R. B. Thompson

The effects of focusing and refraction on Gaussian ultrasonic beams

A scalar theory of the propagation of Gaussian ultrasonic beams through lenses and interfaces is presented. For radiation into a fluid, the Fresnel approximation is employed to derive the laws of propagation of Guassian beams (previously employed in the analysis of coherent optical systems). These are then generalized to situations commonly found in nondestructive evaluation by treating the effects of propagation through lenses and through curved interfaces at oblique incidence. A numerical example illustrates the ease with which insight into diffraction phenomena for complex geometries can be gained by this approach. The limitations imposed on the theory by aberrations and the scalar assumption are discussed, and the relationship of the Gaussian theory to the radiation of piston transducers is explored.

Relative anisotropies of plane waves and guided modes in thin orthorhombic plates: implication for texture characterization

Abstract The angular dependences of the long wavelength velocities of S0 and SH0 modes of orthorhombic (orthotropic) plates are compared to those of the velocities of corresponding plane waves. To first order in the anisotropy, many of the phenomena are as expected. The absolute velocities and anisotropy of the SH0 plate modes are identical to those for plane SH waves and the absolute velocities of the S0 modes propagating along symmetry axes are reduced from the longitudinal plane wave velocities by an amount explained by the change from the plane strain to the plane stress condition. However, for certain classes of materials such as metal polycrystals, the anisotropy of the S0 mode can be substantially different from that of the longitudinal plane waves. This effect is explained through an expansion of the crystallite orientation distribution function in terms of generalized spherical harmonics. Implications of the results for the ultrasonic measurement of preferred grain orientation (texture) in polycrystals is indicated.

A comparison of ultrasonic and X-ray determinations of texture in thin Cu and Al plates

Ultrasonic techniques for determining the orientation distribution coefficients (ODC’s), which define the preferred orientation of polycrystals, are discussed. The theory is reviewed for thin plates of cubic crystallites for which the texture information is deduced from the velocity anisotropy of guided modes. Experimental ultrasonic and X-ray predictions of the ODC’s of up to an order of 4 are compared for plates of commercially pure electrolytic tough pitch (ETP) copper and aluminum. ForW420 andW440 in both samples andW400 in copper, the predictions agree to |ΔW|∼10-3. However, considerably greater differences are reported for the predictions ofW400 in aluminum. Interpretation of these comparisons is assisted by a detailed error analysis for the ultrasonic technique and reference to a number of other recent comparisons of ultrasonic and neutron or X-ray predictions of ODC’s Possible applications of the ultrasonic technique during the production and forming of metal sheet are indicated.

The interaction of ultrasound with contacting asperities: Applications to crack closure and fatigue crack growth

The partial contact of two rough fatigue crack surfaces leads to transmission, reflection, diffraction, and mode conversion of an acoustic signal at those contacts. This paper reviews recent experimental and theoretical efforts to understand and quantify such contact on actual fatigue cracks in greater detail. It is shown that the size and density of individual contacts, or asperities, can be estimated from acoustic measurements. Furthermore, it is shown that this information is useful to provide the static stress across a partially closed crack as well as the “effective” stress intensity range which activates fatigue crack propagation.

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.

Microstructure‐independent acoustoelastic measurement of stress

Measurements are reported of the velocities of horizontally polarized shear waves (fundamental mode) propagating in the plane of aluminum plates under tensile loads applied parallel to the rolling direction. In agreement with the predictions of previous theories, the applied stress is found to be predicted by the expression 2C(ΔV/V), where C is the appropriate second‐order shear elastic constant and ΔV/V is the fractional difference in velocities of waves propagating parallel and perpendicular to the load. The data show that, whereas the individual velocities are strongly influenced by microstructure, the stress prediction based on their difference is not. Included are results illustrating the effects of preferred grain orientation and plastic deformation.

Crack tip shielding by asperity contact as determined by acoustic measurements

Abstract Asperity contact along the fracture surface of a crack is one of the mechanisms of crack closure. This contact shields the crack tip, in part, from the externally applied driving force. We have now succeeded in using information from acoustic transmission and diffraction experiments, obtained under plane strain conditions, to determine the size and density of the contacting asperities in the closure region. We have also succeeded in estimating values for the static stress across a partially closed crack as well as the stress intensity factor,KI (local), which shields the crack tip below the stress intensity factor KIclosure at which the first contact during unloading occurs. It is suggested that when crack closure has an important influence on crack propagation, the shielding stress intensity factor provides information that can be used to estimate the fatigue crack propagation rate.

Quantitative characterization of flaws near a surface using inverse born approximation

Quantitative reconstruction of volumetric flaws near a surface of an elastic solid has been carried out experimentally by analyzing the scattered ultrasonic waves. The inverse Born approximation (developed for flaws in bulk materials) was tested for the first time in the determination of the size, shape, and orientation of near-surface flaws. We have studied spherical solid inclusions at various depths below the surface. In addition we examined an approximately 2:1 prolate spheroidal inclusion which was located one major axis below the surface. The determination of the flaws size, shape, and orientation in terms of an equivalent ellipsoid is realized by performing nonlinear least-squares iteration of the one-dimensional Born inversion results obtained at various scattering directions within a finite aperture. The reconstruction is in good agreement with the actual parameters of the flaw.

Ultrasonic Measurement of Formability in Thin Ferritic Steel Sheet

The formability of rolled sheet metal is strongly influenced by the texture of the polycrystalline metal. For steel sheet, it is desirable to have high drawability to make automobile body parts, etc. In addition, material homogeneity is desired; that is, material cut from different parts of a rolled sheet should have the same plastic deformation when subjected to deep drawing.

Ultrasonic measurements of crack tip shielding by closure

Abstract During fatigue, an existing crack closes partially owing to the compressive stresses set up by the deformed material. It is well established that this crack closure can have pronounced effects on the rate of crack propagation and thus on fatigue life. The present paper deals mainly with our recent efforts which have been concerned with the characterization of crack closure acoustically and the determination of the mechanical effects of closure on the crack tip. Results indicate that closure occurs by asperity contact along the fracture surface and it is this asperity contact which shields the crack tip, in part, from the externally applied driving force on the crack tip. Consequences of this research on the effective stress intensity range and thus on the driving force on a crack will be discussed.