TECHNICAL FIELD
[0001] The present invention relates to an aluminum-alloy material.
BACKGROUND ART
[0002] In various fields, such as industrial products, buildings, and structures, vibration
that is generated during use of equipment, vibration that is imparted from outside
the equipment, and the like sometimes gives rise to a variety of problems. For example,
in transportation equipment, such as automobiles and rail transport, there is a risk
that the comfort of the crew will decrease owing to vibration itself, noise generated
by vibration, and the like. In consumer electronics, acoustic equipment, and the like,
there is a risk that the noise generated by the vibration will cause discomfort to
the user. In addition, for example, in precision equipment, there is a risk that vibration
will cause a hindrance in the operation of the equipment.
[0003] To curtail the occurrence of these problems, various techniques that attenuate vibration
have been proposed. For example, in the fields of buildings, structures, and the like,
methods that incorporate a damping member, such as a damper, methods that use, as
a member that constitutes the building or the like, a member having a shape that readily
attenuates vibration, and the like are widely used. Nevertheless, in methods that
incorporate a damping member, there is a risk that it will lead to an increase in
the number of members in industrial products and the like. In addition, methods that
attenuate vibration owing to the shape of a member are difficult to apply to transportation
equipment, consumer electronics, precision equipment, and the like, in which the dimensions,
masses, and shapes of members are greatly constrained.
[0004] To overcome such problems, methods are being studied in which, taking advantage of
the characteristics of aluminum alloys, which are comparatively lightweight and excel
in workability, industrial products and the like are constructed using members composed
of aluminum alloys having a high damping ability. For example, Patent Document 1 describes
a method of manufacturing an aluminum-alloy damping material in which an aluminum-alloy
ingot containing Fe: 0.5-20 wt%, the remainder being Al and unavoidable impurities,
is subjected to plastic working with a surface-reduction percentage of 30% or more.
PRIOR ART LITERATURE
Patent Documents
SUMMARY OF THE INVENTION
PROBLEMS TO BE SOLVED BY THE INVENTION
[0006] There has been demand in recent years for an aluminum-alloy material having a damping
ability higher than that of the aluminum-alloy damping material described in Patent
Document 1.
[0007] The present invention was conceived considering such a background, and an object
of the present invention is to provide an aluminum-alloy material having a high damping
ability.
MEANS FOR SOLVING THE PROBLEMS
[0008] One aspect of the present invention is an aluminum-alloy material having an Al matrix
and second-phase particles dispersed in the Al matrix,
wherein the value of a metallographic-structure factor F indicated in Equation (1)
below is 0.005 or more.

[0009] Therein, in the above-mentioned Equation (1), L is the total [µm/µm
2] of the perimeters of the second-phase particles, from among the second-phase particles
present in an arbitrary cross section, whose circle-equivalent diameters are 0.2 µm
or more, ρ is the dislocation density [µm
-2], E is the electrical conductivity [% IACS] at 25°C, and A and B are correction coefficients
determined in accordance with the chemical composition of the aluminum-alloy material.
A and B can be values within the ranges of 0.2 × 10
-15 ≤ A ≤ 20 × 10
-15 and 0.1 ≤ B ≤ 1.0, respectively.
EFFECTS OF THE INVENTION
[0010] In the above-mentioned aluminum-alloy material, the value of the metallographic-structure
factor F expressed by the total L of the perimeters of the second-phase particles
having a circle-equivalent diameter of 0.2 µm or more, the dislocation density p,
and the electrical conductivity E, is within the above-mentioned specific range. Thereby,
owing to interactions between the above-mentioned second-phase particles and dislocations
in the Al matrix, vibration imparted from outside of the above-mentioned aluminum-alloy
material can be attenuated with good efficiency. As a result, damping ability can
be increased beyond that of preexisting aluminum-alloy materials.
[0011] Therefore, according to the above-mentioned aspect, an aluminum-alloy material having
excellent damping ability can be provided.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012]
FIG. 1 is an example of a reflection-electron image of an L-LT cross section of an
aluminum-alloy material according to a working example.
FIG. 2 is an example of a binarized image produced by subjecting the reflection-electron
image in FIG. 1 to a binarization process.
FIG. 3 is a side view that shows the principal parts of a loss-factor measuring apparatus
according to the working example.
FIG. 4 is an explanatory diagram that shows one example of an amplitude-frequency
curve according to the working example.
MODES FOR CARRYING OUT THE INVENTION
(Chemical Composition)
[0013] The above-mentioned aluminum-alloy material contains Al (aluminum) and one or two
or more of additional elements for forming second-phase particles in the Al matrix.
For example, Fe (iron), Mn (manganese), Si (silicon), Cu (copper), Mg (magnesium),
Zn (zinc), Ni (nickel), Cr (chrome), Ti (titanium), V (vanadium), Zr (zirconium),
or the like can be used as the additional elements. By adding these additional elements
to the aluminum alloy, second-phase particles that contain the above-mentioned additional
elements can be formed in the Al matrix.
• Fe (iron): 0.30-3.0 mass%
[0014] The above-mentioned aluminum-alloy material may contain 0.30-3.0 mass% of Fe. By
setting the Fe content to 0.30 mass% or more, the amount of second-phase particles
in the Al matrix can be made greater, and thereby the damping ability of the aluminum-alloy
material can be improved. From the viewpoint of further improving the damping ability
of the aluminum-alloy material, the Fe content is preferably set to 0.50 mass% or
more.
[0015] On the other hand, in the situation in which the Fe content is excessively high,
there is a risk that coarse second-phase particles will tend to be formed in the aluminum-alloy
material, leading to a decrease in rollability. By setting the Fe content to 3.0 mass%
or less and preferably to 2.0 mass% or less, the damping ability of the aluminum-alloy
material can be improved while easily avoiding such problems.
• Mn: 0.10-1.50 mass%
[0016] The above-mentioned aluminum-alloy material may contain 0.10-1.50 mass% of Mn. By
setting the Mn content to 0.10 mass% or more, the amount of second-phase particles
in the Al matrix can be made greater, and thereby the damping ability of the aluminum-alloy
material can be further improved. From the viewpoint of further improving the damping
ability of the aluminum-alloy material, the Mn content is more preferably set to 0.20
mass% or more.
