ASTM C747-93(2005)
(Test Method)Standard Test Method for Moduli of Elasticity and Fundamental Frequencies of Carbon and Graphite Materials by Sonic Resonance
Standard Test Method for Moduli of Elasticity and Fundamental Frequencies of Carbon and Graphite Materials by Sonic Resonance
SIGNIFICANCE AND USE
This test method is primarily concerned with the room temperature determination of the dynamic moduli of elasticity and rigidity of slender rods or bars composed of homogeneously distributed carbon or graphite particles.
This test method can be adapted for other materials that are elastic in their initial stress-strain behavior, as defined in Test Method E 111.
This basic test method can be modified to determine elastic moduli behavior at temperatures from −75°C to +2500°C. Thin graphite rods may be used to project the specimen extremities into ambient temperature conditions to provide resonant frequency detection by the use of transducers as described in 6.1.
SCOPE
1.1 This test method covers the measurement of the fundamental transverse, longitudinal, and torsional frequencies of isotropic and anisotropic carbon and graphite materials. These measured resonant frequencies are used to calculate dynamic elastic moduli for any grain orientations.
1.2 The values stated in SI units are to be regarded as the standard.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Standards Content (Sample)
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An American National Standard
Designation: C747 – 93 (Reapproved 2005)
Standard Test Method for
Moduli of Elasticity and Fundamental Frequencies of
Carbon and Graphite Materials by Sonic Resonance
This standard is issued under the fixed designation C747; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope C885 Test Method for Young’s Modulus of Refractory
Shapes by Sonic Resonance
1.1 This test method covers the measurement of the funda-
E111 Test Method forYoung’s Modulus,Tangent Modulus,
mental transverse, longitudinal, and torsional frequencies of
and Chord Modulus
isotropic and anisotropic carbon and graphite materials. These
measured resonant frequencies are used to calculate dynamic
3. Terminology
elastic moduli for any grain orientations.
3.1 Definitions of Terms Specific to This Standard:
1.2 The values stated in SI units are to be regarded as the
3.1.1 elastic modulus—the initial tangent modulus as de-
standard.
fined in Test Method E111.
1.3 This standard does not purport to address all of the
3.1.2 longitudinal vibrations—when the oscillations in a
safety concerns, if any, associated with its use. It is the
slender rod or bar are in a plane parallel to the length
responsibility of the user of this standard to establish appro-
dimension, the vibrations are said to be in the longitudinal
priate safety and health practices and determine the applica-
mode (Fig. 1(a)).
bility of regulatory limitations prior to use.
3.1.3 nodal points—a slender rod or bar in resonance
2. Referenced Documents contains one or more points having zero displacement, called
nodal points. In the longitudinal and torsional fundamental
2.1 ASTM Standards:
resonances of a uniform rod or bar, the mid-length point is the
C215 Test Method for Fundamental Transverse, Longitudi-
nodal point (Fig. 1(a) and Fig. 1(d)). For the fundamental
nal, and Torsional Resonant Frequencies of Concrete
transverseorflexuralresonance,thenodalpointsarelocatedat
Specimens
0.224 L from each end, where L is the length of the specimen
C559 Test Method for Bulk Density by Physical Measure-
(Fig. 1(b) and Fig. 1(c)).
ments of Manufactured Carbon and Graphite Articles
3.1.4 resonance—aslenderrodorbardrivenintooneofthe
above modes of vibration is said to be in resonance when the
This test method is under the jurisdiction of ASTM Committee D02 on
imposed frequency is such that resultant displacements for a
PetroleumProductsandLubricants andisthedirectresponsibilityofSubcommittee
givenamountofdrivingforce(voltage)areatamaximum.The
D02.F0 on Manufactured Carbon and Graphite Products.
resonant frequency is a natural vibration frequency which is
Current edition approved May 1, 2005. Published May 2005. Originally
approved in 1974. Last previous revision approved in 1998 as C747–93 (1998).
determined by the elastic moduli, density, and dimensions of
DOI: 10.1520/C0747-93R05.
the test specimen.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
C747 – 93 (2005)
3.1.5 slender rod or bar—a specimen whose ratio of length
R = ratio of the polar moment of inertia to the shape factor
to minimum cross-sectional dimension is at least 5 but not
for torsional rigidity,
more than 20.
B = aconstantconsistentwiththeunitsof G, R, f, L,and r,
f = frequency of fundamental torsional mode of vibration,
3.1.6 transverse vibrations—whentheoscillationsinaslen-
Hz,
der rod or bar are in a horizontal plane normal to the length
L = length of the specimen, m, and
dimension, the vibrations are said to be in the transverse mode
r = density of the specimen as determined byTest Method
(Fig. 1(b)). This mode is also commonly referred to as the
C559, kg/m .
flexuralmodewhentheoscillationsareinaverticalplane(Fig.
