3.0
Theoretical Basis
3.1
Sound Pressure at a Finite Distance from an
Ultrasonic Probe
All materials are made of atoms (or molecules) which are connected to each other
by inter-atomic elastic forces. The tested material under ultrasonic vibrations is a
structure constituted by sinusoidal oscillations of the atoms (or molecules) of the
medium. While the atoms (or molecules) vibrate about their own central
equilibrium positions the sound energy pass through the medium.
The equation of spherical waves in the medium can be written as
u (r , t ) =
ξ
r
sin(ωt − kx) − − − − − − − −(1)
Where u is the displacement, r is the radial distance from the origin of sound, ξ
is the maximum amplitude of displacement (particle amplitude), t is the time, K
is
the
proportional
constant
and
ω
is
the
angular
frequency
( ω = 2π / T , T = Period) 19, 20, 21, 22.
The average energy stored per unit volume–E is given by following equation
19,23,24,25
.
1 ξ
ρ 2 ω 2 − − − − − − − − − − − −(2)
2 r
2
E=
Where ρ is the density of material.
The “Intensity” (I) of sound is defined as rate of energy transfer through a unit
area perpendicular to the sound propagation direction 21, 25, 26.
Total energy stored/volume= I / (area). (Length) =
14
I
v
I = v.E =
1 v 2 2 1 z 2 2
ρ ξ ω =
ξ ω − −(3)
2 r2
2 r2
Where v is the velocity of sound and z is the acoustic impedance of the medium.
Equation 3 shows that intensities at different distances are, in the case of spherical
waves, inversely proportional27 to the square of the distance from the source
(inverse square law).
The amplitude of alternating stresses on a material by a propagating wave is
called “acoustic pressure” ( P ) and it is defined as21, 25, 26,
P = z ω ξ − − − − − − − − − − − − − − − − − (4)
Also the initial sound pressure (P0) immediately in front of the sound generator is
then can be written as26,
P0 = ρ v ω ξ = ρ v. v .
2π
λ
ξ=
2π ρ v 2ξ
λ
− −(5)
Where λ is the wavelength of sound beam.
This equation for evaluating the amplitude of sound pressure is common for both
plane and spherical waves26. For longitudinal waves this sound pressure is defined
as force per unit surface area at right angles to the wave front, and for transverse
waves it is as shear force per unit surface parallel to the wave front.
Within the test material the sound pressure reduced due to beam spreading
(divergence) and attenuation by absorption and scattering. The pressure at a
distance R from the origin of sound can be obtained by considering in the first
case, the reduction of sound due to beam spreading disregarding the attenuation of
sound energy due to absorption and scattering within the material.
15
Let I 1 and I 2 are intensities at distances R1 and R2 respectively, then from
equation 3,
I1 ∝
1
2
R1
and I 2 ∝
1
.
2
R2
2
Therefore,
I 2 R1
=
I1 R2 2
From equations 3 and 4 it can be proved that sound pressure is proportional to
square root of the sound intensity ( P ∝ I ).Therefore,
2
2
I 2 R1
P
P
R
= 2 = 22 , Hence 2 = 1
I1 R2
P1 R2
P1
If the sound pressure at a unit distance (i.e.R1 = 1) is considered as P0, i.e. initial
sound pressure immediately in front of the sound generator, then the sound
pressure- PR1 at a distance R from a spherical ultrasound point source can be
written as,
PR1 = P0
1
− − − − − − − − − − − − − − − − − (6)
R
Consider a circular type ultrasonic probe (Figure 6). According to Huygen’s
principle all points of probe crystal acts as sound generators and generate
spherical elementary waves having the same frequency27, 28. Consider a small ring
on the probe crystal at a distance x from the centre having a thickness “ dx ”.
16
dx
R2 + X 2
X
O
R
Probe Crystal
Figure 6: Sound pressure from an ultrasonic probe
According to the equation 6, sound pressure in the far field due to this small ring
is,
dp = P0
1
R + x2
2
.(2πx ).dx
Where R is the beam path distance.
As such, total sound pressure ( PR ) at a point in the far field due to the probe
crystal having a radius r is,
PR = ∫ dp = 2πP0 ∫
x
r
0
R + x2
2
.dx
Suppose x = R tan θ
x = 0 →θ = 0
 rp 
x = rp → θ1 = tan −1  
R
2
d x = R sec θ .dθ
17
θ1
R tan θ
∴ PR = 2πP0 ∫
R + R tan θ
2
0
2
2
.R sec 2 θ .dθ
θ1
PR = 2πP0 R ∫ tan θ . sec θ .dθ
0
PR = 2πP0 R[sec θ ]0
θ1
rp + R 2
2
PR = 2πP0 R(
2πP0 rp
PR =
PR =
R
− 1)
2
rp + R 2 + R
2
2 P0 S





2

 rp 
  + 1 + 1 R

R

Where rp and S are the radius and the area of the circular probe.
