Licensed by WEX to CENTRO DE INVESTIGACIÓN EN MATERIALES AV.

Downloaded: 10/12/20074:46:15PM single-user license only, copying and networking pro

Designation: D 1053 – 92a (Reapproved 2001)e1

Standard Test Methods for

Rubber Property—Stiffening at Low Temperatures: Flexible
Polymers and Coated Fabrics1
This standard is issued under the fixed designation D 1053; 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.

This standard has been approved for use by agencies of the Department of Defense.

e1 NOTE—Keywords were added editorially in December 2001.

1. Scope fabric coated with flexible polymer is secured and connected in

1.1 These test methods describe the use of a torsional series to a wire of known torsional constant; the other end of
apparatus for measuring the relative low temperature stiffening the wire is fastened to a torsion head to impart a twist to the
of flexible polymeric materials and fabrics coated therewith. A wire. The specimen is immersed in a chamber filled with a heat
routine inspection and acceptance procedure, to be used as a transfer medium at a specified uniform subnormal temperature.
pass-fail test at a specified temperature, is also described. The torsion head is then twisted 180° and in turn twists the
1.2 These test methods yield comparative data to assess the specimen by an amount (less than 180°) that is dependent on
low temperature performance of flexible polymers and fabrics specimen compliance or inverse stiffness. After a specified
coated therewith. elapsed time, the amount of specimen twist is measured with a
1.3 The values stated in either SI or non-SI units shall be mounted protractor. The angle of twist, which is inversely
regarded separately as the standard. The values in each system related to the stiffness, is plotted versus the specified tempera-
may not be exact equivalents; therefore, each system must be ture. The temperature is then systematically increased in
used independently of the other, without combining values in prescribed increments and the measurements repeated at each
any way. temperature, yielding a twist or inverse stiffness versus tem-
1.4 This standard does not purport to address all of the perature profile for the test specimen. The torsional modulus of
safety concerns, if any, associated with its use. It is the the specimen at any temperature is proportional to the quantity
responsibility of the user of this standard to establish appro- (180-twist)/twist.
priate safety and health practices and determine the applica- 4. Significance and Use
bility of regulatory limitations prior to use.
4.1 These test methods may be used to determine the
2. Referenced Documents subnormal temperature stiffening of flexible polymers or fab-
2.1 ASTM Standards: rics coated with flexible polymers. Temperatures at which the
D 832 Practice for Rubber Conditioning for LowTempera- low temperature modulus is a specified multiple or ratio of the
ture Testing2 modulus at room temperature are interpolated from the twist
D 4483 Practice for Determining Precision for Test Method versus temperature curve. These specified ratios of low-
Standards in the Rubber and Carbon Black Industries2 temperature modulus to room-temperature modulus are called
relative moduli. These temperatures at the relative moduli
3. Summary of Test Method encompass the transition region between the glassy and rub-
3.1 Test Method A describes the measurement, at low bery states of the materials tested.
temperatures, of the stiffening of flexible polymers. 4.2 These test methods offer only a general guide to stiffness
3.2 Test Method B describes the measurement, at low characterization as service conditions of experimental materi-
temperatures, of the stiffening of fabrics coated with flexible als may differ greatly from the test conditions.
polymers.
5. Apparatus
3.3 In these test methods, a specimen of flexible polymer or
5.1 Torsion Apparatus3—The torsion apparatus (Fig. 1)
1
shall consist of a torsion head, A, capable of being turned 180
These test methods are under the jurisdiction of ASTM Committee D11 on
Rubber and are the direct responsibility of Subcommittee D11.14 on Time and
Temperature-Dependent Physical Properties.
3
Current edition approved Sept. 15, 1992. Published March 1993. Originally The original apparatus was described and typical examples of the results of its
published as D1053 – 43 T. Last previous edition D1053 – 92. use were given in a paper by Gehman, Woodford, and Wilkinson, Industrial and
2
Annual Book of ASTM Standards, Vol 09.01. Engineering Chemistry, IECHA, Vol 39, September 1947, p. 1108.

Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.

