Ajit K. Mal

Wave propagation in layered composite laminates under periodic surface loads

Abstract A matrix method is presented for the solution of wave propagation problems in multilayered anisotropic media subjected to time harmonic disturbances. The method is applied to obtain the formal solution of the response of layered composite plates to time harmonic and spatially periodic surface loads. It is shown that the solution leads to stable numerical schemes for the evaluation of the displacement and stress fields within the laminate. Numerical results for specific problems will be presented in a separate paper.

Inversion of leaky Lamb wave data by simplex algorithm

A numerical procedure is presented for the inversion of leaky Lamb wave (LLW) data to determine certain material properties of a waveguide, using a modified version of the simplex algorithm. The technique is capable of computing the parameter values that best fit a particular set of data, given an analytical model of the associated phenomenon containing any number of variables and parameters. The basic theoretical concepts involved are reviewed, and the versatility and simplicity of the method are illustrated by examples. The inversion scheme is used to estimate the elastic properties and thickness of an adhesive layer between two aluminum plates and the elastic constants of a unidirectional graphite/epoxy composite laminate. The limitations of the LLW data in the determination of the elastic constants of a composite are discussed.

Interaction of elastic waves with a Griffith crack

Abstract The problem of the diffraction of normally indicent longitudinal and antiplane shear waves on a Griffith crack located in an infinite, isotropic elastic medium is considered. A Fredholm integral equation of the second kind is derived in each case for the determination of diffracted field. From the integral equation an asymptotic development of the solution is obtained which is valid for wavelength long compared to the crack length. For wavelengths comparable with the size of the crack the integral equation is solved numerically. The stress and the displacement fields in the vicinity of the crack as well as the radiation field at points far away from the crack are computed for a range of values of the frequency.

Scattering of Lamb waves from a rivet hole with edge cracks

Lamb waves propagating in an infinite plate containing a circular hole, with or without edge cracks, are investigated both theoretically and experimentally in this paper. The theoretical analysis is accomplished by means of a hybrid method called the global local finite element method, in which a bounded region enclosing the hole and the cracks is discretized into finite elements, while the field external to this region is represented analytically in terms of Lamb wave modes. The scattered field is calculated through the application of the boundary conditions at the interface between the discretized region and the unbounded exterior. In the experiments the incident Lamb wave of a specific mode is generated by means of a wedge transducer and the waves scattered by the hole is recorded in conventional contact type transducers located on the plate surface. The measured time histories and amplitude spectra of the transmitted and reflected waves are compared with those calculated from the hybrid model. The agreement between the theoretical and experimental results is found to be excellent in the cases considered. Application of the technique to non-destructive evaluation (NDE) of corrosion and fatigue induced defects in aging structural components is discussed.

Elastic waves in a fiber-reinforced composite

Abstract T he propagation of time-harmonic elastic waves in a fiber-reinforced composite is studied. The circular fibers are assumed to be parallel to each other and randomly distributed with a statistically uniform distribution. The direction of propagation and the associated particle motion are considered to be normal to the fibers. It is shown that the average waves in the composite separate into compressional and shear types. General formulae for the complex wave number giving the phase velocity and the damping are obtained. It is shown that these formulae lead to the Hashin-Rosen expressions for the transverse bulk modulus and the lower bound for the transverse rigidity, if the correlation in the positions of the fibers can be ignored. The correlation terms, for exponential correlation, are shown to have a significant effect on the damping property of the composite, especially at high frequencies and concentrations.

Longitudinal shear waves in a fiber-reinforced composite

The propagation of time harmonic longitudinal shear waves in a composite with randomly distributed parallel fibers is studied. Assuming the composite to be statistically uniform, the phase velocity and the damping of the average waves are obtained as functions of the statistical and the mechanical parameters of the system. The theory leads to the well known Hashin and Rosens formula for the axial shear modulus if the correlation in the positions of the fibers are ignored. The correlation terms are shown to have a significant effect on the damping property of the composite, especially at high frequencies and concentrations.

Elastic waves in a multilayered solid due to a dislocation source

Abstract A modified version of the wave number integral approach is applied to the calculation of the motion produced in a multilayered solid by dynamic sources. A new method of pole removal is introduced to facilitate separation of the continuous and the discrete spectral responses of the medium. The well-known numerical difficulties associated with the calculation of the integrands of the continuous spectra and the mode shapes of the discrete spectra are avoided through the use of delta matrices. Special numerical integration schemes are used to calculate the body wave integrals accurately at smaller distances and higher frequencies.

Dynamic elastic moduli of a suspension of imperfectly bonded spheres

An isotropic elastic material containing a random distribution of identical spherical particles of another elastic material is considered. The bonding between the spheres and the matrix is imperfect, so that slip may occur at interfaces when stress is applied to the medium. The shear stresses at the interface is assumed to be proportional to the amount of slip. The velocity and attenuation of the average harmonic elastic waves propagating through such a medium are calculated. The results are valid to the lowest order in frequency for wave lengths long compared with the radius of the sphere. The dynamic elastic moduli are obtained from these results and are compared with available results for welded contact. The variations in the P and S wave velocities for propagation across earthquake faults is discussed.

Interaction of elastic waves with a penny-shaped crack

Abstract The problem of the diffraction of normally incident longitudinal and torsional elastic waves by a penny-shaped crack located in an infinite isotropic elastic medium is considered. The associated integral equations are solved numerically for a range of values of the frequency of the incident waves. The dynamic stress intensity factors are computed as functions of the frequency. The displacement fields on the crack as well as at points far away from the crack are presented graphically.

Multiple scattering of elastic waves in a fiber-reinforced composite

Abstract Propagation of elastic waves in a composite containing randomly distributed parallel fibers is studied in this paper. Both anti-plane (SH waves) and in-plane (P and SV waves) cases are considered. A multiple scattering theory and a statistical averaging procedure are implemented by means of the so-called Generalized Self Consistent Model (GSCM). Multiple scattering in the inhomogeneous medium results in a frequency dependent velocity and attenuation of the waves. The effective phase velocity and attenuation of the coherent waves are calculated for a wide range of frequencies and concentrations. The degree of interaction between the fibers is determined and the average strain calculated in a given inclusion by direct analysis and approximate homogenization is compared. The proposed method recovers three well-known static effective moduli of fiber-reinforced composites in the Rayleigh limit and the results at higher frequencies are physically reasonable.