Ultrasonic Testing Theory - Ndt Research

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ntroduction to Ultrasonic Testing

me - Education Resources - NDT Course Material - Ultrasound

-Introduction toUltrasonic Testin

IntroductionBasic Principles

History

Present State

Future Direction

Physics of UltrasouWave Propagation

Modes of Sound Wave

Properties of Plane W

Wavelength/Flaw Det

Elastic Properties of SAttenuation

Acoustic Impedance

Reflection/Transmissi

Refraction & Snell's La

Mode Conversion

Signal-to-noise Ratio

Wave Interference

Equipment &TransducersPiezoelectric Transduc

Characteristics of PT

Radiated Fields

Transducers Beam Sp

Transducer Types

Transducer Testing I

Transducer Testing II

Transducer Modeling

Couplant

EMATs

Pulser-Receivers

Tone Burst Generator

Function Generators

Impedance Matching

Data Presentation Error Analysis

MeasurementTechniquesNormal Beam Inspect

Angle Beams I

Angle Beams II

Crack Tip Diffraction

Automated Scanning

Velocity Measurement

Measuring Attenuatio

Basic Principles of Ultrasonic Testing

rasonic Testing (UT) uses high frequency sound energy to conduct examinations and make

asurements. Ultrasonic inspection can be used for flaw detection/evaluation, dimensional

asurements, material characterization, and more. To illustrate the general inspection principle, a

ical pulse/echo inspection configuration as illustrated below will be used.

ypical UT inspection system consists of several functional units, such as the pulser/receiver,

nsducer, and display devices. A pulser/receiver is an electronic device that can produce high

tage electrical pulse. Driven by the pulser, the transducer generates high frequency ultrasonic

ergy. The sound energy is introduced and propagates through the materials in the form of waves.

hen there is a discontinuity (such as a crack) in the wave path, part of the energy will be reflected

ck from the flaw surface. The reflected wave signal is transformed into electrical signal by the

nsducer and is displayed on a screen. In the applet below, the reflected signal strength is displayed

sus the time from signal generation to when a echo was received. Signal travel time can be

ectly related to the distance that the signal traveled. From the signal, information about the

lector location, size, orientation and other features can sometimes be gained.

rasonic Inspection is a very useful and versatile NDT method. Some of the advantages of

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ntroduction to Ultrasonic Testing

Spread Spectrum

Signal Processing

Flaw Reconstruction

Calibration MethodsCalibration Methods

Corrections - DAC

Thompson-Gray Mode

UTSIM

Grain Noise Modeling

References/Standards

Selected ApplicatioRail Inspection

Weldments

Reference MaterialUT Material Properties

References

rasonic inspection that are often cited include:

It is sensitive to both surface and subsurface discontinuities.

The depth of penetration for flaw detection or measurement is superior to other NDT methods.

Only single-sided access is needed when the pulse-echo technique is used.

It is high accuracy in determining reflector position and estimating size and shape.

Minimal part preparation required.

Electronic equipment provides instantaneous results.

Detailed images can be produced with automated systems.

It has other uses such as thickness measurements, in addition to flaw detection.

with all NDT methods, ultrasonic inspection also has its limitations, which include:

Surface must be accessible to transmit ultrasound.

Skill and training is more extensive than with some other methods.

It normally requires a coupling medium to promote transfer of sound energy into test

specimen.

Materials that are rough, irregular in shape, very small, exceptionally thin or not homogeneous

are difficult to inspect.

Cast iron and other coarse grained materials are difficult to inspect due to low sound

transmission and high signal noise.

Linear defects oriented parallel to the sound beam may go undetected.

Reference standards are required for both equipment calibration, and characterization of flaws.

e above introduction provides a simplified introduction to the NDT method of ultrasonic testing.

wever, to effectively perform an inspection using ultrasonic, much more about the method needs

be known. The following pages present information on the science involved in ultrasonic

pection, the equipment that is commonly used, some of the measurement techniques used, as well

other information.

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History

Present State

Future Direction


Modes of Sound Wave


Wavelength/Flaw Det


Acoustic Impedance



Mode Conversion


Wave Interference



Radiated Fields

Transducers Beam Sp

Transducer Types



Transducer Modeling

Couplant

EMATs

Pulser-Receivers


Function Generators

Impedance Matching



Angle Beams I

Angle Beams II


Automated Scanning



History of Ultrasonics

or to World War II, sonar, the technique of sending sound waves through water and observing the

urning echoes to characterize submerged objects, inspired early ultrasound investigators to explore

ys to apply the concept to medical diagnosis. In 1929 and 1935, Sokolov studied the use of

rasonic waves in detecting metal objects. Mulhauser, in 1931, obtained a patent for using

rasonic waves, using two transducers to detect flaws in solids. Firestone (1940) and Simons (1945)

veloped pulsed ultrasonic testing using a pulse-echo technique.

ortly after the close of World War II, researchers in Japan began to explore medical diagnostic

pabilities of ultrasound. The first ultrasonic instruments used an A-mode presentation with blips onoscilloscope screen. That was followed by a B-mode presentation with a two dimensional, gray

le imaging.

an's work in ultrasound was relatively unknown in the United States and Europe until the 1950s.

en researchers presented their findings on the use of ultrasound to detect gallstones, breast masses,

d tumors to the international medical community. Japan was also the first country to apply Doppler

rasound, an application of ultrasound that detects internal moving objects such as blood coursing

ough the heart for cardiovascular investigation.

rasound pioneers working in the United States

ntributed many innovations and importantcoveries to the field during the following decades.

searchers learned to use ultrasound to detect

ential cancer and to visualize tumors in living

bjects and in excised tissue. Real-time imaging,

other significant diagnostic tool for physicians,

sented ultrasound images directly on the system's

RT screen at the time of scanning. The introduction

spectral Doppler and later color Doppler depicted

od flow in various colors to indicate speed of flow

d direction.