1
Licensed by WEX to CENTRO DE INVESTIGACIÓN EN MATERIALES AV. Downloaded: 10/12/20074:46:15PM single-user license only, copying and networking pro

D 1053
6.4-mm (0.25-in.) width to facilitate proper contact with each
end of the wider test specimens, that is, Type B or Type C
specimens. The distance between the top and bottom clamps
shall be 25 6 2.5 mm (1.0 6 0.1 in.) for Test Method A and 38
6 2.5 mm (1.5 6 0.1 in.) for Test Method B. The bottom
clamp, K, shall be a fixed part of the test specimen rack. The
top clamp, L, shall act as an extension of the test specimen and
shall not touch the rack while the specimen is being twisted.
Clearance between the top of the test specimen rack and the
test specimen clamp stud is assured by inserting thin spacers
between the two (Note 1). The top clamp shall be secured to a
stud, D, which in turn shall be connected to the screw
connector, E.
NOTE 1—Slotted TFE-fluorocarbon spacers about 1.3 mm (0.050 in.)
thick and 13 mm (0.5 in.) wide have been found satisfactory. At low
temperatures the test specimens stiffen in position and the spacers are
removed prior to test without losing the clearance.
5.5 Temperature Measuring Device—A thermocouple or
thermometer shall be used. Copper-constantan thermocouples,
used in conjunction with a millivoltmeter or digital temperature
indicator, are highly satisfactory. The thermometer, if used,
A Torsion head G Movable protractor shall be calibrated in 1°C divisions and shall have a range from
B Torsion wire H Supporting stand approximately −70 to + 23°C (−95 to + 73.4°F). The thermo-
C Sieve I Specimen rack
couple or the thermometer bulb shall be positioned as nearly
D Clamp stud J Test specimen
E Screw connector K Bottom clamp equidistant from all test specimens as possible, and equidistant
F Pointer L Top clamp between the top and the bottom of the test specimens.
FIG. 1 Schematic Drawing of Apparatus for Low-Temperature 5.6 Heat Transfer Media—The heat transfer medium shall
Stiffness Test be either liquid or gaseous. Any material which remains fluid at
the test temperatures and does not affect the materials being
tested may be used. Among the liquids that have been found
angular degrees in a plane normal to the torsion wire, B. The
suitable for use are acetone, methyl alcohol, ethyl alcohol,
top of the wire shall be fastened to the torsion head passing
butyl alcohol, silicone fluids, and normal hexane. Carbon
through a loosely fitting sleeve, C. The bottom of the wire shall
dioxide or air are the commonly used gaseous media. Vapors of
be fastened to the test specimen clamp stud, D, by means of a
liquid nitrogen are useful for testing at very low temperatures.
screw connector, E. A pointer, F, and movable protractor, G,
shall be provided to permit convenient twist angle measure- NOTE 2—Specifications for materials or products requiring tests using
ment and exact adjustment of the zero point. this standard should specifically state which coolant media are acceptable
5.2 Stand—The torsion apparatus shall be clamped to the for use in this test.
supporting stand, H. It is advantageous to make the vertical 5.7 Temperature Control—Suitable means, automatic or
portion of the stand from a poor thermal conductor.4 The base manual, shall be provided for maintaining a uniform tempera-
of the stand should be of stainless steel or other corrosion- ture of the heat transfer medium within 61.0°C (1.8°F) for
resisting material. both liquid and gaseous media (Note 3).
5.3 Torsion Wires— Torsion wires, made of tempered spring 5.8 Tank or Test Chamber—A tank for liquid heat transfer
wire, shall be 65 6 8 mm (2.56 0.2 in.) long and have media or a test chamber for gaseous media shall be provided.
torsional constants (k) of 0.0125, 0.05, and 0.2 mN·m/° of NOTE 3—Liquid medium immersion baths, low-temperature cabinets,
twist. The color codes for these wires are black, yellow, and and means for controlling temperature are described in Practice D 832.
white, respectively. The 0.05 mN·m/° wire (color code yellow)
5.9 Stirrer or Fan— A stirrer for liquids or a fan or blower
shall be considered standard.
for air, which ensures thorough circulation of the heat transfer
5.4 Test Specimen Rack—A rack, I, made of a poor thermal
medium, shall be provided.
conductor,4 shall be provided for holding the test specimen, J,
5.10 Timer—A stop watch or other timing device calibrated
in a vertical position in the heat transfer medium (coolant). The
in seconds shall be provided.
rack shall be constructed to hold several test specimens; racks
providing spaces for five or ten test specimens are commonly 6. Test Specimens
used. The rack shall be clamped to the stand, H. Two clamps, 6.1 Test Method A— The test specimens shall be cut with a
also made of a poor thermal conductor, shall be provided for suitable die and shall be either Type A strips 40 6 2.5 mm (1.5
holding each test specimen. The faces of these clamps shall be 6 0.1 in.) long and 3.0 6 0.2 mm (0.125 6 0.008 in.) wide or
Type B specimens of the type illustrated in Fig. 2. The standard
thickness of the specimens shall be the thickness of the
4
Phenolic laminate sheet has been found satisfactory for this purpose. material undergoing test, but shall be not less than 1.5 mm

