Ut testing section 2 physics of ultrasound by charlie Chong

Section 2: Physics of Ultrasound

Content: Section 2: Physics of Ultrasound 2.0: Ultrasound Formula 2.1: Wave Propagation 2.2: Modes of Sound Wave Propagation 2.3: Sound Propagation in Elastic Materials 2.4: Properties of Acoustic Plane Wave 2.5: Wavelength and Defect Detection 2.6: Attenuation of Sound Waves 2.7: Acoustic Impedance 2.8: Reflection and Transmission Coefficients (Pressure) 2.9: Refraction and Snell's Law 2.10: Mode Conversion 2.11: Signal-to-Noise Ratio 2.12: The Sound Fields- Dead / Fresnel & Fraunhofer Zones 2.13: Inverse Square Rule/ Inverse Rule 2.14: Resonance 2.15 Measurement of Sound 2.16 Practice Makes Perfect

2.0: Ultrasound Formula

http://www.ndt-ed.org/GeneralResources/Calculator/calculator.htm

Ultrasonic Formula

Parameters of Ultrasonic Waves

2.1: Wave Propagation Ultrasonic testing is based on time-varying deformations or vibrations in materials, which is generally referred to as acoustics. All material substances are comprised of atoms, which may be forced into vibration motion about their equilibrium positions. Many different patterns of vibration motion exist at the atomic level, however, most are irrelevant to acoustics and ultrasonic testing. Acoustics is focused on particles that contain many atoms that move in unison to produce a mechanical wave. When a material is not stressed in tension or compression beyond its elastic limit, its individual particles perform elastic oscillations. When the particles of a medium are displaced from their equilibrium positions, internal (electrostatic) restoration forces arise. It is these elastic restoring forces between particles, combined with inertia of the particles, that leads to the oscillatory motions of the medium. Keywords: â&#x2013; internal (electrostatic) restoration forces â&#x2013; inertia of the particles

Acoustic Spectrum

Acoustic Wave â&#x20AC;&#x201C; Node and Anti-Node The points where the two waves constantly cancel each other are called nodes, and the points of maximum amplitude between them, antinodes.

http://www.physicsclassroom.com/Class/waves/u10l4c.cfm http://www.physicsclassroom.com/Class/waves/h4.gif

Acoustic Wave â&#x20AC;&#x201C; Node and Anti-Node Formation of a standing wave by two waves from opposite directions

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/standw.html

Q151 A point, line or surface of a vibration body marked by absolute or relative freedom from vibratory motion (momentarily?) is referred to as: a) b) c) d)

a node an antinode rarefaction compression

2.2: Modes of Sound Wave Propagation 2.2.1 Modes of Ultrasound In solids, sound waves can propagate in four principle modes that are based on the way the particles oscillate. Sound can propagate as;    

longitudinal waves, shear waves, surface waves, and in thin materials as plate waves.

Longitudinal and shear waves are the two modes of propagation most widely used in ultrasonic testing. The particle movement responsible for the propagation of longitudinal and shear waves is illustrated below.

2.2.2

Propagation & Polarization Vectors

ď Ž Propagation Vector- The direction of wave propagation ď Ž Polarization Vector- The direction of particle motion

Longitudinal and shear waves

Longitudinal and shear waves- Defined the Vectors

Longitudinal and shear waves

2.2.3 Longitudinal Wave Also Knows as:    

longitudinal waves, pressure wave compressional waves. density waves

can be generated in (1) liquids, as well as (2) solids

http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Graphics/Flash/longitudinal.swf

In longitudinal waves, the oscillations occur in the longitudinal direction or the direction of wave propagation. Since compressional and dilational forces are active in these waves, they are also called pressure or compressional waves. They are also sometimes called density waves because their particle density fluctuates as they move. Compression waves can be generated in liquids, as well as solids because the energy travels through the atomic structure by a series of compressions and expansion (rarefaction) movements.

Longitudinal wave: Longitudinal waves (L-Waves) compress and decompress the material in the direction of motion, much like sound waves in air.

Longitudinal Wave

2.2.4

Shear waves (S-Waves)

In air, sound travels by the compression and rarefaction of air molecules in the direction of travel. However, in solids, molecules can support vibrations in other directions, hence, a number of different types of sound waves are possible. Waves can be characterized in space by oscillatory patterns that are capable of maintaining their shape and propagating in a stable manner. The propagation of waves is often described in terms of what are called â&#x20AC;&#x153;wave modes.â&#x20AC;? As mentioned previously, longitudinal and transverse (shear) waves are most often used in ultrasonic inspection. However, at surfaces and interfaces, various types of elliptical or complex vibrations of the particles make other waves possible. Some of these wave modes such as (1) Rayleigh and (2) Lamb waves are also useful for ultrasonic inspection. Keywords: Compression Rarefaction

Shear waves vibrate particles at right angles compared to the motion of the ultrasonic wave. The velocity of shear waves through a material is approximately half that of the longitudinal waves. The angle in which the ultrasonic wave enters the material determines whether longitudinal, shear, or both waves are produced.

Shear waves

In the transverse or shear wave, the particles oscillate at a right angle or transverse to the direction of propagation. Shear waves require an acoustically solid material for effective propagation, and therefore, are not effectively propagated in materials such as liquids or gasses. Shear waves are relatively weak when compared to longitudinal waves. In fact, shear waves are usually generated in materials using some of the energy from longitudinal waves.

http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Graphics/Flash/transverse.swf

Q10: For a shear wave travelling from steel to water incident on the boundary at 10 degrees will give a refracted shear wave in water with an angle of: A. B. C. D.

0 degrees 5 degrees 20 degrees none of the above

2.2.5

Rayleigh Characteristics

Rayleigh waves are a type of surface wave that travel near the surface of solids. Rayleigh waves include both longitudinal and transverse motions that decrease exponentially in amplitude as distance from the surface increases. There is a phase difference between these component motions. In isotropic solids these waves cause the surface particles to move in ellipses in planes normal to the surface and parallel to the direction of propagation – the major axis of the ellipse is vertical. At the surface and at shallow depths this motion is retrograde 逆行, that is the in-plane motion of a particle is counterclockwise when the wave travels from left to right. http://en.wikipedia.org/wiki/Rayleigh_wave

Rayleigh waves are a type of surface acoustic wave that travel on solids. They can be produced in materials in many ways, such as by a localized impact or by piezo-electric transduction, and are frequently used in nondestructive testing for detecting defects. They are part of the seismic waves that are produced on the Earth by earthquakes. When guided in layers they are referred to as Lamb waves, Rayleighâ&#x20AC;&#x201C;Lamb waves, or generalized Rayleigh waves.

Rayleigh waves

Q29: The longitudinal wave incident angle which results in formation of a Rayleigh wave is called: A. B. C. D.

Normal incidence The first critical angle The second critical angle Any angle above the first critical angle

Surface (or Rayleigh) waves travel the surface of a relatively thick solid material penetrating to a depth of one wavelength. Surface waves combine both (1) a longitudinal and (2) transverse motion to create an elliptic orbit motion as shown in the image and animation below.

http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Graphics/Flash/rayleigh.swf

The major axis of the ellipse is perpendicular to the surface of the solid. As the depth of an individual atom from the surface increases the width of its elliptical motion decreases. Surface waves are generated when a longitudinal wave intersects a surface near the second critical angle and they travel at a velocity between .87 and .95 of a shear wave. Rayleigh waves are useful because they are very sensitive to surface defects (and other surface features) and they follow the surface around curves. Because of this, Rayleigh waves can be used to inspect areas that other waves might have difficulty reaching. Wave velocity:  Longitudinal wave velocity =1v,  The velocity of shear waves through a material is approximately half that of the longitudinal waves, (≈0.5v)  Surface waves are generated when a longitudinal wave intersects a surface near the second critical angle and they travel at a velocity between .87 and .95 of a shear wave. ≈(0.87~0.95)x0.5v

The major axis of the ellipse is perpendicular to the surface of the solid.

Surface wave

Surface wave or Rayleigh wave are formed when shear waves refract to 90. The whip-like particle vibration of the shear wave is converted into elliptical motion by the particle changing direction at the interface with the surface. The wave are not often used in industrial NDT although they do have some application in aerospace industry. Their mode of propagation is elliptical along the surface of material, penetrating to a depth of one wavelength. They will follow the contour of the surface and they travel at approximately 90% of the velocity of the shear waves. Depth of penetration of about one wavelength

Direction of wave propagation

Surface wave has the ability to follow surface contour, until it meet a sharp change i.e. a surface crack/seam/lap. However the surface waves could be easily completely absorbed by excess couplant of simply touching the part ahead of the waves.

Transducer Wedge

Surface discontinuity

Specimen

Surface wave - Following Contour

Surface wave

Surface wave – One wavelength deep

Rayleigh Wave

http://web.ics.purdue.edu/~braile/edumod/waves/Rwave_files/image001.gif

Love Wave

http://web.ics.purdue.edu/~braile/edumod/waves/Lwave_files/image001.gif

Love Wave

Other Reading: Rayleigh Waves Surface waves (Rayleigh waves) are another type of ultrasonic wave used in the inspection of materials. These waves travel along the flat or curved surface of relatively thick solid parts. For the propagation of waves of this type, the waves must be traveling along an interface bounded on one side by the strong elastic forces of a solid and on the other side by the practically negligible elastic forces between gas molecules. Surface waves leak energy into liquid couplants and do not exist for any significant distance along the surface of a solid immersed in a liquid, unless the liquid covers the solid surface only as a very thin film. Surface waves are subject to attenuation in a given material, as are longitudinal or transverse waves. They have a velocity approximately 90% of the transverse wave velocity in the same material. The region within which these waves propagate with effective energy is not much thicker than about one wavelength beneath the surface of the metal.