At far field
PR =
R >>> rp .Therefore this equation can be approximated to
P0 S
− − − − − − − − − − − − − − − − − (7 )
R
Therefore equation 7 gives the sound pressure at a distance R from the probe
surface.
3.2
Sound Pressure Received by the Probe from a
Reflector
The sound beam generated by the probe will pass through the material, which is
expected to have defects (reflectors).If sound beam meets any sudden change of
homogeneity, reflection or refraction occurs.
18
Now consider the reflection of sound wave at an interface between two acoustic
media having densities ρ1 and ρ 2 respectively (e.g. reflection of sound energy
from a defect).
The reflected energy coefficient ( Er ) and transmitted energy coefficient ( Et ) are
given by equations 8 and 9.
1
z1 ξ r2ω 2
z − z2 2
ξ
} − − − (8)
Er = 2
= { r }2 = { 1
1
z1 + z 2
ξ
2 2
i
z1 ξi ω
2
1
z2 ξt2ω 2
4 z1 z 2
ξ
2
− − − (9)
= { t }2 =
Et =
1
ξi
( z1 + z 2 ) 2
z1 ξi2ω 2
2
Where z1 and z 2 are the acoustic impedances of the two media respectively 25, 26.
The defects normally contain air, slag or in some case a vacuum. Therefore the
acoustic impedance ratio between the two interfaces is very high (i.e. z1 >>> z 2 )
and hence most of the energy will reflect back to the probe or disperse away
without any transmission of energy through the defects i.e. ER ≈ 1 and
ET ≈ 0 .
Some
of this reflected energy will be received by the probe. The intensity of this
reflected energy is affected by the type, size and orientation of the interface
concerned (defect).
Let we first consider the behaviour of a sound beam at a spherical interface
(spherical reflector).
At a spherical reflector (Figure 7) the sound beam reflects back by forming an
image point behind the reflecting surface if the acoustic impedance ratio between
the two interfaces, is very high21.
19
Let this image distance behind the apex of the spherical reflector be X and it can
be obtained from following formula.
1
1
2
−
=
X
R
r
; Where r is the radius of spherical reflector.
Figure 7: Reflection of ultrasound from a spherical reflector
Now, equation 7 can be used to calculate the acoustic pressure of the reflected
wave in which the distance from the image point is now being taken as the beam
path distance. Here the image point is the source in which the further propagation
process can be recalculated.
Hence the sound pressure at the apex of the reflector due to the probe is
PR = P0 S / R (equation 7). Then the reflected sound pressure as a function of the
distance-d from the apex of the spherical reflector is given by,
P
f
P = R
s
R (d + f (1+ d / R) )
Where P is the sound pressure received by the probe from the spherical reflector
s
and f is focal length where f = rs / 2 .
20
At the probe, d = R .
rs / 2
P
P
f
∴P = R
= 1
s
r 
R (R + f (1 + R / R) ) R 
 R + s .2 
2 

Where rs is the radius of the spherical reflector21.
P5 ==
PS =
P0 S
PR
=
2
R
2 R (R / rs + 1)
2 R ( + 1)
rs
P0 S
− − − − − − − − − − − − − (10)
2 R (R / rs + 1)
2
.
Therefore received sound pressure by the probe due to a spherical reflector at a
distance R is given by the equation 10.
The differential value of the pressure PS is given by,
dPs
P S d  rs  P0 S
=
= 02
drs 2 R drs  R + r  2 R 2


R
− (11)

2 
 ( R + rs ) 
From the equation 11 it can be observed that dPs / drs is always positive. This
means that the tangent of the function of sound pressure of a spherical reflector is
always positive i.e. it is an increasing function and hence a theoretical maximum
value for radius rs can not be achieved.
Similar to a spherical reflector a cylindrical reflector also reflects almost all the
energy if the acoustic impedance difference between the sound material and
defect area is very high.
21
However in this case instead of forming an image point, a cylindrical reflector
forms an image line, which is the source in which the further propagation process
can be recalculated.
Therefore this line source reflects cylindrical waves instead of spherical waves as
in the previous case21. Here the sound pressure decreases only inversely with the
square root of the distance and hence the equation 6 has to be modified as,
1
R
P = P0
The sound pressure at the apex of the cylindrical reflector due to the probe is
PR = P0 S / R (equation 7). Then the reflected sound pressure as a function of the
distance‘d’ from the apex of the cylindrical reflector is given by the following
formula 21.