e United States also produced the earliest hand held "contact" scanner for clinical use, the second

neration of B-mode equipment, and the prototype for the first articulated-arm hand held scanner,

h 2-D images.

ginnings of Nondestructive Evaluation (NDE)

ndestructive testing has been practiced for many decades, with initial rapid developments in

trumentation spurred by the technological advances that occurred during World War II and the

bsequent defense effort. During the earlier days, the primary purpose was the detection of defects.

istory of Ultrasonics

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istory of Ultrasonics

Spread Spectrum

Signal Processing

Flaw Reconstruction


Corrections - DAC

Thompson-Gray Mode

UTSIM




Weldments


References

a part of "safe life" design, it was intended that a structure should not develop macroscopic defects

ring its life, with the detection of such defects being a cause for removal of the component from

vice. In response to this need, increasingly sophisticated techniques using ultrasonics, eddy

rents, x-rays, dye penetrants, magnetic particles, and other forms of interrogating energy emerged.

the early 1970's, two events occurred which caused a major change. The continued improvement

the technology, in particular its ability to detect small flaws, led to the unsatisfactory situation that

re and more parts had to be rejected, even though the probability of failure had not changed.

wever, the discipline of fracture mechanics emerged, which enabled one to predict whether a crack

a given size would fail under a particular load if a material property, fracture toughness, wereown. Other laws were developed to predict the rate of growth of cracks under cyclic loading

tigue). With the advent of these tools, it became possible to accept structures containing defects if

sizes of those defects were known. This formed the basis for new philosophy of "fail safe" or

amage tolerant" design. Components having known defects could continue in service as long as it

uld be established that those defects would not grow to a critical, failure producing size.

new challenge was thus presented to the nondestructive testing community. Detection was not

ough. One needed to also obtain quantitative information about flaw size to serve as an input to

cture mechanics based predictions of remaining life. These concerns, which were felt particularly

ongly in the defense and nuclear power industries, led to the creation of a number of research

grams around the world and the emergence of quantitative nondestructive evaluation (QNDE) as a

w discipline. The Center for Nondestructive Evaluation at Iowa State University (growing out of a

jor research effort at the Rockwell International Science Center); the Electric Power Research

titute in Charlotte, North Carolina; the Fraunhofer Institute for Nondestructive Testing in

arbrucken, Germany; and the Nondestructive Testing Centre in Harwell, England can all trace their

ts to those.

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History

Present State

Future Direction


Modes of Sound Wave


Wavelength/Flaw Det


Acoustic Impedance



Mode Conversion


Wave Interference



Radiated Fields

Transducers Beam Sp

Transducer Types



Transducer Modeling

Couplant

EMATs

Pulser-Receivers


Function Generators

Impedance Matching



Angle Beams I

Angle Beams II


Automated Scanning



Present State of Ultrasonics

rasonic testing (UT) has been practiced for

ny decades now. Initial rapid developments

nstrumentation spurred by the technological

vances from the 1950's continue today.

rough the 1980's and continuing into the

sent computers have provided technicians

h smaller and more rugged instruments with

ater capabilities.

ickness gauging is one example of instruments that have been refined to reduce operator error and

me on task by recording readings. This reduces the need for a "scribe" and allows the technician to

ord as many as 54,000 thickness values before downloading to a computer. Some instruments

ve the capability to capture waveforms as well as thickness readings. The waveform option allows

echnician to view or review the A-scan signal of thickness readings without being present during

inspection. Much research and development has gone into the understanding of sound reflectedm a surfaces that contains pitting or erosion as would be found on the inner surface of a pipe

rying product. This has lead to more consistent and accurate field measurements.

r sometime ultrasonic flaw detectors have incorporated a trigonometric function allowing for fast

d accurate location of indications when performing shear wave inspections. Cathode ray tubes, for

most part, have been replaced with LED or LCD screens. These screens in most cases are

remely easy to view in a wide range of ambient lighting. Bright or low light working conditions

countered by technicians have little effect on the technician's ability to view the screen. Screens

n be adjusted for brightness, contrast, and on some instruments even the color of the screen and

nal can be selected. Transducers can be programed with predetermined instrument settings. The

hnician only has to place the transducer in contact with the instrument, the instrument will then setiables such as range, delay, frequency, and gain as it is directed by the "chip" in the transducer.

ong with computers, robotics have contributed to the advancement of ultrasonic inspections. Early

the advantage of a stationary platform was recognized and used in industry. These systems were

duced by a number of companies. Automated systems produced a system known as the Ultragraph

20A. This system consisted of an immersion tank, bridge, and recording system for a printout of

scan. The resultant C-scan provides a plan or top view of the component. Scanning of

mponents was considerably faster than contact hand scanning, and the system provided a record of

inspection. Limitations included size and shape of the component, and also system cost.

resent State of Ultrasonics

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resent State of Ultrasonics

Spread Spectrum

Signal Processing

Flaw Reconstruction


Corrections - DAC

Thompson-Gray Mode

UTSIM




Weldments


References

mersion systems have advanced in many directions since the the 1960's. While robotics, as we

ow it, did not exist, the "immersion tanks" provided effective and sired inquiry into other means of

pection. Today robotics have allowed immersion transducers to inspect components without the

ed for immersing them in water. Squirter systems allow the transducer to pass over the component

nsmitting sound through a water column. Computers can be programed to inspect large, complex

aped components, with one or multiple transducers collecting information. This information is then

lected by a computer for evaluation, transmission to a customer, and finally archival of an image

t will maintain quality for years to come.