[0017] On the other hand, in the situation in which the Mn content is excessively high,
there is a risk that coarse second-phase particles will tend to form in the aluminum-alloy
material, leading to a decrease in reliability. From the viewpoint of obtaining a
damping-improvement effect while easily avoiding such problems, the Mn content is
preferably set to 1.50 mass% or less and more preferably set to 1.0 mass% or less.
• Si: 0.0050-3.0 mass%
[0018] The above-mentioned aluminum-alloy material may contain 0.0050-3.0 mass% of Si. By
setting the Si content to 0.0050 mass% or more, the amount of second-phase particles
in the Al matrix can be made greater, and thereby the damping ability of the aluminum-alloy
material can be further improved. From the viewpoint of further improving the damping
ability of the aluminum-alloy material, the Si content is more preferably set to 0.050
mass% or more.
[0019] On the other hand, in the situation in which the Si content is excessively high,
there is a risk that coarse second-phase particles will tend to form in the aluminum-alloy
material, leading to a decrease in reliability. In addition, by virtue of the amount
of the additional elements that have formed a solid solution in the Al matrix becoming
large in this situation, there is a risk that it will lead to a decrease in damping
ability. From the viewpoint of avoiding such problems and obtaining the damping-improvement
effect, the Si content is preferably set to 3.0 mass% or less and more preferably
set to 2.0 mass% or less.
• Cu: 0.0030-0.10 mass%
[0020] The above-mentioned aluminum-alloy material may contain 0.0030-0.10 mass% of Cu.
By setting the Cu content to 0.0030 mass% or more, the amount of second-phase particles
in the Al matrix can be made greater, and thereby the damping ability of the aluminum-alloy
material can be further improved. From the viewpoint of further improving the damping
ability of the aluminum-alloy material, the Cu content is more preferably set to 0.010
mass% or more.
[0021] On the other hand, in the situation in which the Cu content is excessively high,
there is a risk that coarse second-phase particles will tend to form in the aluminum-alloy
material, leading to a decrease in reliability. In addition, by virtue of the amount
of the additional elements that have formed a solid solution in the Al matrix becoming
large in this situation, there is a risk that it will lead to a decrease in damping
ability. From the viewpoint of easily avoiding such problems and obtaining the damping-improvement
effect, the Cu content is preferably set to 0.10 mass% or less and more preferably
set to 0.050 mass% or less.
• Mg: 0.0050-3.0 mass%
[0022] The above-mentioned aluminum-alloy material may contain 0.0050-3.0 mass% of Mg. By
setting the Mg content to 0.0050 mass% or more, the amount of second-phase particles
in the Al matrix can be made greater, thereby further improving the damping ability
of the aluminum-alloy material. From the viewpoint of further improving the damping
ability of the aluminum-alloy material, the Mg content is more preferably set to 0.050
mass% or more.
[0023] On the other hand, in the situation in which the Mg content is excessively high,
by virtue of the amount of additional elements that have formed a solid solution in
the Al matrix becoming large, there is a risk that it will lead to a decrease in damping
ability. From the viewpoint of avoiding such problems and obtaining the damping-improvement
effect, the Mg content is preferably set to 3.0 mass% or less and more preferably
set to 1.50 mass% or less.
• Zn: 0.10-0.50 mass%
[0024] The above-mentioned aluminum-alloy material may contain 0.10-0.50 mass% of Zn. By
setting the Zn content to 0.10 mass% or more, the amount of second-phase particles
in the Al matrix can be made greater, thereby further improving the damping ability
of the aluminum-alloy material. From the viewpoint of further improving the damping
ability of the aluminum-alloy material, the Zn content is more preferably set to 0.20
mass% or more.
[0025] On the other hand, in the situation in which the Zn content is excessively high,
by virtue of the amount of additional elements that have formed a solid solution in
the Al matrix becoming large, there is a risk that it will lead to a decrease in damping
ability. From the viewpoint of easily avoiding such problems and obtaining the damping-improvement
effect, the Zn content is preferably set to 0.50 mass% or less and more preferably
set to 0.40 mass% or less.
• Ni: 0.050-0.30 mass%, Cr: 0.050-0.30 mass%, Ti: 0.050-0.30 mass%, and V: 0.050-0.30
mass%
[0026] The above-mentioned aluminum-alloy material may contain one or two or more of elements
from among elements selected from the group consisting of Ni: 0.050-0.30 mass%, Cr:
0.050-0.30 mass%, Ti: 0.050-0.30 mass%, and V: 0.050-0.30 mass%. By setting the content
of these additional elements to 0.050 mass% or more, the damping ability of the aluminum-alloy
material can be further improved. From the viewpoint of further improving the damping
ability of the aluminum-alloy material, the content of these additional elements is
more preferably set to 0.10 mass% or more.
[0027] On the other hand, in the situation in which the content of these additional elements
is excessively high, there is a risk that coarse second-phase particles will tend
to form in the aluminum-alloy material, leading to a decrease in rollability. From
the viewpoint of obtaining the damping-improvement effect while avoiding such problems,
the content of these additional elements is preferably set to 0.30 mass% or less and
more preferably set to 0.20 mass% or less.
• Zr: 0.0010-0.30 mass%
[0028] The above-mentioned aluminum-alloy material may contain 0.0010-0.30 mass% of Zr.
By setting the Zr content to 0.0010 mass% or more, the damping ability of the aluminum-alloy
material can be further improved. From the viewpoint of further improving the damping
ability of the aluminum-alloy material, the Zr content is more preferably set to 0.010
mass% or more.
[0029] On the other hand, in the situation in which the Zr content is excessively high,
there is a risk that coarse second-phase particles will tend to form in the aluminum-alloy
material, leading to a decrease in reliability. From the viewpoint of obtaining the
damping-improvement effect while avoiding such problems, the Zr content is preferably
set to 0.30 mass% or less and more preferably set to 0.20 mass% or less.
[Metallographic Structure]
[0030] The above-mentioned aluminum-alloy material has second-phase particles that are dispersed
in the Al matrix. The second-phase particles are composed of, for example, an Al-Fe-based
compound, Si, an Al-Fe-Mn-based compound, an Al-Fe-Si-based compound, an Al-Mn-based
compound, an Al-Mn-Si-based compound, an Al-Fe-Mn-Si-based compound, an Al-Cu-based
compound, an Al-Mg-based compound, an Mg-Si-based compound, an Al-Mg-Zn-based compound,
an Al-Cu-Zn-based compound, an Al-Ni-based compound, an Al-Cr-based compound, an Al-Ti-based
compound, an Al-V-based compound, an Al-Zr-based compound, or the like. The second-phase
particles may be precipitates or may be crystallized products.