2
Licensed by WEX to CENTRO DE INVESTIGACIÓN EN MATERIALES AV. Downloaded: 10/12/20074:46:15PM single-user license only, copying and networking pro

D 1053
specimens (see Fig. 2), make certain that the tab ends are
completely within the clamps.
9.2 Test Method B— Clamp the specimens in the testing
apparatus in such a manner that 38.0 6 2.5 mm (1.5 6 0.1 in.)
FIG. 2 Type B Specimen of each specimen is free between the clamps.
10. Procedure for Stiffness Measurements in Liquid
(0.060 in.) nor greater than 2.8 mm (0.11 in.), and the Media
difference between maximum and minimum thickness of each 10.1 Place the rack containing the test specimens in the
specimen shall not exceed 0.08 mm (0.003 in.). Values of liquid bath with a minimum of 25 mm (1 in.) of liquid covering
thickness other than standard may be used provided it can be the test specimens. Adjust the bath temperature to 23 6 3°C
shown that they give equivalent results for the material being (73.4 6 5°F). Connect one of the specimens to the torsion head
tested. When specimens taken from the finished article are not by means of the screw connector and the standard 0.05 mN·m/°
of standard thickness, it should be permissible, upon agreement wire. The spacer which provides clearance between the speci-
between the manufacturer and the purchaser, to use a standard- men rack and the specimen clamp stud need not be used for
size specimen, taken from a certified press-cured sheet of the measurements made at room temperature. Adjust the pointer
same compound. reading to zero by rotating the protractor scale. Turn the torsion
6.2 Test Method B— The test specimens (Type C) shall be head quickly but smoothly 180°. After 10 s as indicated by the
cut with a suitable die so that the longer dimension is parallel timer, record the pointer reading. If the reading at 23°C
to one of the diagonals of the fabric (on the bias). The test (73.4°F) does not fall in the range from 120 to 170°, the
specimen shall be a minimum of 44 mm (1.75 in.) long and 6.3 standard torsion wire is not suitable for testing the specimen.
6 0.2 mm (0.250 6 0.008 in.) wide. The standard thickness of Specimens twisting more than 170° shall be tested with a wire
the specimen shall be the thickness of the material undergoing (black) having a torsional constant of 0.0125 mN·m/° of twist.
test. The length of the test specimen shall be trimmed to fit in Specimens twisting less than 120° shall be tested with a wire
the specimen clamps for test. (white) having a torsional constant of 0.2 mN·m/° of twist.
10.2 Return the torsion head to its initial position and
7. Calibration of Torsion Wire disconnect the specimen. Then move the test specimen rack to
7.1 Insert one end of the torsion wire in a vertical position, bring the next test specimen into position for measurement
in a fixed clamp, and attach the lower end of the wire at the (Note 5). All test specimens in the rack shall be measured at 23
exact longitudinal center of a circular cross-section rod of 6 3°C (73.4 6 5°F).
known dimension and weight. For standardization purposes, it
NOTE 5—A modified version of the standard apparatus is now in use in
is suggested that the rod be 200 to 250 mm (8 to 10 in.) long which the rack is stationary while the torsion head is movable and can be
and about 6 mm (0.25 in.) in diameter. Initially, the rod should positioned over the several test specimens in turn.
not be twisted through more than 90°. The rod should be
10.3 Insert the spacers between the specimen rack and the
allowed to oscillate freely in a horizontal plane and the time
specimen clamp studs. Adjust the liquid bath to the lowest
required for 20 oscillations noted in seconds. (An oscillation
temperature desired (Note 6). After this temperature has
includes the swing from one extreme to the other and return.)
remained constant within 6 1°C (6 1.8°F) for 5 min, remove
7.2 Calculate the torsional constant l as follows:
one spacer and test one specimen in the same manner as was
l 5 p2 ml2/3 T 2
(1) used at room temperature. Return the spacer to its original
position after the specimen has been tested (Note 7).
where:
l = restoring force exerted by the wire, N·m/rad of twist, NOTE 6—This varies with the type of material being tested since time
T = period of one oscillation, s, is saved by not starting at a temperature more than 10°C (18°F) lower than
m = mass, kg, and the freezing point of the material. For natural rubber, the lowest tempera-
l = length, m. ture required is usually − 80°C (−112°F); for styrene butadiene rubber, the
lowest temperature is usually − 70°C (−94°F).
7.3 The torsion wires should calibrate within 63 % of their
NOTE 7—Movement of the spacer often tends to alter the pointer
specified torsional constants as given in 5.3. position with respect to the protractor; therefore, the pointer should be
NOTE 4—K = 17.45l, where: K = torsional constant in mN·m/°. adjusted to zero after the spacer has been removed.
10.4 After all specimens have been tested at the lowest
8. Number of Specimens temperature desired, increase the bath temperature by 5°C
8.1 Unless otherwise specified in the detailed specification, (9°F) intervals and make stiffness measurements after condi-
two specimens from each test unit shall be tested. It is good tioning the specimens for 5 min at each temperature. Continue
practice, however, to include a control specimen with known testing until a temperature is reached at which the angular twist
stiffness-temperature characteristics. is within 5 to 10° of the original twist at 23 6 3°C (73.4 6
5°F).
9. Mounting Test Specimens 10.5 Increments of 10°C (18°F) instead of 5°C (9°F) may be
9.1 Test Method A— Clamp the specimens in the testing used, if desired, for the less sensitive parts of the temperature
apparatus in such a manner that 25 6 2.5 mm (1.0 6 0.1 in.) range. The temperature rise may be accelerated by use of an
of each specimen is free between the clamps. For Type B electrical immersion heater. The test may be shortened by