Pc =
PR
R
f
(1 + d / R )(d + f (1 + d / R )
Where Pc is the sound pressure received by the probe from cylindrical surface of a
cylindrical reflector.
At the probe, d = R , Therefore,
Pc ==
Pc =
PR
2R
1
R / rc + 1
P0 S
2R
2
R / rc + 1
=
P0 S
2R
2
R / rc + 1
− − − − − − − − − − − − − −(12)
Where rc is the radius of the cylindrical reflector and R is the beam path distance.
22
The differential value of the pressure Pc is,


 P0 S 
dPc
P0 S d 
1
R
 > 0 − − − (13)
=
=

2
2 
3
1 
drc 2 R drc  R / rc + 1  2 R
 ( R + rc ) 2 .rc 2 
Similar to the case of a spherical reflector dp c / drc is always positive and hence it
is not possible to obtain a theoretical maximum value for radius rc .
When the radius of a spherical or cylindrical reflector increases up to infinity, the
reflector becomes an infinite plate (e.g. a back wall) and then the sound pressure
equation becomes,
PB =
P0 S
PS
= 0 2 − − − − − − − −(14)
2 R (R / ∞ + 1) 2 R
2
Where PB is the sound pressure received by the probe from the back wall of test
piece.
If the reflector has finite dimensions (e.g. flat bottom hole), then the equation for
pressure (PF) becomes,
PF =
P1 ⋅ π rF
R
2
P S πr
πSrF
= 0 . F = P0
− − − − − − − − − − − (15)
R
R
R2
2
2
Where rF is the radius of the flat bottom hole21, 28.
The equations 10, 12, 14 and 15 were derived by assuming the attenuation of
sound is only due to beam spreading.
23
However in natural materials scattering and absorption of sound within the
material, which can be combined to the name “attenuation”, will further weaken
the sound pressure.
Scattering is the result from the fact that the material is not strictly homogeneous
(i.e. scattering from microscopic interfaces). Absorption is the direct conversion
of sound into heat due to internal friction.
The attenuation of sound beam is influenced by the properties of the material21, 25, 26
such as size of the atom, lattice structure and grain size.
The sound pressure P, which decreases as a result of attenuation by scattering and
absorption, can be written in the form of an exponential function.
P = P0 .e −aR − − − − − − − − − − − − − − − − − − − −(16)
Where a is the attenuation constant, which depends on the properties of the
material and R, is the beam path distance (range).
According to the equation 16, defect echo amplitude decreases with increasing of
beam path distance29 as shown in figure 8.
Figure 8: Variation of defect echo amplitude with beam path distance
24
Considering the attenuation effect, equations 10, 12 and 15 can be re-written as
follows by substituting the value for P0 from equation 5. Assume that
r s = rc = rF = r .Then,
PS =
Pc =
PF =
3.3
πρv 2ξS
λR 2 (R / r + 1)
πρv 2ξS
λR
2
R / r +1
e − 2 aR − − − − − − − (17)
e − 2 aR − − − − − − − −(18)
π 2 ρv 2ξSr 2 − 2 aR
e
− − − − − − − − − (19)
λR 2
Factors which Influence the Received Sound
Pressure
The equations (17), (18), (19) show that received sound pressure by the probe due
to a reflector is affected on geometry of the defect (spherical, cylindrical or flat
circular), area of the defect (r), depth to the defect (R),material type (a, ρ , v)
,wavelength of sound ( λ ) and size of the probe (S ).
In addition to above, the received sound pressure might be affected by couplant
type and thickness, impurities within the defect, test surface roughness, probe
parameters and defect orientation. These possibilities are discussed in preceding
paragraphs 3.3.1 to 3.3.8.
25
3.3.1 Effect of Couplant Type
Received Sound Pressure
and
Thickness
on
In ultrasonic testing technique a couplant is used in between the probe and the test
specimen to reduce the acoustic impedance mismatch between air and test
specimen material (e.g. steel). Acoustic impedance (z) is the resistance offered to
the propagation of an ultrasonic wave through a material, which equals to the
multiplication of density of the material ( ρ ) and velocity of ultrasound (v).
If the probe is directly placed on the test piece, the total energy is reflected and no
transmission occurs. By using a couplant, most of the energy can be transmitted
into the test piece (Figure 9).
Figure 9: Reflection and transmission of ultrasound at air-steel interface
The transmission factor depends on impedance of the coupling medium. Different
couplants such as water, grease, oil, etc. give various transmission properties and
therefore same couplant has to be used during a specific test28, 30.
