R. B. Mignogna

Real Time Parallel Computation and Visualization of Ultrasonic Pulses in Solids

Parallel processing has changed the way much computational physics is done. Areas such as condensed matter physics, fluid dynamics, and other fields are making use of massively parallel computers to solve immense and important problems in new ways. Simulating wave propagation is another area that has benefited through the use of parallel processing. This is graphically illustrated in this article by various numerical simulations of ultrasonic pulses propagating through solids carried out on a massively parallel computer. These computations are accompanied by visualizations of the resulting wavefield. The calculations and visualizations, together, can be completed in only seconds to several minutes and compare well with experimental data. The computations and parallel processing techniques described should be important in related fields, such as geophysics, acoustics, and mechanics.

Acousto-elastic measurement of stress and stress intensity factors around crack tips

Abstract Acousto-elasticity predicts that the phase velocity of sound waves in a material will be changed slightly by stress. For a slightly orthotropic plate in a state of plane stress, the shear stress σ xy can be calculated from σ xy = (B sin 2 φ) 2m once measurements of the acoustic birefringence B and the angle φ have been made. The birefringence is the difference in phase velocity between SH waves polarized along the ‘fast’ and ‘slow’ acoustic axes, φ is the angle between the acoustic axes in stressed and unstressed state, and m is an acousto-elastic constant for the material. For symmetrical, two-dimensional crack-opening problems, σ xy can be expressed as a series expansion of stress functions, each of which satisfies the equilibrium equation. The coefficients in the expansion allow the appropriate boundary conditions to be satisfied. The stress intensity factor K 1 is the coefficient of the leading term in the series. Values of σ xy and K 1 for an ASTM standard test specimen made of 2024 aluminium were acousto-elastically determined. These were compared with those obtained from a similar photoelastic specimen. Good agreement was obtained for both σ xy and K 1 .

Texture monitoring in aluminium alloys: a comparison of ultrasonic and neutron diffraction measurement

Abstract Theories have been developed by several authors to calculate velocities of bulk, guided and surface waves in polycrystalline aggregates of cubic metals. These theories can be used to predict the effect of texture on ultrasonic velocity in rolled aluminium and steel sheet, provided that the effects of dislocations, second-phase particles, inclusions, etc. can be ignored. The theories predict that ultrasonic velocities will will be influenced by three orientation distribution coefficients (ODCs). The ODCs are quantitative measures of the texture in the material; in general, more than three ODC are required to completely characterize texture. Neutron diffraction pole figures can also be used to obtain the ODCs. Neutron diffraction measurements of ODC can be compared against ultrasonic values to obtain an independent check on the validity of the ultrasonic theories. In this work, the texture of thin sheets of a commercial grade aluminium alloy was measured with both ultrasonics and neutron diffraction. Several ultrasonic techniques were employed, using bulk, guided and surface waves. Both piezoelectric and electromagnetic-acoustic transducers (EMATs) were used. Quantitative measurements of texture made with different ultrasonic techniques were in good agreement. These ultrasonic measurements also agreed with neutron diffraction measurements, indicating that the dominant features of the effect of texture on wave propagation have been modelled with sufficient accuracy. The extension of the ultrasonic technique to on-line (production) monitoring of texture is considered. In particular, it appears that EMATs are the transducer of choice for on-line texture measurement of rolled sheet, since they are non-contacting.

A comparison of two theories of acoustoelasticity

Abstract The presence of a plane stress field causes small changes in the phase velocities of orthogonally polarized SH waves. The (small) difference in phase velocities (birefringence) can be used for non-destructive stress measurement. However, material anisotropy can affect phase velocity to the same extent as stress. Two theories have been developed which account for the effect of both stress and anisotropy. The theory of Iwashimizu and Kubomura assumes isotropy in the third-order elastic moduli and anisotropy in second-order moduli. A different approach was taken by Okada, who assumed the existence of a matrix analogous to the index of the refraction matrix in optics. In this paper, we generalize the theory of Iwashimizu and Kubomura by retaining anisotropy in third-order moduli. We show how Okadas theory can be made to agree with this more general theory. We also compare the predictions of the various theories with birefringence data obtained from uniaxial tension tests on 2024-T351 aluminium specimens. Both the Okada theory and the theory of Iwashimizu and Kubomura gave good agreement with experiment.