3
Licensed by WEX to CENTRO DE INVESTIGACIÓN EN MATERIALES AV. Downloaded: 10/12/20074:46:15PM single-user license only, copying and networking pro

D 1053
concluding the temperature rise as soon as the range of interest TABLE 1 Relationship Between Specimen Thickness and
has been passed, as described in 13.3. Angular Twist
10.6 Vulcanizates of certain polymers such as dimethyl Thickness, mm (in.) Twist, min angular°
vinyl silicone and cis-1,4-polybutadiene are known to crystal- 1.5 (0.060) 98
lize rapidly (over specific temperature ranges) under conditions 1.8 (0.070) 80
2.0 (0.080) 66
of this test. This should be recognized in interpreting the results 2.3 (0.090) 55
(see Practice D 832). 2.5 (0.100) 46
2.8 (0.110) 40
11. Procedure for Stiffness Measurements in Gaseous
Media (Long-Term Tests)
11.1 For long-term tests at a given temperature, the appara- are calculated for a Young’s modulus value of 69 MPa (10 000
tus shall be used in a suitable low-temperature cabinet or cold psi) for a specimen 25 mm (1.0 in.) long (span) and 3.2 mm
room. Additional specimen racks are required. Mount the test (0.125 in.) wide.
specimens in racks and measure and record the pointer
NOTE 8— Example—A specimen 2.0 mm (0.080 in.) thick, which has
deflection at 23°C (73.4°F) for each specimen. Then store the an angular twist of 66° or more when tested at − 556 0.5°C (−67 6 1°F),
racks in a low-temperature cabinet or cold room whose has a Young’s modulus no greater than 69 MPa (10 000 psi) at this
temperature is regulated at the desired value and measure the temperature.
deflections periodically. Relevant material specifications
should state the conditioning period, which should never be 13. Calculation
less than the time required for the specimens to reach thermal 13.1 Twist Versus Temperature Curve—A plot shall be made
equilibrium with the surrounding gaseous medium. (See Fig. of the pointer reading (angle of twist of the test specimen)
3.) versus the temperature, as illustrated in Fig. 4. This plot can be
used for determining the temperatures corresponding to spe-
12. Routine Inspection and Acceptance
cific relative moduli as described later.
12.1 For routine inspection of materials the stiffness test 13.2 Modulus Proportionality Factor—The modulus pro-
shall be conducted as described in Section 10 with the portionality factor (MPF) of the specimen is equal to the
exceptions that only the standard wire shall be used and that the quantity (180°-twist)/twist. The angle of twist of the test
test shall be conducted at only one temperature. The test specimen at a specific test temperature is measured in degrees.
temperature, exposure time, and type of coolant shall be as Table 2 lists the value of modulus proportionality factors for
stated in the relevant material specification. Unless otherwise every angular degree from 1 to 180.
stated in the material specification, the minimum number of 13.3 Relative Modulus— The relative modulus, or torsional
angular degrees of twist exhibited by the specimens, when stiffness ratio at a specified test temperature, is the ratio of the
tested at the specified temperature, shall be as shown in Table modulus proportionality factor at the temperature to the modu-
1. lus proportionality factor at 23°C (73.4°F). For example:
12.2 Interpolation shall be used for those thicknesses not Twist at 23°C = 160° Twist at − 40°C = 100°
contained within Table 1. The angular twists shown in the table MPF = (180–160)/160 = 0.125 MPF = (180–100)/100 = 0.800
Relative Modulus or Torsional Stiffness Ratio = 0.800/0.125 = 6.4