In addition to couplant type the transmission factor might be affected by the
thickness of couplant. The reason for this can be explained using the figure 10.
The longitudinal waves received from probe, enters into the couplant medium and
reflection, refraction and mode conversion occur.
26
At point A shear waves enter directly into steel medium. Reflected Longitudinal
waves mode converted to shear waves at points C, E… and enter into steel
medium indirectly.
Figure 10: Transmission of sound waves in to steel through a couplant layer
Thus, in summation of the total energy transmitted by these direct and indirect
routes, phase of the individual waves must also be considered, with in phase
waves adding and out-of phase waves canceling. The difference in the path length
depends on the thickness‘t’ of the coupling layer.
When‘t’ is an integral multiple of λ/2, direct and indirect waves are in phase and
maximum energy transmission occurs and hence the flaw echo amplitude gives
maximum value.
When ‘t’ is an odd multiple of λ/4, direct and indirect waves are out of phase and
minimum energy transmission occurs .i.e., when t = n. λ/2
where t is the
couplant thickness, λ is the wave length and n =1, 2, 3, 4, maximum transmission
occurs When t = (2n-1) λ/4 it gives minimum value28,30,31,32 .
27
According to this theoretical argument, a separate experiment was done to
observe the effect of couplant thickness on echo amplitude which is explained in
paragraph 5.2 of chapter 5.
3.3.2 Effect of Impurities within the Defect on Received
Sound Pressure
Generally the interior of defects may contain non-metallic inclusions, oxides,
welding slag, liquids and gas emitted from the welding electrodes or air. The
amount of ultrasonic energy reflected from a defect depends on the difference in
the acoustic impedances (z) of the materials on either side of the boundary at
which reflection occurs9, 30,31,32,33. In the case of normal incidence for steel – air
boundary (e.g. flat bottom hole) almost all the energy reflects because of the high
acoustic impedance difference between steel and air interface. (Zsteel >>> Zair).
Therefore the echo amplitude gives maximum value (figure 11).
Figure 11: Reflection of ultrasound at steel – air interface
If the flat bottom hole contains some impurities such as welding slag, a portion of
energy may transmit through the steel- defect interface, and the amount of energy
transmitted depends on the acoustic impedance difference between the two media
(figure12).
28
Figure 12: Reflection of ultrasound at steel – slag interface
The amount of reflected acoustic pressure (Pr) and transmitted pressure (Pt) are
given by the following equations where Zsteel and Zslag are acoustic impedances of
steel and slag respectively.
Pr =
Pt =
Z steel − Z slag
Z slag + Z steel
2.Z slag
Z slag + Z steel
.................................................(20)
..................................................(21)
Since the acoustic impedance of steel is very high compared to that of impurities
(Z
steel
=46629x103 Kg/m2 .s) it can be expected that almost all of the energy
might be reflected9, 30. To observe this effect, a separate experiment was done as
per paragraph 5.5 of chapter 5.
29
3.3.3 Effect of Roughness of the Test Surface on
Received Sound Pressure
In metal fabrication industry metal surfaces are produced by various machining
and finishing operations, which may gives different surface characteristics
depending on the methods used. If a machined surface is reproduced to a large
enough magnification, it will be found to have a wavy profile with hills and
hollows.
Figure 13 shows an example of an enlarged profile of surface finishes34, 35.
Figure 13: An enlarged profile of surface finishes
The method to measure surface roughness is to find the average height of the
undulations of its contour with reference to a horizontal straight line drawn
through the contour in such a position that the loop areas enclosed above the line
are equal to those below (figure 14).
30
Figure 14: Measurement of Roughness average (Ra)
Roughness average = average height = (a + b +…. + m + n+...) 100
Length x M
= Ra index
Where a+b+... etc is in mm2 and length in mm. M is the vertical magnification.
Ra index is measured in µm.
According to figure 15 it can be observed that defect echo amplitude is affected
by surface roughness of the test material30, 31.
Figure 15: Effect of surface roughness on echo amplitude7
31
The loss of signal amplitude with increase of surface roughness is due to
scattering of ultrasonic energy at the top surface of the test piece and hence
ultrasound energy entering into the test surface is reduced30,31. From the graph it
can be shown that surface roughness should preferably be less than 25 µm to
obtain highest echo amplitude.
Therefore the roughness of surfaces of all the test specimens was measured as per
chapter 5 (Research Methodology) paragraph 5.3.All of those surfaces gave
roughness values less than 25 µm .
Hence it can be concluded that roughness of surfaces of all the test specimens to
be used in the research do not affect seriously on received sound pressure.