Today quantitative theories have been developed to describe theinteraction of the interrogating fields with flaws. Models

incorporating the results have been integrated with solid model

descriptions of real-part geometry's to simulate practical

inspections. Related tools allow NDE to be considered during the

design process on an equal footing with other failure-related

engineering disciplines. Quantitative descriptions of NDE

performance, such as the probability of detection (POD), have

become an integral part of statistical risk assessment.

Measurement procedures initially developed for metals have been

extended to engineered materials such as composites, where

sotropy and inhomogeneity have become important issues. The rapid advances in digitization andmputing capabilities have totally changed the faces of many instruments and the type of algorithms

t are used in processing the resulting data. High-resolution imaging systems and multiple

asurement modalities for characterizing a flaw have emerged. Interest is increasing not only in

ecting, characterizing, and sizing defects, but in characterizing the materials in which they occur.

als range from the determination of fundamental microstructural characteristics such as grain size,

rosity, and texture (preferred grain orientation), to material properties related to such failure

chanisms as fatigue, creep, and fracture toughness. As technology continues to advance,

plications of ultrasound advances. The high-resolution imaging systems in the laboratory today will

tools of the technician tomorrow.

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uture Direction




History

Present State

Future Direction


Modes of Sound Wave


Wavelength/Flaw Det


Acoustic Impedance



Mode Conversion


Wave Interference



Radiated Fields

Transducers Beam Sp

Transducer Types



Transducer Modeling

Couplant

EMATs

Pulser-Receivers


Function Generators

Impedance Matching



Angle Beams I

Angle Beams II


Automated Scanning



Future Direction of Ultrasonic Inspection

oking to the future, those in the field of NDE see an exciting new set of opportunities. Defense and

clear power industries have played a major role in the emergence of NDE. Increasing global

mpetition has led to dramatic changes in product development and business cycles. At the same

me aging infrastructure, from roads to buildings and aircraft, present a new set of measurement and

nitoring challenges for engineers as well as technicians.

mong the new applications of NDE spawned by

se changes is the increased emphasis on the use of

DE to improve productivity of manufacturingcesses. Quantitative nondestructive evaluation

NDE) both increases the amount of information

out failure modes and the speed with which

ormation can be obtained and facilitates the

velopment of in-line measurements for process

ntrol.

e phrase, "you can not inspect in quality, you must build it in," exemplifies the industry's focus on

oiding the formation of flaws. Nevertheless, flaws and the need to identify them, both during

nufacture and in service, will never disappear and continual development of flaw detection and

aracterization techniques are necessary.

vanced simulation tools that are designed for inspectability and their integration into quantitative

ategies for life management will contribute to increase the number and types of engineering

plications of NDE. With growth in engineering applications for NDE, there will be a need to

panded the knowledge base of technicians performing the evaluations. Advanced simulation tools

d in the design for inspectability may be used to provide technical students with a greater

derstanding of sound behavior in materials. UTSIM developed at Iowa State University provides ampse into what may be used in the technical classroom as an interactive laboratory tool.

globalization continues, companies will seek to develop, with ever increasing frequency, uniform

ernational practices. In the area of NDE, this trend will drive the emphases on standards, enhanced

ucational offerings, and simulations that can be communicated electronically.

e coming years will be exciting as NDE will continue to emerge as a full-fledged engineering

cipline.

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History

Present State

Future Direction


Modes of Sound Wave


Wavelength/Flaw Det


Acoustic Impedance



Mode Conversion


Wave Interference



Radiated Fields

Transducers Beam Sp

Transducer Types



Transducer Modeling

Couplant

EMATs

Pulser-Receivers


Function Generators

Impedance Matching



Angle Beams I

Angle Beams II


Automated Scanning



Wave Propagation

rasonic testing is based on time-varying deformations or vibrations in materials, which is

nerally referred to as acoustics. All material substances are comprised of atoms, which may be

ced into vibrational motion about their equilibrium positions. Many different patterns of

rational motion exist at the atomic level, however, most are irrelevant to acoustics and ultrasonic

ting. Acoustics is focused on particles that contain many atoms that move in unison to produce a

chanical wave. When a material is not stressed in tension or compression beyond its elastic limit,

individual particles perform elastic oscillations. When the particles of a medium are displaced

m their equilibrium positions, internal (electrostatic) restoration forces arise. It is these elastic

toring forces between particles, combined with inertia of the particles, that leads to oscillatory

tions of the medium.

solids, sound waves can propagate in four principle modes that are based on the way the particles

illate. Sound can propagate as longitudinal waves, shear waves, surface waves, and in thin

terials as plate waves. Longitudinal and shear waves are the two modes of propagation most

dely used in ultrasonic testing. The particle movement responsible for the propagation of

gitudinal and shear waves is illustrated below.

Wave Propagation

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Wave Propagation

Spread Spectrum

Signal Processing

Flaw Reconstruction


Corrections - DAC

Thompson-Gray Mode

UTSIM




Weldments


References

longitudinal waves, the oscillations occur in the

gitudinal direction or the direction of wave

pagation. Since compressional and dilational forces

active in these waves, they are also called pressure

compressional waves. They are also sometimes

led density waves because their particle density

ctuates as they move. Compression waves can be

nerated in liquids, as well as solids because the

ergy travels through the atomic structure by a series

comparison and expansion (rarefaction)vements.

the transverse or shear wave, the particles oscillate at

ght angle or transverse to the direction of

pagation. Shear waves require an acoustically solid

terial for effective propagation and, therefore, are not

ectively propagated in materials such as liquids or

ses. Shear waves are relatively weak when

mpared to longitudinal waves In fact, shear waves are

ually generated in materials using some of the energy

m longitudinal waves.