[0031] The second-phase particles dispersed in the Al matrix have various particle sizes.
In addition to second-phase particles having a circle-equivalent diameter of 0.2 µm
or more, the aluminum-alloy material may contain second-phase particles having a circle-equivalent
diameter of less than 0.2 µm, but does not have to contain second-phase particles
having a circle-equivalent diameter of less than 0.2 µm. The above-mentioned aluminum-alloy
material can exhibit the functions and effects of improving damping ability as long
as the Al matrix has second-phase particles having a circle-equivalent diameter of
0.2 µm or more.
[0032] In addition, as described above, in the situation in which coarse second-phase particles
are formed in the Al matrix, there is a risk that it will lead to a decrease in rollability.
From the viewpoint of easily avoiding such a problem, the circle-equivalent diameter
of the second-phase particles dispersed in the Al matrix is preferably 20 µm or less.
[Metallographic-Structure Factor F]
[0033] With regard to the above-mentioned aluminum-alloy material, as described above, vibration
can be attenuated by interactions between the second-phase particles dispersed in
the Al matrix and dislocations. For this reason, to increase the damping ability of
the above-mentioned aluminum-alloy material, it is necessary to control not only the
mode of the second-phase particles in the metallographic structure but also the mode
of the dislocations. A characteristic of the metallographic structure relating to
the damping ability of the above-mentioned aluminum-alloy material can be expressed
by the value of the metallographic-structure factor F that appears in Equation (1)
below.

[0034] Therein, symbol L in the above-mentioned Equation (1) is the total [µm/µm
2] of the perimeters of the second-phase particles, from among the above-mentioned
second-phase particles present in an arbitrary cross section, having a circle-equivalent
diameter of 0.2 µm or more; symbol ρ is the dislocation density [µm
-2]; symbol E is the electrical conductivity [% IACS] at 25°C; and symbol A and symbol
B are correction coefficients that are determined in accordance with the chemical
composition of the above-mentioned aluminum-alloy material.
[0035] In a metallographic structure in which the value of the metallographic-structure
factor F is 0.005 or more, the mode of existence of the additional elements contained
in the aluminum-alloy material and the mode of existence of the dislocations in the
matrix tend to be suitable modes for attenuating vibration. For this reason, with
regard to an aluminum-alloy material whose metallographic-structure factor F value
is 0.005 or more, damping ability can be improved. From the viewpoint of further increasing
damping ability, the above-mentioned metallographic-structure factor F value is preferably
0.01 or more and more preferably 0.05 or more. It is noted that, from the viewpoint
of improving damping ability, although there is no upper limit to the metallographic-structure
factor F value, it is difficult in typical manufacturing methods to obtain an aluminum-alloy
material for which the metallographic-structure factor F value is greater than 400.
[0036] In the situation in which the above-mentioned metallographic-structure factor F value
is less than 0.005, because the damping-reduction effect owing to the solid-solution
elements tends to surpass the damping-improvement effect owing to interactions between
the second-phase particles and the dislocations, there is a risk that it will lead
to a decrease in damping ability.
[0037] The individual parameters used in the calculation of the metallographic-structure
factor F value can be determined as below.
• Perimeter L of Second-Phase Particles
[0038] The total L of the perimeters of the second-phase particles having a circle-equivalent
diameter of 0.2 µm or more can be calculated by the following method. First, a cross
section of the above-mentioned aluminum-alloy material is observed using a scanning
electron microscope, and a reflection electron image is acquired. The magnification
during the observation can be set as appropriate from the range of, for example, 1,000-5,000
times.
[0039] The cross section of the observation target is not particularly limited. For example,
in the situation in which the above-mentioned aluminum-alloy material is a rolled
plate, the cross section of the observation target may be a cross section that is
perpendicular to the rolling direction (i.e., an LT-ST plane) or may be a cross section
that is parallel to the rolling direction, such as an L-LT plane (i.e., a cross section
parallel to the plate surface), an L-ST plane, or the like. In addition, in the situation
in which the above-mentioned aluminum-alloy material is an extruded material, the
cross section of the observation target may be a cross section that is parallel to
the extrusion direction or may be a cross section that is perpendicular to the extrusion
direction. Furthermore, the cross section of the observation target may be some other
cross section.
[0040] Next, the reflection electron image is subjected to a binarization process using
an image-processing apparatus or the like to obtain a binarized image, in which the
Al matrix and the second-phase particles are indicated by differing brightnesses.
Second-phase particles having a circle-equivalent diameter of 0.2 µm or more are sampled
from this binarized image; furthermore, the perimeters of these second-phase particles
are calculated. Then, the total of the perimeters of the second-phase particles having
a circle-equivalent diameter of 0.2 µm or more present in the binarized image is converted
to a value per 1 µm
2 of surface area. The value obtained by the above is taken as the value L [µm/µm
2] of the total of the perimeters of the second-phase particles having a circle-equivalent
diameter of 0.2 µm or more.
[0041] The total L of the perimeters of the second-phase particles described above is preferably
0.1 µm/µm
2 or more and is more preferably 0.2 µm/µm
2 or more. By setting the total L of the perimeters of the second-phase particles to
be large, interactions between the second-phase particles and the dislocations can
be made stronger. As a result, the damping ability of the above-mentioned aluminum-alloy
material can be further improved. It is noted that, from the viewpoint of improving
damping ability, there is no upper limit to the above-mentioned total of the perimeters;
however, in common manufacturing methods, it is difficult to obtain an aluminum-alloy
material in which the above-mentioned total L of the perimeters is greater than 3.0
µm/µm
2.
• Dislocation Density ρ
[0042] The dislocation density ρ in the aluminum-alloy material can be measured by the following
method. First, diffraction profiles for a plurality of aluminum-alloy materials are
obtained by X-ray diffractometry. Next, the peak location 2θ of the peaks present
in each of the diffraction profiles and the integration width β of each peak (i.e.,
the full width of each peak) are read.
[0043] Next, based on the Williamson-Hall equation (Equation (2) below), the nonuniform
strain h value of the aluminum-alloy material is calculated from the peak location
2θ value and the integration width β value. It is noted that λ in Equation (2) below
is a symbol that represents the wavelength of the incident X-rays, and D is a symbol
that represents the size of the crystallites.