3.3.4 Effect of Probe Parameters on Received Sound
Pressure
The tool used to scan the test specimen in angle beam Ultrasonic Testing is the
angle beam probe. This probe transmits and receives transverse (shear) waves,
which are characterized by particle displacements perpendicular to the
propagating direction of the waves.
3.3.4.1 Probe Angle
To eliminate generating of any confusing signal by longitudinal waves (particle
displacements are parallel to the propagating direction of wave), the angle of
incidence must be chosen so that after the refraction no more longitudinal waves
can occur but however that the transverse waves still can36. To satisfy this
condition the probe angle (refraction angle -β) should be within 33.5° ≤ β ≤ 90°.
Therefore the used probe angles in the experiment were 45°, 60° and 70°.
32
These transverse waves are more sensitive for smaller defects than longitudinal
waves since it has smaller wavelength compared to that of longitudinal waves.
By using different probe angles (45°, 60° and 70°) waves hit on the same defect at
different angles and hence reflects waves back to the same probe with different
intensity levels.
3.3.4.2 Frequency of Ultrasonic Waves.
The test frequency of shear waves (f) should be such that it gives low attenuation
during passing through the material and high sensitive for small defects.
If the average grain size of the material is in the order of wavelength (λ) then
considerable amount of attenuation of sound beam occur due to scattering of the
same at granular structures. The minimum condition to detect any defect in
ultrasonic testing is that defect size should be grater than or equal to half the
magnitude of wavelength.
By considering above two facts frequency of shear
waves used in this specific research was selected to be within 0.5 to 5.0MHz30.
3.3.4.3 Size of the Probe
The size of the transducer element (S) affects the shape of the transmitted sound
field and hence on the received sound pressure. The shape of the sound field is
determined by near field length and beam divergence.
The position in an ultrasonic beam where the intensity of sound on the beam axis
reaches a final maximum before beginning a uniform reduction with distance is
called near field length30 .
33
The divergence of the sound beam as it travels through a medium forms beam
divergence angle. By considering above two facts 45°, 60° and 70° probe angles
were used in this specific research30.
3.3.5 Effect of Defect Orientation on Received Sound
Pressure
The direction of the sound wave of an obliquely oriented reflector can be
explained using Huygens’ Principle28. This principle says that a wave front of the
incident wave, which has just reached the defect surface, will radiate elementary
spherical waves.
As in geometric sound optics, the direction of the reflected wave, which has the
maximum sound pressure, is such that it follows the Snell’s law21, i.e. the angle of
reflection equals the angle of incidence as shown in figure 16.
Figure 16: Reflection of ultrasound at a defect surface
Only the weak sound pressure, which reflects from the side lobe region returns to
the probe. Consequently, when applying the angle beam technique and using the
same probe as the transmitter and the receiver, detection of obliquely orientated
defects is still possible (Figure 17).However the received sound pressure might be
low.
34
Figure17: Portion of sound pressure received by the probe
This problem can overcome by sending ultrasonic beam perpendicular to the
defect as shown in position 2 of figure 18.
Figure 18: Different probe positions to obtain maximum echo
The probe at the position 2 of figure 18 provide higher signal than at position 1 if
the attenuation loss is corrected.
Beam path length of defect echo signal corresponding to location 2 can be
obtained easily using following equation.
35
R2 =
2T
− R1 − − − − − − − − − − − −(22)
Cosβ
Where R1 and R2 are the beam path lengths corresponding position 1 and 2
respectively, T is the thickness of the specimen.
For vary small defects i.e. defects which are no longer large compared with the
wavelength, the influence of the oblique position disappears altogether21 (e.g.
porosity).As such, it can be concluded that in practice, the oblique position of a
defect does not affect on evaluating of defect parameters as adversely as it may
seen.
3.3.6 Effect of Roughness of Defect Surface on Received
Sound Pressure
Surfaces of natural defects are not smooth as much as artificial ones. Hence the
refraction properties may change for smooth and rough defect surfaces when
struck by an ultrasonic beam. The measure of the qualities rough and smooth is
the wavelength. If the differences in height of the surface irregularities are less
than approximately 1/3 of the wavelength, this surface is considered as smooth21.
A surface of a defect reflects the sound beam as if in the same way as an optical
mirror reflects a light beam in the dark. For an observer outside the reflected
beam the mirror is practically invisible, at the most edge only. With increasing
roughness the surface exposed to the sound beam behaves like a dust-covered
mirror in a light beam. In addition to the reflected beam the light is scattered in
all directions.
36
In the case of ultrasonic pulse-echo method such a rough surface of a defect
returns part of sound beam to the transmitting probe also if the beam is not
incident at right angles. On the other hand, the reflected beam, compared with that
returned by a smooth surface, becomes weaker due to scattering of sound away
from the main beam21.
