Fundamentals of ultrasound

Fundamentals of UltrasonicsFundamentals of Ultrasonics

UltrasonicsUltrasonics

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 waveElastic 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 FunctionWave Function

Equation of progressive wave:

)sin( kxtAy

•Amplitude: A•Wavelength: •Frequency/Time period: f=1/T•Velocity U: U=f=/T•Energy: •Intensity:

2222 AmfE 2222 AfI

Waveform & Wave frontWaveform & Wave front

Waveform: the sequence in time of the motions in a wave

Propagation and Polarization VectorPropagation and Polarization Vector

Propagation vector: the direction of wave propagationPolarization vector: the direction of particle motion

Wave PropagationWave 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 WavesParameters 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 is the Poisson’s Ratio

– Transverse wave:

– Surface wave:

21

)21)(1(

)1(

E

UL

LT UGE

U 5.0)1(2

2121

Ts UU 9.0

AttenuationAttenuation

• 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-x

)(ln

0nepers

A

A

)(log200

10 dBA

A

Types of AttenuationTypes 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.

DiffractionDiffraction

• 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:

4

2Dd

4

2Dd

D

2.1

Acoustic ImpedanceAcoustic Impedance

• Definition: the resistance offered to the propagation of the ultrasonic wave in a material, Z=U. Depend on material properties only.

Reflection-Normal IncidentReflection-Normal Incident

• Reflection coefficient:

• Transmission coefficient:

2

12

122

1122

1122

ZZ

ZZ

UU

UU

I

I

i

rr

ri

TT

ZZ

ZZ

UU

UU

I

I

1

442

12

212

1122

2211

Reflection-Oblique IncidentReflection-Oblique Incident

• Snell’s Law:

• Reflection coefficient:

• Transmission coefficient:

B

A

r

i

U

U

sin

sin

2

22221

2

22221

2

sin//sin1

sin//sin1

iBAi

iBAir

UU

UU

2

22221

2

22221

sin//sin1

sin//4

iBAi

iBAt

UU

UU

Total Refraction AngleTotal Refraction Angle

222

22

21

)(arcsin

21A

rU

ZZ

Mode ConversionMode 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 WaveSurface Skimmed Bulk Wave

•The refracted wave travels along the surface of both media and at the sub-surface of media B

ResonanceResonance

Quality factor

f

f

ff

f

CyclePerDissipatedEnergy

CyclePerSuppliedEnergyQ rr

12

Typical Ultrasound Inspection SystemTypical Ultrasound Inspection System

•Transducer: convert electric signal to ultrasound signal

•Sensor: convert ultrasound signal to electric signal

Types of TransducersTypes of Transducers

• Piezoelectric

• Laser

• Mechanical (Galton Whistle Method)

• Electrostatic

• Electrodynamic

• Magnetostrictive

• Electromagnetic

What is Piezoelectricity?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 CrystalsQuartz Crystals

• Highly anisotropic• X-cut: vibration in the direction perpendicular to the

cutting direction• Y-cut: vibration in the transverse direction

Piezoelectric MaterialsPiezoelectric 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 MaterialsPiezoelectric 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 PropertiesPiezoelectric 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.

orAppliedEnergy Electrical

StoredEnergy Mechanicalk

AppliedEnergy Mechanical

StoredEnergy Electricalk

Piezoelectric PropertiesPiezoelectric 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

Field Electric Applied

tDevelopmenStrain d

j

iij V

xd

Piezoelectric PropertiesPiezoelectric 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

Stress Mechanical Applied

Field ElectricCircuit Open g

SMART Layer for Structural Health SMART Layer for Structural Health MonitoringMonitoring

• 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 SensorPiezoelectric 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 Comparison of different PZ materials for Actuation and SensingActuation and Sensing

Thickness Selection of a PZ transducerThickness 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 TransducerDifferent Types of PZ Transducer

Normal beam transducer Dual element transducer

Angle beam transducerFocus beam transducer

Characterization of Ultrasonic BeamCharacterization 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. DistanceBeam Profile vs. Distance

Beam profile vs. distance

Intensity vs. distance

Laser Generated Ultrasound (cont’)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 GenerationComparison of Ultrasound Generation

Ultrasonic Parameter SelectionUltrasonic 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