At this depth, wave energy is about 4% of the wave energy at the surface, and the amplitude of oscillation decreases sharply to a negligible value at greater depths. Surface waves follow contoured surfaces. For example, surface waves traveling on the top surface of a metal block are reflected from a sharp edge, but if the edge is rounded off, the waves continue down the side face and are reflected at the lower edge, returning to the sending point. Surface waves will travel completely around a cube if all edges of the cube are rounded off. Surface waves can be used to inspect parts that have complex contours.

Q110: What kind of wave mode travel at a velocity slightly below the shear wave and their modes of propagation are both longitudinal and transverse with respect to the surface? a) b) c) d)

Rayleigh wave Transverse wave L-wave Longitudinal wave

Q: Which of the following modes of vibration exhibits the shortest wavelength at a given frequency and in a given material? A. B. C. D.

longitudinal wave compression wave shear wave surface wave

2.2.6

Lamb Wave:

Lamb waves propagate in solid plates. They are elastic waves whose particle motion lies in the plane that contains the direction of wave propagation and the plate normal (the direction perpendicular to the plate). In 1917, the english mathematician horace lamb published his classic analysis and description of acoustic waves of this type. Their properties turned out to be quite complex. An infinite medium supports just two wave modes traveling at unique velocities; but plates support two infinite sets of lamb wave modes, whose velocities depend on the relationship between wavelength and plate thickness.

Since the 1990s, the understanding and utilization of lamb waves has advanced greatly, thanks to the rapid increase in the availability of computing power. Lamb's theoretical formulations have found substantial practical application, especially in the field of nondestructive testing. The term rayleighâ&#x20AC;&#x201C;lamb waves embraces the rayleigh wave, a type of wave that propagates along a single surface. Both rayleigh and lamb waves are constrained by the elastic properties of the surface(s) that guide them. http://en.wikipedia.org/wiki/Lamb_wave http://pediaview.com/openpedia/Lamb_waves

Types of Wave

New!  Plate wave- Love  Stoneley wave  Sezawa

Plate or Lamb waves are the most commonly used plate waves in NDT. Lamb waves are complex vibrational waves that propagate parallel to the test surface throughout the thickness of the material. Propagation of Lamb waves depends on the density and the elastic material properties of a component. They are also influenced a great deal by the test frequency and material thickness. Lamb waves are generated at an incident angle in which the parallel component of the velocity of the wave in the source is equal to the velocity of the wave in the test material. Lamb waves will travel several meters in steel and so are useful to scan plate, wire, and tubes. Lamb wave influenced by: (Dispersive Wave) ■ ■ ■ ■

Density Elastic material properties Frequencies Material thickness

Plate or Lamb waves are similar to surface waves except they can only be generated in materials a few wavelengths thick.

http://www.ndt.net/ndtaz/files/lamb_a.gif

Plate wave or Lamb wave are formed by the introduction of surface wave into a thin material. They are a combination of (1) compression and surface or (2) shear and surface waves causing the plate material to flex by totally saturating the material. The two types of plate waves:

With Lamb waves, a number of modes of particle vibration are possible, but the two most common are symmetrical and asymmetrical. The complex motion of the particles is similar to the elliptical orbits for surface waves. Symmetrical Lamb waves move in a symmetrical fashion about the median plane of the plate. This is sometimes called the extensional mode because the wave is “stretching and compressing” the plate in the wave motion direction. Wave motion in the symmetrical mode is most efficiently produced when the exciting force is parallel to the plate. The asymmetrical Lamb wave mode is often called the “flexural mode” because a large portion of the motion moves in a normal direction to the plate, and a little motion occurs in the direction parallel to the plate. In this mode, the body of the plate bends as the two surfaces move in the same direction. The generation of waves using both piezoelectric transducers and electromagnetic acoustic transducers (EMATs) are discussed in later sections. Keywords: Symmetrical = extensional mode Asymmetrical = flexural mode

When guided in layers they are referred to as Lamb waves, Rayleighâ&#x20AC;&#x201C;Lamb waves, or generalized Rayleigh waves. Lamb waves â&#x20AC;&#x201C; 2 modes

Symmetrical = extensional mode Asymmetrical = flexural mode

Symmetrical = extensional mode

Other Reading: Lamb Wave Lamb waves, also known as plate waves, are another type of ultrasonic wave used in the nondestructive inspection of materials. Lamb waves are propagated in plates (made of composites or metals) only a few wavelengths thick. A Lamb wave consists of a complex vibration that occurs throughout the thickness of the material. The propagation characteristics of Lamb waves depend on the density, elastic properties, and structure of the material as well as the thickness of the test piece and the frequency. Their behavior in general resembles that observed in the transmission of electromagnetic waves through waveguides. There are two basic forms of Lamb waves: ď Ž Symmetrical, or dilatational ď Ž Asymmetrical, or bending

The form is determined by whether the particle motion is symmetrical or asymmetrical with respect to the neutral axis of the test piece. Each form is further subdivided into several modes having different velocities, which can be controlled by the angle at which the waves enter the test piece. Theoretically, there are an infinite number of specific velocities at which Lamb waves can travel in a given material. Within a given plate, the specific velocities for Lamb waves are complex functions of plate thickness and frequency. In symmetrical (dilatational) Lamb waves, there is a compressional (longitudinal) particle displacement along the neutral axis of the plate and an elliptical particle displacement on each surface (Fig. 4a). In asymmetrical (bending) Lamb waves, there is a shear (transverse) particle displacement along the neutral axis of the plate and an elliptical particle displacement on each surface (Fig. 4b). The ratio of the major to minor axes of the ellipse is a function of the material in which the wave is being propagated.

Fig. 4 Diagram of the basic patterns of (a) symmetrical (dilatational) and (b) asymmetrical (bending) Lamb waves. The wavelength, , is the distance corresponding to one complete cycle.

Q1: The wave mode that has multiple or varying wave velocities is: A. B. C. D.

Longitudinal waves Shear waves Transverse waves Lamb waves

2.2.7

Dispersive Wave:

Wave modes such as those found in Lamb wave have a velocity of propagation dependent upon the operating frequency, sample thickness and elastic moduli. They are dispersive (velocity change with frequency) in that pulses transmitted in these mode tend to become stretched or dispersed.

Dispersion refers to the fact that in a real medium such as water, air, or glass, a wave traveling through that medium will have a velocity that depends upon its frequency. Dispersion occurs for any form of wave, acoustic, electromagnetic, electronic, even quantum mechanical. Dispersion is responsible for a prism being able to resolve light into colors and defines the maximum frequency of broadband pulses one can send down an optical fiber or through a copper wire. Dispersion affects wave and swell forecasts at sea and influences the design of sound equipment. Dispersion is a physical property of the medium and can combine with other properties to yield very strange results. For example, in the propagation of light in an optical fiber, the glass introduces dispersion and separates the wavelengths of light according to frequency, however if the light is intense enough, it can interact with the electrons in the material changing its refractive index. The combination of dispersion and index change can cancel each other leading to a wave that can propagate indefinitely maintaining a constant shape. Such a wave has been termed a soliton. http://www.rpi.edu/dept/chem-eng/WWW/faculty/plawsky/Comsol%20Modules/DispersiveWave/DispersiveWave.html

Plate or Lamb waves are generated at an incident angle in which the parallel component of the velocity of the wave in the source is equal to the velocity of the wave in the test material.

Thickness Limitation: One can not generate shear / surface (or Lamb?) wave on a plate that is thinner than Â˝ the wavelength.

2.3: Sound Propagation in Elastic Materials In the previous pages, it was pointed out that sound waves propagate due to the vibrations or oscillatory motions of particles within a material. An ultrasonic wave may be visualized as an infinite number of oscillating masses or particles connected by means of elastic springs. Each individual particle is influenced by the motion of its nearest neighbor and both (1) inertial and (2) elastic restoring forces act upon each particle. A mass on a spring has a single resonant frequency determined by its spring constant k and its mass m. The spring constant is the restoring force of a spring per unit of length. Within the elastic limit of any material, there is a linear relationship between the displacement of a particle and the force attempting to restore the particle to its equilibrium position. This linear dependency is described by Hooke's Law.

Spring model- A mass on a spring has a single resonant frequency determined by its spring constant k and its mass m.

In terms of the spring model, Hooke's Law says that the restoring force due to a spring is proportional to the length that the spring is stretched, and acts in the opposite direction. Mathematically, Hooke's Law is written as F =-kx, where F is the force, k is the spring constant, and x is the amount of particle displacement. Hooke's law is represented graphically it the bottom. Please note that the spring is applying a force to the particle that is equal and opposite to the force pulling down on the particle.