According to this theoretical argument it can be understood that natural defects
can be detected even if the transducers away from the main reflected beam. This
is an advantage in detection of obliquely oriented defects.
3.3.7 Effect of Depth of Defect on Received Sound
Pressure
The intensity of an ultrasonic beam is considerably reduced when passing through
a material. This effect is described as attenuation, which is due to interaction of
ultrasound with the material.
With sound attenuation the echo amplitude of any defect is additionally reduced
proportional to its distance from the surface of the work piece. Various causes of
attenuation exist due to scattering, absorption, surface roughness and diffraction10,
30
.This makes difficulties in using intensity of received sound pressure for
interpretation of defects. Therefore a separate experiment was done to propose a
way to correct for attenuation loss.
This is explained in paragraph 5.4 of chapter 5.
3.3.8 Effect of Defect Area on Received Sound Pressure
From equation 19 it can be shown that if defect area (radius of flat bottom hole) is
increased, the signal amplitude is increased accordingly. To observe this effect a
separate experiment was done as explained in paragraph 5.6 of chapter 5.
37
3.4
Acoustic Energy Equations of Spherical, Cylindrical
and Flat Circular Reflectors
By considering all the above facts which affects on received sound pressure as
explained in paragraphs 3.3.1 to 3.3.8 ,acoustic energy equations for spherical,
cylindrical and flat circular reflectors can be derived from equations (17),(18) and
(19) as follows for angle beam probes having an angle of β .
Let “T” be the sound pressure transmission coefficient of coupling layer, “µ ” be
the transmission coefficient due to surface roughness and “V” be the magnifying
power of the amplifying circuit.Since the sound pressure received by the probe is
directly proportional to flaw echo amplitude (A) on the CRT screen of the
ultrasonic equipment, sound pressure can be replaced with echo amplitude
(A).Therefore the acoustic energy equations for spherical, cylindrical and flat
circular reflectors can be written as,
AS =
πΤµVρv 2ξS 1 − 2 aR
− − − − − − − − − ( 23)
e
λR 2 (R / r + 1)
Ac =
πΤµVρv 2ξS 1 − 2 aR
e
− − − − − − − − − −(24)
λR 2 R / r + 1
AF =
2π 2 Τµρv 2ξr 2 S 1 − 2 aR
e
− − − − − − − −(25)
λR 2
Comparison of these equations shows that echo amplitude is highest in the case of
a flat circular reflector. For a cylindrical reflector it is lower than that for a flat
circular reflector. A spherical reflector gives the lowest value.
A F (flat circular reflector) > A
reflector)
c
38
(cylindrical reflector) > A
s
(spherical
3.5
Comparison of Echo Amplitude from Defects in
Single-V Butt Welded Plates
Defects in single-V butt welded plates are identified according to their nature,
shape and position as isolated pore, porosity, slag, lack of inter-run fusion, lack of
side wall fusion, crack, lack of penetration etc.
These natural defects in the work pieces may differ from artificial, substitute
defects such as flat circular reflectors, cylindrical reflectors and spherical
reflectors.
In general their surfaces is uneven, irregular and of complex shape. Orientations
of these types of defects are not always at right angle to the sound beam.
However for theoretical and practical considerations of the defect echoes, these
natural defects are classified37, 38 as in table 1.
Type of defect
Model
Isolated pore/Porosity/ Slag
Lack of inter-run fusion
Sphere(Spherical reflector)
Side drilled hole (Cylindrical reflector)
Crack/Lack of side wall
fusion
Disc shaped Reflector (Flat circular reflector)
Table 1: Modelling of natural defects in single-V butt welded plates
Therefore, the relationship developed in paragraph 3.4 between various reflectors
can be modified for natural defects in single-V butt welded plates as follows,
AF (crack/lack of side wall fusion) > Ac (lack of inter-run fusion) > As (isolated
pore/porosity/ slag).
39
This relationship is shown in figure 19.
Figure 19: Comparison of amplitude values of common defects in single-V butt
welded steel plates.
Since the amplitude of echo signal affects on various factors as discussed above,
this parameter alone can not be used to identify the type of defect. As such the
possibilities of using few other features such as width of defect echo, position of
probe and change of probe angle also will have to be considered to identify the
type of defect.These features are discussed in paragraphs 3.6, 3.7 and 3.8
respectively.
3.6
Relationship of Defect Type to Width of Echo Signal
As discussed in paragraph 3.3.8 the effect of defect area on defect echo amplitude
makes difficulty in using only the echo amplitude to identify defect type. To
eliminate or minimize this difficulty, echo width, defect position and change of
probe angle might be used along with echo amplitude.
