Reflection And Transmission At Normal Incidence
Reflected and transmitted intensities
When ultrasonic waves are incidence at right angles to the boundary of two media of different acoustic impedance, then some of the waves are reflected and some are transmitted across the boundary.
Figure2.1 Reflections and Transmission at Normal Incidence
Ultrasonic waves are reflected at boundaries where there is a difference in acoustic impedance (Z) of the materials on each side of the boundary. This difference in is commonly referred to as the impedance mismatch. The greater the impedance mismatch, the greater the percentage of energy that will be reflected at the interface or boundary between one medium and another.
The fraction of the incident wave intensity that is reflected can be derived based on the fact that particle velocity and local particle pressures must be continuous across the boundary. When the acoustic impedance of the materials on both sides of the boundary are known, the fraction of the incident wave intensity that is reflected (the reflection coefficient) can be calculated as:
R = Reflection Coefficient
Z1 = Acoustic Impedance of Medium 1
Z2 = Acoustic Impedance of Medium 2
T = Transmission Coefficient
Z1 = Acoustic Impedance of Medium 1
Z2 = Acoustic Impedance of Medium 2
Reflected and transmitted pressures
The relationships which determine the amount of reflected and transmitted acoustic pressures at a boundary for normal incidence are the amount of reflected and transmitted acoustic pressure which is given by:
Pt = Transmitted pressure
Pr = Reflected pressure
Z1 = Acoustic Impedance of Medium 1
Z2 = Acoustic Impedance of Medium 2
Figure2.2 Acoustic pressure values in the case of reflection on the interface steel/water, incident wave in steel (a) or in water (b).
The reason for a higher transmitted acoustic pressure in steel is that the acoustic pressure is proportional to the product of intensity and acoustic impedance although the transmitted intensity in steel is low. The transmitted acoustic pressure is high because of the high acoustic impedance of steel.
Reflection And Transmission At Oblique Incidence
Refraction and mode conversion
When sound travels in a solid material, one form of wave energy can be transformed into another form. For example, when a longitudinal wave hits an interface at an angle, some of the energy can cause particle movement in the transverse direction to start a shear wave.
Mode conversion occurs when a wave encounters an interface between materials of different acoustic impedances and the incident angle is not normal to the interface. It should be noted that mode conversion occurs “every time” a wave encounters an interface at an angle. This mode conversion occurs for both the portion of the wave that passes through the interface and the portion that reflects off the interface.
Figure2.3 Showing mode conversions when longitudinal wave hits an interface at an angle
When sound waves pass through an interface between materials having different acoustic velocities, refraction takes place at the interface. The larger the difference in acoustic velocities between the two materials, the more the sound is refracted.
However, the converted shear wave is not refracted as much as the longitudinal wave because shear waves travel slower than longitudinal waves. Therefore, the velocity difference between the incident longitudinal wave and the shear wave is not as great as it is between the incident and refracted longitudinal waves.
Also, note that when a longitudinal wave is reflected inside the material, the reflected shear wave is reflected at a smaller angle than the reflected longitudinal wave. This is also due to the fact that the shear velocity is less than the longitudinal velocity within a given material.
If ultrasonic waves strike a boundary at an oblique angle, then the reflection and transmission of the waves become more complicated than that with normal incidence. At oblique incidence, the phenomena of mode conversion (i.e. a change in the nature of the wave motion) and refraction (a change in the direction of wave propagation) occur.
Snell’s Law describes the relationship between the angles and the velocities of the waves. Snell’s law equates the ratio of material velocities to the ratio of the sine’s of incident and refracted angles, as shown in the following equation:
θI= Angle of the Incident Wave
θR= Angle of the Reflected Wave
V1 = Velocity of Incident Wave
V2 = Velocity of Reflected Wave
First and second critical angles
When a longitudinal wave moves from a slower to a faster material (and thus the wave is refracted), there is an incident angle that makes the angle of refraction for the “longitudinal wave” to become 90°. This is angle is known as “the first critical angle”.