[0044] No. 1

[0045] As shown in the above-mentioned Equation (2), the value of the nonuniform strain
h is equal to one half the value of the slope of a straight line in which the βcosθ/λ
values serve as the ordinate of a graph and the sinθ/λ values serve as the abscissa.
Accordingly, first, for all peaks present in each of the diffraction profiles, a Williamson-Hall
plot is prepared by plotting all data points in a graph such that the ordinate values
are βcosθ/λ and the abscissa values are sinθ/λ. Subsequently, a straight-line approximation
of these data points is determined using the least squares method. The nonuniform
strain h value can be calculated by halving the slope of this straight-line approximation.
[0046] It is noted that, in situation in which, for example, the crystal grains of the aluminum-alloy
material are coarse, sometimes the intensity of a peak relating to a specific crystal
orientation in a diffraction profile becomes extremely low. In that situation, the
integration width of that peak is strongly affected by the background, and there are
situations in which a data point that constitutes an abnormal value appears in the
Williamson-Hall plot. In this situation, upon eliminating the relevant data point
from the Williamson-Hall plot, the measurement location should be modified, a diffraction
profile should once again be obtained for the aluminum-alloy material in which the
relevant data point was obtained, and data points should be added to the Williamson-Hall
plot using a procedure the same as that mentioned above.
[0047] The dislocation density ρ value can be calculated by substituting the nonuniform
strain h value in Equation (3) below. It is noted that b in Equation (3) below is
a symbol that represents the Burgers vector of the aluminum. The b value is, specifically,
0.2863 nm.
No. 2

[0048] The dislocation density ρ of the above-mentioned aluminum-alloy material is preferably
10 µm
-2 or more, more preferably 20 µm
-2 or more, and yet more preferably 50 µm
-2 or more. By setting the dislocation density ρ to be large, interactions between the
second-phase particles and the dislocations can be made stronger. As a result, the
damping ability of the above-mentioned aluminum-alloy material can be further improved.
It is noted that, from the viewpoint of improving damping ability, there is no upper
limit to the dislocation density ρ of the aluminum-alloy material; however, in typical
manufacturing methods, it is difficult to obtain an aluminum-alloy material in which
the dislocation density is greater than 2,000 µm
-2.
• Electrical Conductivity E
[0049] The electrical conductivity E of the above-mentioned aluminum-alloy material at 25°C
is 50% IACS or more. The electrical conductivity E of the aluminum-alloy material
increases as the additional elements precipitate or crystallize as second-phase particles
and the smaller the amount of the additional elements, which have formed a solid solution
in the Al matrix becomes. By setting the electrical conductivity E of the above-mentioned
aluminum-alloy material to 50% IACS or more, the amount of the additional elements
that has formed a solid solution, which becomes a hindrance to dislocation movements,
can be reduced. As a result, the damping ability improvement effect owing to interactions
between the dislocations and the second-phase particles can be further increased.
From the viewpoint of further improving damping ability, the electrical conductivity
of the above-mentioned aluminum-alloy material at 25°C is more preferably 55% IACS
or higher.
[0050] In the situation in which the above-mentioned electrical conductivity E is less than
50% IACS, dislocation movements tend to become impeded due to the additional elements
that have formed a solid solution in the Al matrix. As a result, there is a risk that
interactions between the dislocations and the second-phase particles will tend not
to occur, leading to a decrease in damping ability.
[0051] It is noted that, from the viewpoint of increasing damping ability, although there
is no limit to the electrical conductivity E value, the electrical conductivity value
is 64% IACS or less due to the physical properties of the aluminum alloy.
• Correction Coefficients A, B
[0052] Correction coefficient A and correction coefficient B of the above-mentioned metallographic-structure
factors can be various values in accordance with the type and amount of the additional
elements contained in the aluminum-alloy material. As the reason for this, it is conceivable
that, for example, when the types and the amounts of the additional elements change,
the phase that constitutes the second-phase particles changes, and thereby the contribution
of the interactions between the second-phase particles and the dislocations changes,
or that, when the types and the amounts of the additional elements change, the extent
to which dislocation movements are impeded due to the additional elements that have
formed a solid solution in the Al matrix changes.
[0053] Specifically, the range of the correction coefficient A value is 0.2 × 10
-15 ≤ A ≤ 20 × 10
-15, and the range of the correction coefficient B value is 0.1 ≤ B ≤ 1.0. The same correction
coefficient A value and the same correction coefficient B value can be used for aluminum-alloy
materials, among the multiple aluminum-alloy materials in which the types or amounts
of additional elements differ, in which the additional element type of the highest
content is the same. For example, in the situation in which the above-mentioned aluminum-alloy
material contains 0.3-3.0 mass% of Fe as the highest content additional element, 2.0
× 10
-15 can be used as the A value, and 0.4851 can be used as the B value.
[0054] The correction coefficient A value and the correction coefficient B value can be
determined by the following method. First, multiple types of aluminum-alloy materials
are prepared, in which the highest content additional element is in common, and the
content of that additional element, the content of other additional elements, the
manufacturing conditions, and the like differ. Furthermore, the values of the previously
described total L of the perimeters, the dislocation density p, and the electrical
conductivity E for these aluminum-alloy materials are calculated. Furthermore, the
correction coefficient A value and the correction coefficient B value can be determined
by approximating, using the above-mentioned Equation (1), a plot prepared using these
values.
[Damping Ability]
[0055] The damping ability of the above-mentioned aluminum-alloy material can be evaluated
based on a correction-loss coefficient η
c (refer to Equation (4) below) obtained by correcting a loss factor η, which is determined
by a free-resonance method, for the sample shape of the above-mentioned aluminum-alloy
material.

[0056] It is noted that symbol t in the above-mentioned Equation (4) is the thickness [mm]
of the test piece used in the measurement of the loss factor η. The length of the
test piece used in the measurement of the loss factor η is 60 mm, and the width is
8 mm.
[0057] The correction-loss coefficient η
c is preferably 1.6 × 10
-3 or more, more preferably 1.8 × 10
-3 or more, and yet more preferably 2.0 × 10
-3 or more. In this situation, the damping ability of the above-mentioned aluminum-alloy
material can be further improved. From the viewpoint of improving damping ability,
there is no upper limit to the correction-loss coefficient η
c; however, in an aluminum-alloy material having a metallographic-structure factor
F in the above-mentioned specific range, the correction-loss coefficient η
c is normally 300 × 10
-3 or less.
