Transcript Acoustic Emission as a Wave Phenomenon

Acoustic Emission Wave
Propagation and Source Location
Dr. Boris Muravin
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Outline
•
•
•
•
Introduction.
Types of Acoustic Emission waves.
Wave propagation modes.
Wave propagation modes in various geometries
and materials.
• Wave propagation effects (attenuation,
dispersion, scattering and other).
• Group and phase velocity.
• Dispersion curves.
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Introduction
• Acoustic Emission (AE) is a phenomenon of stress wave
radiation caused by a dynamic reconstruction of material’s
structure that accompanies processes of deformation and
fracture.
• Crack propagation is one of the macroscopic sources of AE.
Cracks and other discontinuities in a material concentrate
stresses. Crack jumps accompanied by a rapid release of
potential energy, a small part of which is released in form
of stress waves.
• Stress waves are generated when the rate of the stress field
change locally is such that the stresses cannot be
instantaneously transmitted to the different areas of the
body.
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Types of Acoustic Emission Waves
Type of AE waves generated depend on material
properties, its mechanical behavior and level of
stresses at the source. AE waves can be:
• Elastic.
• Non-linear elastic.
• Elastic-plastic.
• Elastic-viscoplastic and other.
Anelastic waves attenuate at short distances and
therefore elastic waves are mostly detected and
analyzed in acoustic emission testing.
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Modes of Elastic Waves Propagation
• Longitudinal (dilatational, P-) wave is the wave in which the oscillations
occurring in the direction of the wave propagation.
• Shear (or transverse, or distortional, or equivolumal, S-) wave is the wave
in which the oscillations occurring perpendicular to the direction of the
wave propagation.
• Rayleigh (or surface) wave is the wave with elliptic particle motion in
planes normal to the surface and parallel to the direction of the wave
propagation.
• Lamb (or plate) wave is the wave with particles motion in perpendicular to
the plate.
• Stoneley (or interfacial) wave is the wave at interface between two semiinfinite media.
• Love wave is the wave in a layered media, parallel to the plane layer and
perpendicular to the wave propagation direction.
• Creeping wave is the wave that is diffracted around the shadowed surface
of a smooth obstacle.
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Example of AE Signal
0.8
0.6
Rayleigh wave
P wave
S wave
0.4
Volts
0.2
0
-0.2
-0.4
-0.6
-0.8
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Longitudinal, Shear, Rayleigh and Love
Waves
Reference:
http://web.ics.purdu
e.edu/~braile/edum
od/slinky/slinky.htm
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Wave Modes in Different Geometries
•
•
•
In infinite media there are only two
types of waves: dilatational (P) and
distortional (S).
Semi-infinite media there are also
Rayleigh and Lateral (Head) waves.
Head waves produced by interaction of
longitudinal wave with free surface.
In double bounded media like plates
there are also Lamb waves.
t = 10 mm
Symmetric
t = 5 mm
Antisymmetric
In thinnest plates only Lamb wave
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arrivals are visible.
Wave Speed in Different Materials
Material
Acoustic
Longitudinal
Impedance,
wave (C1), Shear (C2), Rayleigh
Lamb (Cp),
106
km/sec
km/sec (Cr), km/sec km/sec kg/(m2*sec)
Aluminum
6.3
3.1
2.9
5.1
17
Brass
4.4
2.1
2.0
3.5
36
Cast iron
5.0
3.0
2.7
4.7
36
Copper
4.7
2.3
2.1
3.8
42
Lead
2.2
0.7
0.7
1.2
25
Magnesium
5.8
3.1
2.9
5.0
10
Nickel
5.6
3.0
2.8
4.8
49
Steel
5.9
3.2
3.0
5.1
46
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Wave speeds derivation:
C1 
  2

C2 


0.862  1.14
 C2
1 
2
CP 
 C2
1 
CR 
λ and μ – Lame constants
ν – Poisson’s ratio
ρ – material density
Properties of Elastic Waves in SemiInfinite Media
• Rayleigh waves carry 67% of total energy (for ν=0.25).
• Shear 26%.
• Longitudinal 7%.
• Longitudinal and shear waves decay at a rate 1/r in
the region away of the free surfaces.
• Along the surface they decay faster, at a rate 1/r2.
• Rayleigh waves decays much slower, at a rate of
1/sqrt(r).
Reference: “Dynamic Behavior of Materials” by M. Meyers
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Wave Propagation Effects
The following phenomena take place as AE waves propagate along the structure:

Attenuation: The gradual decrease in AE amplitude due to energy loss
mechanisms, from dispersion, diffraction or scattering.

Dispersion: A phenomenon caused by the frequency dependence of speed for
waves. Sound waves are composed of different frequencies hence the speed of the
wave differs for different frequency spectrums.

Diffraction: The spreading or bending of waves passing through an aperture or
around the edge of a barrier.

Scattering: The dispersion, deflection of waves encountering a discontinuity in the
material such as holes, sharp edges, cracks inclusions etc….


