acoustic emission wave propagation and source location

Acoustic Emission Wave Propagation and Source Location

Dr. Boris Muravin

More at www.muravin.com

More about AE at www.muravin.com

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.


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.


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.


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 semi-infinite 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.


Example of AE Signal


Longitudinal, Shear, Rayleigh and Love Waves

Reference:http://web.ics.purdue.edu/~braile/edumod/slinky/slinky.htmMore about AE at www.muravin.com

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

t = 5 mm

In thinnest plates only Lamb wave arrivals are visible .

Symmetric

Antisymmetric


Wave Speed in Different Materials

2

2

2

1

1

2

1

14.1862.0

2

CC

CC

C

C

P

R

Wave speeds derivation:

λ and μ – Lame constantsν – Poisson’s ratioρ – material density


Properties of Elastic Waves in Semi-Infinite 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. MeyersMore about AE at www.muravin.com

Wave Propagation EffectsThe 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 Attenuation tests have to be performed on actual structures during their inspection.actual structures during their inspection.

The attenuation curves allow to estimate The attenuation curves allow to estimate amplitude or energy of a signal at a given amplitude or energy of a signal at a given distance from a sensor. distance from a sensor.


Group and Phase VelocityLord 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


Dispersion Curves

Example calculated for steel 347 plate (10mm thick)

Triple pointNon-dispersive part of A0 mode


Use of Dispersion CurvesDispersion 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.


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.


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.


Effective Velocity• Another parameter necessary for time difference location method is effective

velocity.• Effective velocity can be established 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. For example, in linear location it can be about 10% of sensors spacing.

• Detection of different wave modes arrival times separately and evaluation of their 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 background noise conditions.

• Another parameter necessary for time difference location method is effective velocity.

• Effective velocity can be established 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. For example, in linear location it can be about 10% of sensors spacing.

• Detection of different wave modes arrival times separately and evaluation of their 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.


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

2distance from first hit sensor

D = distance between sensors

wave velocity

d D T V

d

V


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.


Two Dimensional Source Location

1,2 1 2

2

2 2 21 2

2 2 2 22 1 2

2 2 22 1

1 1,2 2

2 2 21,2

21,2

sin

( )

sin ( cos )

2 cos

1

2 cos

t V R R

Z R

Z R D R

R R D R

R R D D

R t V R

D t VR

t V D

Sensor 1

Sensor 2

Sensor 1

1

2

1,2

2

distance between sensor 1 and 2

distance between sensor 1 and source

distance between sensor 2 and source

time differance between sensor 1 and 2

angle between lines and

line perpend

D

R

R

t

R D

Z

icular to D

Z D

R3R2

R1

R1

R2R3

Sensor 2

Sensor 3

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.


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 2, ,( )i obs i calct t

2 2 2 2, 1 1

,

,

1( ) ( ) ( ) ( )

The calculated time difference between the sensor and the first hit sensor, where and are the unknown coordinates of the source.

T

i calc i s i s s s

i calc s s

i obs

t x x y y x x y yV

t i x y

t

he observed time difference

Chi Squared error function that minimized in over-determined source location.


-0.1 0 0.1-0.1

0

0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

3

6

9

X [m]

4

7

1

2

5

8

Y [m]

Z [

m]

VyyxxyyxxttT iiii2

012

012

02

01 )()()()(

N

imeasuredi TT

1

22

),( 00 yx

Minimization on χ2 :

(xo,yo)– location of source(xi,yi)– location of sensor iti – arrival time to sensor it1- arrival time to sensor 1

The time delay between the signal arrival to two sensors:

•At least 3 sensors are required for location.•However, more sensors increase the accuracy of the source location

),( 00 yx

2D Location on Cylinder


Source

((((*))))

x),( 11 Ex ),( 00 Ex

I

),( 22 Ex ),( 33 Ex

0302

0201

3

2

2

1 lnlnxxxx

xxxx

EE

EE

)(0

0xxi

ieEE

Xo – location of sourceXi – location of sensor iEo – energy at sourceEi – energy at sensor iβ - the decay constant

Energy attenuation in line:

* 3 sensors are required for location for unknown β(for known β 2 sensors are required for location)

Energy Attenuation Location


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.

Velocity vs. Angle

0

1000

2000

3000

4000

5000

6000

7000

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Angle [Degrees]

Vel

oci

ty [

m/s

]

R=0.9m

R=0.45m2 2 2 2

1 1,

, ,1

,

( ) ( ) ( ) ( )

The time difference recorded by the sensor relative to the first hit sensor

i s i s s si calc

i

i calc

x x y y x x y yt

v v

t i


Ch 1

Ch 2

Δt

Normalized cross-correlation function

Δt)}(max{

21 )()()(

tC

ChCh

tt

dttSStC

Cross-correlation function

Cross-correlation based Location

Cross-correlation method is typically applied for location of continuous AE signals.

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.


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.


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 ARBITRARYSURFACE BY GEODESIC CURVE EVOLUTION”, Advances in Acoustic Emission - 2007


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.


acoustic emission wave propagation and source location

Documents

surface wave

p wave

plate wave

s wave

interfacial wave

creeping wave

wave propagation direction

wave propagation modes