[0058] It is noted that techniques for measuring the loss factor include, in addition to
the free-resonance method, methods such as, for example, cantilever-vibration methods.
However, as a result of diligent investigation conducted by the present inventors,
it became clear that, in the situation in which the loss factor value in the cantilever-vibration
method varies with the shape of the test piece and the length of the test piece is
long, particularly as described in Patent Document 1, there is a tendency for the
loss factor value to become larger than in the situation in which the length of the
test piece is short-regardless of whether the chemical compositions were the same
or the metallographic structures were the same. Accordingly, the value of the loss
factor in the cantilever-vibration method and the value of the loss factor obtained
using the free-resonance method could not be simply compared.
[0059] In addition, as a result of diligent investigation conducted by the present inventors,
it became clear that, in the free-resonance method as well, the value of the loss
factor varied in accordance with the thickness, the surface area, and the like of
the test pieces. It is conceivable that this was caused by friction or the like between
the test piece and the air during the measurement. Accordingly, the value of the loss
factor in the free-resonance method could not be simply compared with the values of
the correction-loss coefficients.
• Crystal Grains
[0060] The above-mentioned aluminum-alloy material preferably includes a fibrous structure
and more preferably is composed of a fibrous structure. In this situation, the damping
ability of the above-mentioned aluminum-alloy material can be further improved.
[0061] It is noted that a fibrous structure refers to a structure that comprises numerous
crystal grains that have been stretched in a processing direction by wrought working
such as rolling, extrusion, forging, and the like. For example, in the situation in
which a cross section of the fibrous structure parallel to the processing direction
was observed using a metallurgical microscope at a magnification of 25-100 times,
the fibrous structure was observed as a stripe-shaped pattern extending in the processing
direction. In addition, an equiaxial structure refers to a structure that comprises
numerous equiaxial crystal grains. For example, in the situation in which a cross
section of the equiaxial structure parallel to the processing direction was observed
using a metallurgical microscope at a magnification of 25-100 times, the equiaxial
structure was observed as a granular pattern, in which the difference between the
major axis and the minor axis was relatively small.
[0062] The above-mentioned aluminum-alloy material can be manufactured by, for example,
casting an ingot having the above-mentioned specific chemical composition, and then
performing, in accordance with the casting method, an appropriate combination of wrought
working, such as rolling, extrusion, and forging, and heat treatment on the above-mentioned
ingot.
[0063] For example, as one aspect of the manufacturing method, a method can be used in which,
after casting a slab, which serves as an ingot, using a DC-casting method, hot rolling
and cold rolling are sequentially performed, as the wrought working, on the slab.
[0064] The casting speed in the DC casting is preferably within the range of 20-100 mm/min.
By setting the casting speed to within the above-mentioned specific range, the formation
of coarse second-phase particles can be curtailed.
[0065] In the present aspect, after the DC casting has been performed, a homogenization
treatment may be performed by heating the slab prior to performing the hot rolling,
or the hot rolling may be performed without performing the homogenization treatment.
In the situation in which the homogenization treatment is to be performed, the heating
temperature can be set as appropriate from the range of, for example, 200°C-550°C.
The heating temperature of the homogenization treatment is preferably 500°C or lower
and more preferably 340°C or lower. In this situation, the second-phase particles
in the Al matrix can be made finer, and thereby the perimeters of the second-phase
particles can be made even larger. As a result, the damping ability due to interactions
between the dislocations and the second-phase particles can be further improved.
[0066] In addition, in the homogenization treatment, the heating may be ended immediately
after the temperature of the slab has reached the above-mentioned heating temperature,
or the above-mentioned heating temperature may be held for a fixed time. The hold
time in the latter situation can be set to 50 h or less.
[0067] In the situation in which the heating temperature of the homogenization treatment
is lower than 200°C, there is a risk that the homogenization of the slab will become
insufficient. In addition, in the situation in which the heating temperature of the
homogenization treatment is above 550°C or in the situation in which the hold time
is more than 50 h, there is a risk that coarse second-phase particles will tend to
form in the slab, leading to a decrease in damping ability.
[0068] Next, a hot-rolled plate is manufactured by hot rolling the slab. The temperature
of the slab at rolling start of the hot rolling is preferably 200°C-550°C. In the
situation in which the temperature of the slab at rolling start is lower than 200°C,
it is difficult to perform hot rolling because the slab tends not to deform. In the
situation in which the temperature of the slab at rolling start is above 550°C, there
is a risk that coarse second-phase particles will tend to form in the slab, leading
to a decrease in damping ability.
[0069] The above-mentioned hot rolling may be performed while the temperature of the slab
after casting is within the above-mentioned specific range. In the situation in which
the temperature of the slab after casting is lower than the above-mentioned specific
temperature, the temperature of the slab can still be set to the above-mentioned specific
range by heating the slab prior to performing the hot rolling.
[0070] In the situation in which the slab is to be heated prior to the hot rolling, the
heating may be ended immediately after the temperature of the slab has reached a desired
temperature, or the desired temperature may be held for a fixed time. The hold time
in the situation of the latter can be set to 30 h or less. In the situation in which
the hold time is more than 30 h, there is a risk that coarse second-phase particles
will tend to form in the slab, leading to a decrease in damping ability.
[0071] In the present aspect, after the hot rolling has been performed and before the cold
rolling is performed, annealing may be performed by heating the hot-rolled plate.
The heating temperature of this annealing can be set as appropriate in the range of
200°C-400°C. In the situation in which the heating temperature of the annealing is
lower than 200°C, there is a risk that the annealing effect will become insufficient.
In the situation in which the heating temperature of the annealing is higher than
400°C, there is a risk that coarse second-phase particles will tend to form in the
hot-rolled plate, leading to a decrease in damping ability.
[0072] With regard to the above-mentioned annealing, heating may be ended immediately after
the above-mentioned heating temperature has been reached, or the above-mentioned heating
temperature may be held for a fixed time. The hold time in the situation of the latter
can be set to 10 h or less. In the situation in which the hold time is more than 10
h, there is a risk that coarse second-phase particles will tend to form in the hot-rolled
plate, leading to a decrease in damping ability.
