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.     

Analytical methods for modeling of ultrasonic nondestructive testing of anisotropic media

Many modern structural materials exhibit anisotropic elastic behavior leading to complicated wave propagation phenomena. To ensure the reliability of ultrasonic nondestructive testing techniques, these material properties as well as the influence of microstructural inhomogeneities and the effects of interfaces on ultrasonic wave propagation have to be taken into account. In this respect, mathematical modeling provides an efficient method of assisting analysis. Two computationally efficient analytical approaches--a Gaussian beam and a point source superposition technique--are presented, which are well-suited for performing ultrasonic wave propagation and scattering simulations for anisotropic media. Results for homogeneous as well as inhomogeneous anisotropic media like composites and weld material are presented.     

Experimental analysis of the linear and nonlinear behaviour of composites with delaminations

An analysis of the linear and nonlinear vibration responses of composites with delaminations is presented. The effect of delamination size on the linear and nonlinear vibration response is studied. The composite material used in this paper is a glass fibre reinforced plastic (GFRP) having delaminations at the plies interfaces. The experimental procedure consists in inducing the specimen on its resonance flexural modes with different excitation levels (amplitudes) for six bending modes and for each delamination length. The presence of the nonlinearity introduced by the delamination was clearly identified by the variation of natural frequencies for increasing excitation levels. Then, nonlinear elastic parameters for progressive delamination length were determined and discussed for the first six bending modes. The linear and the nonlinear elastic parameters were compared in their sensitive modes.     

FREE VIBRATIONS OF SIMPLY SUPPORTED AND MULTILAYERED MAGNETO-ELECTRO-ELASTIC PLATES

Analytical solutions are derived for free vibrations of three-dimensional, linear anisotropic, magneto-electro-elastic, and multilayered rectangular plates under simply supported edge conditions. For any homogeneous layer, we construct the general solution in terms of a simple formalism that resembles the Stroh formalism, from which any physical quantities can be solved for given boundary conditions. In particular, the dispersion equation that characterizes the relationship between the natural frequency and wavenumber can be obtained in a simple form. For multilayered plates, we derive the dispersion relation in terms of the propagator matrices. The present solution includes all previous solutions, such as piezoelectric, piezomagnetic, and purely elastic solutions as special cases, and can serve as benchmarks to various thick plate theories and numerical methods used for the modelling of layered composite structures. Typical natural frequencies and mode shapes are presented for sandwich piezoelectric/piezomagnetic plates. It is shown clearly that some of the modes are purely elastic while others are fully coupled with piezoelectric/piezomagnetic quantities, with the latter depending strongly upon the material property and stacking sequence. These frequency and mode shape features could be of particular interest to the analysis and design of various “smart” sensors/actuators constructed from magneto-electro-elastic composite laminates.     

Elastic properties of spherically anisotropic piezoelectric composites

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezo-electric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.     

Ultrasonic measurement of elastic constants in fiber-reinforced polymer composites under influence of absorbed moisture

This paper presents an attempt to quantify hygral aging in fiber-reinforced polymer composites by the elastic constants C11 and C33. Quantitative ultrasonic measurements of the elastic constants for three different unidirectional as well as three different cross-ply specimens were compared. The specimens were manufactured with different moisture resistant surfaces and immersed in water for 24 h. By calculating the elastic constants, it was taken into account that hygral aging was accompanied by absorption of moisture in the polymer matrix. Moisture changed the laminate dimensions significantly, and typically moisture expansion coefficients are reported. Moreover, as the ultrasonic pulse form changed in the anisotropic materials, different broadband methods were used to calculate the elastic constants.     

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.     

Electromechanical response of 2-2 layered piezoelectric composites: A micromechanical model based on the asymptotic homogenization method

A micromechanical model based on the asymptotic homogenization technique has been developed to predict the complete elastic, dielectric and piezoelectric properties of a general 2-2 layered piezoelectric composite where the constituent phases are elastically anisotropic and piezoelectrically active. Two classes of layered piezoelectric composites (i.e. longitudinally and transversely layered) are considered in two widely different ceramic- and polymer-based systems and their effective properties are obtained in the limits of both large-volume (i.e. bulk) and small-volume (i.e. thin-film) systems. It is demonstrated that: (i) in the bulk, ceramic–ceramic layered composite system, the elastic, piezoelectric, and dielectric properties of the composites vary linearly with volume fraction of the second phase, while in the bulk ceramic–polymer layered composite system, the corresponding properties vary non-linearly with volume fraction of the second phase; (ii) in the prismatic (thin-film) layered piezoelectric composite system, the non-vanishing, effective elastic, piezoelectric and dielectric properties vary linearly with the volume fraction of the second phase for both the longitudinally and transversely layered composite structures in the ceramic–ceramic and the ceramic–polymer composite systems; (iii) the ceramic–polymer piezoelectric layered composites that incorporate a low density polymeric phase with lower acoustic impedance generally exhibit enhanced piezoelectric coupling constants and lowered acoustic impedance; (iv) the longitudinally layered composites exhibit higher piezoelectric coupling constants and lower acoustic impedance compared to that of the transversely layered composites; and (v) the best combination of properties for applications such as hydrophones (i.e. the highest piezoelectric coupling constants and the lowest acoustic impedance) is obtained in the ceramic–polymer, longitudinally layered, thin-film, piezoelectric composites.     

Guided waves in anisotropic and quasi-isotropic aerospace composites: Three-dimensional simulation and experiment

Three-dimensional (3D) elastic wave simulations can be used to investigate and optimize nondestructive evaluation (NDE) and structural health monitoring (SHM) ultrasonic damage detection techniques for aerospace materials. 3D anisotropic elastodynamic finite integration technique (EFIT) has been implemented for ultrasonic waves in carbon fiber reinforced polymer (CFRP) composite laminates. This paper describes 3D EFIT simulations of guided wave propagation in undamaged and damaged anisotropic and quasi-isotropic composite plates. Comparisons are made between simulations of guided waves in undamaged anisotropic composite plates and both experimental laser Doppler vibrometer (LDV) wavefield data and dispersion curves. Time domain and wavenumber domain comparisons are described. Wave interaction with complex geometry delamination damage is then simulated to investigate how simulation tools incorporating realistic damage geometries can aid in the understanding of wave interaction with CFRP damage. In order to move beyond simplistic assumptions of damage geometry, volumetric delamination data acquired via X-ray microfocus computed tomography is directly incorporated into the simulation. Simulated guided wave interaction with the complex geometry delamination is compared to experimental LDV time domain data and 3D wave interaction with the volumetric damage is discussed.     

Free vibration of three-dimensional anisotropic layered composite nanoplates based on modified couple-stress theory

Based on the modified couple-stress theory, three-dimensional analytical solutions of free vibration of a simply supported, multilayered and anisotropic composite nanoplate are derived by solving an eigenvalue system and using the propagator matrix method. By expanding the solutions of the extended displacements in terms of two-dimensional Fourier series, the final governing equations of motion with modified couple-stress effect are reduced to an eigenvalue system of ordinary differential equations. Analytical expressions for the natural frequencies and mode shapes of multilayered anisotropic composite plates with modified couple-stress effect are then derived via the propagator matrix method. Numerical examples are carried out for homogeneous thick-plates and sandwich composite plates to show the effect of the non-local parameter in different layers and stacking sequence on the mode shapes. The present solutions can serve as benchmarks to various thick-plate theories and numerical methods, and could be further useful for designing layered composite structures involving small scale.