Attenuation tests have to be performed on
actual structures during their inspection.
The attenuation curves allow to estimate
amplitude or energy of a signal at a given
distance from a sensor.
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Group and Phase Velocity
Lord Rayleigh: “It have often been remarked that when a group of waves advances
into still water, the velocity of the group is less than that of the individual waves of
which it is composed; the waves appear to advance through the group, dying away
as they approach its interior limit” (1945, Vol. I, p. 475).
• Group velocity is the velocity of propagation of a group of waves of similar
frequency.
• Phase velocity is the velocity at which the phase of the wave propagates in the
media.
Reference:
http://www.owrc.com/waves/waveSpeed/
waveSpeed.html
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Dispersion Curves
Non-dispersive
part of A0 mode
Triple point
Example calculated
for steel 347 plate (10mm thick)
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Use of Dispersion Curves
Dispersion curves can be effectively used for accurate location
and characterization of AE sources. Examples:
• Filtering AE waveforms at frequency of the triple point (200
kHz), one can improve location accuracy. This is because all
modes at this frequency have similar speed and the
threshold will be triggered by the same wave mode at all
sensors.
• Filtering AE waveforms over non-dispersive range of A0
mode (80-180 kHz) can improve location accuracy even
further. In this technique a wider frequency range of the
original signal remain after filtration while the frequency
content of the mode remain unchanged over the distance.
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Principals of Acoustic Emission Source
Location
• Time difference based on Time of Arrival
locations.
• Cross-correlation time difference location.
• Zone location.
• Attenuation based locations.
• Geodesic location.
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Time of Arrival Evaluation
• Most of existing location procedures require
evaluation of time of arrival (TOA) of AE waves
to sensors.
• TOA can detected as the first threshold
crossing by AE signal, or as a time of peak of
AE signal or as a time of first motion. TOA can
be evaluated for each wave mode separately.
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Effective Velocity
••
•
•
•
•
•
•
Another
Another parameter
parameter necessary
necessary for
for time
time difference
difference location
location method
method is
is effective
effective
velocity.
velocity.
Effective velocity can be established experimentally with or without considering
Effective
can be established
different velocity
wave propagation
modes. experimentally with or without considering
different
wave propagation
modes.
When propagation
modes are
not separated, the error in evaluation of AE source
location
can be significant.
Fornot
example,
in linear
it can be about
of
When propagation
modes are
separated,
the location
error in evaluation
of AE10%
source
sensors
locationspacing.
can be significant. For example, in linear location it can be about 10% of
Detection
of different wave modes arrival times separately and evaluation of their
sensors spacing.
velocities can significantly improve location accuracy. Nevertheless, detection and
Detection
times separately
and evaluation
of theirin
separationof
ofdifferent
differentwave
wavemodes
modesarrival
is computationally
expensive
and inaccurate
case
of complex
geometries
or under
high background
noise conditions.
velocities
can significantly
improve
location
accuracy. Nevertheless,
detection and
separation of different wave modes is computationally expensive and inaccurate in
case of complex geometries or under high and variable background noise
conditions.
Material
Effective velocity
in a thin rod
[m/s]
Shear
[m/s]
Longitudinal
[m/s]
Brass
3480
2029
4280
Steel 347
5000
3089
5739
More5000
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3129
6319
Aluminum
Linear Location
• Linear location is a time difference method commonly used to locate AE
source on linear structures such as pipes, tubes or rods. It is based on
evaluation of time difference between arrival of AE waves to at least two
sensors.
• Source location is calculated based on time difference and effective wave
velocity in the examined structure. Wave velocity usually experimentally
evaluated by generating artificially AE at know distances from sensors.
1
 D  T V 
2
d  distance from first hit sensor
d
D = distance between sensors
V  wave velocity
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One Sensor Linear Location
• It is possible to use one sensor to evaluate the distance
from AE source (but not direction).
• The principal of this location is based on phenomenon of
different velocity of propagation of different wave modes.
• Such location method can be used on short rods, tubes or
pipes, when mode detection and separation can be
effectively performed.
Rayleigh wave
0.8
Time shift is a function
of propagation distance
0.6
0.4
Volts
0.2
P wave
S wave
0
-0.2
-0.4
-0.6
-0.8
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Two Dimensional Source Location
For location of AE sources on a plane minimum three sensors are used. The source is
situated on intersection of two hyperbolas calculated for the first and the second
sensors detected AE signal and the first and the third sensor.
t1,2V  R1  R2
D  distance between sensor 1 and 2
Z  R2 sin 
R1  distance between sensor 1 and source
Z 2  R12  ( D  R2 ) 2
 R2 2 sin 2   R12  ( D  R2 cos  ) 2
R2 2  R12  D 2  2 D cos 
R1  t1,2V  R2
2
2 2
1 D  t1,2 V
 R2 
2 t1,2V  D cos 
R2  distance between sensor 2 and source
t1,2  time differance between sensor 1 and 2
  angle between lines R2 and D
Z  line perpendicular to D
Sensor 2
Sensor 3
Sensor 2
R2
R3
R2

