ASTM E2001-98

NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
Designation: E 2001 – 98
Standard Guide for
Resonant Ultrasound Spectroscopy for Defect Detection in
Both Metallic and Non-metallic Parts
This standard is issued under the fixed designation E 2001; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope 4.1.1 In addition to its basic research applications in phys-
ics, materials science, and geophysics, Resonant Ultrasound
1.1 This guide describes a procedure for detecting defects in
Spectroscopy (RUS) has been used successfully as an applied
metallic and non-metallic parts using the resonant ultrasound
nondestructive testing tool. Resonant ultrasound spectroscopy
spectroscopy method. The procedure is intended for use with
in commercial, nondestructive testing has a few recognizable
instruments capable of exciting and recording whole body
names including, RUS Nondestructive Testing, Acoustic Reso-
resonant states within parts which exhibit acoustical or ultra-
nance Spectroscopy (ARS), and Resonant Inspection. Early
sonic ringing. It is used to distinguish acceptable parts from
references to this body of science often are termed the“ swept
those containing defects, such as cracks, voids, chips, density
sine method.” It was not until 1990 (2) that the name Resonant
defects, tempering changes, and dimensional variations that are
Ultrasound Spectroscopy appeared, but the two techniques are
closely correlated with the elastic properties of the material.
synonymous. RUS based techniques are becoming commonly
1.2 This standard does not purport to address all of the
used in the manufacture of steel, ceramic, and sintered metal
safety concerns, if any, associated with its use. It is the
parts. In these situations, a part is vibrated mechanically, and
responsibility of the user of this standard to establish appro-
defects are detected based on changes in the pattern of
priate safety and health practices and determine the applica-
vibrational resonances or variations from theoretically calcu-
bility of regulatory limitations prior to use.
lated or empirically acceptable spectra. RUS measures all
2. Referenced Documents resonances, in a defined range, of the part rather than scanning
for individual defects. In a single measurement, RUS-based
2.1 ASTM Standards:
techniques potentially can test for numerous defects including
E 1316 Terminology for Nondestructive Examinations
cracks and dimensional variations. Since the RUS measure-
3. Terminology
ment yields a whole body response, it is often difficult to
discriminate between defect types, that is, cracks or other
3.1 Definitions—The definitions of terms relating to con-
discontinuities. Nevertheless, on certain types of parts, it can
ventional ultrasonics can be found in Terminology E 1316.
be accurate, fast, inexpensive and require no human judgment,
3.2 Definitions of Terms Specific to This Standard:
making 100 % inspection possible in selected circumstances.
3.2.1 resonant ultrasonic spectroscopy (RUS), n—a nonde-
Many theoretical texts (3) discuss the relationship between
structive examination method, which employs resonant ultra-
resonances and elastic constants and include the specific
sound methodology for the detection and assessment of varia-
application of RUS to the determination of elastic constants
tions and mechanical properties of a test object. In this
(4). The technology received a quantum increase in attention
procedure, whereby a rigid part is caused to resonate, the
when Migliori published a review article, including the requi-
resonances are compared to a previously defined resonance
site inexpensive electronic designs and procedures from which
pattern. Based on this comparison the part is judged to be either
materials properties could be measured quickly and accurately
acceptable or unacceptable.
(5). The most recent applications include studies in ultrasonic
4. Summary of the Technology (1)
attenuation, modulus determinations, thermodynamic proper-
ties, structural phase transitions, superconducting transitions,
4.1 Introduction:
magnetic transitions, and the electronic properties of solids. A
compendium of these applications may be found in the
This guide is under the jurisdiction of ASTM Committee E-07 on Nondestruc-
Migliori (1) text. Resonant ultrasound spectroscopy also found
tive Testing and is the direct responsibility of Subcommittee E07.06 on Ultrasonic
use in the study of the elastic properties of the Apollo moon
Method.
rocks (6).
Current edition approved Dec. 10, 1998. Published February 1999.