1(c)). Either the transverse or flexural mode of specimen
5. Significance and Use
vibration will yield the correct fundamental frequency, subject
5.1 This test method is primarily concerned with the room
to the geometric considerations given in 9.1.
temperature determination of the dynamic moduli of elasticity
3.1.7 torsional vibrations—when the oscillations in each
and rigidity of slender rods or bars composed of homoge-
cross-sectional plane of a slender rod or bar are such that the
neously distributed carbon or graphite particles.
plane twists around the length dimension axis, the vibrations
5.2 This test method can be adapted for other materials that
are said to be in the torsional mode (Fig. 1(d)).
are elastic in their initial stress-strain behavior, as defined in
Test Method E111.
4. Summary of Test Method
5.3 This basic test method can be modified to determine
elastic moduli behavior at temperatures from −75°C to
4.1 The dynamic methods of determining the elastic moduli
+2500°C. Thin graphite rods may be used to project the
are based on the measurement of the fundamental resonant
specimen extremities into ambient temperature conditions to
frequencies of a slender rod of circular or rectangular cross
provide resonant frequency detection by the use of transducers
section. The resonant frequencies are related to the specimen
as described in 6.1.
dimensions and material properties as follows:
4.1.1 Transverse or Flexural Mode—The equation for the
6. Apparatus
fundamental resonant frequency of the transverse or flexural
6.1 The fundamental resonant frequencies for the different
mode of vibration is as follows:
modes of vibration of a test specimen can be determined by
E 5 CMf (1) severalestablishedtestingprocedures.Theapparatusdescribed
herein uses phonograph record pickup cartridges as a conve-
where:
nient method of generating and detecting these frequencies.A
E = elastic modulus, Pa,
typical testing apparatus is shown schematically in Fig. 2.
C = a dimensional constant that depends upon the shape
6.1.1 Driving Circuit—The driving circuit consists of a
and size of the specimen, and Poisson’s ratio. The
variable-frequency oscillator and a record pickup cartridge
units of C are to be consistent with those of E, M, and
assembly. It is recommended that a variable-frequency oscil-
f,
lator be used in conjunction with a digital-frequency counter.
M = mass of the specimen, kg, and
f = frequency of fundamental transverse or flexural mode
of vibration, Hz.
4.1.2 Longitudinal Mode—The equation for the fundamen-
tal resonant frequency of the longitudinal mode of variation is
as follows:
2 2
E 5 Df L r (2)
where:
E = elastic modulus, Pa,
D = a constant consistent with the units of E, f, and L,
f = frequency of fundamental longitudinal mode of vibra-
tion, Hz,
L = length of the specimen, m, and
r = density of the specimen as determined byTest Method
C559, kg/m .
4.1.3 Torsional Mode—The equation for the fundamental
resonant frequency of the torsional mode of vibration is as
follows:
2 2
G 5RBf L r (3)
FIG. 2 Schematic Diagram of Typical Dynamic Elastic Modulus
where:
Detection Apparatus
G = modulus of rigidity, Pa,
C747 – 93 (2005)
The oscillator shall have sufficient power output to induce 8.2 Transverse Fundamental Resonance Frequency:
detectable vibrations in the test specimen at frequencies above
8.2.1 Place the specimen on the supports, which are located
and below the fundamental frequency under consideration.
at the fundamental transverse nodal points (0.224 L from each
Means for controlling the output of the oscillator shall be end).Placethedrivingandpickup-unitvibratingneedlesonthe
provided. The vibrating needle of the driving unit shall be
specimen center line at its extreme opposite ends with a
small in mass as compared to the test specimen, and a means minimal contact pressure consistent with good response. The
shallbeprovidedtomaintainaminimalcontactpressureonthe
vibrating direction of the driving and pickup needles must be
specimen. Either a piezoelectric or magnetic driving unit perpendicular to the length of the specimen (Fig. 1(b)).
meeting these requirements may be used.
8.2.2 Force the test specimen to vibrate at various frequen-
6.1.2 Pickup Circuit—The pickup circuit consists of a
cies and simultaneously observe the amplified output on an
recordpickupcartridge,amplifier,optionalhigh-passfilter,and
indicating meter or oscilloscope. Record the frequency of
an indicating meter or cathode-ray oscilloscope. The pickup
vibration of the specimen that results in a maximum displace-
unit shall generate a voltage proportional to the amplitude,
ment,havingawell-definedpeakontheindicator,wherenodal
velocity, or acceleration of the test specimen. Either a piezo-
point tracking indicates fundamental transverse resonance.
electric or magnetic pickup unit meeting these conditions may
8.2.3 A basic understanding of Lissajous patterns as dis-
be used. The amplifier shall have a controllable output of
played on an oscilloscope cathode ray tube (CRT), will aid in
sufficient magnitude to sharply peak out the resonant frequen-
the proper identification of the modes of vibration and har-
cies on the indicating meter or the cathode-ray oscilloscope
monic frequencies observed. As the oscillator frequency level
display tube. It may be necessary to use a high-pass filter in
is increased from a point well below expected resonance, a
order to reduce room noise and spurious vibrations. The
single closed loop Lissajous pattern tilted from the horizontal
indicating meter may be a voltmeter, microammeter or oscil-
reference plane, will eventually be displayed on the CRT. This
loscope. An oscilloscope is recommended because it enables
pattern denotes a resonance mode. The nodal points dynamic
the operator to positively identify resonances, including higher
modulus tracking guide template (Fig. 3) may be used to
order harmonics, by Lissajous figure analysis.
identify any resonant mode.