This paragraph discusses how the echo width varies for different types of defects.
In ultrasonic testing the piezo electric transducer is excited by a short voltage
pulse of less than 10 µSec duration, generally consist of band of frequencies.
40
Among these frequencies, the transducer vibrates with maximum amplitude at the
frequency known as resonance frequency of the transducer which is related to its
thickness ( f = v / 2t where t is the thickness of the transducer and v is the
velocity of sound in piezo electric crystal). This will generate short ultrasonic
pulses which contain a short group of waves (decayed or damped waves)7.
The width of such a pulse is affected by wavelength ( λ ) and number of waves (n)
contains in the pulse. Therefore,
Pulse width = λ x n
In addition to above, the pulse width is also affected by degree of damping of the
pulse7.
This pulse width is an inherent characteristic of the specific transducer used and is
a constant value.
When the sound beam hits on a defect, part of sound energy is reflected. The
width of pulse is further affected by the geometry of the reflecting surface i.e.,
spherical, cylindrical or flat circular.
.
Figure 20: Width of an echo signal from a defect
41
Now we consider the theoretical factors on how the width of echo signal vary for
different reflectors such as back wall or flat circular reflector , crack , lack of
sidewall fusion, isolated pore, porosity and slag.
3.6.1 Back Wall or Flat Circular Reflector
When the ultrasound beam hits on a flat surface, each points of the same act as
generators of ultrasound waves and generates spherical elementary waves28. These
sound waves reach the probe at different time intervals and display on the CRT
screen with different beam path distances. Due to this reason the echo width may
enlarge in addition to its inherent beam width due to probe characteristic as
mentioned in paragraph 3.6.This is graphically shown in figure 21.
Figure 21: Echo signal from back wall or flat circular reflector
3.6.2 Crack and Lack of Sidewall Fusion
Compared to back wall or flat circular reflector, crack has a flat or curved but
wavy surface. As such, echo from a crack might give an intense echo but its width
might be slightly larger than that of a back wall or flat circular reflector because
of its wavy surface.
42
Lack of sidewall fusion might give sharp echoes similar to back wall or flat
circular reflector37, 38.
3.6.3 Isolated Pore and Porosity
The outer shape of an isolated pore is rounded. As such only those rays which hit
the pore perpendicularly are reflected back to the receiving probe. The other
entire rays incident at an angle to the pore are radiated away and dispersed.
Due to this reason the width of echo signal might be very small compared to crack
and lack of sidewall fusion.
Cluster of isolated pores forms porosity. Hence porosity gives lot of tiny echoes
having similar shapes as isolated pores as shown in figure 22.
Figure 22: Echo signal from porosity
3.6.4 Slag (Inclusions)
Slag inclusion has a rugged shape, which offers many small targets at different
beam path distances. These will reflect sound back to the probe at different target
points9, 37, 38.
43
As shown in figure 23 reflected sound from a slag may provide a broad and fussy
signal having a pine shape compared to that of an isolated pore.
Figure 23 Echo signal from a slag
3.7
Relationship between Defect Type and Position
As explained in paragraph 3.6, the echo amplitude alone cannot be used to
identify defect type and few other features of defect such as echo width, defect
position and change of probe angle have to be used along with echo amplitude.
This paragraph explains the theoretical background on how the probe position
relates to the type of defect.
Defects such as lack of fusion and lack of penetration have preferred locations in
the weld joint. Hence observing the location of the defect will support to identify
those types of defects.
3.7.1 Identification of Lack of Sidewall Fusion
In single–v butt-welded steel joints lack of fusion occurs at 1st and 2nd fusion faces
(figure 24) whereas lack of inter-run fusion occurs at the weld seam between
inter-run passes6, 39, 40, 41.
44
Figure 24: Position of the probe with respect to the weld center line
Therefore lack of sidewall fusion has a preferred location in the weld seam. Hence
it can be identified knowing the position of the probe with respect to the weld
centerline i.e. stand off distance (X).
Mathematical equations for X can be derived using probe angle (B), root face (B1
), beam path distance (R) and material thickness (T) as explained in case 1 to
case 4.
Case1: Single traverse technique and defect is at 1st fusion face
Let we first consider that defect is at the 1st fusion face and sound beam directly
hits on the defect (case 1).
If the horizontal distance to the defect from weld center line is L then,
tan( B1 / 2) =
L
T − R cos B
L = (T − R cos B). tan( B1 / 2)
45
L can be derived using R as L = X − R sin B
From above equations following relationship can be obtained.