13.4 Temperature for Values of Relative Modulus—To de-

termine the temperature at which the relative modulus is 2, 5,
10, and 100, Table 3 shall be used in conjunction with the twist
versus temperature curve for the specimen. The first column of
Table 3 lists each degree in the range from 120 to 170, so that

FIG. 3 Illustrative Chart for Long-Time Test FIG. 4 Illustrative Chart of Twist Versus Temperature

4
Licensed by WEX to CENTRO DE INVESTIGACIÓN EN MATERIALES AV. Downloaded: 10/12/20074:46:15PM single-user license only, copying and networking pro

D 1053
TABLE 2 Modulus Proportionality Factors
Twist, X,° (180 − X)/X Twist, X,° (180 − X)/X Twist, X,° (180 − X)/X Twist, X,° (180 − X)/X
1 179 51 2.53 101 0.782 151 0.192
2 89 52 2.46 102 0.765 152 0.184
3 59 53 2.40 103 0.748 153 0.176
4 44 54 2.33 104 0.731 154 0.169
5 35 55 2.27 105 0.714 155 0.161

6 29 56 2.21 106 0.698 156 0.154

7 24.7 57 2.16 107 0.682 157 0.146
8 21.5 58 2.10 108 0.667 158 0.141
9 19.0 59 2.05 109 0.651 159 0.132
10 17.0 60 2.00 110 0.636 160 0.125

11 15.4 61 1.95 111 0.622 161 0.1180

12 14.0 62 1.90 112 0.607 162 0.1111
13 12.8 63 1.86 113 0.593 163 0.1043
14 11.86 64 1.81 114 0.579 164 0.0975
15 11.00 65 1.77 115 0.565 165 0.0909

16 10.25 66 1.73 116 0.552 166 0.0843

17 9.59 67 1.69 117 0.538 167 0.0778
18 9.00 68 1.65 118 0.525 168 0.0714
19 8.47 69 1.61 119 0.513 169 0.0651
20 8.00 70 1.571 120 0.500 170 0.0588

21 7.57 71 1.535 121 0.488 171 0.0527

22 7.1 72 1.500 122 0.475 172 0.0465
23 6.83 73 1.466 123 0.463 173 0.0405
24 6.50 74 1.432 124 0.452 174 0.0345
25 6.20 75 1.400 125 0.440 175 0.0286

26 5.92 76 1.368 126 0.429 176 0.0227

27 5.67 77 1.337 127 0.417 177 0.0169
28 5.43 78 1.308 128 0.406 178 0.0112
29 5.21 79 1.278 129 0.395 179 0.0056
30 5.00 80 1.250 130 0.385 180 0

31 4.81 81 1.222 131 0.374

32 4.62 82 1.195 132 0.364
33 4.45 83 1.169 133 0.353
34 4.29 84 1.143 134 0.343
35 4.14 85 1.118 135 0.333

36 4.00 86 1.093 136 0.324

37 3.86 87 1.069 137 0.314
38 3.74 88 1.045 138 0.304
39 3.62 89 1.022 139 0.295
40 3.50 90 1.000 140 0.286

41 3.39 91 0.978 141 0.277

42 3.29 92 0.956 142 0.267
43 3.19 93 0.935 143 0.258
44 3.09 94 0.915 144 0.250
45 3.00 95 0.895 145 0.241