Elastic Model

Elastic Model / Longitudinal Wave

Elastic Model / Shear Wave

The Speed of Sound Hooke's Law, when used along with Newton's Second Law, can explain a few things about the speed of sound. The speed of sound within a material is a function of the properties of the material and is independent of the amplitude of the sound wave. Newton's Second Law says that the force applied to a particle will be balanced by the particle's mass and the acceleration of the particle. Mathematically, Newton's Second Law is written as F = ma. Hooke's Law then says that this force will be balanced by a force in the opposite direction that is dependent on the amount of displacement and the spring constant (F = -kx). Therefore, since the applied force and the restoring force are equal, ma = -kx can be written. The negative sign indicates that the force is in the opposite direction.

F= ma = -kx

Since the mass m and the spring constant k are constants for any given material, it can be seen that the acceleration a and the displacement x are the only variables. It can also be seen that they are directly proportional. For instance, if the displacement of the particle increases, so does its acceleration. It turns out that the time that it takes a particle to move and return to its equilibrium position is independent of the force applied. So, within a given material, sound always travels at the same speed no matter how much force is applied when other variables, such as temperature, are held constant.

aâ&#x2C6;?x

What properties of material affect its speed of sound? Of course, sound does travel at different speeds in different materials. This is because the (1) mass of the atomic particles and the (2) spring constants are different for different materials. The mass of the particles is related to the density of the material, and the spring constant is related to the elastic constants of a material. The general relationship between the speed of sound in a solid and its density and elastic constants is given by the following equation:

Elastic constant â&#x2020;&#x2019; spring constants

Density â&#x2020;&#x2019; mass of the atomic particles

Where V is the speed of sound, C is the elastic constant, and p is the material density. This equation may take a number of different forms depending on the type of wave (longitudinal or shear) and which of the elastic constants that are used. The typical elastic constants of a materials include:  Young's Modulus, E: a proportionality constant between uniaxial stress and strain.  Poisson's Ratio, n: the ratio of radial strain to axial strain  Bulk modulus, K: a measure of the incompressibility of a body subjected to hydrostatic pressure.  Shear Modulus, G: also called rigidity, a measure of a substance's resistance to shear.  Lame's Constants, l and m: material constants that are derived from Young's Modulus and Poisson's Ratio.

Q163 Acoustic velocity of materials are primary due to the material's: a) b) c) d)

density elasticity both a and b acoustic impedance

Q50: The principle attributes that determine the differences in ultrasonic velocities among materials are: A. B. C. D.

Frequency and wavelength Thickness and travel time Elasticity and density Chemistry and permeability

When calculating the velocity of a longitudinal wave, Young's Modulus and Poisson's Ratio are commonly used.

When calculating the velocity of a shear wave, the shear modulus is used. It is often most convenient to make the calculations using

Lame's Constants, which are derived from Young's Modulus and Poisson's Ratio.

E/N/G

It must also be mentioned that the subscript ij attached to C (Cij) in the above equation is used to indicate the directionality of the elastic constants with respect to the wave type and direction of wave travel. In isotropic materials, the elastic constants are the same for all directions within the material. However, most materials are anisotropic and the elastic constants differ with each direction. For example, in a piece of rolled aluminum plate, the grains are elongated in one direction and compressed in the others and the elastic constants for the longitudinal direction are different than those for the transverse or short transverse directions.

V longitudinal V transverse

Examples of approximate compressional sound velocities in materials are: Aluminum - 0.632 cm/microsecond 1020 steel - 0.589 cm/microsecond Cast iron - 0.480 cm/microsecond. Examples of approximate shear sound velocities in materials are: Aluminum - 0.313 cm/microsecond 1020 steel - 0.324 cm/microsecond Cast iron - 0.240 cm/microsecond. When comparing compressional and shear velocities, it can be noted that shear velocity is approximately one half that of compressional velocity. The sound velocities for a variety of materials can be found in the ultrasonic properties tables in the general resources section of this site.

Longitudinal Wave Velocity: VL The velocity of a longitudinal wave is described by the following equation:

VL E Îź P

= Longitudinal bulk wave velocity = Youngâ&#x20AC;&#x2122;s modulus of elasticity = Poisson ratio = Material density

Shear Wave Velocity: VS The velocity of a shear wave is described by the following equation:

Vs E Îź P G

= Shear wave velocity = Youngâ&#x20AC;&#x2122;s modulus of elasticity = Poisson ratio = Material density = Shear modulus

2.4: Properties of Acoustic Plane Wave Wavelength, Frequency and Velocity Among the properties of waves propagating in isotropic solid materials are wavelength, frequency, and velocity. The wavelength is directly proportional to the velocity of the wave and inversely proportional to the frequency of the wave. This relationship is shown by the following equation.

The applet below shows a longitudinal and transverse wave. The direction of wave propagation is from left to right and the movement of the lines indicate the direction of particle oscillation. The equation relating ultrasonic wavelength, frequency, and propagation velocity is included at the bottom of the applet in a reorganized form. The values for the wavelength, frequency, and wave velocity can be adjusted in the dialog boxes to see their effects on the wave. Note that the frequency value must be kept between 0.1 to 1 MHz (one million cycles per second) and the wave velocity must be between 0.1 and 0.7 cm/us.

http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/applet_2_4/applet_2_4.htm

Java don’t work? Uninstalled → Reinstalled → Then → http://jingyan.baidu.com/article/9f63fb91d0eab8c8400f0e08.html

Java donâ&#x20AC;&#x2122;t work? http://jingyan.baidu.com/article/9f63fb91d0eab8c8400f0e08.html

As can be noted by the equation, a change in frequency will result in a change in wavelength. Change the frequency in the applet and view the resultant wavelength. At a frequency of .2 and a material velocity of 0.585 (longitudinal wave in steel) note the resulting wavelength. Adjust the material velocity to 0.480 (longitudinal wave in cast iron) and note the resulting wavelength. Increase the frequency to 0.8 and note the shortened wavelength in each material. In ultrasonic testing, the shorter wavelength resulting from an increase in frequency will usually provide for the detection of smaller discontinuities. This will be discussed more in following sections. Keywords: the shorter wavelength resulting from an increase in frequency will usually provide for the detection of smaller discontinuities

The velocities sound waves The velocities of the various kinds of sound waves can be calculated from the elastic constants of the material concerned, that is the modulus of elasticity E (measured in N/m2), the density p in kg/m3, and Poisson's ratio Îź (a dimensionless number). for longitudinal waves:

for transverse waves:

The two velocities of sound are linked by the following relation:

For all solid materials Poisson's ratio Îź lies between 0 and 0.5, so that the numerical value of the expression

always lies between 0 and 0.707. In steel and aluminum, Îź= 0.28 and 0.34, respectively,

= 0.55 and 0.49 respectIvely. --

2.5: Wavelength and Defect Detection 2.5.1 Sensitivity & Resolution In ultrasonic testing, the inspector must make a decision about the frequency of the transducer that will be used. As we learned on the previous page, changing the frequency when the sound velocity is fixed will result in a change in the wavelength of the sound. The wavelength of the ultrasound used has a significant effect on the probability of detecting a discontinuity. A general rule of thumb is that a discontinuity must be larger than one-half the wavelength to stand a reasonable chance of being detected.

Sensitivity and resolution are two terms that are often used in ultrasonic inspection to describe a technique's ability to locate flaws. Sensitivity is the ability to locate small discontinuities. Sensitivity generally increases with higher frequency (shorter wavelengths). Resolution is the ability of the system to locate discontinuities that are close together within the material or located near the part surface. Resolution also generally increases as the frequency increases.

Keywords:  Discontinuity must be larger than one-half the wavelength to stand a reasonable chance of being detected.  Sensitivity is the ability to locate small discontinuities. Sensitivity generally increases with higher frequency (shorter wavelengths).  Resolution is the ability of the system to locate discontinuities that are close together within the material or located near the part surface.  Resolution also generally increases as the frequency increases, pulse length decrease, bandwidth increase (highly damp)

2.5.2

Grain Size & Frequency Selection

The wave frequency can also affect the capability of an inspection in adverse ways. Therefore, selecting the optimal inspection frequency often involves maintaining a balance between the favorable and unfavorable results of the selection. Before selecting an inspection frequency, the material's grain structure and thickness, and the discontinuity's type, size, and probable location should be considered. As frequency increases, sound tends to scatter from large or course grain structure and from small imperfections within a material. Cast materials often have coarse grains and other sound scatters that require lower frequencies to be used for evaluations of these products. (1) Wrought and (2) forged products with directional and refined grain structure can usually be inspected with higher frequency transducers.

Keywords:  Coarse grains →Lower frequency to avoid scattering and noise,  Fine grains →Higher frequency to increase sensitivity & resolution.

Since more things in a material are likely to scatter a portion of the sound energy at higher frequencies, the penetrating power (or the maximum depth in a material that flaws can be located) is also reduced. Frequency also has an effect on the shape of the ultrasonic beam. Beam spread, or the divergence of the beam from the center axis of the transducer, and how it is affected by frequency will be discussed later. It should be mentioned, so as not to be misleading, that a number of other variables will also affect the ability of ultrasound to locate defects. These include the pulse length, type and voltage applied to the crystal, properties of the crystal, backing material, transducer diameter, and the receiver circuitry of the instrument. These are discussed in more detail in the material on signalto-noise ratio.

