- Wave Characteristics.
- Reflection.
- Refraction.
- Mode Conversion.
- Critical Angles.
- Diffraction.
- Resonance.
- Attenuation.
- Basic Instrumentation.
- Transducers and Coupling.
- Special Equipment Features.
- Review Questions.
- Approaches to Testing.
- Measuring System Performance.
- Reference Reflectors.
- Calibration.
- Review Questions.
- Signal Interpretation.
- Causes of Variability.
- Special Issues.
- Weld Inspection.
- Immersion Testing.
- Production Testing.
- Inservice Inspection.
- Code Bodies and Their UT Standards.
- ASTM International.
- American Society of Mechanical Engineers.
- American Welding Society.
- American Petroleum Society.
- Aerospace Industries Association.
- National Board of Boilers and Pressure Vessel Inspectors.
- Military Standards.
- Flaw Sizing Techniques.
- Time of Flight Diffraction.
- Advantages of Time of Flight.
- Disadvantages of Time of Flight.
- How Phased Array Works.
- Practical Applications of Phased Array.
- Waves.
- Dispersion.
- Dispersion Curves.
- Bulk vs. Guided Waves.
- Source Influence.
- Applications.
- Pipe.
- Review Questions.
- Review Questions.
2 Ultrasonic Testing Method l Chapter 1
The velocity at which bulk waves travel is deter-
mined by the material’s elastic moduli and density.
The expressions for longitudinal and transverse
waves are given in Equations 2 and 3, respectively.
where
VL = longitudinal bulk wave velocity,
VT = transverse (shear) wave velocity,
G = shear modulus,
E = Young’s modulus of elasticity,
μ = Poisson’s ratio, and
= material density.
Typical values of bulk wave velocities in com-
mon materials are given in Table 2. From Table 2 it is
seen that, in steel, a longitudinal wave travels at 5.
km/s, while a shear wave travels at 3 km/s. In alu-
minum, the longitudinal wave velocity is 6 km/s
while the shear velocity is 3 km/s. The wave-
lengths of sound for each of these materials are cal-
culated using Equation 1 for each applicable test
frequency used. For example, a 5 MHz L-wave in
water has a wavelength equal to 1483/5(10) 6 m or
0 mm.
When sound waves are confined within bound-
aries, such as along a free surface or between the
surfaces of sheet materials, the waves take on a very
different behavior, being controlled by the confining
boundary conditions. These types of waves are
called guided waves, i., they are guided along the
respective surfaces and exhibit velocities that are
dependent upon elastic moduli, density, thickness,
surface conditions and relative wavelength interac-
tions with the surfaces. For rayleigh waves, the use-
ful depth of penetration is restricted to about one
wavelength below the surface. The wave motion is
that of a retrograde ellipse. Wave modes such as
those found with lamb waves have a velocity of
propagation dependent upon the operating fre-
quency, sample thickness and elastic moduli. They
are dispersive (velocity changes with frequency) in
that pulses transmitted in these modes tend to
become stretched or dispersed as they propagate in
these modes and/or materials which exhibit fre-
quency-dependent velocities.
Reflection.
Ultrasonic waves, when they encounter a discrete
change in materials, as at the boundary of two dis-
similar materials, are usually partially reflected. If
the incident waves are perpendicular to the material
interface, the reflected waves are redirected back
toward the source from which they came. The degree
to which the sound energy is reflected is dependent
upon the difference in acoustic properties, i.,
acoustic impedances, between the adjacent materials.
Acoustic impedance (Equation 4) is the product
of a wave’s velocity of propagation and the density
of the material through which the wave is passing.
where
Z = acoustic impedance,
= density, and
V = applicable wave velocity.
Table 2 lists the acoustic impedances of several
common materials.
The degree to which a perpendicular wave is
reflected from an acoustic interface is given by the
energy reflection coefficient. The ratio of the
reflected acoustic energy to that which is incident
upon the interface is given by Equation 5.
where
R = coefficient of energy reflection for normal
incidence,
Z = respective material acoustic impedances,
Z 1 = incident wave material,
Z 2 = transmitted wave material, and
T = coefficient of energy transmission.
Note: T + R = 1
ρ + μ
ρ
Z = ρ ×V
R Z Z Z Z 2 1 2 2 1 2 ( ) ( )( )
− μ
ρ + μ − μ
V E 1 L 1 1 2 Table 2: Acoustic velocities, densities and acoustic impedance of common materials. Material VL (m/s) VT (m/s) Z ρ (g/cm 3 ) Steel 5900 3230 45 7. Aluminum 6320 3130 17 2. Plastic glass 2730 1430 3 1. Water 1483 ---- 1 1. Quartz 5800 2200 15 2.