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-IntroductionUltrasonic

Testing


History

Present State

Future Direction

Physics ofUltrasoundWave Propagati

Modes of Sound

WavesProperties of Pla

Waves

Wavelength/Flaw

Detection

Elastic Propertie

Solids

Attenuation

Acoustic Impeda

Reflection/

Transmission

Refraction & Sne

Law

Mode ConversioSignal-to-noise

Wave Interferen

Equipment &TransducersPiezoelectric

Transducers

Characteristics o

Radiated Fields

Transducers Bea

Spread

Transducer TypeTransducer Test

Transducer Test

Transducer Mod

Couplant

EMATs

Pulser-Receivers

Tone Burst Gene

Function Genera

Impedance Matc

Data Presentatio

Error Analysis

Modes of Sound Wave Propagation

air, sound travels by compression and rarefaction of air molecules in the direction of travel. However, in

ids, molecules can support vibrations in other directions, hence, a number of different types (modes) of

und waves are possible. As mentioned previously, longitudinal and transverse (shear) waves are most

en used in ultrasonic inspection. However, at surfaces and interfaces, various types of elliptical or

mplex vibrations of the particles make other waves possible. Some of these wave modes such as

yleigh and Lamb waves are also useful for ultrasonic inspection.

e table below summarizes many, but not all, of the wave modes possible in solids.

Wave Types in Solids Particle Vibrations

ongitudinal Parallel to wave direction

ansverse (Shear) Perpendicular to wave direction

urface - Rayleigh Elliptical orbit - symmetrical mode

ate Wave - Lamb Component perpendicular to surface (extensional wave)

ate Wave - Love Parallel to plane layer, perpendicular to wave direction

oneley (Leaky Rayleigh Waves) Wave guided along interface

ezawa Antisymmetric mode

ngitudinal and transverse waves were discussed on the previous page, so let's touch on surface and plate

ves here.

rface or Rayleigh waves travel the surface of a relative thick solid material penetrating to a depth of one

velength. The particle movement has an elliptical orbit as shown in the image and animation below.

yleigh waves are useful because they are very sensitive to surface defects and since they will follow the

face around, curves can also be used to inspect areas that other waves might have difficulty reaching.


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MeasurementTechniquesNormal Beam

Inspection

Angle Beams I

Angle Beams II

Crack Tip Diffrac

Automated Scan

Velocity

Measurements

Measuring AttenSpread Spectrum

Signal Processin

Flaw Reconstruc

Calibration MeCalibration Meth

Corrections - DA

Thompson-Gray

UTSIM

Grain Noise Mod

References/Stan

SelectedApplicationsRail Inspection

Weldments

Reference MatUT Material Prop

References

te waves can be propagated only in very thin metals. Lamb

ves are the most commonly used plate waves in NDT. Lamb

ves are a complex vibrational wave that travels through the

ire thickness of a material. Propagation of Lamb waves

pends on density, elastic, and material properties of a

mponent, and they are influenced by a great deal by selected

quency and material thickness. With Lamb waves, a number

modes of particle vibration are possible, but the two most

mmon are symmetrical and asymmetrical. The complextion of the particles is similar to the elliptical orbits for

face waves.

e generation of waves using both piezoelectric transducers and electromagnetic acoustic transducers

MATs) are discussed in later sections.

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History

Present State

Future Direction


Modes of Sound Wave


Wavelength/Flaw Det


Acoustic Impedance



Mode Conversion


Wave Interference



Radiated Fields

Transducers Beam Sp

Transducer Types



Transducer Modeling

Couplant

EMATs

Pulser-Receivers


Function Generators

Impedance Matching



Angle Beams I

Angle Beams II


Automated Scanning



Properties of Acoustic Plane Wave

avelength, Frequency and Velocity

mong the properties of waves propagating in isotropic solid materials are wavelength, frequency,

d velocity. The wavelength is directly proportional to the velocity of the wave and inversely

portional to the frequency of the wave. This relationship is shown by the following equation.

e applet below shows a longitudinal and transverse wave. The direction of wave propagation is

m left-to-right and the movement of the lines indicate the direction of particle oscillation. The

uation relating ultrasonic wavelength, frequency, and propagation velocity is included at the

tom of the applet in a reorganized form. The values for the wavelength, frequency, and wave

ocity can be adjusted in the dialog boxes to see their effects on the wave. Note that the value must

set to keep the frequency value between 0.1 to 1 MHz or million cycles per second, and the wave

ocity must be between 0.1 and 0.7 cm/us.

can be noted by the equation, a change in frequency will result in a change in wavelength. Change

frequency in the applet and view the resultant wavelength. At a frequency of .2 and a material

ocity of 0.585 (longitudinal wave in steel) note the resulting wavelength. Adjust the material

ocity to 0.480 (longitudinal wave in cast iron) note the resulting wavelength. Increase the

quency to 0.8 and note the shortened wavelength in each material.

ultrasonic testing, the shorter wavelength resulting from an increase in frequency will usually

vide for the detection of smaller discontinuities. This will be discussed more in following

terials.

roperties of Acoustic Plane Wave

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Wavelength & Defect Detection




History

Present State

Future Direction


Modes of Sound Wave


Wavelength/Flaw Det


Acoustic Impedance



Mode Conversion


Wave Interference



Radiated Fields

Transducers Beam Sp

Transducer Types



Transducer Modeling

Couplant

EMATs

Pulser-Receivers


Function Generators

Impedance Matching



Angle Beams I

Angle Beams II


Automated Scanning



Wavelength and Defect Detection

ultrasonic testing the inspector must make a decision about the frequency of the transducer that

l be used. As we learned on the previous page, changing the frequency when the sound velocity is

ed will result in a change in the wavelength of the sound. The wavelength of the ultrasound used

significant affect on the probability of detecting a discontinuity. A rule of thumb in industrial

pections is that discontinuities that are larger than one-half the size of wavelength can be usually

detected.