Phase and group velocity considerations for dynamic modulus measurement in anisotropic media

Abstract In anisotropic media, the direction of energy propagation does not necessarily coincide with the wave normal, i.e. the energy flux vector does not coincide with the wave normal. Since, experimentally, one measures group velocity not phase velocity, one must therefore be careful in interpreting ultrasonic wave speed measurements in anisotropic media. This is of particular importance in elastic property reconstruction where acoustic velocity measurements are used as the basis for determining anisotropic material properties. In this work, the consequences of energy flux deviation from the wave normal are considered for typical experimental geometries. Particular attention is devoted to developing appropriate relationships between the phase velocity and ultrasonic transit time measurements, as these relations are most useful for elastic property reconstruction. In all the cases considered, it is shown that the phase velocity can be directly calculated from appropriate time delay measurements.

Dynamic full-field visualization of ultrasound interacting with material defects: experiment and simulation

Full-field visualization of ultrasound interacting with a material defect allows the dynamic stress (strain) field to be investigated. Many real materials and structures contain defects such as voids, inclusions and cracks throughout their volume which affect the ultrasound propagating past or through the defects. Understanding the interaction of the ultrasound with these defects is critical to interpreting the received signals in an ultrasonic test. A numerical simulation has been developed based on parallel computer processing. The importance of the numerical simulation is in its capability to model very complex geometries and material property variation. However, validation and fine tuning require comparison of the model to experiment. An experimental apparatus permitting visualization and digitization of ultrasound in transparent media is used to obtain images that are compared to images generated using the parallel simulation. The experimental apparatus is based on optical birefringence, i.e. photoelasticity. A description of the experimental apparatus and the model are given, along with images obtained from a glass matrix with a void and two different solid inclusions. The described comparisons appear to be quite good, but are qualitative at the current time. Quantitative comparison of experiment to simulation is the goal of this work.

Use of a transient wave propagation code for 3D simulation of cw radiated transducer fields

In order to compute continuous wave (cw) ultrasonic wave fields in complex media, where analytical approaches are extremely difficult, numerical simulations on large computational grids must be employed. The use of a time domain code, normally used for transient wave propagation in heterogeneous media, is used here as a tool to simulate continuous wave fields. As a starting point, the case of the three-dimensional pressure field radiated from a circular aperture in water is computed. These numerical simulations are performed on a massively parallel computer and compared with experiment and known theory. The computations are performed on very large three-dimensional grids that span the near to the far field. As a trial case, a numerical computation of the radiated field from a continuous-wave excited transducer in a baffle is compared with an analytical evaluation using the Rayleigh surface integral and experiment. In addition, results are presented that show the effect of a small defect placed in the beam. To do this, a small cylindrical copper scatterer was placed in the near field, in both the computation and an accompanying experiment. These cases are done in preparation for using the same approach for computing cw fields radiated from a transducer into complex heterogeneous media.

Computational and experimental investigation of the fields generated by a 1-3 piezocomposite transducer.

Large-scale three-dimensional numerical simulations using the finite-difference time domain technique are used to compute the continuous wave fields associated with a composite transducer. The interior of the transducer is made of a periodic array of square rods. This lattice causes elastic wave Bragg diffraction similar to electrons in a periodic lattice. A low frequency mode shape is assumed for the rods. This prescribed motion includes longitudinal and transverse components. It is shown that the transverse motion in the rod gives rise to shear waves causing standing waves (lateral resonances) in the polymer regions. This is also confirmed by experimental results presented here and other independent analytical and experimental work. The full-scale numerical simulation is performed on a large parallel supercomputer and permits modeling of not only the composite transducer but the radiated pressure from near to far field. In addition, cover plates and edge effects are included, unlike analytical treatments. Although only mechanical effects are included, the wave propagation approach captures many essential features.

Ultrasonic Texture Analysis for Polycrystalline Aggregates of Cubic Materials Displaying Orthotropic Symmetry

The study of the applications of the acoustoelastic effect, i.e. the stress-dependence of the propagation velocity of ultrasonic waves in deformed elastic media, has undergone considerable progress in recent years.1 Techniques for the determination of applied and residual stresses have been proposed both for bulk2–5 and for surface6–9 ultrasonic waves. However, for the practical application of these techniques to fabricated materials, the difficulty of separating the often competing effects of stress and texture remains a vexing problem.

The Use of Ultrasonics for Texture Monitoring in Aluminum Alloys

Many alloys of common metals (such as aluminum and steel) are polycrystalline aggregates having preferred orientation (texture) of the single crystals making up the aggregate. Texture often affects mechanical properties, such as response of material to deep drawing which occurs in the manufacture of aluminum cans.