The first critical angle can be found from Snell’s law by putting in an angle of 90° for the angle of the refracted ray. At the critical angle of incidence, much of the acoustic energy is in the form of an inhomogeneous compression wave, which travels along the interface and decays exponentially with depth from the interface. This wave is sometimes referred to as a “creep wave”.
Because of their inhomogeneous nature and the fact that they decay rapidly, creep waves are not used as extensively as Rayleigh surface waves in NDT.
When the incident angle is equal or greater than the first critical angle, only the mode-converted shear wave propagates into the material. For this reason, most angle beam transducers use a shear wave so that the signal is not complicated by having two waves present.
In many cases, there is also an incident angle that makes the angle of refraction for the “shear wave” to become 90°. This is known as the “second critical angle” and at this point, all of the wave energy is reflected or refracted on a surface following shear wave or shear creep wave. Slightly beyond the second critical angle, surface (Rayleigh) waves will be generated.
The incident angle for angle-beam transducers is somewhere between the first and second critical angles such that a shear wave, at a desired angle, is introduced into the material being inspected.
Figure2.4 Showing the first and second critical angle
The figure shows the mode of waves introduced into a steel surface as a function of the incident angle of the wave generated by the transducers. It can be seen from the figure that the incident angle for angle beam (shear) transducers ranges between 30° to 55°. But it is important to remember that, due to refraction, the angle of the shear wave inside the material is completely different from the incident angle.
The characteristics of the ultrasonic beam
The ultrasonic beam
The region in which ultrasonic waves are propagated from an ultrasonic transducers is known as the ultrasonic beam. Two distinct regions of the beam exist and are classified as the near field region and far field region.
The region located near the transducers surface is called the near field. In the near field, the acoustic field is basically cylindrical, with a diameter slightly less than the diameter of the emitter, and the intensity of the acoustic waves oscillates along the axis of the transducers.
As the characteristic distances of these oscillations are often much smaller than the dimensions of the measured volumes, they do not significantly affect Doppler information collected in this region. The length of the near field, Z, is determined by the position of the last maximum of the acoustic intensity.
If the length of the near field is important, the oscillations of the acoustic waves may affect the measurement. Therefore it is not recommended to realize measurements in this region in such a case.
Figure2.5 Showing the near field
N = Near Field
D = Transducer Diameter
V = Velocity
The zone lying beyond Z is called the far field. In the far field, the intensity of the acoustic waves along the axis varies as the inverse of the square of the distance from the transducers and small oscillations appear in the radial direction. Most of the acoustic energy is contained in a cone of which the half angle, ‘d’ is characterized by the wavelength and the diameter of the emitter.
Figure2.6 Showing the far field
As discussed on the previous page, round transducers are often referred to as piston source transducers because the sound field resembles a cylindrical mass in front of the transducer. However, the energy in the beam does not remain in a cylinder but instead spreads out as it propagates through the material.
The phenomenon is usually referred to as beam spread but is sometimes also referred to as beam divergence or ultrasonic diffraction. It should be noted that there is actually a difference between beam spread and beam divergence.
Beam spread is a measure of the whole angle from side to side of the main lobe of the sound beam in the far field. Beam divergence is a measure of the angle from one side of the sound beam to the central axis of the beam in the far field. Therefore, beam spread is twice the beam divergence.
Attenuation of ultrasonic beams
The intensity of an ultrasonic beam that is sensed by a receiving transducer is considerably less than the intensity of the initial transmission. The factors that are primarily responsible for the loss in beam intensity are discussed below:
Scattering of ultrasonic waves
The scattering of ultrasonic waves is due to the fact that the material in which the ultrasonic wave is traveling is not absolutely homogeneous. The inhomogeneities can be anything that will present a boundary between two materials of different acoustic impedance such as an inclusion or pores and possibly grain boundaries containing contaminants.
Certain materials are inherently inhomogeneous, such as cast iron which is composed of a matrix of grains and graphite particles which differ greatly in density and elasticity. Each grain in the agglomeration has radically different acoustic impedance and consequently produces severe scattering.
