Fundamentals of Ultrasonics
Ultrasonics
Definition: the science and exploitation of elastic waves in
solids, liquids, and gases, which have a frequency above
20KHz.
Frequency range: 20KHz-10MHz
Applications:
• Non-destructive detection (NDE)
• Medical diagnosis
• Material characterization
• Range finding
• ……
Elastic wave
Definition: An elastic wave carries changes in stress and
velocity. Elastic wave is created by a balance between the
forces of inertia and of elastic deformation.
Particle motion: elastic wave induced material motion
Wavespeed: the propagation speed of the elastic wave
Particle velocity is much smaller than wavespeed
Wave Function
Equation of progressive wave:
y  A sin( t  kx)
•Amplitude: A
•Wavelength: l
•Frequency/Time period: f=1/T
•Velocity U: U=fl=l/T
•Energy: E  2 2mf 2 A2
•Intensity:
I  2 2  f 2 A2
Waveform & Wave front
Waveform: the sequence in time of the motions in a wave
Propagation and Polarization Vector
Propagation vector: the direction of wave propagation
Polarization vector: the direction of particle motion
Wave Propagation
• Body wave: wave propagating inside an object
– Longitudinal (pressure) wave: deformation is parallel to
propagation direction
– Transverse (shear) wave: deformation is perpendicular
to propagation direction, vT=0.5vL, generated in solid
only
• Surface wave: wave propagating near to and
influenced by the surface of an object
– Rayleigh wave: The amplitude of the waves decays
rapidly with the depth of propagation of the wave in the
medium. The particle motion is elliptical. vR=0.5vT
– Plate Lamb wave: for thin plate with thickness less than
three times the wavelength
Parameters of Ultrasonic Waves
Velocity: the velocity of the ultrasonic wave of
any kind can be determined from elastic moduli,
density, and poisson’s ratio of the material
12


E (1  m )
– Longitudial wave: U L  


(
1

m
)(
1

2
m
)


 is density and m is the Poisson’s Ratio
12


E
– Transverse wave: U T  

2

(
1

m
)


– Surface wave:
U s  0.9UT
12
G 
 
 
 0.5U L
Attenuation
• Definition: the rate of decrease of energy when an
ultrasonic wave is propagating in a medium. Material
attenuation depends on heat treatments, grain size,
viscous friction, crystal structure, porosity, elastic
hysterisis, hardness, Young’s modulus, etc.
• Attenuation coefficient: A=A0e-ax
 A
a  ln   (nepers )
 A0 
 A
a  20 log 10   (dB)
 A0 
Types of Attenuation
• Scattering: scattering in an inhomogeneous
medium is due to the change in acoustic
impedance by the presence of grain boundaries
inclusions or pores, grain size, etc.
• Absorption: heating of materials, dislocation
damping, magnetic hysterisis.
• Dispersion: frequency dependence of
propagation speed
• Transmission loss: surface roughness &
coupling medium.
Diffraction
• Definition: spreading of energy into high and
low energy bands due to the superposition of
plane wave front.
D2
• Near Field: d 
4l
• Far Field:
D2
d
4l
• Beam spreading angle:   1.2l
D
Acoustic Impedance
• Definition: the resistance offered to the
propagation of the ultrasonic wave in a
material, Z=U. Depend on material properties
only.
Reflection-Normal Incident
• Reflection coefficient:
2
 Z 2  Z1 
I r   2U 2  1U1 
ar   
 

I i   2U 2  1U1 
 Z 2  Z1 
2
• Transmission coefficient:
IT
4 1U1 2U 2
4Z1Z 2
aT 


 1 ar
2
2
I i  2U 2  1U1 
Z 2  Z1 
Reflection-Oblique Incident
• Snell’s Law: sin i  U A
sin  r U B
• Reflection coefficient:
 1  sin 2    /   U 2 / U 2  sin 2 
i
1
2
A
B
i
ar  
 1  sin 2    /   U 2 / U 2  sin 2 
i
1
2
A
B
i





2
• Transmission coefficient:
41 /  2  U A2 / U B2  sin 2 i
at 
 1  sin 2    /   U 2 / U 2  sin 2  

i
1 2
A
B
i


2
Total Refraction Angle


2
2
Z1  Z 2 

 r  arcsin
 (  2   2 )U 2 
A 
 1
2
Mode Conversion
When a longitudinal wave is incident at the
boundary of A & B, two reflected beams are
obtained.
Selective excite different type of ultrasonic
wave
Surface Skimmed Bulk Wave
•The refracted wave travels along the
surface of both media and at the subsurface of media B
Resonance
Quality factor
Energy Supplied Per Cycle
fr
fr
Q