3 Physical Properties
In the case of water-to-steel, approximately 88%
of the incident longitudinal wave energy is reflected
back into the water, leaving 12% to be transmitted
into the steel. 1 These percentages are arrived at using
Equation 5 with Zst= 45 and Zw = 1. Thus, R =
(45 − 1) 2 /(45 + 1) 2 = (43.5/46) 2 = 0, or
88%, and T = 1 – R = 1 − 0 = 0, or 12%.
Refraction.
When a sound wave encounters an interface at an
angle other than perpendicular (oblique incidence),
reflections occur at angles equal to the incident angle
(as measured from the normal or perpendicular axis).
If the sound energy is partially transmitted beyond
the interface, the transmitted wave may be 1) refract-
ed (bent), depending on the relative acoustic veloci-
ties of the respective media, and/or 2) partially con-
verted to a mode of propagation different from that of
the incident wave. Figure 1(a) shows normal reflec-
tion and partial transmission, while Figure 1(b) shows
oblique reflection and the partition of waves into
reflected and transmitted wave modes.
Referring to Figure 1(b), Snell’s law may be stated as:
For example, at a water-plastic glass interface,
the refracted shear wave angle is related to the inci-
dent angle by:
sinβ = (1430/1483)sinα = (0)sinα
For an incident angle of 30°,
sinβ = 0 × 0 and β = 28°
Mode Conversion.
It should be noted that the acoustic velocities (V 1
and V 2 ) used in Equation 6 must conform to the
modes of wave propagation that exist for each given
case. For example, a wave in water (which supports
only longitudinal waves) incident on a steel plate at
an angle other than 90° can generate longitudinal,
shear, as well as heavily damped surface or other
wave modes, depending on the incident angle and
test part geometry. The wave may be totally reflect-
ed if the incident angle is sufficiently large. In any
case, the waves generated in the steel will be refract-
ed in accordance with Snell’s law, whether they are
longitudinal or shear waves.
Figure 2 shows the distribution of transmitted
wave energies as a function of the incident angle for
β =
α
V V sin 2 sin 1 V 1 V 2 β β α α (V 1 > V 2 ) Z 1 Z 2 R I T Oblique incidence Normal incidence Figure 1: (a) Reflected ( R) and transmitted ( T) waves at normal incidence, and (b) reflected and
refracted waves at angled (α) incidence.
Energy flux coefficient
- 0
- 9
- 8
- 7
- 6
- 5
- 4
- 3
- 2
- 1 4 8 12 16 20 24 28 32 36 40 Transmi ed shear wave Transmi ed longitudinal wave
Incidence angle (degrees)
Reflected L-wave Figure 2: Reflection and transmission coefficients versus incident angle for water/aluminum interface. (a) (b)
- When Equation 5 is expressed for pressure waves rather than the energy contained in the waves, the terms in parentheses are not squared.
edges of reflective interfaces, such as near the tip of
a fatigue crack, specular reflections occur along the
“flat” surfaces of the crack and cylindrical wavelets
are launched from the edges. Since the waves are
coherent, i., the same frequency (wavelength) and
in phase, their redirection into the path of subse-
quent advancing plane waves results in incident and
reflected (scattered) waves interfering, i., forming
regions of reinforcement (constructive interference)
and cancellation (destructive interference).
This “interfering” behavior is characteristic of
continuous waves (or pulses from “ringing” ultra-
sonic transducers) and, when applied to edges and
apertures serving as sources of sound beams, is
known as wave diffraction. It is the fundamental
basis for concepts such as transducer beam spread
(directivity), near field wavelength-limited disconti-
nuity detection sensitivity, and assists in the sizing of
discontinuities using dual transducer (crack-tip dif-
fraction) techniques. Figure 3 shows examples of
plane waves being changed into spherical or cylindri-
cal waves as a result of diffraction from point reflec-
tors, linear edges and (transducer-like) apertures.
Beam spread and the length of the near field for
round sound sources may be calculated using
Equations 8 and 9.
where
= beam divergence half angle,
= wavelength in the media,
D = diameter of the aperture (transducer),
N = length of the near field (fresnel zone).
Note: The multiplier of 1 in Equation 8 is for
the theoretical null. 1 is used for the 20 dB down
point (10% of peak), 0 is used for the 10 dB
down point (32% of peak) and 0 for the 6 dB
down point (50% of peak).
For example, a 20 mm diameter, L-wave
transducer, radiating into steel and operating at
a frequency of 2 MHz, will have a near field
given by:
and half-beam spread angle given by:
If the 10% peak value was desired rather than the
theoretical null, the 1 would be changed to 1 and
would equal 9°. Using the multiplier of 0 for the
6 dB down value, the half angle becomes 6°.