It is possible to encounter scattering in a material of just one crystal type if the crystals exhibit velocities of different values when measured along axes in different directions. A material of this type is said to be Anisotropic. If individual grains are randomly oriented throughout a material, scattering will occur as if the material is composed of different types of crystals or phases.
Materials exhibiting these qualities not only decrease the returned ultrasonic signal because of scattering, but also often produce numerous small echoes which may mask or “camouflage” real indications.
Absorption of ultrasonic waves
Absorption of ultrasonic waves is the result of the conversion of a portion of the sound energy into heat. In any material not at absolute zero temperature the particles are in random motion as a result of the heat content of the material. As the temperature increases, there will be an increase in particle activity.
As an ultrasound wave propagates through the material it excites the particles. As these particles collide with unexcited particles, energy is transmitted causing them to oscillate faster and through larger distances. This motion persists after the sound wave has passed on, so an energy of the passing wave has been converted to heat in the material.
Loss due to coupling and surface roughness
The third cause of attenuation is transmission loss due to the coupling medium and the surface roughness. When a transducer is placed on a very smooth surface of a specimen using a couplant, the amplitude of signal from the back surface varies with the thickness of the couplant.
The transmission loss due to surface roughness is best observed when a reference calibration block is used. A reference block is generally made of a material acoustically equivalent to the test specimen. However, the test specimen cannot always have the same surface roughness as the calibration block.
This difference leads to a transfer loss at the contact surface. In addition to the amount of sound lost due to the above causes, there are other factors to consider, such as losses in scattering due to the surface roughness of a reflector and spreading of the sound beam. In this instance, attenuation is considered as the sum of all these factors since they all affect the amount of sound transmitted to and returned from an area of interest in the test material. The attenuation losses during propagation in a material are shown in figure 2.7.
In this instance, attenuation is considered as the sum of all these factors since they all affect the amount of sound transmitted to and returned from an area of interest in the test material. The attenuation losses during propagation in a material are shown in figure 2.7.
Figure2.7 Attenuation loss during transmission
An important property of ultrasonic waves is there ability, or tendency, to “bend around” and pass obstacles which are comparable in size to their wavelength. This wave interference or diffraction occurs if the wave impinges upon a small inclusion or pore in the metal.
A portion of the energy bends around the defect and reflection is much reduced. A second example of this phenomenon is the bending of ultrasonic waves near the edge of a specimen .This bending may divert the ultrasonic wave from where it would normally be received, to some other point.
Figure 2.8 Diffraction of ultrasound in solid
Piezoelectric and ferroelectric transducers
The term “Piezoelectricity” refers to the production of bound electrical charges on the surfaces of a material or crystal specimen by the imposition of some form of “stress”. Piezoelectricity is the ability of certain crystals to generate a voltage in response to applied mechanical stress. Crystals which acquire a charge when compressed, twisted or distorted are said to be piezoelectric.
The word is derived from the Greek piezo, which means to push. The piezoelectric effect, known as piezoelectricity, was discovered by brothers Pierre and Jacques Curie when they were 21 and 24 years old in 1880. The brothers Curie predicted and demonstrated the piezoelectric effect in their laboratory by using such common materials as tinfoil, glue, wire, magnets, and a jeweler’s saw.
Nanomotion’s unique line of piezoelectric motors utilizes the reverse piezoelectric effect. The piezoelectric effect is reversible in that piezoelectric crystals, when subjected to an externally applied voltage, can change shape, or distort, by a small amount.
This distortion, which is approximately 0.1% of the size of the original piezoelectric crystal, is measured in nanometers, but nevertheless is sufficient to allow for useful application in a range of areas, such as precision motion applications and ultra fine focusing of optical assemblies.
Figure2.9 Direct piezoelectric effect
Figure2.10 Inverse piezoelectric effect
Types of piezoelectric transducers
Piezoelectric transducers can be classified into two groups. The classification is made based on the type of piezoelectric material which is used in the manufacture of the transducer. If the transducers are made from single crystal materials in which the piezoelectric effect occurs naturally, they are classified as piezoelectric crystal Transducers. On the other hand, the transducers which are made from polycrystalline material in which the piezoelectric effect has to be induced by polarization, are termed polarized ceramic transducers.