nsitivity and resolution are two terms that are often used in ultrasonic inspection to describe a

hnique's ability to locate flaws. Sensitivity is the ability to locate small discontinuities. Sensitivitynerally increases with higher frequency (shorter wavelengths). Resolution is the ability of the

tem to locate discontinuities that are close together within the material or located near the part

face. Resolution also generally increases as the frequency increases.

e wave frequency can also affect the capability of an inspection in adverse ways. Therefore,

ecting the optimal inspection frequency often involves maintaining a balance between favorable

d unfavorable results of the selection. Before selecting an inspection frequency, the grain structure,

terial thickness, size, type, and probable location of the discontinuity should be considered. As

quency increases, sound tends to scatter from large or course grain structure and from small

perfections within a material. Cast materials often have coarse grains and other sound scatters that

uire lower frequencies to be used for evaluations of these products. Wrought and forged productsh directional and refined grain structure, can usually be inspected with higher frequency

nsducers.

nce more things in a material are likely to scatter a portion of the sound energy at higher

quencies, the penetrating power (or the maximum depth in a material that flaws can be located) is

o reduced. Frequency also has an effect on the shape of the ultrasonic beam. Beam spread, or the

ergence of the beam from the center axis of the transducer, and how it is affected by frequency

l be discussed later.

hould be mentioned, so as not to be misleading, that a number of other variables will also affect

ability of ultrasound to locate defects. These include pulse length, type and voltage applied to the

stal, properties of the crystal, backing material, transducer diameter, and the receiver circuitry of

instrument. These are discussed in more detail in the material on signal-to-noise ratio.

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History

Present State

Future Direction


Modes of Sound Wave


Wavelength/Flaw Det


Acoustic Impedance



Mode Conversion


Wave Interference



Radiated Fields

Transducers Beam Sp

Transducer Types



Transducer Modeling

Couplant

EMATs

Pulser-Receivers


Function Generators

Impedance Matching



Angle Beams I

Angle Beams II


Automated Scanning



Sound Propagation in Elastic Materials

the previous pages, it was pointed out that sound waves

pagate due to the vibrations or oscillatory motions of

ticles within a material. An ultrasonic wave may be

ualized as an infinite number of oscillating masses or

ticles connected by means of elastic springs. Each

ividual particle is influenced by the motion of its nearest

ghbor and both inertial and elastic restoring forces act upon

h particle.

mass on a spring has a single resonant frequency determined by its spring constant k and its mass

The spring constant is the restoring force of a spring per unit of length. Within the elastic limit of

y material, there is a linear relationship between the displacement of a particle and the force

empting to restore the particle to its equilibrium position. This linear dependency is described by

oke's Law.

terms of the spring model, Hooke's Law says that

restoring force due to a spring is proportional to

length that the spring is stretched, and acts in the

posite direction. Mathematically, Hooke's Law istten, F = -kx, where F is the force, k is the spring

nstant, and x is the amount of particle

placement. Hooke's law is represented graphically

he right. Please note that the spring is applying a

ce to the particle that is equal and opposite to the

ce pulling down on the particle.

e Speed of Sound

oke's Law when used along with Newton's Second Law can explain a few things about the speedsound. The speed of sound within a material is a function of the properties of the material and is

ependent of the amplitude of the sound wave. Newton's Second Law says that the force applied to

article will be balanced by the particle's mass and the acceleration of the the particle.

athematically, Newton's Second Law is written as F = ma. Hooke's Law then says that this force

l be balanced by a force in the opposite direction that is dependent on the amount of displacement

d the spring constant (F = -kx). Therefore, since the applied force and the restoring force are equal,

=-kx can be written. The negative sign indicates that the force is in the opposite direction.

nce the mass m and the spring constant k are constants for any given material, it can be seen that

acceleration a and the displacement x, are the only variables. It can also be seen that they are

lastic Properties of Solids

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ectly proportional. So if the displacement of the particle increases, so does its acceleration. It turns

that the time that it takes a particle to move and return to its equilibrium position is independent

the force applied. So, within a given material, sound always travels at the same speed no matter

w much force is applied when other variables, such as temperature, are held constant.

hat properties of material affect its speed of sound?

course, sound does travel at different speeds in different materials. This is because the mass of the

mic particles and the spring constants are different for different materials. The mass of the

ticles is related to the density of the material, and the spring constant is related to the elastic

nstants of a material. The general relationship between the speed of sound in a solid and its density

d elastic constants is given by the following equation:

here V is the speed of sound, C is the elastic constant, and p is the material density. This equation

y take a number of different forms depending on the type of wave (longitudinal or shear) and

ich 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 substance's resistance to shear.

Lame's Constants, l and m: material constants that are derived from Young's Modulus and

Poisson's Ratio.

hen calculating the velocity of a longitudinal wave, Young's Modulus and Poisson's Ratio are

mmonly used. When calculating the velocity of a shear wave, the shear modulus is used. It is often

st convenient to make the calculations using Lame's Constants, which are derived from Young's

odulus and Poisson's Ratio.

must also be mentioned that the subscript ij attached to C in the above equation is used to indicate

directionality of the elastic constants with respect to the wave type and direction of wave travel.

sotropic materials, the elastic constants are the same for all directions within the material.

wever, most materials are anisotropic and the elastic constants differ with each direction. For

ample, in a piece of rolled aluminum plate, the grains are elongated in one direction and

mpressed in the others and the elastic constants for the longitudinal direction are different thanse for the transverse or short transverse directions.

amples 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.

amples of approximate shear sound velocities in materials are:




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Aluminum - 0.313 cm/microsecond

1020 steel - 0.324 cm/microsecond

Cast iron - 0.240 cm/microsecond.

hen comparing compressional and shear velocities it can be noted that shear velocity is

proximately one half that of compressional. The sound velocities for a variety of materials can be

nd in the ultrasonic properties tables in the general resources section of this site.