X = T tan( B1 / 2) + R[sin B − cos B. tan( B1 / 2)]....................(26)
Similarly equations (27), (28) and (29) can be derived for case2, case3 and case 4
respectively.
Case2: Double traverse technique and defect is at 1st fusion face
X = R[sin B + cos β . tan( B1 / 2)] − T . tan( B1 / 2)....................(27)
Case3: Single traverse technique and defect is at 2nd fusion face
X = R[sin B + cos B. tan( B1 / 2)] − T . tan( B1 / 2)...................(28)
Case4: Double traverse technique and defect is at 2nd fusion face
X = T tan B1 / 2 + R[sin B − cos B. tan( B1 / 2)]....................(29)
According to above theoretical relationships, if stand off distance satisfies any of
the above conditions the defect might be recognized as lack of sidewall fusion.If
X does not satisfy any of the conditions above it might be either due to a lack of
inter-run fusion or any other type of defect42.
46
3.7.2 Identification of Defects in Weld Root
Let t is the root face. If t satisfies following condition the echo signal will be due
to a defect in the weld root. This defect might be either due to an isolated pore,
porosity, a slag, a crack or a lack of penetration.
t ≥ T − R cos β ............................................................(30)
Method to identify lack of penetration from other defects in weld root is explained
in paragraph 3.8.
3.8
Usage of Different Probe Angles to Identify Lack of
Penetration
As discussed in paragraph 3.6, the echo amplitude alone cannot be used to
identify defect type and few other features of defect such as echo width, defect
position and change of probe angle have to be used along with echo amplitude.
This paragraph discuss on the possibilities of using different sound beam
directions i.e. change of probe angle, to identify Lack of Penetration
In angle beam ultrasonic testing the shear waves are transmitted in to the test
specimen at an angle to the interface (normally 450, 600 and 700) and reflection
and refraction occur at the boundary face.
At some incident angles mode
conversion occurs i.e. shear waves convert into longitudinal waves (figure 25).
47
Figure 25: Reflection, refraction and mode conversion at an air – steel interface.
The correlation between the angle of incidence and reflection coefficient of sound
pressure for steel-air interface37, 38 is shown in figure 26.
Figure 26: Sound pressure of reflected waves vs. angle of incidence37
In figure 26 the angle of incidence of longitudinal waves is shown by the lower
horizontal scale and the angle of incidence of shear waves by the upper horizontal
scale. The vertical scale shows the reflection coefficient rc , rc =
Pr
× 100% , Where
Pi
Pi and Pr are incident and reflected sound pressures respectively (figure 27).
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Figure 27: Reflected and transmitted sound pressure at an interface.
According to figure 26 shear waves are totally reflected and no mode conversion
occur when those strikes the steel-air interface at an angle larger than 33.20 which
is called the critical angle for shear waves transmitting in steel with an air
interface. This property of shear waves might be used to observe behavior of
sound waves at a right-angled corner.
As shown in figure 28 at the point ‘P’ shear waves from a 700 angle beam probe
meet back surface of a steel plate at an angle of 700 which is more than the critical
angle for shear waves39,40.Therefore at this point total reflection occurs. Those
reflected shear waves then meet the vertical surface at the point ‘Q’ at an angle of
200 .Since this angle is less
than the critical angle for shear waves, mode
conversion occur at the point ‘Q’.
Figure 28: Reflection of shear waves at a right angled corner by a 70° angle probe.
From figure 26, it can be shown that the reflected sound pressure of the shear
waves at the point Q is 50% of the incident sound pressure and the other portion
of the waves are converted to longitudinal waves, which propagate at an angle
38.7°
49
C

 5900

φ L =Sin −1  L x Sin20 °  =Sin −1 
x Sin20° =38.7°
 3230

CS

Therefore the transducer cannot receive the longitudinal waves reflected at point
Q and it receives only the shear waves.
Consequently, the received sound
pressure is 50% of the initial sound pressure, if attenuation due to beam spread
and scattering is disregarded43.
By a similar process, calculation shows that a corner reflects 100% of the sound
pressure from a 450 shear wave probe and only 13% from a 600 shear wave probe
(figure 29)
(b) 600 Angle probe
(a) 450 Angle probe
Figure 29: Reflection of shear waves at a right-angled corner by 450 and 600 angle
probes.
Figure 30 shows comparison of percentages of echo amplitude from probe angles
45°, 60° and 70°.
50
Figure 30: Comparison of percentages of echo amplitude from probe angles
450, 600 and 700
Since lack of penetration is mostly similar to a right angle corner above
relationship can be used to identify lack of penetration from other root defects in
single –V butt-welded steel plates44.
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