Estimation of the Length of the Near Zone of a Rectangular Transducer

Self Cite

This paper was prepared upon request from the organizers of the XVIII St. Petersburg conference "Ultrasonic Flaw Detection in Metal Structures. UZDM 2004." The progress made in the theoretical issues of ultrasonic flaw detection over the past 20 years is briefly considered, and some practical issues are discussed. Specific problems that are waiting to be solved are formulated, and the author's opinions about the prospects of developments in ultrasonic flaw detection are presented. The preparation of the paper was much facilitated by book [1], which was published recently. WAVES AND THEIR PROPERTIES New or Rarely Used Types of WavesHead waves are presently well known, but this topic involves concepts that need to be discussed. Longitudinal head waves are waves that propagate along a surface. They are also called surface-longitudinal waves. The term head wave is only widespread among defectoscopists in Russia. Acousticians consider it to be a type of leaky surface waves [2]. Foreign seismoacousticians and defectoscopists call it a creep wave or lateral wave. There are differences between these waves. For example, when these waves propagate near the surface of a convex cylinder, a wave propagating along the surface is called a creep wave, whereas a wave propagating along a bisecant is called a lateral wave. The utilization of head waves for flaw detection was proposed by N.P. Razygraev (TsNIITMASh) in 1974 [3]. Figure 1 shows a system of waves that appear when a longitudinal wave falls from the plastic wedge of a probe to the interface of a metal, e.g., steel, at the first critical angle [4, p. 649]. A longitudinal wave with wavefront P has the highest velocity. From the angle probe, this wave, which may be a head wave creeping along the surface, propagates as a diverging bundle of rays. This explains the dependence shown in Fig. 2 for the amplitude of the echo signal obtained from flat-bottomed holes that have different depths h and probe-reflector distances. Rays at an angle of about 80 ° have the maximum amplitude.When a longitudinal wave propagates along the surface, this wave alone cannot satisfy the boundary condition on the free surface of a test object (TO) since the stresses are equal to zero. At each point of the surface, it generates transverse wave S that propagates at an angle to a surface normal. This angle equals the third critical angle. The condition at the free surface is satisfied due to this transverse wave. The transverse wave carries away energy; as a result, wave C rapidly decays. The wavefront of transverse waves H is an inclined plane. It is this wave H that is called the head wave in acoustics and in the foreign literature on flaw detection, whereas Russian defectoscopists call it a shear side wave. The transverse wave generates longitudinal wave P , which is delayed in time with respect to wave P mentioned above; however, some theoreticians doubt the existence of wave P .The head wave is usually excited and received by means of angle-type send/receive probes with an incidence angle equal t...

Section: The Acoustic Field Of a Probe And Controlling Such A Fieldmentioning

confidence: 99%

Progress in the theory of ultrasonic flaw detection. Problems and prospects

Ermolov¹

2004

Self Cite

“…This method for obtaining solutions was widely used in the work of V.N. Danilov and coworkers [1][2][3].The experience acquired in the exact solving of acoustic wave problems virtually cannot be used for our purpose, since the existence and uniqueness of the solution to the inverse problem have not been demonstrated in the most general case. The methods for obtaining solutions mentioned above are not universal.…”

mentioning

confidence: 98%

“…This method for obtaining solutions was widely used in the work of V.N. Danilov and coworkers [1][2][3].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Models of the formation of ultrasonic signals in image reconstruction problems