Coarse grains â&#x2020;&#x2019;Lower frequency to avoid scattering and noise, Fine grains â&#x2020;&#x2019;Higher frequency to increase sensitivity & resolution.

http://www.cnde.iastate.edu/ultrasonics/grain-noise

Detectability variable:      

pulse length, type and voltage applied to the crystal, properties of the crystal, backing material, transducer diameter, and the receiver circuitry of the instrument.

Keywords:  Higher the frequency, greater the scattering, thus less penetrating.  Higher the frequency better sensitivity and better resolution  If the grain size is 1/10 the wavelength, the ultrasound will be significantly scattered.

Q7: When a material grain size is on the order of ______ wavelength or larger, excessive scattering of the ultrasonic beam affect test result. A. B. C. D.

1 Â˝ 1/10 1/100

2.5.3

Further Reading on Attenuation

Q94: In general, which of the following mode of vibration would have the greatest penetrating power in a coarse grain material if the frequency of the wave are the same? a) b) c) d)

Longitudinal wave Shear wave Transverse wave All the above modes would have the same penetrating power

Q: The random distribution of crystallographic direction in alloys with large crystalline structures is a factor in determining: A. B. C. D.

Acoustic noise levels Selection of test frequency Scattering of sound All of the above

Q168: Heat conduction, viscous friction, elastic hysteresis, and scattering are four different mechanism which lead to: A. B. C. D.

Attenuation Refraction Beam spread Saturation

Q7: When the material grain size is in the order of ____ wavelength or larger, excessive scattering of the ultrasound beam may affect test result: A. B. C. D.

1 Â˝ 1/10 1/100

2.7: Acoustic Impedance Acoustic impedance is a measured of resistance of sound propagation through a part.

From the table air has lower acoustic impedance than steel and for a given energy Aluminum would travel a longer distance than steel before the same amount of energy is attenuated.

Transmission & Reflection Animation: http://upload.wikimedia.org/wikipedia/commons/3/30/Partial_transmittance.gif

Sound travels through materials under the influence of sound pressure. Because molecules or atoms of a solid are bound elastically to one another, the excess pressure results in a wave propagating through the solid. The acoustic impedance (Z) of a material is defined as the product of its density (p) and acoustic velocity (V).

Z = pV Acoustic impedance is important in: 1. the determination of acoustic transmission and reflection at the boundary of two materials having different acoustic impedances. 2. the design of ultrasonic transducers. 3. assessing absorption of sound in a medium.

The following applet can be used to calculate the acoustic impedance for any material, so long as its density (p) and acoustic velocity (V) are known. The applet also shows how a change in the impedance affects the amount of acoustic energy that is reflected and transmitted. The values of the reflected and transmitted energy are the fractional amounts of the total energy incident on the interface. Note that the fractional amount of transmitted sound energy plus the fractional amount of reflected sound energy equals one. The calculation used to arrive at these values will be discussed on the next page.

http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/applet_2_6/applet_2_6.htm

Reflection/Transmission Energy as a function of Z

Q2.8: The acoustic impedance of material used to determined: A. Angle of refraction at the interface B. Attenuation of material C. Relative amount of sound energy coupled through and reflected at an interface D. Beam spread within the material

2.8: Reflection and Transmission Coefficients (Pressure) Ultrasonic waves are reflected at boundaries where there is a difference in acoustic impedances (Z) of the materials on each side of the boundary. (See preceding page for more information on acoustic impedance.) This difference in Z is commonly referred to as the impedance mismatch. The greater the impedance mismatch, the greater the percentage of energy that will be reflected at the interface or boundary between one medium and another. The fraction of the incident wave intensity that is reflected can be derived because particle velocity and local particle pressures must be continuous across the boundary.

When the acoustic impedances of the materials on both sides of the boundary are known, the fraction of the incident wave intensity that is reflected can be calculated with the equation below. The value produced is known as the reflection coefficient. Multiplying the reflection coefficient by 100 yields the amount of energy reflected as a percentage of the original energy.

Since the amount of reflected energy plus the transmitted energy must equal the total amount of incident energy, the transmission coefficient is calculated by simply subtracting the reflection coefficient from one. Formulations for acoustic reflection and transmission coefficients (pressure) are shown in the interactive applet below. Different materials may be selected or the material velocity and density may be altered to change the acoustic impedance of one or both materials. The red arrow represents reflected sound and the blue arrow represents transmitted sound.

http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/applet_2_7/applet_2_7.htm

Reflection Coefficient:

Note that the reflection and transmission coefficients are often expressed in decibels (dB) to allow for large changes in signal strength to be more easily compared. To convert the intensity or power of the wave to dB units, take the log of the reflection or transmission coefficient and multiply this value times 10. However, 20 is the multiplier used in the applet since the power of sound is not measured directly in ultrasonic testing. The transducers produce a voltage that is approximately proportionally to the sound pressure. The power carried by a traveling wave is proportional to the square of the pressure amplitude. Therefore, to estimate the signal amplitude change, the log of the reflection or transmission coefficient is multiplied by 20.

Using the above applet, note that the energy reflected at a water-stainless steel interface is 0.88 or 88%. The amount of energy transmitted into the second material is 0.12 or 12%. The amount of reflection and transmission energy in dB terms are -1.1 dB and -18.2 dB respectively. The negative sign indicates that individually, the amount of reflected and transmitted energy is smaller than the incident energy.

If reflection and transmission at interfaces is followed through the component, only a small percentage of the original energy makes it back to the transducer, even when loss by attenuation is ignored. For example, consider an immersion inspection of a steel block. The sound energy leaves the transducer, travels through the water, encounters the front surface of the steel, encounters the back surface of the steel and reflects back through the front surface on its way back to the transducer. At the water steel interface (front surface), 12% of the energy is transmitted. At the back surface, 88% of the 12% that made it through the front surface is reflected. This is 10.6% of the intensity of the initial incident wave. As the wave exits the part back through the front surface, only 12% of 10.6 or 1.3% of the original energy is transmitted back to the transducer.

Incident Wave other than Normal? â&#x20AC;&#x201C; Oblique Incident

http://www.slideshare.net/crisevelise/fundamentals-ofultrasound?related=1&utm_campaign=related&utm_medium=1&utm_sourc e=29

Incident Wave other than Normal? â&#x20AC;&#x201C; Oblique Incident

Q: The figure above shown the partition of incident and reflected wave at water-Aluminum interface at an incident angle of 20, the reflected and transmitted wave are: A. B. C. D.

60% and 40% 40% and 60% 1/3 and 2/3 80% and 20%

Note: if normal incident the reflected 70% Transmitted 30%

Further Reading (Olympus Technical Note) The boundary between two materials of different acoustic impedances is called an acoustic interface. When sound strikes an acoustic interface at normal incidence, some amount of sound energy is reflected and some amount is transmitted across the boundary. The dB loss of energy on transmitting a signal from medium 1 into medium 2 is given by: dB loss of transmission = 10 log10 [ 4Z1Z2 / (Z1+Z2)2] The dB loss of energy of the echo signal in medium 1 reflecting from an interface boundary with medium 2 is given by: dB loss of Reflection = 10 log10 [ (Z1-Z2)2 / (Z1+Z2)2]

For example: The dB loss on transmitting from water (Z = 1.48) into 1020 steel (Z = 45.41) is -9.13 dB; this also is the loss transmitting from 1020 steel into water. The dB loss of the backwall echo in 1020 steel in water is -0.57 dB; this also is the dB loss of the echo off 1020 steel in water. The waveform of the echo is inverted when Z2<Z1. Finally, ultrasound attenuates as it progresses through a medium. Assuming no major reflections, there are three causes of attenuation: diffraction, scattering and absorption. The amount of attenuation through a material can play an important role in the selection of a transducer for an application. http://olympus-ims.com/data/File/panametrics/UT-technotes.en.pdf

Further Reading: Reflection & Transmission for Normal Incident

http://www.slideshare.net/crisevelise/fundamentals-ofultrasound?related=1&utm_campaign=related&utm_me dium=1&utm_source=29

Q6: For an ultrasonic beam with normal incidence the transmission coefficient is given by:

http://webpages.ursinus.edu/lriley/courses/p212/lectures/node19.html#eq:acousticR http://sepwww.stanford.edu/sep/prof/waves/fgdp8/paper_html/node2.html

2.9: Refraction and Snell's Law

Refraction and Snell's Law When an ultrasonic wave passes through an interface between two materials at an oblique angle, and the materials have different indices of refraction, both reflected and refracted waves are produced. This also occurs with light, which is why objects seen across an interface appear to be shifted relative to where they really are. For example, if you look straight down at an object at the bottom of a glass of water, it looks closer than it really is. A good way to visualize how light and sound refract is to shine a flashlight into a bowl of slightly cloudy water noting the refraction angle with respect to the incident angle.

Vs1 Only If this medium support shear wave i.e. Solid

VL1

VS2

VL2

Refraction takes place at an interface due to the different velocities of the acoustic waves within the two materials. The velocity of sound in each material is determined by the material properties (elastic modulus and density) for that material. In the animation below, a series of plane waves are shown traveling in one material and entering a second material that has a higher acoustic velocity. Therefore, when the wave encounters the interface between these two materials, the portion of the wave in the second material is moving faster than the portion of the wave in the first material. It can be seen that this causes the wave to bend.

http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Graphics/Flash/waveRefraction.swf

http://www.ni.com/white-paper/3368/en

Snell's Law describes the relationship between the angles and the velocities of the waves. Snell's law equates the ratio of material velocities V1 and V2 to the ratio of the sine's of incident (Ɵ1°) and refracted (Ɵ2°) angles, as shown in the following equation.