Annual Book of ASTM Standards, Vol 03.03.
The boldface numbers in parentheses refer to the list of references at the end of
this guide.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E2001–98
4.1.2 This guide is intended to provide a practical introduc- their frequencies remain constant for fixed length, independent
tion to RUS-based nondestructive test (NDT), highlighting
of diameter. A crack will reduce the ability of the part to resist
successful applications and outlining failures, limitations, and twisting, thereby reducing the effective stiffness, and thus, the
potential weaknesses. Vibrational resonances are considered
frequency of a torsional mode. A large defect can be detected
from the perspective of defect detection in 4.2. In 4.3 and 4.4,
readily by its effect on the first few modes; however, smaller
a review of some of the types of RUS measurements are
defects have much more subtle effects on stiffness, and
presented. In 4.5, some example implementations and configu-
therefore, require higher frequencies (high-order modes) to be
rations of RUS systems and their applications are presented.
detected. Detection of very small defects may require using the
Finally, the guide concludes with a discussion of constraints,
frequency corresponding to the fiftieth, or even higher, mode.
which limit the effectiveness of RUS.
Some modes do not produce strain in the end of the cylinder,
4.2 Mode Shapes and Defects:
therefore, they cannot detect end defects. To detect this type of
4.2.1 Resonant ultrasound spectroscopy/NDT techniques,
defect, a more complex mode is required, the description of
operate by driving a part at given frequencies and measuring its
which is beyond the scope of this specification. A defect in the
mechanical response (Fig. 1 contains a schematic for the RUS
end will reduce the effective stiffness for this type of mode, and
apparatus). The process proceeds in small frequency steps over
thus, will shift downward the frequency of the resonance. In
some previously determined region of interest. During such a
general, it must be remembered that most modes will exhibit
sweep, the drive frequency typically brackets a resonance.
complex motions, and for highly symmetric objects, can be
When the excitation frequency is not matched to one of the
linear combinations of several degenerate modes, as discussed
part’s resonance frequencies, very little energy is coupled to
in 4.3.2.
the part; that is, there is essentially no vibration. At resonance,
4.3 General Approaches to RUS/NDT:
however, the energy delivered to the part is coupled generating
4.3.1 Test Evaluation Methods (1)—Once a fingerprint has
much larger vibrations. A part’s resonance frequencies are
been established, for conforming parts, numerous algorithms
determined by its dimensions (to include the shape and
can be employed to either accept or reject the part. For
geometry) and by the density and the elastic constants of the
example, if a frequency 650 Hz can be identified for all
material. The required frequency window for a scan depends
conforming parts, the detection of a peak outside of this
on the size of the part, its mechanical rigidity, and the size of
boundary condition will cause the computer code to signal a
the defect being sought.
“test reject” condition. The code, rather than the inspector,
4.2.2 Vibrational resonances produce a wide range of dis-
makes the accept/reject decision. The following sections will
tortions. These distortions include shapes, which bend and
expand on some of these sorting criteria.
twist. It is known that increasing the length of a cylinder will
lower some resonant frequencies. Similarly, reducing the
4.3.2 Frequency Shifts:
stiffness, that is, reducing the relevant elastic constant, lowers
4.3.2.1 Resonant ultrasound spectroscopy measurements
the associated resonant frequency for most modes; thus, for a
generally produce strains (even on resonance) that are well
given part, the resonant frequencies are measures of stiffness,
within the elastic limit of the materials under test, that is, the
and knowledge of the mode shape helps to determine what
atomic displacements are small in keeping with the “nonde-
qualities of the part affect those frequencies. If a defect, such as
structive” aspect of the testing. If strains are applied above the
a crack, is introduced into a region under strain, it will reduce
elastic limit, a crack will tend to propagate, causing a mechani-
the effective stiffness, that is, the part’s resistance to deforma-
cal failure. Note that certain important engineering properties,
tion, and will shift downward the frequency of resonant modes
for example, the onset of plastic deformation, yield strength,
that introduce strain at the crack. This is one basis for detecting
etc., generally are not derivable from low-strain elastic prop-
defects with RUS-based techniques.
erties. Sensitivity of the elastic properties of an object to the
4.2.3 The torsional modes represent a twisting of a cylinder
presence of a crack depends on the stiffness and geometry of
about its axis. These resonances are easily identified because
the sample under test. This concept is expanded upon under
4.4.3.
