of the single transmitter and multiple receiver compact array was developed to experimentally validate the blind inversion approach on a quasi-isotropic graphite-epoxy composite plate. This technique finds application in the area of material characterization and structural health monitoring of anisotropic platelike structures.

Structural health monitoring of anisotropic plates using ultrasonic guided wave STMR array patches

Structural health monitoring (SHM) of plate-like structures used in aerospace industries, using transducer arrays located suitably on the structure, such as the single-transmitter multiple-receiver (STMR) array [Wilcox PD, Lowe M, Cawley P. Lamb and SH wave transducer arrays for the inspection of large areas of thick plates. Review of progress in quantitative nondestructive evaluation, vol. 19A. Melville, NY, USA: American Institute of Physics; 1999. p. 1049–56; Wilcox PD. Guided wave beam steering from omni-directional transducer arrays. Review of progress in quantitative nondestructive evaluation, vol. 22A. Melville, New York, USA: American Institute of Physics; 2002. p. 761–8], has been demonstrated here. The reconstruction of the material state was carried out by utilizing a phased addition reconstruction algorithm. In addition to the signals from damage sites, the ultrasonic guided wave-based reconstruction procedures also need the complete set of elastic moduli as a continuous input throughout the SHM process. In the present study, two flexible printed circuit board (PCB)-based patches: ((i). single-quadrant, double-ring STMR material characterization (MC) array and (ii). Full-ring STMR SHM array) were developed for accomplishing both objectives, i.e. (a) online MC and (b) SHM of anisotropic plate-like structures, respectively. Experiments were conducted on 3.15 mm graphite-epoxy composite plate using PCB-based STMR arrays, the feasibility of accomplishing both objectives was demonstrated.

Fatigue residual strength of circular laminate graphite–epoxy composite plates damaged by transverse load

The research dealt with the relation between damage and tension–tension fatigue residual strength (FRS) in a quasi-isotropic carbon fibre reinforced epoxy resin laminate. The work was organized in two phases: during the first one, composite laminates were damaged by means of an out-of-plane quasi-static load that was supposed to simulate a low velocity impact; in the second phase, fatigue tests were performed on damaged and undamaged specimens obtained from the original composite laminates. During the quasi-static transverse loading phase, damage progression was monitored by means of acoustic emission (AE) technique. The measurement of the strain energy accumulated in the specimens and of the acoustic energy released by fracture events made it possible to estimate the amount of induced damage and evaluate the quasi-static residual tensile strength of the specimens. A probabilistic failure analysis of the fatigue data, reduced by the relative residual strength values, made it possible to relate the FRS of damaged specimens with the fatigue strength of undamaged ones.

Locating point of impact in anisotropic fiber reinforced composite plates

The conventional triangulation technique cannot predict the point of impact in an anisotropic composite plate because the triangulation technique assumes that the wave speed is independent of the direction of propagation which is not the case for anisotropic plates. An alternative method based on the optimization scheme was proposed by Kundu et al. [T. Kundu, S. Das, K.V. Jata, Point of impact prediction in isotropic and anistropic plates from the acoustic emission data, J. Acoust. Soc. Am. 122, 2007, 2057–2066] to locate the point of impact in plates by analyzing the time of arrival of the ultrasonic signals received by the passive sensors attached to the plate. In this paper, that objective function is modified further to overcome the inherent difficulties associated with multiple singularities and to maximize the efficiency of the acoustic emission data for multiple receiving sensors. With this modified objective function the impact point on an anisotropic composite plate is predicted from the acoustic emission data. Experiments are carried out by dropping steel and ping pong balls on a graphite-epoxy composite plate and recording acoustic signals by passive transducers adhesively bonded to the plate at three different locations. The impact point is predicted by the proposed method and compared with the actual location of impact.

Determination of material symmetries from ultrasonic velocity measurements: A genetic algorithm based blind inversion method

The determination of material symmetries and principle plane orientations of anisotropic plates, whose planes of symmetries are not known, are calculated using a Genetic Algorithm (GA) based blind inversion method. Ultrasonic phase velocity profiles were used as input data to the inversion. During each blind inversion, the material was initially assumed to be dependent on 21 elastic moduli (general anisotropy). A Genetic Algorithm based method was exploited to identify the “statistically significant” elastic moduli using the coefficient of variation ( C V) to derive a reduced set of elastic moduli. The unknown material symmetry and the principle planes (angles between the geometrical coordinates and the material symmetry coordinates) were evaluated using the method proposed by Cowin and Mehrabadi [Cowin SC, Mehrabadi MM. On the identification of material symmetry for anisotropic elastic materials. Quart J Mech Appl Math 1987;40(4):451–76], Cowin [Cowin SC. Properties of the anisotropic elasticity tensor. Quart J Mech Appl Math 1989;42(2):249–66] and Sun [Sun M. Optical recovery of elastic properties for a general anisotropic material through ultrasonic measurements. M.S. thesis, The Graduate School, University of Maine, August 2002]. This procedure was verified using simulated ultrasonic velocity data sets on materials with transversely isotropic, orthotropic, monoclinic and triclinic symmetries. Experimental validation was also performed on a unidirectional graphite-epoxy [0] 7s material, a quasi-isotropic graphite-epoxy [0/45/90/-45] 7s fiber reinforced composite plate, and plate cut at 45° to the fibers from a unidirectional graphite-epoxy composite plate.