Where: VL1 is the longitudinal wave velocity in material 1. VL2 is the longitudinal wave velocity in material 2.

Note that in the diagram, there is a reflected longitudinal wave (VL1' ) shown. This wave is reflected at the same angle as the incident wave because the two waves are traveling in the same material, and hence have the same velocities. This reflected wave is unimportant in our explanation of Snell's Law, but it should be remembered that some of the wave energy is reflected at the interface. In the applet below, only the incident and refracted longitudinal waves are shown. The angle of either wave can be adjusted by clicking and dragging the mouse in the region of the arrows. Values for the angles or acoustic velocities can also be entered in the dialog boxes so the that applet can be used as a Snell's Law calculator.

Snell Law

http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/applet_2_8/applet_2_8.htm

Snell Law

When a longitudinal wave moves from a slower to a faster material, there is an incident angle that makes the angle of refraction for the wave 90o. This is know as the first critical angle. The first critical angle can be found from Snell's law by putting in an angle of 90Â° for the angle of the refracted ray. At the critical angle of incidence, much of the acoustic energy is in the form of an inhomogeneous compression wave, which travels along the interface and decays exponentially with depth from the interface. This wave is sometimes referred to as a "creep wave." Because of their inhomogeneous nature and the fact that they decay rapidly, creep waves are not used as extensively as Rayleigh surface waves in NDT. However, creep waves are sometimes more useful than Rayleigh waves because they suffer less from surface irregularities and coarse material microstructure due to their longer wavelengths.

Snell Law

Refraction and mode conversion occur because of the change in L-wave velocity as it passes the boundary from one medium to another. The higher the difference in the velocity of sound between two materials, the larger the resulting angle of refraction. L-waves and S-waves have different angles of refraction because they have dissimilar velocities within the same material. s the angle of the ultrasonic transducer continues to increase, L-waves move closer to the surface of the UUT. The angle at which the L-wave is parallel with the surface of the UUT is referred to as the first critical angle. This angle is useful for two reasons. Only one wave mode is echoed back to the transducer, making it easy to interpret the data. Also, this angle gives the test system the ability to look at surfaces that are not parallel to the front surface, such as welds.

Example: Snell’s Law L-wave and S-wave refraction angles are calculated using Snell’s law. You also can use this law to determine the first critical angle for any combination of materials.

Where: Ɵ2° = angle of the refracted beam in the UUT Ɵ1° = incident angle from normal of beam in the wedge or liquid V1 = velocity of incident beam in the liquid or wedge V2 = velocity of refracted beam in the UUT

For example, calculate the first critical angle for a transducer on a plastic wedge that is examining aluminum. V1 = 0.267 cm/µs (for L-waves in plastic) V2 = 0.625 cm/µs (for L-waves in aluminum) Ɵ2° = 90 degree (angle of L-wave for first critical angle) Ɵ1° = unknown The plastic wedge must have a minimum angle of 25.29 ° to transmit only Swaves into the UUT. When the S-wave angle of refraction is greater than 90°, all ultrasonic energy is reflected by the UUT.

Snell Law: First critical angle

Snell Law: 1st / 2nd Critical Angles

Q155 Which of the following can occur when an ultrasound beam reaches the interface of 2 dissimilar materials? a) b) c) d)

Reflection refraction mode conversion all of the above

Q. Both longitudinal and shear waves may be simultaneously generated in a second medium when the angle of incidence is: a) between the normal and the 1st critical angle b) between the 1st and 2nd critical angle c) past the second critical angle d) only at the second critical angle

Q: When angle beam contact testing a test piece, increasing the incident angle until the second critical angle is reached results in: A. B. C. D.

Total reflection of a surface wave 45 degree refraction of the shear wave Production of a surface wave None of the above

Typical angle beam assemblies make use of mode conversion and Snell's Law to generate a shear wave at a selected angle (most commonly 30°, 45°, 60°, or 70°) in the test piece. As the angle of an incident longitudinal wave with respect to a surface increases, an increasing portion of the sound energy is converted to a shear wave in the second material, and if the angle is high enough, all of the energy in the second material will be in the form of shear waves. There are two advantages to designing common angle beams to take advantage of this mode conversion phenomenon.  First, energy transfer is more efficient at the incident angles that generate shear waves in steel and similar materials.  Second, minimum flaw size resolution is improved through the use of shear waves, since at a given frequency, the wavelength of a shear wave is approximately 60% the wavelength of a comparable longitudinal wave.

Snell Law:

http://techcorr.com/services/Inspection-and-Testing/Ultrasonic-Shear-Wave.cfm

Depth & Skip

More on Snell Law Like light, when an incident ultrasonic wave encounters an interface to an adjacent material of a different velocity, at an angle other than normal to the surface, then both reflected and refracted waves are produced. Understanding refraction and how ultrasonic energy is refracted is especially important when using angle probes or the immersion technique. It is also the foundation formula behind the calculations used to determine a materials first and second critical angles. First Critical Angle Before the angle of incidence reaches the first critical angle, both longitudinal and shear waves exist in the part being inspected. The first critical angle is said to have been reached when the longitudinal wave no longer exists within the part, that is, when the longitudinal wave is refracted to greater or equal than 90Â°, leaving only a shear wave remaining in the part.

Second Critical Angle The second critical angle occurs when the angle of incidence is at such an angle that the remaining shear wave within the part is refracted out of the part. At this angle, when the refracted shear wave is at 90Â° a surface wave is created on the part surface Beam angles should always be plotted using the appropriate industry standard, however, knowing the effect of velocity and angle on refraction will always benefit an NDT technician when working with angle inspection or the immersion technique. The above calculator uses the following equation: ultrasonic snells law formula Where: A1 = The angle of incidence. V1 = The incident material velocity A2 = The angle of refraction V2 = The refracted material velocity

http://www.ndtcalc.com/calculators.html

2.10: Mode Conversion When sound travels in a solid material, one form of wave energy can be transformed into another form. For example, when a longitudinal waves hits an interface at an angle, some of the energy can cause particle movement in the transverse direction to start a shear (transverse) wave. Mode conversion occurs when a wave encounters an interface between materials of different acoustic impedances and the incident angle is not normal to the interface. From the ray tracing movie below, it can be seen that since mode conversion occurs every time a wave encounters an interface at an angle, ultrasonic signals can become confusing at times.

Mode Conversion

http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Graphics/Flash/ModeConversion/ModeConv.swf

In the previous section, it was pointed out that when sound waves pass through an interface between materials having different acoustic velocities, refraction takes place at the interface. The larger the difference in acoustic velocities between the two materials, the more the sound is refracted. Notice that the shear wave is not refracted as much as the longitudinal wave. This occurs because shear waves travel slower than longitudinal waves. Therefore, the velocity difference between the incident longitudinal wave and the shear wave is not as great as it is between the incident and refracted longitudinal waves. Also note that when a longitudinal wave is reflected inside the material, the reflected shear wave is reflected at a smaller angle than the reflected longitudinal wave. This is also due to the fact that the shear velocity is less than the longitudinal velocity within a given material.

Snell's Law holds true for shear waves as well as longitudinal waves and can be written as follows

= Where: VL1 is the longitudinal wave velocity in material 1. VL2 is the longitudinal wave velocity in material 2. VS1 is the shear wave velocity in material 1. VS2 is the shear wave velocity in material 2.

Snell's Law

In the applet below, the shear (transverse) wave ray path has been added. The ray paths of the waves can be adjusted by clicking and dragging in the vicinity of the arrows. Values for the angles or the wave velocities can also be entered into the dialog boxes. It can be seen from the applet that when a wave moves from a slower to a faster material, there is an incident angle which makes the angle of refraction for the longitudinal wave 90 degrees. As mentioned on the previous page, this is known as the first critical angle and all of the energy from the refracted longitudinal wave is now converted to a surface following longitudinal wave. This surface following wave is sometime referred to as a creep wave and it is not very useful in NDT because it dampens out very rapidly.

Reflections

Creep wave

VS1

VS2

Beyond the first critical angle, only the shear wave propagates into the material. For this reason, most angle beam transducers use a shear wave so that the signal is not complicated by having two waves present. In many cases there is also an incident angle that makes the angle of refraction for the shear wave 90 degrees. This is known as the second critical angle and at this point, all of the wave energy is reflected or refracted into a surface following shear wave or shear creep wave. Slightly beyond the second critical angle, surface waves will be generated. Keywords: â&#x2013; Longitudinal creep wave â&#x2013; Shear creep wave

Snell Law- 1st & 2nd Critical Angles

Note that the applet defaults to compressional velocity in the second material. The refracted compressional wave angle will be generated for given materials and angles. To find the angle of incidence required to generate a shear wave at a given angle complete the following: 1. Set V1 to the longitudinal wave velocity of material 1. This material could be the transducer wedge or the immersion liquid. 2. Set V2 to the shear wave velocity (approximately one-half its compressional velocity) of the material to be inspected. 3. Set Q2 to the desired shear wave angle. 4. Read Q1, the correct angle of incidence.