[0073] Subsequently, by performing one or more passes of cold rolling on the hot-rolled
plate, the above-mentioned aluminum-alloy material can be obtained. With regard to
the cold rolling, the rolling is preferably performed such that the total rolling
reduction becomes 50% or more. That is, the difference between the thickness of the
hot-rolled plate after hot rolling has been performed and before the cold rolling
and the thickness of the desired aluminum-alloy material is preferably 50% or more
of the thickness of the above-mentioned hot-rolled plate. Thereby, the dislocation
density of the above-mentioned aluminum-alloy material can be further increased, and
thereby the damping ability of the above-mentioned aluminum-alloy material can be
further improved.
[0074] In the situation in which the number of passes of the cold rolling is two or more
passes, an intermediate annealing can also be performed by heating the hot-rolled
plate between passes of the cold rolling. The heating temperature of the intermediate
annealing can be set as appropriate in the range of 200°C-400°C. In the situation
in which the heating temperature of the intermediate annealing is lower than 200°C,
there is a risk that the intermediate-annealing effect will become insufficient. In
the situation in which the heating temperature of the intermediate annealing is higher
than 400°C, there is a risk that coarse second-phase particles will tend to form in
the aluminum-alloy material, leading to a decrease in damping ability.
[0075] In addition, with regard to the intermediate annealing, the heating may be ended
immediately after the above-mentioned heating temperature has been reached, or the
above-mentioned heating temperature may be held for a fixed time. The hold time in
the situation of the latter can be set to 10 h or less. In the situation in which
the hold time is more than 10 h, there is a risk that coarse second-phase particles
will tend to form in the aluminum-alloy material, leading to a decrease in damping
ability.
[0076] In the situation in which the above-mentioned intermediate annealing is to be performed,
it is preferable to perform the rolling such that the rolling reduction after the
intermediate annealing becomes 50% or more. That is, the difference between the thickness
of the hot-rolled plate after the intermediate annealing has been performed and before
resuming the cold rolling and the thickness of the desired aluminum-alloy material
is preferably 50% or more of the thickness of the hot-rolled plate before the cold
rolling resumes. Thereby, the dislocation density of the above-mentioned aluminum-alloy
material can be increased, and thereby the damping ability of the above-mentioned
aluminum-alloy material can be improved.
[0077] In the present aspect, a final annealing may be performed by heating the aluminum-alloy
material after the cold rolling. The heating temperature of the final annealing can
be set as appropriate in the range of 100°C-200°C. In the situation in which the heating
temperature of the final annealing is less than 100°C, there is a risk that the final
annealing effect will become insufficient. In the situation in which the heating temperature
of the final annealing is higher than 200°C, there is a risk that the dislocation
density will greatly decrease due to the rearrangement, the disappearance, or the
like of the dislocations, leading to a decrease in damping ability.
[0078] In addition, in the final annealing, the heating may be ended immediately after the
above-mentioned heating temperature has been reached, or the above-mentioned heating
temperature may be held for a fixed time. The hold time in the situation of the latter
can be set to 10 h or less. In the situation in which the hold time is more than 10
h, there is a risk that the dislocation density will decrease due to the rearrangement,
the disappearance, or the like of the dislocations, leading to a decrease in damping
ability.
[0079] As another aspect of the method of manufacturing the above-mentioned aluminum-alloy
material, it is also possible to use a method in which a strip is cast as the ingot
by a continuous-casting method, such as a twin-roll continuous casting and hot rolling
method, a twin-belt casting method, or the like, after which the strip is cold rolled
as the wrought working.
[0080] The casting speed of the continuous casting is preferably within the range of 500-3,000
mm/min. By setting the casting speed to within the above-mentioned specific range,
the formation of coarse second-phase particles can be curtailed.
[0081] After the continuous casting has been performed, the above-mentioned aluminum-alloy
material can be obtained by performing one or more passes of the cold rolling on the
strip. With regard to the cold rolling, it is preferable to perform the rolling such
that the total rolling reduction becomes 50% or more, the same as the process condition
for the situation in which the DC casting described above is performed. That is, the
difference between the thickness of the strip after the continuous casting has been
performed and before the cold rolling is performed and the thickness of the desired
aluminum-alloy material is preferably 50% or more of the thickness of the above-mentioned
strip. Thereby, the dislocation density of the above-mentioned aluminum-alloy material
can be further increased, thereby further improving the damping ability of the above-mentioned
aluminum-alloy material.
[0082] In addition, in the present aspect as well, the same as the situation in which the
DC casting described above is performed, the intermediate annealing may be performed
between passes of the cold rolling, or the final annealing may be performed after
the cold rolling has been completed. The process conditions of the intermediate annealing,
the process conditions of the final annealing, and the functions and effects thereof
according to the present aspect are the same as the process conditions of the situation
in which the DC casting described above is performed.
Working Examples
[0083] Working examples of the above-mentioned aluminum-alloy material will now be explained,
with reference to FIG. 1 to FIG. 4. It is noted that the specific aspects of the aluminum-alloy
material according to the present invention are not limited to the aspects of the
working examples described below, and the configuration of the working examples can
be modified as appropriate within a range that does not depart from the gist of the
present invention.
[0084] Aluminum-alloy materials according to the present example were manufactured by the
following method. First, ingots having the chemical compositions listed in Table 1
were cast using a DC casting method. After heating these ingots at the heating temperatures
listed in the "Pre-Rolling Temperature" column in Table 1, they were hot rolled to
manufacture hot-rolled plates having the thicknesses listed in Table 1. The obtained
hot-rolled plates were cold rolled such that their total rolling reductions became
the values listed in Table 1. In addition, with regard to Test Materials 10-12 and
Test Material 14, after the cold rolling was completed, a final annealing was performed
at the heating temperatures listed in the "Final Annealing" column in Table 1. Based
on the above, Test Materials 1-12 having a thickness of 0.75 mm and Test Materials
13-14 having a thickness of 2.0 mm, as listed in Table 1, were obtained. It is noted
that, with regard to Test Materials 15, 16 listed in Table 1, because the Fe content
and Mn content in the ingots were excessively high, coarse second-phase particles
readily formed. Consequently, it was difficult to roll these test materials.
[0085] In these test materials, the method of calculating the metallographic-structure factor
F value, the method of calculating the correction-loss coefficient η
c, and the method of evaluating the mode of the crystal grains were as below.
[Method of Calculating the Metallographic-Structure Factor F]
[0086] The metallographic-structure factor F value was calculated by substituting, in Equation
(1) below, the value of the total L [µm/µm
2] of the perimeters of the second-phase particles having a circle-equivalent diameter
of 0.2 µm or more obtained by the method below, the value of the dislocation density
ρ [µm
-2], and the value of the electrical conductivity E [% IACS]. It is noted that, in the
present example, the correction coefficient A value was 2.0 × 10
-15, and the correction coefficient B value was 0.4851. The metallographic-structure
factor F values of the test materials were as listed in Table 2.

