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# Fundamentals of ultrasound

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### Fundamentals of ultrasound

1. 1. Fundamentals of Ultrasonics
2. 2. Ultrasonics <ul><li>Definition : the science and exploitation of elastic waves in solids, liquids, and gases, which have a frequency above 20KHz. </li></ul><ul><li>Frequency range : 20KHz-10MHz </li></ul><ul><li>Applications : </li></ul><ul><li>Non-destructive detection (NDE) </li></ul><ul><li>Medical diagnosis </li></ul><ul><li>Material characterization </li></ul><ul><li>Range finding </li></ul><ul><li>…… </li></ul>
3. 3. Elastic wave <ul><li>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. </li></ul><ul><li>Particle motion : elastic wave induced material motion </li></ul><ul><li>Wavespeed : the propagation speed of the elastic wave </li></ul><ul><li>Particle velocity is much smaller than wavespeed </li></ul>
4. 4. Wave Function <ul><li>Equation of progressive wave : </li></ul><ul><li>Amplitude : A </li></ul><ul><li>Wavelength :  </li></ul><ul><li>Frequency/Time period : f=1/T </li></ul><ul><li>Velocity U : U= f  =  /T </li></ul><ul><li>Energy: </li></ul><ul><li>Intensity: </li></ul>
5. 5. Waveform & Wave front Waveform : the sequence in time of the motions in a wave
6. 6. Propagation and Polarization Vector Propagation vector : the direction of wave propagation Polarization vector : the direction of particle motion
7. 7. Wave Propagation <ul><li>Body wave : wave propagating inside an object </li></ul><ul><ul><li>Longitudinal (pressure) wave: deformation is parallel to propagation direction </li></ul></ul><ul><ul><li>Transverse (shear) wave: deformation is perpendicular to propagation direction, v T =0.5v L, generated in solid only </li></ul></ul><ul><li>Surface wave : wave propagating near to and influenced by the surface of an object </li></ul><ul><ul><li>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. v R =0.5v T </li></ul></ul><ul><ul><li>Plate Lamb wave: for thin plate with thickness less than three times the wavelength </li></ul></ul>
8. 8. Parameters of Ultrasonic Waves <ul><li>Velocity : the velocity of the ultrasonic wave of any kind can be determined from elastic moduli, density, and poisson’s ratio of the material </li></ul><ul><ul><li>Longitudial wave: </li></ul></ul><ul><ul><ul><li>is density and  is the Poisson’s Ratio </li></ul></ul></ul><ul><ul><li>Transverse wave: </li></ul></ul><ul><ul><li>Surface wave: </li></ul></ul>
9. 9. Attenuation <ul><li>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. </li></ul><ul><li>Attenuation coefficient : A=A 0 e -  x </li></ul>
10. 10. Types of Attenuation <ul><li>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. </li></ul><ul><li>Absorption : heating of materials, dislocation damping, magnetic hysterisis. </li></ul><ul><li>Dispersion : frequency dependence of propagation speed </li></ul><ul><li>Transmission loss : surface roughness & coupling medium. </li></ul>
11. 11. Diffraction <ul><li>Definition : spreading of energy into high and low energy bands due to the superposition of plane wave front. </li></ul><ul><li>Near Field : </li></ul><ul><li>Far Field : </li></ul><ul><li>Beam spreading angle : </li></ul>
12. 12. Acoustic Impedance <ul><li>Definition: the resistance offered to the propagation of the ultrasonic wave in a material, Z=  U. Depend on material properties only. </li></ul>
13. 13. Reflection-Normal Incident <ul><li>Reflection coefficient: </li></ul><ul><li>Transmission coefficient: </li></ul>
14. 14. Reflection-Oblique Incident <ul><li>Snell’s Law: </li></ul><ul><li>Reflection coefficient: </li></ul><ul><li>Transmission coefficient: </li></ul>
15. 15. Total Refraction Angle
16. 16. Mode Conversion <ul><li>When a longitudinal wave is incident at the boundary of A & B, two reflected beams are obtained. </li></ul><ul><li>Selective excite different type of ultrasonic wave </li></ul>
17. 17. Surface Skimmed Bulk Wave <ul><li>The refracted wave travels along the surface of both media and at the sub-surface of media B </li></ul>
18. 18. Resonance Quality factor
19. 19. Typical Ultrasound Inspection System <ul><li>Transducer : convert electric signal to ultrasound signal </li></ul><ul><li>Sensor : convert ultrasound signal to electric signal </li></ul>
20. 20. Types of Transducers <ul><li>Piezoelectric </li></ul><ul><li>Laser </li></ul><ul><li>Mechanical (Galton Whistle Method) </li></ul><ul><li>Electrostatic </li></ul><ul><li>Electrodynamic </li></ul><ul><li>Magnetostrictive </li></ul><ul><li>Electromagnetic </li></ul>
21. 21. What is Piezoelectricity? <ul><li>Piezoelectricity means “pressure electricity”, which is used to describe the coupling between a material’s mechanical and electrical behaviors. </li></ul><ul><ul><li>Piezoelectric Effect </li></ul></ul><ul><ul><ul><li>when a piezoelectric material is squeezed or stretched, electric charge is generated on its surface. </li></ul></ul></ul><ul><ul><li>Inverse Piezoelectric Effect </li></ul></ul><ul><ul><ul><li>Conversely, when subjected to a electric voltage input, a piezoelectric material mechanically deforms. </li></ul></ul></ul>