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History

Present State

Future Direction


Modes of Sound Wave


Wavelength/Flaw Det


Acoustic Impedance



Mode Conversion


Wave Interference



Radiated Fields

Transducers Beam Sp

Transducer Types



Transducer Modeling

Couplant

EMATs

Pulser-Receivers


Function Generators

Impedance Matching



Angle Beams I

Angle Beams II


Automated Scanning



Attenuation of Sound Waves

hen sound travels through a medium, its intensity diminishes with

tance. In idealized materials, sound pressure (signal amplitude) is only

uced by the spreading of the wave. Natural materials, however, all

duce an effect which further weakens the sound. This further weakening

ults from two basic causes, which are scattering and absorption. The

mbined effect of scattering and absorption is called attenuation.

enuation of sound within a material itself is often not of intrinsic interest. However, natural

perties and loading conditions can be related to attenuation. Attenuation often serves as aasurement tool that leads to the formation of theories to explain physical or chemical phenomenon,

ich decreases the ultrasonic intensity.

rasonic attenuation is the decay rate of mechanical radiation at ultrasonic frequency as it

pagates through material. A decaying plane wave is expressed as:

this expression A0 is the amplitude of the propagating wave at some location. The amplitude A is

reduced amplitude after the wave has traveled a distance z from that initial location. The

antity is the attenuation coefficient of the wave traveling in the z-direction. The dimensions of

are nepers/length, where a neper is a dimensionless quantity. e is Napier's constant which is

ual to approximately 2.71828.

e units of the attenuation value in nepers/length can be converted to decibels/length by dividing by

151. Decibels is a more common unit when relating the amplitudes of two signals.

enuation is generally proportional to the square of sound frequency. Quoted values of attenuation

often given for a single frequency, or an attenuation value averaged over many frequencies may

given. Also, the actual value of the attenuation coefficient for a given material is highly dependent

the way in which the material was manufactured. Thus, quoted values of attenuation only give a

gh indication of the attenuation and should not be automatically trusted. Generally, a reliable

ue of attenuation can only be obtained by determining the attenuation experimentally for the

ticular material being used.

enuation can be determined by evaluating the multiple backwall reflections seen in a typical A-

n display like the one shown in the image above. The number of decibels between two adjacent

ttenuation of Sound Waves

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nals is measured and this value is divided by the time interval between them. This calculation

duces a attention coefficient in decibels per unit time Ut. This value can be converted to nepers/

gth by the following equation.

here v is the velocity of sound in meters per second and Ut is decibels per second.

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coustic Impedance




History

Present State

Future Direction


Modes of Sound Wave


Wavelength/Flaw Det


Acoustic Impedance



Mode Conversion


Wave Interference



Radiated Fields

Transducers Beam Sp

Transducer Types



Transducer Modeling

Couplant

EMATs

Pulser-Receivers


Function Generators

Impedance Matching



Angle Beams I

Angle Beams II


Automated Scanning



Acoustic Impedance

und travels through materials under the influence of sound pressure. Because molecules or atoms

a solid are bound elastically to one another, the excess pressure results in a wave propagating

ough the solid.

e acoustic impedance (Z) of a material is defined as the product of density (p) and acoustic

ocity (V) of that material.

Z = pV

oustic impedance is important in

1. the determination of acoustic transmission and reflection at the boundary of two materials

having different acoustic impedance

2. the design of ultrasonic transducers.

3. assessing absorption of sound in a medium.

e following figure will help you calculate the acoustic impedance for any material, so long as you

ow its density (p) and acoustic velocity (V). You may also compare two materials and "see" how

y reflect and transmit sound energy. The red arrow represents energy of the reflected sound, whileblue arrow represents energy of the transmitted sound. The

lected energy is the square of the difference divided by the sum of the acoustic impedances of the

o materials.

Note that Transmitted Sound Energy + Reflected Sound Energy = 1

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History

Present State

Future Direction


Modes of Sound Wave


Wavelength/Flaw Det


Acoustic Impedance



Mode Conversion


Wave Interference



Radiated Fields

Transducers Beam Sp

Transducer Types



Transducer Modeling

Couplant

EMATs

Pulser-Receivers


Function Generators

Impedance Matching



Angle Beams I

Angle Beams II


Automated Scanning



Reflection and Transmission Coefficients (Pressure)

rasonic waves are reflected at boundaries where there are differences in acoustic impedance, Z.

is is commonly referred to as impedance mismatch. The fraction of the incident-wave intensity in

lected waves can be derived because particle velocity and local particle pressures are required to

continuous across the boundary between materials.

rmulation for acoustic reflection and transmission coefficients (pressure) are shown in the

eractive figure below. Different materials may be selected or you may alter the material velocity or

nsity to change the acoustic impedance of one or both materials. The red arrow represents reflected

und, while the blue arrow represents transmitted sound.

te that reflection and transmission coefficients are often expressed in decibels (dB), where decibels

defined as 20 times the log of the reflection or transmission coefficient.

multiplying the resulting numbers by 100, the energy reflected can be calculated in percent of

ginal energy. Using the above applet, note that the energy reflected at a water steel interface is

8 or 88%. 0.12 or 12% is transmitted into the component. If reflection and transmission at

erfaces is followed through the component, and loss by attenuation is ignored, a small percentagethe original energy returns to the transducer.

suming acoustic energy at the transducer is 100% and energy transmitted into a component at a

ter steel interface is 12% as discussed above. At the second interface (back surface) 88% or

56% would be reflected and 12% transmitted into the water. The final interface would allow only

% of 10.56 or 1.26% of the original energy to be transmitted back to the transducer.