Resonance.
Another form of wave interference occurs when nor-
mally incident (at normal incidence) and reflected
plane waves interact (usually within narrow, parallel
interfaces). The amplitudes of the superimposed
acoustic waves are additive when the phase of the
doubly reflected wave matches that of the incoming
incident wave and creates “standing” (as opposed to
traveling) acoustic waves. When standing waves
occur, the item is said to be in resonance, i., res-
onating. Resonance occurs when the thickness of the
item equals half a wavelength 2 or its multiples, i.,
when T = V/2F. This phenomenon occurs when
piezoelectric transducers are electrically excited at
their characteristic (fundamental resonant) frequency.
It also occurs when longitudinal waves travel through
thin sheet materials during immersion testing.
Attenuation.
Sound waves decrease in intensity as they travel away
from their source, due to geometrical spreading,
scattering and absorption. In fine-grained, homoge-
neous and isotropic elastic materials, the strength of
the sound field is affected mainly by the nature of the
radiating source and its attendant directivity pattern.
Tight patterns (small beam angles) travel farther than
widely diverging patterns.
λ
φ =
λ
D sin 1. sin 1 5 10 20 10 2 10 1 10° 3 3 6 ( ) ( ) ( )
φ =
− − N 20 10 2 10 4 5 10 200 5. 10 33 mm 3 2 6 3 3 < ( ) ( )>( ) ( )
− − 5 Physical Properties 2. If a layer between two differing media has an acoustic imped- ance equal to one-quarter wavelength, 100% of the incident acoustic energy, at normal incidence, will be transmitted through the dual interfaces because the interfering waves in the layer combine to serve as an acoustic impendence trans- former.
When ultrasonic waves pass through common
polycrystalline elastic engineering materials (that
are generally homogeneous but contain evenly dis-
tributed scatterers, e., gas pores, segregated inclu-
sions and grain boundaries), the waves are partially
reflected at each discontinuity and the energy is
said to be scattered into many different directions.
Thus, the acoustic wave that starts out as a coherent
plane wave front becomes partially redirected as it
passes through the material.
The relative impact of the presence of scattering
sources depends upon their size in comparison to the
wavelength of the ultrasonic wave. Scatterers much
smaller than a wavelength are of little consequence.
As the scatterer size approaches that of a wavelength,
scattering within the material becomes increasingly
troublesome. The effects on such signal attenuation
can be partially compensated by using longer wave-
length (lower frequency) sound sources, usually at
the cost of decreased sensitivity to discontinuities
and resolution.
Some scatters, such as columnar grains in
stainless steels and laminated composites, exhibit
highly anisotropic elastic behavior. In these cases,
the incident wave front becomes distorted and often
appears to change direction (propagate better in
certain preferred directions) in response to the
material’s anisotropy. This behavior of some materi-
als can significantly complicate the analysis of the
signals.
Sound waves in some materials are absorbed by
the processes of mechanical hysteresis, internal fric-
tion or other energy loss mechanisms. These
processes occur in nonelastic materials such as
plastics, rubber, lead and nonrigid coupling materi-
als. As the mechanical wave attempts to propagate
through such materials, part of its energy is given
up in the form of heat and is not recoverable.
Absorption is usually the reason that testing of
soft and pliable materials is limited to relatively
thin sections.
Attenuation is measured in terms of the energy
loss ratio per unit length, e., decibels per inch or
decibels per meter. Values range from less than
10 dB/m for aluminum to over 100 dB/m or more
for some castings, plastics and concrete.
Table 3 shows some typical values of attenuation
for common NDT applications. Be aware that atten-
uation is highly dependent upon operating frequen-
cy and thus any stated values must be used with
caution.
Because many factors affect the signals returned
in pulse-echo testing, direct measurement of mate-
rial attenuation can be quite difficult. Detected sig-
nals depend heavily upon operating frequency,
boundary conditions, and waveform geometry
(plane or other), as well as the precise nature of the
materials being evaluated. Materials are highly vari-
able due to their thermal history, balance of alloying
or other integral constituents (aggregate, fibers,
matrix uniformity and water/void content, to name
a few), as well as mechanical processing (forging,
rolling, extruding and the preferential directional
nature of these processes).
6 Ultrasonic Testing Method l Chapter 1 Table 3: Attenuation values for common materials. Nature of Material Attenuation*(dB/m) Principal Cause Normalized steel 70 Scatter Aluminum 6061-T6511 90 Scatter Stainless steel, 3XX 110 Scatter/Redirection Plastic (clear acrylic) 380 Absorption
- Frequency of 2 MHz, longitudinal wave mode
8 Ultrasonic Testing Method l Chapter 1
