Discuss about Plate waves and How Ultrasonic waves are used for ultrasonic testing

1. NON –DESTRUCTIVE TESTING(RME-080)
BASICS OF ULTRASONIC TESTING-2
Prepared By : Rohit Sahu
Assistant Professor (ME)
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DEPARTMENT OF MECHANICAL ENGINEERING
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provided by the presenter are for educational purposes only. Nothing conveyed or provided
should be considered legal, accounting or tax advice.

2. BASICS OF ULTRASONIC TESTING-2
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 for example, elliptical or other complex kind of paths in the movement of the particles, as the
sound moves through the medium.
 So, this kind of elliptical or other complex vibration, which are generated on the surface are known
as surface or Rayleigh waves, which are generated in relatively thick samples. if the sound is
moving in this direction, so, you can have a particle movement path, like in an elliptical path. So,
this will be the movement of the particles and through this kind of movement, you will generate the
motion for the waves in the horizontal direction. So, this kind of waves which are generated at
surfaces or interfaces, in thick materials, they are known as surface or Rayleigh waves.
*Source- NPTEL Lecture 16 Theory and Practice of Non Destructive Testing by Dr. Ranjit Bauri Dept. of Metallurgical & Materials Engineering IIT Madras, Ultrasonic Testing

3. BASICS OF ULTRASONIC TESTING-2
And in thin plates, plate waves generated and this can be further divided into two
categories; one is known as Lamb and the other one is known as Love. So, Lamb is the
component of the vibration, which is perpendicular to the surface and Love is parallel to
the plane layer and perpendicular to the direction of the waves. So, these are two
different types of plate waves that you can find on thin plates; one is Lamb and another
is Love.
And in the lamb waves, you can have a symmetric lamb, like this, symmetric lamb or
these are also known as extensional waves and you could also have asymmetric, as
shown in the image and this is in flexible mode. So, these are different types of
ultrasonic waves.
Source- NPTEL Lecture 16 Theory and Practice of Non Destructive Testing by Dr. Ranjit Bauri Dept. of Metallurgical & Materials Engineering IIT Madras, Ultrasonic Testing
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4. BASICS OF ULTRASONIC TESTING-2
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 for example, if you talk loudly in an empty room, the walls will reflect the sound and
you will get an echo. So, while doing ultrasonic testing, these ultrasonic waves are
sent into the sample and when these waves are reflected back, they are collected by
a transducer, which finally will generate the signal, if there is any defect. So, this
defect will also act as a reflector, which can reflect the sound waves, but in that case
the reflection interface is much smaller compared to a wall. So, that means, the
energy which is there in the reflected waves should be enough for the transducer or
the instrument to collect this signal back.
 The energy in the transmitted sound waves will depend on the sound pressure,
which is created by these traveling waves. You might know that sound waves travel
through a medium by oscillatory movement of the atoms or the particles and this
movement is due to the local pressure, which is created by sound. So, this pressure
is the excess pressure above the atmospheric pressure.
 When sound waves are travelling through a medium, this local pressure provides
some movement to the atoms and due to the bonding between the atoms, it creates
an oscillatory movement, which in turn, will create a wave.
Source- NPTEL Lecture 16 Theory and Practice of Non Destructive Testing by Dr. Ranjit Bauri Dept. of Metallurgical & Materials Engineering IIT Madras, Ultrasonic Testing

5. BASICS OF ULTRASONIC TESTING-2
So, let us say, this local pressure which is created by the sound is P
and it provides a velocity to the particles or the atoms, which is Q,
because this will provide some movement to the particles of the atom.
the velocity of that movement is Q. So, P will be proportional to Q.
P α Q
Higher the P, higher will be the movement between the atoms. Now, if
you introduce a proportionality constant. Equation can be write
P = ZQ
This Z is known as acoustic impedance. So, this is nothing but the total
resistance to the movement of sound waves through a particular
medium.
Source- NPTEL Lecture 16 Theory and Practice of Non Destructive Testing by Dr. Ranjit Bauri Dept. of Metallurgical & Materials
Engineering IIT Madras, Ultrasonic Testing
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6. BASICS OF ULTRASONIC TESTING-2
 And the energy of the transmitted beam, the energy in the
transmitted waves, E, is again dependent on the pressure P,
 Where ρ is the density of the medium and V is the velocity of
sound waves through the medium.
 So, you should have enough energy, first of all in the
transmitted sound waves which go to the sample and then,
when it is reflected back, that reflected waves also should
have enough energy, so that the instrument which is used for
doing ultrasonic testing should be able to capture it.
*Source- NPTEL Lecture 16 Theory and Practice of Non Destructive Testing by Dr. Ranjit Bauri Dept. of Metallurgical & Materials
Engineering IIT Madras, Ultrasonic Testing
6