eflection and Transmission

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-Introductito Ultrason

Testing

IntroductionBasic Principle

History

Present State

Future Directi

Physics ofUltrasoundWave Propaga

Modes of Sou

WavesProperties of

Waves

Wavelength/F

Detection

Elastic Proper

Solids

Attenuation

Acoustic Impe

Reflection/

Transmission

Refraction & S

Law

Mode ConversSignal-to-nois

Ratio

Wave Interfer


Transducers

Characteristic

PT

Radiated Field

Transducers BSpread

Transducer Ty

Transducer Te

I

Transducer Te

II

Transducer

Modeling

Couplant

EMATs

Pulser-Receiv

Tone Burst

Refraction and Snell's Law

hen an ultrasound wave passes through an interface between two materials at an

ique angle, and the materials have different indices of refraction, it produces both

lected and refracted waves. This also occurs with light and this makes objects you

across an interface appear to be shifted relative to where they really are. For

ample, if you look straight down at an object at the bottom of a glass of water, it

ks closer than it really is. A good way to visualize how light and sound refract is

shine a flashlight into a bowl of slightly cloudy water noting the refraction angle

h respect to the incidence angle.

fraction takes place at an interface due to the different velocities of the acoustic waves within the two

terials. The velocity of sound in each material is determined by the material properties (elastic modules

d density) for that material. In the animation below, a series of plane waves are shown traveling in one

terial and entering a second material that has a higher acoustic velocity. Therefore, when the wave

counters the interface between these two materials, the portion of the wave in the second material isving faster than the portion of the wave in the first material. It can be seen that this causes the wave to

nd.

ell's Law describes the relationship between the angles and the velocities of the waves. Snell's law equates

ratio of material velocities v1 and v2 to the ratio of the sine's of incident (Θ1) and refraction (Θ2) angles,

efraction and Snell's Law

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efraction and Snell's Law

Generators

Function Gene

Impedance

Matching

Data Presenta

Error Analysis

MeasuremenTechniquesNormal Beam

InspectionAngle Beams

Angle Beams

Crack Tip Diff

Automated

Scanning

Velocity

Measurement

Measuring

Attenuation

Spread Spect

Signal Process

Flaw Reconstr

CalibrationMethodsCalibration Me

Corrections -

Thompson-Gr

Model

UTSIM

Grain Noise

Modeling

References/

Standards

SelectedApplicationsRail Inspectio

Weldments

ReferenceMaterialUT Material

Properties

References

shown in the following equation.

Where:

VL1

is the longitudinal wave velocity in material 1.

VL2 is the longitudinal wave velocity in material 2.

te that in the diagram, there is a reflected longitudinal wave (VL1) shown. This wave is reflected at the

me angle as the incident wave because the two waves are traveling in the same material and, therefore,

ve the same velocities. This reflected wave is unimportant in our explanation of Snell's Law, but it should

remembered that some of the wave energy is reflected at the interface. In the applet below, only theident and refracted longitudinal waves are shown. The angle of either wave can be adjusted by clicking

d dragging the mouse in the region of the arrows. Values for the angles or acoustic velocities can also be

ered in the dialog boxes so the that applet can be used as a Snell's Law calculator.

hen a longitudinal wave moves from a slower to a faster material, there is an incident angle that makes the

gle of refraction for the wave 90°. This is know as the first critical angle. The first critical angle can be

nd from Snell's law by putting in an angle of 90° for the angle of the refracted ray. At the critical angle ofidence, much of the acoustic energy is in the form of an inhomogeneous compression wave, which travels

ng the interface and decays exponentially with depth from the interface. This wave is sometimes referred

as a "creep wave." Because of there inhomogeneous nature and the fact that they decay rapidly, creep

ves are not used as extensively as Rayleigh surface waves in NDT. However, creep waves are sometimes

ful because they suffer less from surface irregularities and coarse material microstructure, due to their

ger wavelengths, than Rayleigh waves.

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History

Present State

Future Direction


Modes of Sound Wave


Wavelength/Flaw Det


Acoustic Impedance



Mode Conversion


Wave Interference



Radiated Fields

Transducers Beam Sp

Transducer Types



Transducer Modeling

Couplant

EMATs

Pulser-Receivers


Function Generators

Impedance Matching



Angle Beams I

Angle Beams II


Automated Scanning



Mode Conversion

hen sound travels in a solid material, one form of wave energy can be transformed into another

m. For example, when a longitudinal waves hits an interface at an angle, some of the energy can

use particle movement in the transverse direction to start a shear (transverse) wave. Mode

nversion, occurs when a wave encounters an interface between materials of different acoustic

pedance and the incident angle is not normal to the interface. From the ray tracing movie below it

n be seen that since mode conversion occurs every time a wave encountered interface at an angle,

rasonic signals can become confusing at times.

the previous section it was pointed out that when sound waves pass through an interface between

terials having different acoustic velocities, refraction takes place at the interface. The larger the

ference in acoustic velocities between the two materials, the more the sound is refracted. Notice

t the shear wave is not refracted as much as the longitudinal wave. This occurs because shear

ves travel slower than longitudinal waves. Therefore, the velocity difference between the incident

gitudinal wave and the shear wave is not as great as it is between the incident and refracted

gitudinal waves. Also note that when a longitudinal wave is reflected inside the material, the

lected shear wave is reflected at a smaller angle than the reflected longitudinal wave. This is also

e to the fact that the shear velocity is less than the longitudinal velocity within a given material.

Mode Conversion

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Mode Conversion

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

here:



VS1 is the shear wave velocity in material 1.