22. 22. Quartz Crystals <ul><li>Highly anisotropic </li></ul><ul><li>X-cut: vibration in the direction perpendicular to the cutting direction </li></ul><ul><li>Y-cut: vibration in the transverse direction </li></ul>
23. 23. Piezoelectric Materials <ul><li>Piezoelectric Ceramics (man-made materials) </li></ul><ul><ul><li>Barium Titanate (BaTiO 3 ) </li></ul></ul><ul><ul><li>Lead Titanate Zirconate (PbZrTiO 3 ) = PZT, most widely used </li></ul></ul><ul><ul><li>The composition, shape, and dimensions of a piezoelectric ceramic element can be tailored to meet the requirements of a specific purpose. </li></ul></ul>Photo courtesy of MSI, MA
24. 24. Piezoelectric Materials <ul><li>Piezoelectric Polymers </li></ul><ul><ul><li>PVDF (Polyvinylidene flouride) film </li></ul></ul><ul><li>Piezoelectric Composites </li></ul><ul><ul><li>A combination of piezoelectric ceramics and polymers to attain properties which can be not be achieved in a single phase </li></ul></ul>Image courtesy of MSI, MA
25. 25. Piezoelectric Properties <ul><li>Anisotropic </li></ul><ul><li>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. </li></ul>
26. 26. Piezoelectric Properties <ul><li>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. </li></ul><ul><ul><li>k xy , 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. </li></ul></ul><ul><ul><li>Typical k values varies from 0.3 to 0.75 for piezoelectric ceramics. </li></ul></ul>or
27. 27. Piezoelectric Properties <ul><li>The piezoelectric charge constant, d, relates the mechanical strain produced by an applied electric field, </li></ul><ul><ul><li>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. </li></ul></ul><ul><ul><li>The unit is Meters/Volt, or Coulombs/Newton </li></ul></ul>
28. 28. Piezoelectric Properties <ul><li>The piezoelectric constants relating the electric field produced by a mechanical stress are termed the piezoelectric voltage constant, g, </li></ul><ul><ul><li>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. </li></ul></ul><ul><ul><li>The unit of g is volt meters per Newton </li></ul></ul>
29. 29. SMART Layer for Structural Health Monitoring <ul><li>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. </li></ul>Image courtesy of FK Chang, Stanford Univ.
30. 30. Piezoelectric Wafer-active Sensor <ul><li>Read paper: </li></ul><ul><ul><li>“ Embedded Non-destructive Evaluation for Structural Health Monitoring, Damage Detection, and Failure Prevention” by V. Giurgiutiu, The Shock and Vibration Digest 2005; 37; 83 </li></ul></ul><ul><li>Embedded piezoelectric wafer-active sensors (PWAS) is capable of performing in-situ nondestructive evaluation (NDE) of structural components such as crack detection. </li></ul>Image courtesy of V. Giurgiutiu, USC
31. 31. Comparison of different PZ materials for Actuation and Sensing
32. 32. Thickness Selection of a PZ transducer <ul><li>Transducer is designed to vibrate around a fundamental frequency </li></ul><ul><li>Thickness of a transducer element is equal to one half of a wavelength </li></ul>
33. 33. Different Types of PZ Transducer Normal beam transducer Dual element transducer Angle beam transducer Focus beam transducer
34. 34. Characterization of Ultrasonic Beam <ul><li>Beam profile or beam path </li></ul><ul><li>Near field: planar wave front </li></ul><ul><li>Far field: spherical wave front, intensity varies as the square of the distance </li></ul><ul><li>Determination of beam spread angle </li></ul><ul><li>Transducer beam profiling </li></ul>Near field planar wave front
35. 35. Beam Profile vs. Distance Beam profile vs. distance Intensity vs. distance
36. 36. Laser Generated Ultrasound (cont’) <ul><li>Thermal elastic region : ultrasound is generated by rapid expansion of the material </li></ul><ul><li>Ablation region : ultrasound is generated by plasma formed by surface vaporization </li></ul>
37. 37. Comparison of Ultrasound Generation
38. 38. Ultrasonic Parameter Selection <ul><li>Frequency : </li></ul><ul><ul><li>Penetration decreases with frequency </li></ul></ul><ul><ul><ul><li>1-10MHz: NDE work on metals </li></ul></ul></ul><ul><ul><ul><li><1MHz: inspecting wood, concrete, and large grain metals </li></ul></ul></ul><ul><ul><li>Sensitivity increases with frequency </li></ul></ul><ul><ul><li>Resolution increases with frequency and bandwidth but decrease with pulse length </li></ul></ul><ul><ul><li>Bream spread decrease with frequency </li></ul></ul><ul><li>Transducer size: </li></ul><ul><ul><li>active area controls the power and beam divergence </li></ul></ul><ul><ul><li>Large units provide more penetration </li></ul></ul><ul><ul><li>Increasing transducer size results in a loss of sensitivity </li></ul></ul><ul><li>Bandwidth </li></ul><ul><ul><li>A narrow bandwidth provides good penetration and sensitivity but poor resolution </li></ul></ul>