Genetic algorithm based reconstruction of the elastic moduli of orthotropic plates using anultrasonic guided wave single-transmitter-multiple-receiver SHM array

The reconstruction of all nine unknown elastic moduli of orthotropic platestructures has been achieved using a single-transmitter-multiple-receiver(STMR) compact structural health monitoring (SHM) array. This methoduses the velocity measurement of the fundamental guided Lamb wave modes(S0 and A0), generated from a central transmitter, and received by a sparse array of receivers thatencircle the transmitter. The measured velocities are then used in an inversionalgorithm based on genetic algorithms. A prototype compact STMR array wasdeveloped and used in the measurement. Simulated data were used to demonstrate thefeasibility of the technique. Experiments were conducted on 3.15 mm graphite–epoxycomposite plate using a PZT based STMR array as well as laser vibrometer baseddisplacement measurement. Experimental Lamb wave velocity data were used tovalidate the present technique. This technique finds application in the areas ofmaterial characterization and SHM of anisotropic plate-like structures used inaerospace and automobile components made using fiber reinforced composites.

Stresses in a thin, circular aeolotropic plate subjected to uniform lateral load

Closed form, approximate stress solutions for simply supported cubic and orthotropic plates subjected to a lateral pressure are presented and compared with a series solution. The accuracy of the approximate solutions depends on the degree of anisotropy. For cubic plates exhibiting significant anisotropy, the approximate solution is within ∼10% of the series solution. For a graphite–epoxy composite plate of orthotropic symmetry, the approximate solution is within 10% of the series solution for the maximum stress at the plate centre and within 23% for the minimum stress at the plate centre. Single crystal plates tend to exhibit a large tangential stress where the stiff directions intersect the plate edges, implying that the edges of brittle single crystal test specimens must either be prepared better than those of isotropic specimens or have more of the plate overhanging the support.

Experimental observations of intersonic crack growth in asymmetrically loaded unidirectional composite plates

Abstract Some recent experimental observations of highly dynamic crack growth events in thick unidirectional composites are presented. The specimens used in this study were 48-ply thick unidirectional graphite–epoxy composite plates which were either symmetrically (mode I) or asymmetrically (mode II) loaded by impact in a one-point bend configuration with an edge pre-notch machined in the fibre direction. Moderate impact speeds of up to 57 ms−1 were used. The lateral shearing interferometric technique of coherent gradient sensing in conjunction with high-speed photography was used to visualize the failure process in real time. Mode-I cracks propagated subsonically with crack speeds increasing to the neighbourhood of the Rayleigh wave speed. For asymmetric mode-II types of loading the results revealed highly unstable and intersonic shear-dominated crack growth along the fibres. These cracks propagated with unprecedented speeds reaching 7400 ms−1, a speed which is more than three times the shear wave speed ...

Exact solutions for dynamic analysis of composite plates with distributed piezoelectric layers

Exact solutions are presented for analyzing dynamics of composite plates with piezoelectric layers bonded at the top and the bottom surfaces. The expressions for mechanical displacements, stresses, electric displacements and potential are derived from constitutive relations and field equations for the piezoelectric medium under applied surface traction and electric potential. The procedure is illustrated with a simply supported symmetric cross-ply (0°/90°/0°) graphite–epoxy composite plate covered with piezoelectric material polyvinylidene fluoride (PVDF). Results are in good agreement with those obtained from finite element model.

A Model of Embedded Fiber Optic Fabry-Perot Temperature and Strain Sensors

A model was developed for embedded intrinsic and extrinsic Fabry-Perot fiber optic sensors. This model relates the strains and the temperature changes in the material surrounding the sensor to the reflected light intensity. The model consists of three parts. Submodel I relates the temperature and the strains in the material to the temperature and the strains inside the sensor. Submodel 2 relates the temperature and the strains inside the sensor to the change in sensor length and to the changes in the optical properties of the sensor. Submodel 3 relates the changes in sensor length and optical properties to the changes in the intensity of the reflected light. On the basis of the model, a computer code SENSOR1 was written which can be used to calculate the reflected light intensity for specified strains and temperature changes inside the material. The model and the code were verified by measuring changes in the light in tensity of an intrinsic Fabry-Perot sensor embedded in a graphite-epoxy composite plate subjected to loads varying with time. The changes in light intensities were measured and were also calculated by the code. The measured and calculated light intensities were found to be in good agreement.

Modification of Lamb wave spectrum in fluid coupled plate

It has been accepted previously that for most practical eases when a plate is immersed in a liquid the Lamb wave spectrum is only slightly perturbed due to energy loss related to leakage of the wave from the plate to the liquid. In contrast it was recently discovered by D. E. Chimenti and A. H. Nayfeh [Appl. Phys. Lett. 49 (9) (1986)] that for leaky Lamb waves in a graphite epoxy composite plate in water a strong anomaly appears in the topology of the S0 mode as a function of frequency. Although it was caused by the fluid, the reason for this anomaly was still not clear. The nature of the anomalous behavior of leaky Lamb waves is discussed in this paper. It is shown that for an understanding of the spectrum topology, the full complex spectrum of propagating and nonpropagating modes should be considered. It is demonstrated that the topological changes in the S0 mode are related to its nearness to the first complex branch of the spectrum. Increasing liquid density leads to interaction between these modes and mutual interchange between their branches in the complex plane. It is shown that, in general, as the density of the immersion liquid increases from zero to infinity the complex spectrum of plate modes gradually transforms from a spectrum of Lamb waves in a free plate to a spectrum of waves in a plate clamped on its surfaces with slip (boundary conditions σxy = 0, Uy = 0).