46 2.91 96 0.875 146 0.233

47 2.83 97 0.856 147 0.224
48 2.75 98 0.837 148 0.216
49 2.67 99 0.818 149 0.208
50 2.60 100 0.800 150 0.200

the value corresponding to the twist of the specimen at 23°C (73.4°F) is found to be 160°. Referring to Table 3, the angles of twist
(73.4°F) can be selected. Successive columns give the twist corresponding to relative modulus values of 2, 5, 10, and 100 are,
angles which correspond to values of 2, 5, 10, and 100 for the respectively, 144, 111, 80, and 13. Referring again to the curve in Fig. 4,
relative modulus. The temperatures corresponding to these the temperatures at which these angles of twist occur are found to
be − 38°C, − 47°C, − 50°C, and − 56°C (−39°F, − 44°F, − 46°F,
angles are then read from the twist versus temperature curve
and − 49°F), respectively.
for the specimen and are designated at T 2, T5, T 10, and T100,
respectively. Table 3 can be used during a test to determine 13.5 Apparent Modulus of Rigidity—Annex A1 describes
when a particular T value has been obtained so that the test may the procedure for determining the apparent modulus of rigidity
then be concluded. or torsional modulus in megapascals, and Young’s Modulus,
NOTE 9— Example—The twist versus temperature curve for a hevea using the angular twist values determined at the test tempera-
gum compound is given in Fig. 4. From this curve the twist at 23°C ture, test specimen cross-sectional area measurements, and

5
Licensed by WEX to CENTRO DE INVESTIGACIÓN EN MATERIALES AV. Downloaded: 10/12/20074:46:15PM single-user license only, copying and networking pro

D 1053
TABLE 3 Twist Angles for Designated Values of the Relative ing type, source, manufacturer’s code designation, form, date
Modulus made, etc.,
Twist at Twist for Twist for Twist for Twist for 14.1.2 Thickness and type of specimen,
23°C,° RM = 2,° RM = 5,° RM = 10,° RM = 100,°
14.1.3 Details of conditioning of specimens prior to test,
120 90 51 30 3 14.1.4 Torsional constant of torsion wire used,
121 91 52 31 4
122 92 53 31 4 14.1.5 Type of heat transfer medium used,
123 93 54 32 4 14.1.6 Exposure time,
124 95 55 33 4
125 96 56 33 4
14.1.7 Temperatures, in degrees Celsius, at which the rela-
tive modulus is 2, 5, 10, and 100. These temperatures shall be
126 97 57 34 4 designated, respectively, as T2, T5, T10, and T100, and
127 98 58 35 4
128 99 59 36 4
14.1.8 When requested or specified, the torsional modulus
129 101 61 36 5 or torsional stiffness ratio at a specified test temperature.
130 102 62 37 5 14.2 Room-Temperature Rigidity Modulus—The report
131 103 63 38 5
shall also include the room-temperature rigidity modulus as
132 104 64 39 5 calculated in the Annex. This is used as a basis for judging the
133 105 65 40 5 actual stiffness attained at T2, T5, T10, T100.
134 107 66 41 5
135 108 68 42 5
14.3 Long-Time Tests— For long-time tests, the results shall
be presented as plots of the ratio of modulus to original
136 109 69 42 5 modulus at the test temperature versus time, the modulus ratio
137 111 70 43 6
138 112 71 45 6
being plotted on a logarithmic scale, as illustrated in Fig. 3.
139 113 72 46 6 14.3.1 When required by control specifications or as agreed
140 114 74 47 6 upon between the producer and the user, the results of
141 116 75 48 6
long-time tests may be reported as the relative modulus or
142 117 77 49 7 torsional stiffness ratio as determined according to 13.2.
143 119 78 50 7 14.4 Routine Inspection and Acceptance—For routine in-
144 120 80 51 7
145 121 82 53 7
spection of materials, the results shall include the test tempera-
ture, the average specimen thickness, and the average value for
146 123 83 54 7 the twist, in angular degrees, obtained at the test temperature.
147 124 85 55 7
148 126 87 57 8 15. Precision and Bias 5
149 127 88 58 8
150 129 90 60 9 15.1 This precision and bias section has been prepared in
accordance with Practice D 4483. Refer to Practice D 4483 for
151 130 92 62 9
152 132 94 62 9 terminology and other statistical calculation details.
153 133 96 65 10 15.2 The precision results in this precision and bias section
154 134 97 67 10 give an estimate of the precision of this test method with the
155 136 100 69 11
materials (rubbers) used in the particular interlaboratory pro-
156 138 102 71 11 gram as described as follows. The precision parameters should
157 139 104 73 12 not be used for acceptance or rejection testing of any group of
158 140 106 75 12
159 142 108 78 13 materials without documentation that they are applicable to
160 144 111 80 13 those particular materials and the specific testing protocols that
include this test method.
161 146 113 82 14
162 147 116 85 15 15.3 A Type 1 (interlaboratory) precision was evaluated.
163 149 118 88 16 Both repeatability and reproducibility are short term; a period
164 151 121 91 17 of a few days separates replicate test results. A test result is the
165 152 124 94 18
average value, as specified by this test method, obtained on
166 154 126 98 19 two determination(s) or measurement(s).
167 156 130 101 20 15.4 For Test Method A, four different materials were used
168 158 133 105 22
169 159 136 109 24 in the interlaboratory program, these were tested in four
170 161 139 113 26 laboratories on two different days. The results of the precision
calculations for repeatability and reproducibility are given in
Table 4, in ascending order of material average or level, for
supplemental tabular information. each of the materials evaluated.
NOTE 10—When the computed value for apparent modulus of rigidity
15.5 With the approximation to 0°C of T2 measurements of
exceeds 69 MPa (10 000 psi), the rubber is generally considered to be too Materials 1-A and 1-B, all temperatures at the relative moduli
stiff to be serviceable at the specified temperature. have been transformed to the kelvin scale to avoid excessively
large (r) and (R) values.
14. Report
14.1 Report the following information: 5
Supporting data are available from ASTM Headquarters. Request RR: D11-
14.1.1 Complete identification of the material tested includ- 1036.

