Determination of the elastic constants of composite materials from ultrasonic group velocity measurement

A non-destructive test procedure based on the ultrasonic point-source/point-receiver (PS/PR) technique is described in this thesis. In the procedure group velocity data determined from the signals detected in an anisotropic composite specimen is processed to recover the matrix of elastic constants of the material.;The composites are modeled as homogeneous, elastically anisotropic materials, whose elastic constants or stiffness are related to the speeds of the elastic waves propagating in them. It is shown that the wave arrivals in the PS/PR waveforms detected in the far field from the source correspond closely to the group velocities of plane waves propagating in the associated directions. Since there is no explicit equation relating the group velocities and the material stiffness, the inverse problem of recovering the elastic constants from the wavespeed data is solved by an algorithm consisting of an inner minimization loop to determine the wave normals and an outer optimization loop to recover the elastic constants. The solution to the forward problem is used to identify the arrivals of specific wave modes in the signals detected for a particular source/receiver geometry. A procedure for processing the arrivals of quasi-transverse waves propagating along directions through cuspidal regions of the wave surface is also developed. To evaluate the operation of the procedure, the sensitivity of the algorithm for recovering the elastic constants from perturbed wavespeed data was determined. Also considered was the use of only quasi-longitudinal wavespeed data to recover a subset of the material's elastic constants.;Experiments were carried out using the PS/PR measurement configuration. The point source was a monopolar force with a step-unloading time-function which was obtained from the fracture of a small-diameter glass capillary on the surface of a specimen. Such a source generates ultrasonic signals that exhibit a broad angular spectrum in the material. The point-receiver was a small-aperture capacitive transducer whose output is proportional to the local vertical displacement of the medium over a broad bandwidth. The processing algorithm was first evaluated using wavespeed data obtained in a single crystal specimen of zinc, a material whose matrix of elastic constants is known. Then a number of composite specimens, including several uni-directional fiber-reinforced and cross-ply laminate composite plates, were tested. For transversely isotropic materials, the full set of elastic constants were recovered. For the orthotropic materials, a partial set of the elastic constants was recovered. The results were compared with those obtained using conventional ultrasonic measurement procedures.