[0087] The methods of measuring the L, p, and E values will be explained below.
• Total L of Perimeters of Second-Phase Particles Having a Circle-Equivalent Diameter
of 0.2 µm or More
[0088] First, the plate surface of the test material was polished to expose an L-LT plane
(a plane parallel to the plate surface). Five observation locations randomly selected
from the L-LT plane were observed using a scanning electron microscope, and reflection
electron images at a magnification of 2,000 times were acquired. In the reflection
electron images, the Al matrix and the second-phase particles dispersed in the Al
matrix were indicated by brightnesses that differ from one another. For example, in
FIG. 1, second-phase particles 12 in an aluminum-alloy material 1 are indicated with
a brightness that is brighter than that of an Al matrix 11.
[0089] Next, a binarized image shown in FIG. 2 was prepared by subjecting the reflection
electron image to a binarization process using an image-processing apparatus or the
like. It is noted that, in FIG. 2, for the sake of convenience, after the binarization
process was performed, an inversion process was performed in which white and black
were switched. The threshold of the binarization process should be set as appropriate
such that the contours of the second-phase particles 12 in the reflection electron
image are maintained even after the binarization process.
[0090] After having sampled, from the binarized image, the second-phase particles 12 having
a circle-equivalent diameter of 0.2 µm or more, the perimeter of each of the second-phase
particles 12 (i.e., the length of the contour of the second-phase particle 12) was
measured. By dividing the total of these perimeters by the total of the surface area
of the visual field, the total L [µm/µm
2] of the perimeters of the second-phase particles 12 having a circle-equivalent diameter
of 0.2 µm or more listed in Table 2 was calculated.
• Dislocation Density ρ
[0091] First, an X-ray diffraction profile of each test material was acquired using an X-ray
diffraction apparatus. The conditions of the X-ray diffractions were as below.
Measuring apparatus: "SmartLab (registered trademark)" manufactured by Rigaku Corporation
Incident X-ray: Cu-Kα line (λ = 0.15405 nm)
Tube voltage: 40 kV
Tube current: 20 mA
Sampling width: 0.004°
Scanning speed: 0.2°/min
2θ scan range: 40°-80°
[0092] A Williamson-Hall plot was prepared using the acquired X-ray diffraction profiles
and the method described above. Furthermore, after calculating the nonuniform strain
h from the slope of the straight-line approximation in the Williamson-Hall plot, the
dislocation density ρ value was calculated by substituting the obtained h value in
the above-mentioned Equation (3). The dislocation density ρ values of the test materials
are listed in Table 2. In addition, the values calculated by multiplying the total
L values of the perimeters of the second-phase particles calculated using the above-described
method by the dislocation density ρ values are listed in the "L × ρ" column in Table
2.
• Electrical Conductivity E
[0093] For example, an electrical-conductivity meter ("Sigma Tester Model 2.069" manufactured
by Foerster Japan Limited) was used in the measurement of the electrical conductivity
E. The electrical conductivity E of each of the test materials at 25°C is listed in
Table 2. It is noted that, to set the temperature of each of the test materials to
25°C, for example, the test materials should be left stationary for approximately
1 h in a temperature-controlled chamber at 25°C. In addition, in the situation in
which the above-mentioned electrical-conductivity meter is used, the measurement frequency
can be set to, for example, 480 kHz.
[Mode of Crystal Grains]
[0094] Each test material was cut parallel to the rolling direction to expose an L-ST plane.
After having polished the L-ST plane, an oxide film having a polarization dependent
on the crystal orientation was formed on the surface of the sample by performing anodization.
Subsequently, three observation locations randomly selected from the L-ST plane were
observed at a magnification of 100 times using a polarizing microscope, and micrographs
were acquired. In addition, the aspect ratio, that is, the ratio of the crystal grain
length to the crystal grain thickness, was calculated for each individual crystal
grain in the micrograph using an image-processing apparatus or the like.
[0095] Furthermore, in the situation in which equiaxial crystal grains (i.e., recrystallized
grains) were not present in the micrograph and the average value of the aspect ratios
was 10 or more, it was determined that the test material was composed of a fibrous
structure; in the situation in which equiaxial crystal grains were present in the
micrograph and the average value of the aspect ratios was less than 10, it was determined
that the test material included an equiaxial structure. It is noted that, in the situation
in which the aspect ratios of the crystal grains were extremely high, the number of
crystal grains for which both ends in the rolling direction were present within the
visual field became few, and therefore the average of the aspect ratios could not
be calculated accurately. In this situation, it was determined whether the average
of the aspect ratios was or was not 10 or more by comparing it with a sample for which
the average of the aspect ratios was 10.
[Correction-Loss Coefficient ηc]
[0096] First, the loss factor η was measured by a free-resonance method using strip-shaped
test pieces, which were collected from the test materials, having a length of 60 mm
and a width of 8 mm.
[0097] A free-resonance-type internal-friction measuring apparatus ("JE-RT" manufactured
by Nihon Techno-Plus Co. Ltd.) was used in the measurement of the loss factor η. As
shown in FIG. 3, the measuring apparatus 2 comprises a drive electrode 21 and an amplitude
sensor 22, which faces the drive electrode 21. A strip-shaped test piece S is disposed
horizontally between the drive electrode 21 and the amplitude sensor 22, and the strip-shaped
test piece S is fixed by fine wires 23 at locations where vibration nodes form. In
this state, the strip-shaped test piece S can be caused to vibrate by supplying an
alternating current to the drive electrode 21 to cause a Coulomb force to act upon
the strip-shaped test piece S. Furthermore, by using the amplitude sensor 22 to measure
the amplitude of the strip-shaped test piece S, the waveform of the vibration can
be obtained.
[0098] In the present example, an electrostatic force was generated from the drive electrode
21 to forcibly cause the strip-shaped test piece S to vibrate, and the amplitude of
the strip-shaped test piece S was measured. At this time, the amplitude-frequency
curve was obtained, as shown in FIG. 4, by causing the strip-shaped test piece S to
vibrate while sweeping the frequencies of the vibration. It is noted that the ordinate
in FIG. 4 represents the common logarithm of the magnitude of the amplitude, and the
abscissa represents the frequency [Hz].