Transverse wave can be introduced into the test material by various methods: 1. Inclining the incident L-wave at an angle beyond the first critical angle, yet short of second critical angle using a wedge. 2. In immersion method, changing the angle of the normal search unit manipulator, 3. Off-setting the normal transducer from the center-line for round bar or pipe. for 45Â° refracted transverse wave, the rule of thumb is the offset d= 1/6 of rod diameter

Offset of Normal probe above circular object

θ1

θ2

Calculate the offset for following conditions: Aluminum rod being examined is 6" diameter, what is the off set needed for (a) 45 refracted shear wave (b) Logitudinal wave to be generated? (L-wave velocity for AL=6.3x105cm/s, T-wave velocity for AL=3.1x105 cm/s, Wave velocity in water=1.5X105 cm/s) Question (a)

Refraction and mode conversion at non-perpendicular boundaries

http://static4.olympus-ims.com/data/Flash/HTML5/incident_angle/IncidentAngle.html?rev=5E62

Refraction and mode conversion at non-perpendicular boundaries

Q1. From the above figures, if the incident angle is 50 Degree, what are the sound wave in the steel? Answer: 65 Degree Shear wave in steel. Q2. If 50 Degree longitudinal wave in steel is used what is the possible problem? Answer: If 50 degree Longitudinal wave is generated in steel, shear wave at 28 degree is also generated and this may cause fault indications.

Q118: At the water-steel interface, the angle of incidence in water is 7 degree. The principle mode of vibration that exist in steel is: A. B. C. D.

Longitudinal Shear Both A & B (Possible incorrect answer) Surface

Hint: The keyword is â&#x20AC;&#x153;the principle modeâ&#x20AC;?

Q: On Calculation: Incident angle= 7° Refracted longitudinal wave = 29.11° Refracted shear wave = 15.49°

Q72. In a water immersion test, ultrasonic energy is transmitted into steel at an incident angle of 14. What is the angle of refracted shear wave within the material? Vs = 3.2 x 105 cm/s, Vw = 1.5 x 105 cm/s a) b) c) d)

45째 23째 31째 13째

Q1. If you were requested to design a plastid shoe to generate Rayleigh wave in aluminum, what would be the incident angle of the ultrasonic energy? VA = 3.1 x 105 cm/s, Vp = 2.6 x 105 cm/s a) b) c) d)

37째 57째 75째 48째

Q53. The term used to determined the relative transmittance and reflectance of an ultrasonic energy at an interface is called: a) b) c) d)

Acoustic attenuation Interface reflection Acoustic impedance ratio Acoustic frequency

2.11: Signal-to-Noise Ratio In a previous page, the effect that frequency and wavelength have on flaw detectability was discussed. However, the detection of a defect involves many factors other than the relationship of wavelength and flaw size. For example, the amount of sound that reflects from a defect is also dependent on the acoustic impedance mismatch between the flaw and the surrounding material. A void is generally a better reflector than a metallic inclusion because the impedance mismatch is greater between air and metal than between two metals. Often, the surrounding material has competing reflections. Microstructure grains in metals and the aggregate of concrete are a couple of examples. A good measure of detectability of a flaw is its signal-to-noise ratio (S/N). The signal-to-noise ratio is a measure of how the signal from the defect compares to other background reflections (categorized as "noise"). A signal-to-noise ratio of 3 to 1 is often required as a minimum.

The absolute noise level and the absolute strength of an echo from a "small" defect depends on a number of factors, which include: 1. 2. 3. 4. 5. 6. 7.

The probe size and focal properties. The probe frequency, bandwidth and efficiency. The inspection path and distance (water and/or solid). The interface (surface curvature and roughness). The flaw location with respect to the incident beam. The inherent noisiness of the metal microstructure. The inherent reflectivity of the flaw, which is dependent on its acoustic impedance, size, shape, and orientation. 8. Cracks and volumetric defects can reflect ultrasonic waves quite differently. Many cracks are "invisible" from one direction and strong reflectors from another. 9. Multifaceted flaws will tend to scatter sound away from the transducer.

The following formula relates some of the variables affecting the signal-tonoise ratio (S/N) of a defect:

Sound Volume: Area x pulse length

Material properties Flaw geometry: Figure of merit FOM and amplitudes responds

Rather than go into the details of this formulation, a few fundamental relationships can be pointed out. The signal-to-noise ratio (S/N), and therefore, the detectability of a defect: 1. Increases with increasing flaw size (scattering amplitude). The detectability of a defect is directly proportional to its size. 2. Increases with a more focused beam. In other words, flaw detectability is inversely proportional to the transducer beam width. 3. Increases with decreasing pulse width (delta-t). In other words, flaw detectability is inversely proportional to the duration of the pulse (â&#x2C6;&#x2020;t) produced by an ultrasonic transducer. The shorter the pulse (often higher frequency), the better the detection of the defect. Shorter pulses correspond to broader bandwidth frequency response. See the figure below showing the waveform of a transducer and its corresponding frequency spectrum.

Acoustic Volume: wxwyâ&#x2C6;&#x2020;t

Determining cross sectional area using reflector- A Scan (6db drop)

Determining cross sectional area using reflector- C Scan

â&#x20AC;&#x153;Sonic pulse volumeâ&#x20AC;? and S/N (defect resolution)

4. Decreases in materials with high density and/or a high ultrasonic velocity. The signal-to-noise ratio (S/N) is inversely proportional to material density and acoustic velocity. 5. Generally increases with frequency. However, in some materials, such as titanium alloys, both the "Aflaw" and the "Figure of Merit (FOM)" terms in the equation change at about the same rate with changing frequency. So, in some cases, the signal-to-noise ratio (S/N) can be somewhat independent of frequency.

Pulse Length

Pulse Length Affect Resolution

2.12: The Sound Fields 2.12.1 Wave Interaction or Interference Before we move into the next section, the subject of wave interaction must be covered since it is important when trying to understand the performance of an ultrasonic transducer. On the previous pages, wave propagation was discussed as if a single sinusoidal wave was propagating through the material. However, the sound that emanates from an ultrasonic transducer does not originate from a single point, but instead originates from many points along the surface of the piezoelectric element. This results in a sound field with many waves interacting or interfering with each other.

Transducer cut-out

http://ichun-chen.com/ultrasonic-transducer

When waves interact, they superimpose on each other, and the amplitude of the sound pressure or particle displacement at any point of interaction is the sum of the amplitudes of the two individual waves. First, let's consider two identical waves that originate from the same point. When they are in phase (so that the peaks and valleys of one are exactly aligned with those of the other), they combine to double the displacement of either wave acting alone. When they are completely out of phase (so that the peaks of one wave are exactly aligned with the valleys of the other wave), they combine to cancel each other out. When the two waves are not completely in phase or out of phase, the resulting wave is the sum of the wave amplitudes for all points along the wave.

UT Transducer

http://www.fhwa.dot.gov/publications/research/infrastructure/structures/04042/index.cfm#toc

UT Transducer- Surface creep wave transducer

UT Transducer

Wave Interaction

Complete in-phase

Complete out of-phase

not in-phase

When the origins of the two interacting waves are not the same, it is a little harder to picture the wave interaction, but the principles are the same. Up until now, we have primarily looked at waves in the form of a 2D plot of wave amplitude versus wave position. However, anyone that has dropped something in a pool of water can picture the waves radiating out from the source with a circular wave front. If two objects are dropped a short distance apart into the pool of water, their waves will radiate out from their sources and interact with each other. At every point where the waves interact, the amplitude of the particle displacement is the combined sum of the amplitudes of the particle displacement of the individual waves. With an ultrasonic transducer, the waves propagate out from the transducer face with a circular wave front. If it were possible to get the waves to propagate out from a single point on the transducer face, the sound field would appear as shown in the upper image to the right. Consider the light areas to be areas of rarefaction and the dark areas to be areas of compression.

With an ultrasonic transducer, the waves propagate out from the transducer face with a circular wave front. If it were possible to get the waves to propagate out from a single point on the transducer face, the sound field would appear as shown in the upper image to the right. Consider the light areas to be areas of rarefaction and the dark areas to be areas of compression.

However, as stated previously, sound waves originate from multiple points along the face of the transducer. The lower image to the right shows what the sound field would look like if the waves originated from just two points. It can be seen that where the waves interact, there are areas of constructive and destructive interference. The points of constructive interference are often referred to as nodes.

The points of constructive interference are often referred to as nodes

29. It is possible for a discontinuity smaller than the transducer to produce indications of fluctuating amplitude as the search unit is moved laterally if testing is being performed in the: (a) Fraunhofer zone (b) Near field (c) Snell field (d) Shadow zone

Q5: Acoustic pressure along the beam axis moving away from the probe has various maxima and minima due to interference. At the end of the near field pressure is: a) a maximum b) a minimum c) the average of all maxima and minima d) none of the above Q4: For a plane wave, sound pressure is reduced by attenuation in a _______ fashion. a) linear b) exponential c) random d) none of the above

Intensity

2.12.2 Variations in sound intensity

Distance

Of course, there are more than two points of origin along the face of a transducer. The image below shows five points of sound origination. It can be seen that near the face of the transducer, there are extensive fluctuations or nodes and the sound field is very uneven. In ultrasonic testing, this in known as the near field (near zone) or Fresnel zone. The sound field is more uniform away from the transducer in the far field, or Fraunhofer zone, where the beam spreads out in a pattern originating from the center of the transducer. It should be noted that even in the far field, it is not a uniform wave front. However, at some distance from the face of the transducer and central to the face of the transducer, a uniform and intense wave field develops.