7. BASICS OF ULTRASONIC TESTING-2
 To get an expression for P and Q, if the wave is represented by an equation,
Y= YO sin(ωt-kx)
 So, if this be the wave, where YO is the amplitude, t is time, ω is the
angular frequency, which is,
ω=2πf
Where f is the frequency and k is known as wave number, which is equal to,
k λ=2 π
 λ is the wavelength. So, if this be the wave, then the velocity which is given to the particles or to
the atoms Q is, this, Q=dy ⁄ dt
So, Q will be equal to this. Q= ω YO sin(ωt-kx)
 The effect of sound waves, when it travels through a medium, it provides this velocity Q and the
resistance to the movement of sound wave is given by, that parameter acoustic impedance. So,
based upon this transmitted beam energy, it will enter a particular sample or a particular
medium and then, when it encounters an interface, a part of this sound beam will be reflected
back. And the energy of that reflected beam, that will depend on this particular parameter,
acoustic impedance, as to what is the change of impedance across that reflecting interface.
 Source- NPTEL Lecture 16 Theory and Practice of Non Destructive Testing by Dr. Ranjit Bauri Dept. of Metallurgical & Materials Engineering IIT Madras, Ultrasonic Testing
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8. BASICS OF ULTRASONIC TESTING-2
So, that is, what will decide the energy in the
reflected beam and if the energy is enough in this
echo or in this reflected beam, then, you can use an
instrument, a transducer to capture that energy and
convert that into a signal, which can be shown in the
display of the system and that is how, you will get to
know about presence of defects, if that reflecting
interface be a defect..
It is based upon the reflection of sound waves from a
discontinuity, which provides a reflecting interface to
the sound waves, which are propagating through the
sample
*Source- NPTEL Lecture 16 Theory and Practice of Non Destructive Testing by Dr. Ranjit Bauri Dept. of
Metallurgical & Materials Engineering IIT Madras, Ultrasonic Testing
8

9. BASICS OF ULTRASONIC TESTING-2
 acoustic impedance, how this particular parameter will decide the energy in the reflected
beam, because that is what is our concern for this particular technique.
 We need to capture the echoes or the reflected sound beams, which are coming out from the
sample and whether you would be able to capture it or not that would depend on the energy
which is there in this reflected sound wave. And, this energy in the reflected beam will depend
on the change of the acoustic impedance, Z, across that reflecting interface.
 What basically happens when the sound waves encounters an interface or a discontinuity?
these discontinuities or the boundaries will give rise to a change in Z and this change can be
detected when the sound waves are reflected from these boundaries, because the energy in
the reflected beam will depend on this change.
 So, if you have two medium; one and two, with the acoustic impedance Z1 and Z2 , so, across
this boundary there is a change in the impedance and if you have sound waves coming and
getting reflected back from this boundary, then, the energy in this reflected beam that would
depend on this change,
Energy in the reflected beam α (Z2- Z1)
*Source- NPTEL Lecture 17 Theory and Practice of Non Destructive Testing by Dr. Ranjit Bauri Dept. of Metallurgical & Materials
Engineering IIT Madras, Ultrasonic Testing
9

10. BASICS OF ULTRASONIC TESTING-2
 So, now let us say, you have this medium one and the sound waves are
moving through it at a particular velocity. So, this is the incident wave, we
will call that as I and in its path, if the wave encounters an interface, that
means, if there is a change in the medium or there is some discontinuity,
then, this acoustic impedance will change. So, let us say, in medium 1, it is
Z1 and in medium 2 or across this interface it is Z2.
*Source- NPTEL Lecture 17 Theory and Practice of Non Destructive Testing by Dr. Ranjit Bauri Dept. of Metallurgical &
Materials Engineering IIT Madras, Ultrasonic Testing 10

11. BASICS OF ULTRASONIC TESTING-2
 So, when there is a change in the impedance and when the sound encounters an
interface, a part of the sound wave will be reflected and a part of it will be
transmitted. So, this is the transmitted wave and this one is the reflected, let us call
them as T and R. So, the energy of this reflected beam, which is our concern for
doing NDT, will depend on, what is this impedance change across this interface.
 this interface could be the defect itself. So, when the sound waves encounter the
discontinuity, it will reflect a part of the sound waves and the energy of that reflected
wave will depend on the change in the acoustic impedance across that interface.
And that can be calculated, because across the path of the sound beam, the whole
thing is continuous in the sense, if i be the incident beam as we have written, then,
you can write like,
Qi +Qr = Qt
This parameter Q, we have already defined, that is the velocity given to the atoms or we
can also say that,
Pi +Pr = Pt
*Source- NPTEL Lecture 17 Theory and Practice of Non Destructive Testing by Dr. Ranjit Bauri Dept. of Metallurgical & Materials Engineering IIT Madras,
Ultrasonic Testing
11

12. BASICS OF ULTRASONIC TESTING-2
 So, this is across the interface, since this is continuous
these individual components can be estimated and the
fraction of energy into the reflected wave would depend
on, so, if we call that as , so that would depend on the
change in the acoustic impedance,
Fraction of Energy Reflected, RE= (Z2- Z1) ⁄ (Z1+ Z2)
So, if you have enough energy in the reflected wave
coming out from a flaw, then, this can be easily captured
through an instrument and then, you can generate a
defect signal and get the indications about the presence of
defects and flaws on a given sample
*Source- NPTEL Lecture 17 Theory and Practice of Non Destructive Testing by Dr. Ranjit Bauri Dept. of Metallurgical & Materials
Engineering IIT Madras, Ultrasonic Testing
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