1. Fundamentals of Ultrasonics

2. 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 ……
Acoustics: waves of lower frequencies

3. Particle velocity is much smaller than wavespeed
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
Acoustics: waves of lower frequencies

4. Wave Function Equation of progressive wave: Amplitude: A Wavelength: l
Frequency/Time period: f=1/T
Velocity U: U=fl=l/T
Energy:
Intensity:
Acoustics: waves of lower frequencies

5. Waveform & Wave front
Waveform: the sequence in time of the motions in a wave
Acoustics: waves of lower frequencies

6. Propagation and Polarization Vector
Propagation vector: the direction of wave propagation
Polarization vector: the direction of particle motion
Acoustics: waves of lower frequencies

7. 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
Acoustics: waves of lower frequencies

8. 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
Longitudial wave:
is density and m is the Poisson’s Ratio
Transverse wave:
Surface wave:
Acoustics: waves of lower frequencies

9. 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
Acoustics: waves of lower frequencies

10. 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.
Acoustics: waves of lower frequencies

11. Diffraction
Definition: spreading of energy into high and low energy bands due to the superposition of plane wave front.
Near Field:
Far Field:
Beam spreading angle:
Acoustics: waves of lower frequencies

12. Acoustic Impedance
Definition: the resistance offered to the propagation of the ultrasonic wave in a material, Z=rU. Depend on material properties only.
Acoustics: waves of lower frequencies

13. Reflection-Normal Incident
Reflection coefficient:
Transmission coefficient:
Acoustics: waves of lower frequencies

14. Reflection-Oblique Incident
Snell’s Law:
Reflection coefficient:
Transmission coefficient:
Acoustics: waves of lower frequencies

15. Total Refraction Angle
Acoustics: waves of lower frequencies

16. Selective excite different type of ultrasonic wave
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
Acoustics: waves of lower frequencies

17. Surface Skimmed Bulk Wave
The refracted wave travels along the surface of both media and at the sub-surface of media B
Acoustics: waves of lower frequencies

18. Resonance
Quality factor
Acoustics: waves of lower frequencies

19. Typical Ultrasound Inspection System
Transducer: convert electric signal to ultrasound signal
Sensor: convert ultrasound signal to electric signal

20. Mechanical (Galton Whistle Method) Electrostatic Electrodynamic
Types of Transducers
Piezoelectric
Laser
Mechanical (Galton Whistle Method)
Electrostatic
Electrodynamic
Magnetostrictive
Electromagnetic
Acoustics: waves of lower frequencies

21. 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.

22. Quartz Crystals Highly anisotropic
X-cut: vibration in the direction perpendicular to the cutting direction
Y-cut: vibration in the transverse direction

23. 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

24. 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

25. 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.

26. 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. or

27. 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

28. 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

29. 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.

30. 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

31. Comparison of different PZ materials for Actuation and Sensing

32. 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

33. Different Types of PZ Transducer
Normal beam transducer
Dual element transducer
Angle beam transducer
Focus beam transducer

34. 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

35. Beam Profile vs. Distance
Intensity vs. distance

36. 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

37. Comparison of Ultrasound Generation

38. 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