6
Licensed by WEX to CENTRO DE INVESTIGACIÓN EN MATERIALES AV. Downloaded: 10/12/20074:46:15PM single-user license only, copying and networking pro

D 1053
TABLE 4 Type 1 Precision for Test Method A—Amount of Twist at 23°CA
Average Within Laboratories Between Laboratories
Material Level
(°) Sr r (r) SR R (R)

1-A 152.3 0.71 2.01 1.3 2.22 6.28 4.1

1-B 155.4 0.64 1.81 1.2 1.20 3.40 2.2
3 164.0 1.02 2.89 1.8 1.17 3.31 2.0
2 168.7 1.02 2.89 1.7 1.49 4.22 2.5
4 169.1 0.75 2.12 1.3 0.75 2.12 1.3

Pooled Values 161.9 0.90 2.55 1.6 1.57 4.44 2.7

T2, K
Average Within Laboratories Between Laboratories
Level
Material
Sr r (r) SR R (R)
(°)
4 223.2 0.81 2.31 1.0 2.13 6.02 2.7
3 230.3 0.98 2.76 1.2 0.98 2.76 1.2
2 248.9 2.30 6.51 2.6 4.58 12.96 5.2
1-B 272.6 0.14 0.41 0.2 2.40 6.80 2.5
1-A 273.5 0.55 1.56 0.7 2.54 7.19 2.6

Pooled Values 250.7 1.23 3.49 1.4 2.59 7.33 2.9

T5, K
4 218.7 0.45 1.27 0.6 2.80 7.93 3.6
3 223.3 0.22 0.62 0.3 0.48 1.37 0.6
2 240.8 0.63 1.78 0.7 0.63 1.78 0.7
1-A 267.0 0.40 1.14 0.4 1.90 5.39 2.0
1-B 267.5 0.29 0.81 0.3 0.35 0.99 0.4

Pooled Values 243.4 0.43 1.22 0.5 1.80 5.08 2.1

T10, K
Average Within Laboratories Between Laboratories
Material Level
(°) Sr r (r) SR R (R)

4 217.1 0.35 0.98 0.5 2.65 7.49 3.5

3 219.5 0.52 1.46 0.7 2.60 7.36 3.4
2 237.8 0.33 0.93 0.4 0.33 0.93 0.4
1-A 265.1 0.40 1.12 0.4 2.39 6.77 2.6
1-B 265.9 0.27 0.78 0.3 0.27 0.78 0.3

Pooled Values 239.9 0.38 1.08 0.4 2.03 5.74 2.4

T100, K
Average Within Laboratories Between Laboratories
Material Level
(°) Sr r (r) SR R (R)

4 212.0 0.78 2.22 1.0 2.53 7.17 3.4

3 213.5 0.37 1.04 0.5 2.45 6.94 3.3
2 230.4 0.27 0.75 0.3 2.15 6.09 2.6
1-B 259.5 0.59 1.68 0.6 1.80 5.09 2.0
1-A 259.8 0.41 1.16 0.4 2.28 6.44 2.5

Pooled Values 235.0 0.52 1.47 0.6 2.26 6.39 2.7

A
Sr = repeatability standard deviation.
r = repeatability = 2.83 times the square root of the repeatability variance.
(r) = repeatability (as percent of material average).
SR = reproducibility standard deviation.
R = reproducibility = 2.83 times the square root of the reproducibility variance.
(R) = reproducibility (as percent of material average).