[0099] The loss factor η of each test material was calculated, using a full width at half
maximum method, based on the amplitude-frequency curve shown in FIG. 4. First, the
frequency at which the amplitude on the amplitude-frequency curve becomes maximal
was derived, and this frequency was taken as resonance frequency f
0. Next, a full width at half maximum Δf of the resonance peak was derived. The full
width at half maximum Δf was calculated specifically as follows. First, within the
range at which the frequency was lower than the resonance frequency f
0, a frequency f
1, at which the amplitude value was half of the amplitude value A
0 at the resonance frequency f
0, was derived. Next, in the range in which the frequency was higher than the resonance
frequency f
0, a frequency f
2, at which the amplitude value became half the amplitude value A
0 at the resonance frequency f
0, was derived. The value of the difference f
2-f
1 between the frequency f
2 and the frequency f
1 thus derived is the full width at half maximum Δf.
[0100] By substituting the resonance frequency f
0 and the full width at half maximum Δf, which were obtained above, in Equation (5)
below, the loss factor η was calculated.
[0101] No. 3

[0102] Furthermore, by substituting the loss factor η thus obtained in Equation (4) below,
the correction-loss coefficient η
c was calculated. The correction-loss coefficient η
c value of each test material is listed in Table 2.
Table 1
| Test Material Symbol |
Chemical Composition (mass%) |
Hot Rolling |
Cold Rolling |
Final Annealing |
Thickness (mm) |
| Fe |
Other Elements |
A1 |
Pre-Rolling Temp. (°C) |
Hot-Rolled Plate Thickness (mm) |
Rolling Reduction (%) |
Heating Temp. (°C) |
|
| 1 |
1.0 |
- |
Bal. |
500 |
3.0 |
75 |
- |
0.75 |
| 2 |
1.5 |
- |
Bal. |
500 |
3.0 |
75 |
- |
0.75 |
| 3 |
2.0 |
- |
Bal. |
500 |
3.0 |
75 |
- |
0.75 |
| 4 |
1.0 |
Mn: 0.30 |
Bal. |
500 |
3.0 |
75 |
- |
0.75 |
| 5 |
1.0 |
Mn: 0.60 |
Bal. |
500 |
3.0 |
75 |
- |
0.75 |
| 6 |
1.0 |
Mn: 0.90 |
Bal. |
500 |
3.0 |
75 |
- |
0.75 |
| 7 |
1.5 |
Zr: 0.15 |
Bal. |
500 |
3.0 |
75 |
- |
0.75 |
| 8 |
1.5 |
Mn: 0.30 |
Bal. |
500 |
3.0 |
75 |
- |
0.75 |
| 9 |
1.0 |
- |
Bal. |
300 |
3.0 |
75 |
- |
0.75 |
| 10 |
1.5 |
- |
Bal. |
500 |
3.0 |
75 |
100 |
0.75 |
| 11 |
1.5 |
- |
Bal. |
500 |
3.0 |
75 |
200 |
0.75 |
| 12 |
1.0 |
Mn: 0.90 |
Bal. |
500 |
3.0 |
75 |
600 |
0.75 |
| 13 |
1.5 |
- |
Bal. |
300 |
5.0 |
60 |
- |
2.0 |
| 14 |
0.2 |
Si: 0.70, Mg: 0.70 |
Bal. |
580 |
5.0 |
60 |
520 |
2.0 |
| 15 |
5.0 |
- |
Bal. |
Rolling Difficulty |
| 16 |
2.0 |
Mn: 2.0 |
Bal. |
Rolling Difficulty |
Table 2
| Test Material Symbol |
Total L of Perimeters (µm/µm2) |
Dislocation Density ρ (µm-2) |
Electrical Conductivity E (% IACS) |
Metallo graphic-Structure Factor F |
Crystal Grains |
Loss Factor η |
Correction-Loss Coefficient ηc |
| 1 |
0.36 |
436 |
60.0 |
1.37 |
Fibrous |
3.01×10-3 |
3.39×10-3 |
| 2 |
0.58 |
420 |
60.9 |
3.30 |
Fibrous |
3.70×10-3 |
4.08×10-1 |
| 3 |
0.68 |
449 |
59.0 |
1.64 |
Fibrous |
3.04×10-3 |
3.42×10-3 |
| 4 |
0.46 |
551 |
57.9 |
0.80 |
Fibrous |
2.22×10-3 |
2.60×10-3 |
| 5 |
0.37 |
590 |
56.9 |
0.42 |
Fibrous |
1.96×10-3 |
2.34×10-3 |
| 6 |
0.52 |
610 |
54.4 |
0.18 |
Fibrous |
1.70×10-3 |
2.08×10-3 |
| 7 |
0.38 |
438 |
53.1 |
0.05 |
Fibrous |
2.77×10-3 |
3.15×10-3 |
| 8 |
0.58 |
535 |
57.2 |
0.70 |
Fibrous |
2.54×10-3 |
2.92×10-3 |
| 9 |
0.45 |
547 |
59.6 |
1.77 |
Fibrous |
3.17×10-3 |
3.55×10-3 |
| 10 |
0.38 |
358 |
60.8 |
1.75 |
Fibrous |
3.18×10-3 |
3.56×10-3 |
| 11 |
0.38 |
71 |
61.4 |
0.47 |
Fibrous |
2.08×10-3 |
2.46×10-3 |
| 12 |
0.58 |
12 |
51.5 |
0.00 |
Equiaxial |
1.19×10-3 |
1.57×10-3 |
| 13 |
0.32 |
499 |
55.5 |
0.16 |
Fibrous |
1.19×10-3 |
2.59×10-3 |
| 14 |
0.02 |
67 |
54.5 |
0.00 |
Fibrous |
0.16×10-3 |
1.56×10-3 |
| 15 |
Rolling Difficulty |
| 16 |
Rolling Difficulty |
[0103] As shown in Table 1 and Table 2, the metallographic-structure factor F values of
Test Materials 1-11 and Test Material 13 were within the above-mentioned specific
ranges. Consequently, the correction-loss coefficient η
c values of these test materials were 1.6 × 10
-3 or more. For this reason, these test materials had excellent damping ability.
[0104] The metallographic-structure factor F values of Test Material 12 and Test Material
14 were smaller than the above-mentioned specific ranges. Consequently, the damping
ability of these test materials was inferior to Test Materials 1-11 and Test Material
13.