VS2 is the shear wave velocity in material 2.

the applet below, the shear (transverse) wave ray path has been added. The ray paths of the waves

n be adjusted by clicking and dragging in the vicinity of the arrows. Values for the angles or the

ve velocities can also be entered into the dialog boxes. It can be seen from the applet that when a

ve moves from a slower to a faster material, there is an incident angle which makes the angle ofraction for the longitudinal wave 90 degrees. As mentioned on the previous page, this is know as

first critical angle and all of the energy from the refracted longitudinal wave is now converted to a

face following longitudinal wave. This surface following wave is sometime referred to as a creep

ve and it is not very useful in NDT because it dampens out very rapidly. Beyond the first critical

gle, only the shear wave propagates down into the material. For this reason, most angle beam

nsducers use a shear wave so that the signal is not complicated by having two wave present. In

y cases, there is also an incident angle that makes the angle of refraction for the shear wave 90

grees. This is know as the second critical angle and at this point, all of the wave energy is reflected

refracted into a surface following shear wave or shear creep wave. Slightly beyond the second

tical angle, surface waves will be generated.




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Mode Conversion

te that the applet defaults to compressional velocity in the second material. The refracted

mpressional wave angle will be generated for given materials and angles. To find the angle of

idence required to generate a shear wave at a given angle complete the

lowing:

1. Verify V1 is the longitudinal wave velocity for wedge or immersion liquid.

2. Change V2 to the shear wave velocity (approximately one-half compressional) for the

material to be inspected.

3. Change Q2 to the desired shear wave angle.

4. Read Q1, the correct angle of incidence.



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ignal-to-Noise Ratio




History

Present State

Future Direction


Modes of Sound Wave


Wavelength/Flaw Det


Acoustic Impedance



Mode Conversion


Wave Interference



Radiated Fields

Transducers Beam Sp

Transducer Types



Transducer Modeling

Couplant

EMATs

Pulser-Receivers


Function Generators

Impedance Matching



Angle Beams I

Angle Beams II


Automated Scanning



Signal-to-Noise Ratio

a previous page, the effect that frequency or wavelength has on flaw detectability was discussed.

wever, the detection of a defect involves many factors other than the relationship of wavelength

d flaw size. For example, the amount of sound that reflects from a defect is also dependent acoustic

pedance mismatch between the flaw and the surrounding material. A void is generally a better

lector than a metallic inclusion because the impedance mismatch is greater between air and metal

n between metal and another metal.

ten, the surrounding material has competing reflections. Microstructure grains in metals and the

gregate of concrete are a couple of examples. A good measure of detectability of a flaw is its signal-

noise ratio (S/N). The signal-to-noise ratio is a measure of how the signal from the defect

mpares to other background reflections (categorized as "noise"). A signal to noise ratio of 3 to 1 is

en required as a minimum. The absolute noise level and the absolute strength of an echo from a

mall" defect depends on a number of factors:

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.

Cracks and volumetric defects can reflect ultrasonic waves quite differently. Many cracks are

"invisible" from one direction and strong reflectors from another.

Multifaceted flaws will tend to scatter sound away from the transducer.

e following formula relates some of the variables affecting the signal-to-noise ratio (S/N) of a

fect:

ther than go into the details of this formulation, a few fundamental relationships can be pointed

. The signal-to-noise ratio (S/N), and therefore the detectability of a defect

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increases with increasing flaw size (scattering amplitude). The detectability of a defect is

directly proportional to its size.

increases with a more focused beam. In other words, flaw detectability is inversely

proportional to the transducer beam width.

increases with decreasing pulse width (delta-t). In other words, flaw detectability is inversely

proportional to the duration of the pulse 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.

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.

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 with about rate with

changing frequency. So, in some cases, the signal-to-noise ratio (S/N) can be somewhat

independent of frequency.

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Wave Interaction


-Introduction Ultrasonic

Testing


History

Present State

Future Direction

Physics ofUltrasoundWave Propagation

Modes of Sound W

Properties of PlanWaves

Wavelength/Flaw

Detection

Elastic Properties

Solids

Attenuation

Acoustic Impedan

Reflection/Transm

Refraction & Snel

Mode Conversion

Signal-to-noise R

Wave Interferenc


Transducers

Characteristics of

Radiated Fields

Transducers Beam

Spread

Transducer Types

Transducer Testin

Transducer Testin

Transducer ModeCouplant

EMATs

Pulser-Receivers

Tone Burst Gener

Function Generat

Impedance Match

Data Presentation

Error Analysis

MeasurementTechniquesNormal Beam

Wave Interaction or Interference

fore we move into the next section, the subject of wave interaction must be covered since it is

portant when trying to understand the performance of an ultrasonic transducer. On the previous pages,

ve propagation was discussed as if a single sinusoidal wave was propagating through the material.

wever, the sound that emanates from an ultrasonic transducer does not originate from a single point,

instead originates from many points along the surface of the piezoelectric element. This results in a

und field with many waves interacting or interfering with each other.

hen waves interact, they superimpose on each other, and the amplitude of the sound pressure or particle

placement at any point of interaction is the sum of the amplitudes of the two individual waves. First,

s consider two identical wave that originate from the same point. When they are in phase (so that the

aks and valleys of one are exactly aligned with those of the the other), they combine to double the

placement of either wave acting alone. When they are completely out of phase (so that the peaks of

e wave are exactly aligned with the valleys of the other wave), they combine to cancel each other out.

hen the two waves are not completely in phase or out of phase, the resulting wave is the sum of the

ve amplitudes for all points along the wave.

hen the origins of the two interacting waves is not the same, it is a little

der to picture the wave interaction, but the principles are the same. Up

il now, we have primarily looked at waves in the form of a 2d plot ofve amplitude versus wave position. However, anyone that has dropped

mething in a pool of water, can picture the waves radiating out from the

urce with a circular wave front. If two objects are dropped a short distance

art into the pool of water, their waves will radiate out from their sources

d interact with each other. At every point where the waves interact, the

plitude of the particle displacement is the combined sum of the amplitude

the particle displacement of the individual waves.

th an ultrasonic transducer, the waves propagate out from the transducer

e with a circular wave front. If it were possible to get them to propagate

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