The sound wave exit from a transducer can be separated into 2 zones or areas; The Near Field (Fresnel) and the Far Field (Fraunhofer).

2.12.3 Fresnel & Fraunhofer Zone Fresnel Field, the Near Field are region directly adjacent to the transducer and characterized as a collection of symmetrical high and low pressure regions cause by interference wave fronts emitting from the continuous or near continuous sound sources.

http://blog.3bscientific.com/science_education_insight/2013/04/3b-scientific-makes-waves-with-new-physics-education-kit.html

The Near Field (Fresnel) and the Far Field (Fraunhofer).

The Near Field (Fresnel)â&#x20AC;&#x201C; Wave Interference (Maxima & Minima) The sound field of a transducer is divided into two zones; the near field and the far field. The near field is the region directly in front of the transducer where the echo amplitude goes through a series of maxima and minima and ends at the last maximum, at distance N from the transducer.

Near Field Effect: Because of the variations within the near field it can be difficult to accurately evaluate flaws using amplitude based techniques.

Far Field

â&#x2020;? Amplitude

Near Field Yo+

Distance from Transducer face â&#x2020;&#x2019;

Fresnel / Fraunhofer Zone

Near field (near zone) or Fresnel zone

far field (far zone) or Fraunhofer zone

Near field (near zone) or Fresnel zone

Focus

Crystal

Accoustical axis far field (far zone) or Fraunhofer zone

Angle of divergence

Near field Zf

Far field

ď §6

Near/ Far Fields

http://miac.unibas.ch/PMI/05-UltrasoundImaging.html

Near/ Far Fields

where Îą is the radius of the transducer and Îť the wavelength.

where D is the diameter of the transducer and Îť the wavelength. K= is the spread factor K=1.22 for null edges K=1.08 for 20dB down point (10% of peak) K=0.88 for 10dB down point (32% of peak) K=0.7(0.56?) for 6dB down point (50% of peak) Source for K, ASNT Study Guide UT by Matthew J Golis

The curvature and the area over which the sound is being generated, the speed that the sound waves travel within a material and the frequency of the sound all affect the sound field. Use the Java applet below to experiment with these variables and see how the sound field is affected.

http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/appletUltrasoundPropagation/Applet.html

Fresnel & Fraunhofer Zone

10dB, K-0.88

6dB, K=0.7? Or 0.56?

Fresnel & Fraunhofer Zone

http://static1.olympus-ims.com/data/Flash/HTML5/beamSpread/BeamSpread.html?rev=6C43

http://www.olympus-ims.com/en/ndt-tutorials/transducers/wave-front/

Q: Where does beam divergence occur? A. B. C. D.

Near field Far field At the crystal None of the above

Q4: A transducer has a near field in water of 35 mm. When used in contact on steel the near zone will be about: a) 47 mm b) 35 mm c) 18 mm d) 9 mm Q8: A rectangular probe, 4 mm X 8 mm, will have its maximum half angle of divergence: a) in the 4 mm direction b) in the 8 mm direction c) in no particular orientation d) constant in all directions

Q160 Beam divergence is a function of the dimensions of the crystal and the wavelength of the beam transmitted through a medium, and it: A. B. C. D.

increase if the frequency or the crystal diameter is decrease Decrease if the frequency or the crystal diameter is decrease increase if the frequency is increase and the diameter is decrease decrease if the frequency is increase and the crustal diameter is decrease

Q52: What is the transducer half-angle beam spread of a 1.25cm diameter 2.25 MHz transducer in water (VL= 1.5 x 105 cm/s)? A. B. C. D.

2.5 degree 3.75 degree 37.5 degree 40.5 degree

2.12.4 Dead Zone In ultrasonic testing, the interval following the initial pulse where the transducer ring time of the crystal that prevents detection or interpretation of reflected energy (echoes). In contact ultrasonic testing, the area just below the surface of a test object that can not be inspected because of the transducer is still ringing down and not yet ready to receive signals. The dead is minimized by the damping medium behind the crystal. The dead zone increase when the probe frequency decrease and it only found in single crystal contact techniques.

Dead Zone - The interval following the surface of a test object to the nearest inspectable depth. Any interval following a reflected signal where no direct echoes from discontinuities cannot be detected, due to characteristics of the equipment. dead zone after echo and dead zone after initial pulse, both are common phenomena. Actually the dead zone cannot be determined as a single figure without additional parameters, hence the echo can be recognized, however, signal quality is important. Useful parameters are linearity or signal in a nice ratio that can describe the echo amplitude quality within a dead zone. For this reason standards such as GE specifications are needed to check equipment capability. The appearance of inference effects, within the dead zone, has to be considered as well. Definition by: http://www.ndt.net/ndtaz/content.php?id=103

Dead Zone -The initial pulse is a technical necessity. It limits the detectability of near-surface discontinuities. Reflectors in the dead zone, the nonresolvable area immediately beneath the surface, cannot be detected (Figure 8-10). The dead zone is a function of the width of the initial pulse which is influenced by the probe type, test instrument discontinuities and quality of the interface. The dead zone can be verified with an International Institute of Welding (IIW) calibration block. With the time base calibrated to 50 mm, and the transducer on position A (Figure 8-11), the extent of the dead zone can be inferred to be either less than or greater than 5 mm. With the probe at position B, the dead zone can be said to be either less than or greater than 10 mm. This is done by ensuring that the peak from the Perspex insert appears beyond the trailing edge of the initial pulse start. Excessive dead zones are generally attributable to a probe with excessive ringing in the crystal.

Dead Zone Illustration http://www.ndt.net/ndtaz/content.php?id=103

Dead Zone

http://www.ni.com/white-paper/5369/en/

Q: On an A-scan display, the â&#x20AC;&#x153;dead zoneâ&#x20AC;? refers to: A. The distance contained within the near field B. The area outside the beam spread C. The distance covered by the front surface pulse with and recovery time D. The area between the near field and the far field

Q36: To eliminate the decrease in sensitivity close to a wall which is parallel to the beam direction, the transducer used should be: A. B. C. D.

As small as possible As low frequency as possible Both A & B Large and with a frequency as high as possible

Q45: The length of the near field for a 2.5cm diameter, 5MHz transducer placed in oil with V=1.4 x 105 cm/s is approximately: A. B. C. D.

0.028 cm 6.25 cm 22.3 cm 55.8 cm

2.13: Inverse Square Rule/ Inverse Rule Large Reflector, a reflector larger than the extreme edge of beam / 3D away from the Near Zone- Inverse Rule

Large Reflector Inverse Rule

Small Reflector, a reflector smaller than the extreme edge of beam / 3D away from the Near Zone â&#x20AC;&#x201C; Inverse Square Rule

Small Reflector Inverse Square Rule

2.14: Resonance Another form wave interference occurred when the normal incidence and reflected plane wave interact within a narrow parallel interface. When the phase of the reflected wave match that of incoming incident wave, the amplitude of the superimposed wave doubling, creating a standing wave.

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/string.html#c3

Resonance occurred when the thickness of the material is equal to half the wave length or multiple of it. It also occur when longitudinal wave travel thru a thin sheet of materials during immersion testing.

Fundamental Frequency The lowest resonant frequency of a vibrating object is called its fundamental frequency. Most vibrating objects have more than one resonant frequency and those used in musical instruments typically vibrate at harmonics of the fundamental. A harmonic is defined as an integer (whole number) multiple of the fundamental frequency. Vibrating strings, open cylindrical air columns, and conical air columns will vibrate at all harmonics of the fundamental. Cylinders with one end closed will vibrate with only odd harmonics of the fundamental. Vibrating membranes typically produce vibrations at harmonics, but also have some resonant frequencies which are not harmonics. It is for this class of vibrators that the term overtone becomes useful - they are said to have some non-harmonic overtones.

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/funhar.html

Thickness of Crystal at Fundamental Frequency Fundamental resonance frequency Harmonic resonance frequency

= V/f = N. V/f (N = integer)

Piezoelectric crystal will has the greatest sensitivity when it is driven at its fundamental frequency, this occurs when the thickness of the crystal is at Â˝ Îť. If the thickness is given, the fundamental frequency could be calculated:

Transducers Piezoelectric Thickness: The resonant phenomenon occurred when piezoelectric are electrically excited at their characteristic (fundamental resonance) frequency.

http://bme240.eng.uci.edu/students/09s/patelnj/Ultrasound_for_Nerves/Ultrasound_Background.html

Resonance UT Testing- The diagram below shown how resonance is used to measured thickness and detect defect. However pulse-echo methods have been refined to perform most of function of flaw detections and resonant instruments are rarely used.

Application Case#1: The specimen's geometry determines the number of its natural frequencies: a rod has few whilst a complex work-piece has many such frequencies. Typically, the information that can be obtained by acoustic resonance analysis includes cracks, structural properties, cavities, layer separation, chipping, density fluctuations etc. Damping behaviour depends firstly on the material, and secondly, on how the specimen is positioned during its excitation. In order to achieve high frequency resolution, signal duration ("ringing duration") should be as long as possible (> 50 ms).