4.3.2.2 Fig. 2 shows an example of the resonance spectrum
for a conical ceramic part. Several specific types of modes are
present in this scan, and their relative shifts could be used to
detect defects as discussed above; however, the complexity is
such that, for NDT purposes, some selections must be made so
that only a portion of such a large amount of information is
used. For simple part geometries, the mode type and frequency
can be calculated, and selection of diagnostic modes can be
based on these results. For complex geometries, empirical
approaches have been developed to identify efficiently diag-
nostic modes for specific defects. In this process, a technician
measures the spectra for a batch of known good and bad parts.
The spectra are compared to identify diagnostic modes whose
FIG. 1 Schematic of the Essential Electronic Building Blocks to
Employ RUS in a Manufacturing Environment shift correlates with the presence of the defect. The key is to
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E2001–98
FIG. 2 Typical Broad-Spectrum Scan
isolate a few resonances, which differ from one another, when diameter of the cylinder. Because the part is symmetric, both
known defects are present in the faulty parts. modes have the same stiffness, and therefore, the same fre-
4.3.3 Peak Splitting—One of the techniques employed for quency (the modes are said to be degenerate and appear to be
axially symmetric parts is identified in texts on basic wave a single resonance). When the symmetry is broken by a chip,
physics (7). Some test procedures are based on simple fre- however, the effective diameter is reduced for one of the
quency changes while others include the recognition that orthogonal modes. This increases the frequency for that mode,
symmetry is broken when a defect is present in a homoge- so both modes are seen. In addition, a crack or inclusion affects
neous, isotropic symmetrical part. These techniques employ the symmetry. This splitting of the resonances is illustrated in
splitting of degeneracies or simply “splitting.” A cylinder Fig. 3, which shows spectra for a good part and two defective
actually has two degenerate bending modes, both orthogonal to parts. The part is a steel cylinder. Fig. 3 also demonstrates a
its axis. The bending stiffness for both of these modes, and useful feature of this particular technique, that is, the size of the
therefore their resonance frequency, is proportional to the splitting is proportional to the size of the defect. It is important
FIG. 3 Shown is a Bending Mode Within a Resonance Spectrum of an Acceptable Steel Cylinder (a), One With a Small Defect (b), and
One With a Large Crack (c).
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E2001–98
to recognize that not all resonance peaks are degenerate. Pure used. Statistical analysis will reveal which resonances have
torsional modes, for example, are not degenerate, so they
significant correlations with the desired physical attribute.
cannot be used for splitting.
4.3.5.2 Usually, these measurements are performed in con-
4.3.4 Phase Information and Peak Splittings:
junction with crack/chip/seam detection. Resonant ultrasound
4.3.4.1 In practice, the same empirical approach described
spectroscopy techniques often have to accommodate shifts in
for frequency shifts is used to identify diagnostic modes whose
resonance frequencies associated with density differences in
splittings correlate with the size of a defect of interest. The
addition to those resulting from dimensional variations with
sensitivity of this type of measurement is enhanced by the
sintered parts (ceramics and powder metals). As long as the
interference, which occurs between closely-spaced peaks. The
part is within the tolerance limits, and no other critical defect
destructive interference develops into a visible spectral split-
is present, it is acceptable to pass the item. This is accom-
ting which would not be noticeable with the amplitude spec-
plished by varying the frequency window that is scanned. Fig.
trum (the real and quadrature components add to form the
4 illustrates the ability to determine the thickness of an alumina
amplitude response). Most commercial systems function rea-
was
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