R3
R1
Z
D
Sensor 1
R1
Sensor 1
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Over-determined Source Location
• Generally, it is necessary 2 sensors for linear, 3
sensors for 2D and 4 sensors for 3D locations.
• When more sensors detect AE wave from a
source than necessary it is possible to use this
information to improve location accuracy by error
minimization optimization methods.
 2  (ti,obs ti ,calc )2
ti ,calc 

Chi Squared error function that minimized in over-determined
source location.
( xi  xs ) 2  ( yi  ys ) 2  ( x1  xs ) 2  ( y1  ys ) 2
 V1
ti ,calc  The calculated time difference between the i sensor and the first hit sensor, where xs and ys are the unknown coordinates of the source.
ti ,obs  The observed time difference
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2D Location on Cylinder
 (x  x )  ( y  y )

The time delay between the signal arrival to two sensors:
Ti  ti  t1 
2
i
0
i
0
2
 ( x1  x0 ) 2  ( y1  y0 ) 2 V
1
(xo,yo)– location of source
(xi,yi)– location of sensor i
ti – arrival time to sensor i
t1- arrival time to sensor 1
0.8
0.7
2
3
0.6
N
 2   Ti  Tmeasured 2
0.5
Z [m]
Minimization on
χ2 :
i 1
4
0.4
0.3
5
6
0.2
0.1
7
0
( x0 , y0 )
0.1
•At least 3 sensors are required for location.
•However, more sensors increase the accuracy of the
source location
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Y
( x0 , y0 )
8
9
0
-0.1
[m]
-0.1
0.1
0
X [m]
Energy Attenuation Location
Energy attenuation in line:
Ei  E0e
  ( xi  x0 )
Xo – location of source
Xi – location of sensor i
Eo – energy at source
Ei – energy at sensor i
β - the decay constant
 E2  x1  x0  x2  x0
 E1 
ln  ln  
 E2 
 E3  x2  x0  x3  x0
* 3 sensors are required for location for unknown β
(for known β 2 sensors are required for location)
Source
((((*))))
I
( x1 , E1 )
( x0 , E0 )
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2
2
(x , E )
( x3 , E3 )
x
Location in Anisotropic Materials
•
•
In anisotropic materials, the velocity of wave propagation is different in different
direction.
In order to achieve appropriate results in source location it is necessary to evaluate
velocity profile as a function of propagation direction and incorporate this into the
calculation of time differences as done in the example of the composite plate.
R=0.9m
R=0.45m
Velocity
[m/s]
6035
5137
4671
4600
4649
5182
6141
Angle [Degrees]
0
18
36
45
54
72
90
Velocity
[m/s]
6101
5224
4843
4741
4784
5164
6345
Angle [Degrees]
0
18
36
45
54
72
90
Velocity vs. Angle
7000
6000
ti ,calc 
( xi  xs )2  ( yi  ys )2
v ,i

( x1  xs ) 2  ( y1  ys ) 2
v ,1
Velocity [m/s]
5000
4000
R=0.9m
R=0.45m
3000
2000
1000
0
ti ,calc
5 10 15 20
Morerelative
about AE
 The time difference recorded by the i sensor
to at
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first hit0 sensor
25
30
35
40
45
50
Angle [Degrees]
55
60
65
70
75
80
85
90
Cross-correlation based Location
Δt
Ch 1
Cross-correlation is another method for location of AE
sources based on estimation of time shifts between AE
signals detected by different sensors. It is usually
applied for continuous AE signals when it is impractical
to estimate the time of wave arrival but possible to
estimate time shifts between sensors.
Cross-correlation function
C (t )   SCh1 ( )  SCh 2 (  t )dt
Ch 2
t  t max{C (t )}
Δt
Cross-correlation method is typically applied for
location of continuous AE signals.
Normalized cross-correlation function
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Zone Location
• Zone location is based on the principle that the sensor with the highest
amplitude or energy output will be closest to the source.
• Zone location aims to trace the waves to a specific zone or region around
a sensor.
• Zones can be lengths, areas or volumes depending on the dimensions of
the array.
• With additional sensors added, a sequence of signals can be detected
providing a more accurate result.
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Geodesic Location
• This time-difference location method is based on calculation of the
shortest wave path over the mesh of the object by the principle of
minimum energy.
• The method allows to solve location problems in complex
geometries but computationally expensive.
Reference:
G. PRASANNA, M. R. BHAT and C. R. L.
MURTHY, “ACOUSTIC EMISSION SOURCE
LOCATION ON AN ARBITRARY
SURFACE BY GEODESIC CURVE EVOLUTION”,
Advances in Acoustic Emission - 2007
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Other Location Methods
• FFT and wavelet transforms are be used to
improve location by evaluation of modal
arrival times.
• Cross-correlation between signals envelopes.
• There are works proposing use of neural
network methods for location of continuous
AE.
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