6.1.3 Specimen Supports—The supports shall permit the
8.2.4 Move the pickup cartridge needle slowly toward the
specimen to oscillate without significant restriction in the
specimen center and observe the Lissajous pattern loop.
desired mode. This is accomplished for all modes by support-
Fundamental transverse resonance is indicated when the fol-
ing the specimen at its transverse fundamental nodal points
lowing conditions prevail:
(0.224 L from each end). The supports should have minimal
8.2.4.1 Thelooppatternflattenstoahorizontallinewiththe
area in contact with the specimen and shall be of cork, rubber,
pickup needle over the specimen support.
or similar material. In order to properly identify resonant
8.2.4.2 The CRT pattern opens up to a full loop in a
frequencies, the receiver record pickup cartridge must be
direction normal to its original direction, with the pickup
movable along the total specimen length. Provisions shall be
needle over the specimen center.
made to adjust contact pressures of both record pickup car-
8.2.5 Return the pickup needle to its original position at the
tridges in order to accommodate specimen size variations. The
specimen end.
entire specimen support structure shall be mounted on a
8.2.6 Spurious resonating frequency modes may mask or
massive base plate resting on vibration isolators.
attenuate the fundamental transverse frequency indication.
Investigation of higher order harmonic resonating frequencies
7. Test Specimens
by use of the tracking guide template (Fig. 3) will help to
7.1 Selection and Preparation of Specimens—In the selec-
identify the correct fundamental frequency mode.Aplot of the
tion and preparation of test specimens, take special care to
ratio of harmonic to fundamental frequency for transverse
obtain representative specimens that are straight, uniform in
mode of vibration (Fig. 4) may then be used to calculate the
cross section, and free of extraneous liquids.
fundamental transverse resonant frequency mode.
7.2 Measurement of Weight and Dimensions—Determine
8.3 Longitudinal Fundamental Resonance Frequency:
the weight and the average length of the specimens within
8.3.1 Leave the specimen supported at the fundamental
60.5%. Determine average specimen cross-sectional dimen-
transverse mode nodal points as in 8.2.1. Rotate the driving
sion within 61%.
unit and pickup cartridge needles so as to induce vibrations
7.3 Limitations on Dimensional Ratio— Specimens having
parallel to the specimen length (Fig. 1(a)).
eitherverysmallorverylargeratiosoflengthtothicknessmay
8.3.2 Force the test specimen to vibrate as in 8.2.2. Record
bedifficulttoexciteinthefundamentalmodesofvibration.For
the frequency of vibration of the test specimen, where nodal
this method, the ratio must be between 5 and 20 (slender rod
point tracking indicates fundamental longitudinal resonance.
limitations).
The second harmonic longitudinal resonant frequency is twice
8. Procedure
the fundamental longitudinal resonant frequency.
8.4 Torsional Fundamental Resonance Frequency:
8.1 Switch on all electrical equipment and allow to stabilize
in accordance with the manufacturers’ recommendations. (Use 8.4.1 Leave the specimen supported as in 8.2.1. Rotate the
of a metal bar as a calibration standard is recommended to driving unit and pickup cartridge needles so as to induce
check equipment response and accuracy. Dimensional mea- vibrations perpendicular to the length of the sample (Fig. 1
surements and weight shall meet the requirements of 7.2.) (d)).
C747 – 93 (2005)
FIG. 3 Nodal Points Dynamic Modulus Tracking Guide Template
9. Calculation
9.1 Calculate the dynamic modulus of elasticity for the
transverse or flexural mode of vibration from the fundamental
transverse frequency, weight, and dimensions of the test
specimen as follows:
Dynamic E 5 CMf (4)
where units are as defined in 3.1.1. The evaluation of the
constant C, because of the complexity of its determination, is
in tabular form. Eq 4 may be rewritten in the forms:
Dynamic E ~pascals!5 A Mf /dforrodswith
c
circularcrosssections (5)
where d is the diameter of the rod in metres, and
Dynamic E ~pascals!5 A Mf /wforbarswith
R
squareorrectangularcrosssections (6)
where w is the width dimension of the bar in metres.
9.1.1 Values of A and A are shown in Annex A1 under
c R
Table A1.1 and Table A1.2. The value of A is given as a
c
function of the diameter-to-length ratio of the sample. The
...
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