15.6 The precision of this test method may be expressed in procedures, that differ by more than this tabulated r (for any
the format of the following statements which use an appropri- given level) must be considered as derived from different or
ate value of r, R, (r), or (R), to be used in decisions about test nonidentical sample populations.
results. The appropriate value is that value of r or R associated 15.8 Reproducibility— The reproducibility, R, of this test
with a mean level in Table 4 closest to the mean level under method has been established as the appropriate value tabulated
consideration at any given time, for any given material, in in Table 4. Two single test results obtained in two different
routine testing operations. laboratories, under normal test method procedures, that differ
15.7 Repeatability— The repeatability, r, of this test method by more than the tabulated R (for any given level) must be
has been established as the appropriate value tabulated in Table considered to have come from different or nonidentical sample
4. Two single test results, obtained under normal test method populations.

7
Licensed by WEX to CENTRO DE INVESTIGACIÓN EN MATERIALES AV. Downloaded: 10/12/20074:46:15PM single-user license only, copying and networking pro

D 1053
15.9 Repeatability and reproducibility expressed as a per- 16. Keywords
cent of the mean level, (r) and ( R), have equivalent application
16.1 apparent modulus of rigidity; coated fabric; fabrics;
statements as above for r and R. For the (r) and (R) statements,
flexible polymers; low temperature; low temperature modulus;
the difference in the two single test results is expressed as a
low temperature test; modulus proportionality factor; MPF;
percent of the arithmetic mean of the two test results.
15.10 Bias—In test method terminology, bias is the differ- polymer; relative modulus; rigidity modulus; stiffening; stiff-
ence between an average test value and the reference (or true) ness; stiffness measurement in gaseous media; stiffness mea-
test property value. Reference values do not exist for this test surement in liquid media; subnormal temperature; torsion;
method since the value (of the test property) is exclusively twist versus temperature; rigidity modulus
defined by the test method. Bias, therefore, cannot be deter-
mined.

ANNEX

(Mandatory Information)

A1. APPARENT MODULUS OF RIGIDITY

A1.1 Apparent Modulus of Rigidity—When it is desired to TABLE A1.1 Values of Factor µ for Various Ratios of a/b
calculate the apparent modulus of rigidity or torsional modu- a/b µ a/b µ
lus, the free length of the test specimen must be accurately 1.00 2.249 2.25 3.842
measured and the following equation used (Note A1.1): 1.05 2.359 2.50 3.990
1.10 2.464 2.75 4.111
916K L~180 2 X! 1.15 2.563 3.00 4.213
G5 (A1.1) 1.20 2.658 3.50 4.373
a b3 µ X
1.25 2.748 4.00 4.493
where: 1.30 2.833 4.50 4.586
G = apparent modulus of rigidity, MPa, 1.35 2.914 5.00 4.662
K = torsional constant of wire, mN·m/°, 1.40 2.990 6.00 4.773
L = measured free length (span) of the test specimen, mm, 1.45 3.063 7.00 4.853

a = width of test specimen, mm, 1.50 3.132 8.00 4.913

b = thickness of test specimen, mm, 1.60 3.260 9.00 4.960
µ = factor based on ratio of a/b taken from Table A1.1, and 1.70 3.375 10.00 4.997
X = angle of twist of test specimen, 1.75 3.428 20.00 5.165
1.80 3.479 50.00 5.226
To obtain Young’s modulus, multiply the modulus of rigid- 1.90 3.573 100.00 5.300
ity, G, by 3. 2.00 3.659

NOTE A1.1—There have been recent attempts to verify this equation

without total success. Thus, it should be used with that knowledge.

ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentioned
in this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the risk
of infringement of such rights, are entirely their own responsibility.

This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years and
if not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standards
and should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of the
responsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you should
make your views known to the ASTM Committee on Standards, at the address shown below.

This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,
United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the above
address or at 610-832-9585 (phone), 610-832-9555 (fax), or service@astm.org (e-mail); or through the ASTM website
(www.astm.org).