From the natural frequencies it is possible to calculate specimen-specific characteristics and assign them to quality attributes, e. g. pass / OK, cracked, material structure, hardness deviation / partly hardened etc. Application Acoustic resonance testing can be applied to all work pieces that "sound". Summary Resonance analysis is a qualitative method, i.e. it can differentiate between defective and non-defective parts, so that it is especially suitable for quality assurance in the series production cycle. It compares the actual oscillatory situation with the target one derived from a learning base. This learning base is established by using defined standard parts. The number of self-resonant frequencies is determined by the geometry of the object under test. For instance a bar has few resonant frequencies, while a complex lattice-type object has many natural resonances. After a systematic engineering approach, it is possible to compensate the influence of the production scatter. http://ndttechnologies.com/products/AcousticResonance.html

Application Case#2: Electromagnetic Acoustic Resonance Nondestructive Testing (NDT) Equipment Datasheets Coating Thickness Gauge -- DTG-500 from OMEGA Engineering, Inc. Digital coating thickness gauge with a range of 0 to 40.0 mils (0 to 1000 micrometers). SPECIFICATIONS. Display: 3-digit LCD with max readout of 1999 counts. Range: 0 to 40 mils/0 to 1000 Âľm. Resolution: 0. Instrument Information Instrument Type: Coating Thickness Instrument Technology: Electromagnetic Acoustic Resonance Form Factor: Portable / Handheld / Mobile

http://www.globalspec.com/specsearch/PartSpecs?partid={0DBF141D-6832-4F31-9AB8B87F063BFDC4}&vid=99786&comp=2975

Q: The formula used to determine the fundamental resonance frequency is: A. B. C. D.

F= V/T F= V/2T F= T/V F= VT

Q: When maximum sensitivity is required from a transducer: A. A straight beam unit should be used B. A large diameter crystal should be used C. The piezoelectric element should be driven at its fundamental frequency D. The bandwidth of the transducer should be as large as possible

Q7: The resonance frequency of 2cm thick plate of Naval Brass (V=4.43 x 105 cm/s) is: A. B. C. D.

0,903 MHz 0.443 MHz 0.222 MHz 0.111 MHz

Q35: Resonance testing equipment generally utilized: A. B. C. D.

Pulsed longitudinal; waves Continuous longitudinal waves Pulsed shear wave Continuous shear waves

2.15 Measurement of Sound

dB is a measures of ratio of 2 values in a logarithmic scale given by following equation:

Unlike the SPL (standard pressure level) used in noise measurement, in UT testing, we do not know the exactly ultrasonic sound level energy generated by the probe (neither is it necessary). The used of the ratio of 2 values given by the above equation is used .

Ultrasonic Formula - Signal Amplitude Gain/Loss Expressed in dB The dB is a logarithmic unit that describes a ratio of two measurements. The equation used to describe the difference in intensity between two ultrasonic or other sound measurements is:

where: â&#x2C6;&#x2020;I is the difference in sound intensity expressed in decibels (dB), P1 and P2 are two different sound pressure amplitude measurements, and the log is to base 10.

The Decibel The equation used to describe the difference in intensity between two ultrasonic or other sound measurements is:

where: â&#x2C6;&#x2020;I is the difference in sound intensity expressed in decibels (dB), P1 and P2 are two different sound pressure measurements, and the log is to base 10. What exactly is a decibel? The decibel (dB) is one tenth of a Bel, which is a unit of measure that was developed by engineers at Bell Telephone Laboratories and named for Alexander Graham Bell. The dB is a logarithmic unit that describes a ratio of two measurements. The basic equation that describes the difference in decibels between two measurements is:

where: delta X is the difference in some quantity expressed in decibels, X1 and X2 are two different measured values of X, and the log is to base 10. (Note the factor of two difference between this basic equation for the dB and the one used when making sound measurements. This difference will be explained in the next section.)

Why is the dB unit used? Use of dB units allows ratios of various sizes to be described using easy to work with numbers. For example, consider the information in the table.

From this table it can be seen that ratios from one up to ten billion can be represented with a single or double digit number. Ease to work with numbers was particularly important in the days before the advent of the calculator or computer. The focus of this discussion is on using the dB in measuring sound levels, but it is also widely used when measuring power, pressure, voltage and a number of other things.

Use of the dB in Sound Measurements Sound intensity is defined as the sound power per unit area perpendicular to the wave. Units are typically in watts/m2 or watts/cm2. For sound intensity, the dB equation becomes:

However, the power or intensity of sound is generally not measured directly. Since sound consists of pressure waves, one of the easiest ways to quantify sound is to measure variations in pressure (i.e. the amplitude of the pressure wave). When making ultrasound measurements, a transducer is used, which is basically a small microphone. Transducers like most other microphones produced a voltage that is approximately proportionally to the sound pressure (P). The power carried by a traveling wave is proportional to the square of the amplitude. Therefore, the equation used to quantify a difference in sound intensity based on a measured difference in sound pressure becomes:

I Îą P2 , I Îą V2

where I=intensity, P=amplitude, V=voltage

Therefore, the equation used to quantify a difference in sound intensity based on a measured difference in sound pressure becomes:

(The factor of 2 is added to the equation because the logarithm of the square of a quantity is equal to 2 times the logarithm of the quantity.)

Since transducers and microphones produce a voltage that is proportional to the sound pressure, the equation could also be written as:

where: â&#x2C6;&#x2020;I is the change in sound intensity incident on the transducer and V1 and V2 are two different transducer output voltages.

Revising the table to reflect the relationship between the ratio of the measured sound pressure and the change in intensity expressed in dB produces From the table it can be seen that 6 dB equates to a doubling of the sound pressure. Alternately, reducing the sound pressure by 2, results in a â&#x20AC;&#x201C; 6 dB change in intensity.

Sound Levels- Relative

Sound Levels- Relative dB

Practice:

â&#x20AC;&#x153;Absolute" Sound Levels Sound pressure level (SPL) or sound level is a logarithmic measure of the effective sound pressure of a sound relative to a reference value. It is measured in decibels (dB) above a standard reference level. The standard reference sound pressure in air or other gases is 20 ÂľPa, which is usually considered the threshold of human hearing (at 1 kHz). http://en.wikipedia.org/wiki/DB_SPL#Sound_pressure_level

“Absolute" Sound Levels Whenever the decibel unit is used, it always represents the ratio of two values. Therefore, in order to relate different sound intensities it is necessary to choose a standard reference level. The reference sound pressure (corresponding to a sound pressure level of 0 dB) commonly used is that at the threshold of human hearing, which is conventionally taken to be 2×10−5 Newton per square meter, or 20 micropascals (20μPa). To avoid confusion with other decibel measures, the term dB(SPL) is used.

dB meter 97.3dB against standards sound pressure level 20log(P/20X10-6)=97.3 Absolute level =10 97.3/20 x 20 X 10-6 =1.46564 N/M2 Actual Sound pressure →

↖ Standard reference pressure 20 μMpa

Absolute: The standard reference sound pressure in air or other gases is 20 µPa, which is usually considered the threshold of human hearing (at 1 kHz). Actual Sound pressure →

↖ Standard reference pressure 20 μMpa

Sound pressure level in dB as a ratio to standard reference in logarithmic scale. Absolute: 76db= 20log(P/20 μPa) Log(P/20 μPa)=3.8dB P= 103.8 x 20 μPa =126191 μPa http://www.ncvs.org/ncvs/tutorials/voiceprod/equation/chapter9/index.html

Exercise: Find the absolute sound level in ÎźPa for the following measurement of air traffic noise.

Exercise: ANSWER Find the absolute sound level in ÎźPa for the following measurement of air traffic noise. SPL= 95.8 dB= 20log(P/20x10-6) log(P/20x10-6)= 95.8/20 P= 1095.8/20 x 20x10-6 P= 1.233 N/M2#

Practice:

Relative dB: Example Calculation 1 Two sound pressure measurements are made using an ultrasonic transducer. The output voltage from the transducer is 600 mv for the first measurement and 100 mv for the second measurement. Calculate the difference in the sound intensity, in dB, between the two measurements?

The sound intensity changed by -15.56dB. In other words, the sound intensity decreased by 15.56 dB

Example Calculation 2 If the intensity between two ultrasonic measurements increases by 6 dB, and the first measurement produces a transducer output voltage of 30 mv, what was the transducer output voltage for the second measurement?

Example Calculation 3 Consider the sound pressure difference between the threshold of human hearing, 0 dB, and the level of sound often produce at a rock concert, 120 dB. How much is the rock concert sound greater than that of the threshold of human hearing.

What is the absolute rock concert sound pressure?

2.16 Practice Makes Perfect

Practice Makes Perfect 28. An advantage of using lower frequencies during ultrasonic testing is that: (a) Near surface resolution is improved (b) Sensitivity to small discontinuities is improved (c) Beam spread is reduced (d) Sensitivity to unfavorable oriented flaws is improved

Q104: If an ultrasonic wave is transmitted through an interface of two materials in which the first material has a higher acoustic impedance value but the same velocity value as the secong material, the angle of refraction will be: a) b) c) d)

A greater than the incidence Less than the angle of incidence The same as the angle of incidence Beyond the critical angle.

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