Piezoelectric crystal transducers
Transducer crystals are custom made to order from Quartz, Lithium Niobate, Tourmaline, Gallium Orthophosphate or Lead Zirconate Titanate (PZT) . Transducers themselves are used in many applications, such as ultrasonic pressure measurement, level sensing, distance sensing, micro-positioning, non-destructive testing of solids and acoustic-optical experiments. Soldered wire leads, suitable to the size and frequency of the crystals, are available.
Single-Crystal Quartz can be fabricated to generate compressional, shear, length extensional and torsional waves for use in numerous applications.
Figure2.11 System coordinates in a quartz crystal (simplified) and positions at X and Y-cut crystals.
Single Crystal Quartz is often used in research applications due to its high repeatability, superior aging characteristics, and purity of modes. Crystal Quartz is the standard to which other transducer materials are compared. It is not as efficient as other materials and its extremely high Q may be detrimental in certain applications.
Available frequency range is between 50Khz and 100Mhz depending on shape and size.
Lithium Niobate possesses a high Curie temperature and excellent piezoelectric coupling coefficient making it attractive for ultrasonic device applications. Lithium Niobate possesses a number of useful cuts that are now extensively used in transducer applications. Two compressional cuts are popular, the Z-cut and the 36°C rotated Y-cut. It is suitable for applications from 250 Khz to 40 Mhz.
Lithium Niobate possesses very large piezoelectric coupling coefficients – several times larger than quartz – and very low acoustic losses. Because of its Curie temperature of 1150°C, it can be utilized in high-temperature applications.
Gallium Orthophosphate, GaPO4 is a single crystal material developed in the 1980s primarily for the manufacture and design of high-temperature sensors. The material is purely piezoelectric (no pyroelectric discharge) and has excellent high-temperature properties up to 970°C, with excellent stability of many physical constants.
In addition, the material has high electric resistivity and a high piezoelectric constant and sensitivity. Various angles of orientation are available and element sizes are around 1″ diameter.
Lead Zirconate Titanate (PZT)
Lead Zirconate Titanate (PZT) is available in a variety of grades with a wide range of properties to fulfill the many diverse applications of piezoelectricity. We can supply discs, blocks, tubes, rings and custom shapes from various grades of material in both compressional and shear wave modes.
Frequency range is 100Khz to 20Mhz ± 5%. PZT is ideal for a broad range of applications such as nano-positioning, medical therapeutics, flow sensing and non-destructive testing to name but a few.
The shape can be round, square, rectangular, triangular and wedged, conical, tubular, cylindrical, spherical and annular.
Polarized ceramic transducers
The active element of most acoustic transducers used today is a piezoelectric ceramic, which can be cut in various ways to produce different wave modes. A large piezoelectric ceramic element can be seen in the image of a sectioned low-frequency transducer. Preceding the advent of piezoelectric ceramics in the early 1950’s, piezoelectric crystals made from quartz crystals and magnetostrictive materials were primarily used.
The active element is still sometimes referred to as the crystal by old timers in the NDT field. When piezoelectric ceramics were introduced, they soon became the dominant material for transducers due to their good piezoelectric properties and their ease of manufacture into a variety of shapes and sizes.
They also operate at low voltage and are usable up to about 300oC. The first piezoceramic in general use was barium titanate, and that was followed during the 1960’s by lead zirconate titanate compositions, which are now the most commonly employed ceramic for making transducers. New materials such as piezo-polymers and composites are also being used in some applications.
Figure2.12 Polarized ceramic transducer
The thickness of the active element is determined by the desired frequency of the transducer. Thin wafer element vibrates with a wavelength that is twice its thickness. Therefore, piezoelectric crystals are cut to a thickness that is 1/2 the desired radiated wavelength. The higher the frequency of the transducer, the thinner the active element. The primary reason that high-frequency contact transducers are not produced is because the element is very thin and too fragile.
Next: CHAPTER 3