This paper presents the solution of the materials characterization problem in which the elastic constants of an anisotropic material are determined from ultrasonic wavespeed measurements made in nonprincipal directions of a specimen. The ultrasonic waves were generated via the point-source/point-receiver technique using a pulsed laser as a source and a miniature, point-like transducer as a receiver. Data were acquired during a scan of the source along one of the principal acoustic axes of symmetry of the material. In each waveform the arrivals of the quasi-longitudinal and the two quasi-shear bulk modes were measured and the elastic constants of the material were then recovered using an optimization algorithm. Experimental results are presented for a transversely isotropic, unidirectional fiberglass/polyester and a single crystal specimen of silicon. It was found that the nonlinear fit between the measured and the recovered longitudinal slowness values is excellent. Some discrepancies are observed in the data for the two shear modes. These are shown to be related to the complexity of the detected signals.

In this paper is described a method by which a pointlike source of acoustic emission can be located in an anisotropic plate. The method is applicable for a source in an anisotropic solid of arbitrary symmetry as long as the principal acoustic axes of the material are known a priori. It is shown that from the time-of-flight differences of particular features in the waveforms detected by any pair of sensors, a set of nonlinear transcendental equations can be formed in which the coefficient of each term in the equations is related to the time-of-flight differences, the geometrical parameters of the array, and the wave speeds of quasiwaves propagating along each source/receiver path. For waves propagating in principal planes, the analytical expressions for the wave speed values are used. Extension to nonprincipal planes is obtained by computing the eigenvalues of the Green-Christoffel tensor. Determination of the optimum location of the source is found by minimizing the Euclidean functional associated with the set of transcendental nonlinear equations. The results obtained with numerical simulations of twoand three-dimensional source-location problems are presented to illustrate several characteristic features of the solution. Also shown are the results of two-dimensional sourcelocation measurements made on specimens of a unidirectional fiberglass reinforced composite material. The results demonstrate the efficiency ,of the algorithm in locating a source of emission.

No abstract

The elastodynamic response of a thick plate, with the axis of transverse isotropy normal to the plate surface, is calculated by double numerical inverse transforms, a method particularly well-suited for calculations of responses in the near field of layered structures. Applications of these calculations include point-source/point-receiver ultrasonics, quantitative acoustic emission measurements, and seismology. The singularities of the integrand are eliminated by the introduction of a small, but nonzero, imaginary part to the frequency. We discuss issues of numerical efficiency and accuracy in the evaluation of the resulting integrals. The method can be generalized to calculate the responses in materials of more general symmetry, in viscoelastic materials and to include the effects of finite aperture sources and receivers. The calculated responses are compared to those measured in a single crystal specimen of zinc.

Analytical and optimization methods of determining all elastic constants of elastically anisotropic solids from the group velocities measured in various directions in the symmetry planes are described. The group velocities in various directions of the specimen are measured, using broadband pointlike and line-type sources in combination with pointlike detectors, and changing a source-to-detector orientation. The mixed index elastic constants of the specimen are determined using analytic formulas that relate the elastic constants to the group velocity in an arbitrary direction on the symmetry plane. It is demonstrated that given the numerous group velocity data, one can efficiently determine the elastic constants by first converting them into phase velocity data and then applying the least-squares optimization methods to the phase velocity data. Examples are provided with specimens of transversely isotropic zinc, cubic silicon, and orthotropic fiber-reinforced poly ether ether kethon.