Barkhatov

2005

Theoretical concepts of the formation in articles of ultrasonic signals that are used in image reconstruction algorithms are considered. The approximations and limitations of these models are analyzed.Let us consider the issue of what physical regularities responsible for the formation of ultrasonic signals are used in problems of constructing flaw images.A model describing the sounding of articles can be developed on the basis of exact solutions to the wave equation. This model will yield solutions for all effects in wave processes: emission and reflection of waves, wave interference and diffraction phenomena, transformation of modes upon wave reflections, excitation of damped and traveling waves at the interfaces of continuous media, etc. It is known that the wave equation in a solid with boundary conditions (surfaces of flaws and boundaries of articles) yields a great number of solutions for the waves propagating in an article that travel along all possible boundaries, as well as for reemitted waves. In addition, solutions for waves with increasing and declining amplitudes also appear. Solving the problem in an analytical form implies selecting physically achievable wave processes, i.e., a sort of "artificial selection." It often occurs that, when multiple boundary conditions are specified, the wave problem becomes so complex that no analytical solution can be obtained. There is a widespread approach in which partial solutions of the wave equation are used, and a solution to a more complex problem is combined from these. In this case, the ability of an analyst to see constituents of the solution is required, since their incorrect choice can lead to gross errors. This method for obtaining solutions was widely used in the work of V.N. Danilov and coworkers [1][2][3].The experience acquired in the exact solving of acoustic wave problems virtually cannot be used for our purpose, since the existence and uniqueness of the solution to the inverse problem have not been demonstrated in the most general case. The methods for obtaining solutions mentioned above are not universal. The mathematical description applied to each problem is original.Scattering theory is a branch of mathematics in which problems of obtaining information on the inhomogeneity of a medium are solved by using responses to actions of various natures: optical and radioactive radiation, electromagnetic waves, and ultrasonic waves [4][5][6]. A specific feature of this approach is the condition that the size of the region under inspection is many times larger than the typical size of inhomogeneities inside the medium. A scattering operator is introduced that interrelates the wave fluxes arriving at the region under observation and leaving it. This operator contains all the information about the internal structure of the medium. An inhomogeneity is usually represented as a spatial distribution of the medium's density ρ ( x , y , z ) or the velocity of sound. Scattering theory studies asymptotic solutions to the wave equation. The methods of this theory a...

Progress in the theory of ultrasonic flaw detection. Problems and prospects

Ermolov¹

2004

Self Cite

This paper was prepared upon request from the organizers of the XVIII St. Petersburg conference "Ultrasonic Flaw Detection in Metal Structures. UZDM 2004." The progress made in the theoretical issues of ultrasonic flaw detection over the past 20 years is briefly considered, and some practical issues are discussed. Specific problems that are waiting to be solved are formulated, and the author's opinions about the prospects of developments in ultrasonic flaw detection are presented. The preparation of the paper was much facilitated by book [1], which was published recently.RUSSIAN JOURNAL OF NONDESTRUCTIVE TESTING Vol. 40 No. 10 2004 ERMOLOV L.V. Yuozonene [5] reported that the existence of surface-longitudinal waves follows from the characteristic Rayleigh equation, which is known to be used to prove the existence of Rayleigh-type surface waves. However, V.N. Danilov [6] showed this interpretation of the complex roots of the characteristic equation to be wrong. If the Poisson's coefficient is >0.26, the equation has a single root that corresponds to the Rayleigh wave. The root found by Yuozonene is a root of the characteristic equation after it has been squared (which has to be done when solving the equation), but not a root of the initial equation.Shear head waves. In [7, paper no. 1.28], M.V. Asadchaya et al. report that subsurface vertically polarized transverse waves exist and can be used. Their velocity is almost twice as high as that of subsurface longitudinal waves; hence, the depth of the layer that is subject to inspection decreases accordingly. The most efficient method for exciting waves when inspecting metals is to use piezoelectric probes with wedges made of Plexiglas arranged according to the duet scheme. The directional diagram of these waves is analyzed experimentally. Rayleigh SH-waves. The authors of [4, p. 3160] reported that they developed piezoelectric probes for radiating and receiving angular horizontally polarized transverse waves, including ones with a refraction angle of 90 ° . It should be noted that a surface horizontally polarized transverse wave is not a Rayleigh wave, since the latter is a combination of a vertically polarized transverse wave and a longitudinal wave, which together ensure that the stresses at the surface of a solid are equal to zero. In the case of the surface SHwaves under consideration, the longitudinal wave cannot interact with the transverse wave, since the oscillations occur in different planes. Measurement of the Attenuation CoefficientWhen measuring the attenuation of waves, it is necessary to take into account the diffraction attenuation of ultrasonic rays in the probe's acoustic field and the incomplete reflection of ultrasound from the TOprobe boundary upon repeated reflections in the test object. In many cases, these corrections are not taken into account in studies on the measurement of the attenuation coefficient. A detailed procedure for the measurement of the attenuation coefficient including illustrative examples is presented in manual [8]. It is sta...