Energy Dissipated Per Cycle f 2  f1 f
Typical Ultrasound Inspection System
•Transducer: convert electric signal to ultrasound signal
•Sensor: convert ultrasound signal to electric signal
Types of Transducers
• Piezoelectric
• Laser
• Mechanical (Galton Whistle Method)
• Electrostatic
• Electrodynamic
• Magnetostrictive
• Electromagnetic
What is Piezoelectricity?
• Piezoelectricity means “pressure electricity”, which is
used to describe the coupling between a material’s
mechanical and electrical behaviors.
– Piezoelectric Effect
• when a piezoelectric material is squeezed or stretched, electric
charge is generated on its surface.
– Inverse Piezoelectric Effect
• Conversely, when subjected to a electric voltage input, a
piezoelectric material mechanically deforms.
Quartz Crystals
• Highly anisotropic
• X-cut: vibration in the direction perpendicular to the
cutting direction
• Y-cut: vibration in the transverse direction
Piezoelectric Materials
• Piezoelectric Ceramics (man-made materials)
– Barium Titanate (BaTiO3)
– Lead Titanate Zirconate (PbZrTiO3) = PZT, most widely used
– The composition, shape, and dimensions of a piezoelectric
ceramic element can be tailored to meet the requirements of a
specific purpose.
Photo courtesy of MSI, MA
Piezoelectric Materials
• Piezoelectric Polymers
– PVDF (Polyvinylidene flouride) film
• Piezoelectric Composites
– A combination of piezoelectric ceramics and
polymers to attain properties which can be not be
achieved in a single phase
Image courtesy of MSI, MA
Piezoelectric Properties
• Anisotropic
• Notation: direction X, Y, or Z is represented by
the subscript 1, 2, or 3, respectively, and shear
about one of these axes is represented by the
subscript 4, 5, or 6, respectively.
Piezoelectric Properties
• The electromechanical coupling coefficient,
k, is an indicator of the effectiveness with which
a piezoelectric material converts electrical
energy into mechanical energy, or vice versa.
– kxy, The first subscript (x) to k denotes the direction along which
the electrodes are applied; the second subscript (y) denotes the
direction along which the mechanical energy is developed. This
holds true for other piezoelectric constants discussed later.
– Typical k values varies from 0.3 to 0.75 for piezoelectric
ceramics.
Mechanical Energy Stored
k
Electrical Energy Applied
or
k
Electrical Energy Stored
Mechanical Energy Applied
Piezoelectric Properties
• The piezoelectric charge constant, d,
relates the mechanical strain produced by an
applied electric field,
– Because the strain induced in a piezoelectric material by an
applied electric field is the product of the value for the electric
field and the value for d, d is an important indicator of a
material's suitability for strain-dependent (actuator)
applications.
– The unit is Meters/Volt, or Coulombs/Newton
Strain Development
d
Applied Electric Field
xi
dij 
Vj
Piezoelectric Properties
• The piezoelectric constants relating the
electric field produced by a mechanical
stress are termed the piezoelectric
voltage constant, g,
– Because the strength of the induced electric field in
response to an applied stress is the product of the
applied stress and g, g is important for assessing a
material's suitability for sensor applications.
– The unit of g is volt meters per Newton
Open Circuit Electric Field
g
Applied Mechanical Stress
SMART Layer for Structural Health
Monitoring
• Smart layer is a think dielectric film with built-in piezoelectric sensor
networks for monitoring of the integrity of composite and metal
structures developed by Prof. F.K. Chang and commercialized by the
Acellent Technology, Inc. The embedded sensor network are
comprised of distributed piezoelectric actuators and sensors.
Image courtesy of FK Chang, Stanford Univ.
Piezoelectric Wafer-active Sensor
•
Read paper:
– “Embedded Non-destructive Evaluation for
Structural Health Monitoring, Damage Detection,
and Failure Prevention” by V. Giurgiutiu, The
Shock and Vibration Digest 2005; 37; 83
•
Embedded piezoelectric wafer-active sensors
(PWAS) is capable of performing in-situ
nondestructive evaluation (NDE) of structural
components such as crack detection.
Image courtesy of V. Giurgiutiu, USC
Comparison of different PZ materials for
Actuation and Sensing
Thickness Selection of a PZ transducer
• Transducer is designed to vibrate around a
fundamental frequency
• Thickness of a transducer element is
equal to one half of a wavelength
Different Types of PZ Transducer
Normal beam transducer
Angle beam transducer
Dual element transducer
Focus beam transducer
Characterization of Ultrasonic Beam
• Beam profile or beam path
• Near field: planar wave front
• Far field: spherical wave front, intensity varies as
the square of the distance
• Determination of beam spread angle
• Transducer beam profiling
Near field planar wave front
Beam Profile vs. Distance
Beam profile
vs. distance
Intensity vs.
distance
Laser Generated Ultrasound (cont’)
• Thermal elastic region: ultrasound is generated
by rapid expansion of the material
• Ablation region: ultrasound is generated by
plasma formed by surface vaporization
Comparison of Ultrasound Generation
Ultrasonic Parameter Selection
• Frequency:
– Penetration decreases with frequency
• 1-10MHz: NDE work on metals
• <1MHz: inspecting wood, concrete, and large grain metals
– Sensitivity increases with frequency
– Resolution increases with frequency and bandwidth but decrease with
pulse length
– Bream spread decrease with frequency
• Transducer size:
– active area controls the power and beam divergence
– Large units provide more penetration
– Increasing transducer size results in a loss of sensitivity
• Bandwidth
– A narrow bandwidth provides good penetration and sensitivity but poor
resolution