ASTM E143-20

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it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E143 − 13 E143 − 20
Standard Test Method for
Shear Modulus at Room Temperature
This standard is issued under the fixed designation E143; 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope*
1.1 This test method covers the determination of shear modulus of structural materials. This test method is limited to materials
in which, and to stresses at which, creep is negligible compared to the strain produced immediately upon loading. Elastic properties
such as shear modulus, Young’s modulus, and Poisson’s ratio are not determined routinely and are generally not specified in
materials specifications. Precision and bias statements for these test methods are therefore not available.
1.2 For materials that follow nonlinear elastic stress-strain behavior, the value of tangent or chord shear modulus is useful for
estimating the change in torsional strain to corresponding stress for a specified stress or stress-range, respectively. Such
determinations are, however, outside the scope of this standard. (See for example Ref (1).)
1.3 Units—The values stated in inch-poundSI units are to be regarded as standard. The values given in parentheses are
mathematical conversions to SI units that are provided for information only and are not considered No other units of measurement
are included in this standard.
1.4 This standard may involve hazardous materials, operations, and equipment. This standard does not purport to address all
of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate
safety safety, health, and healthenvironmental practices and determine the applicability of regulatory limitations prior to use.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
E6 Terminology Relating to Methods of Mechanical Testing
E8/E8M Test Methods for Tension Testing of Metallic Materials
E111 Test Method for Young’s Modulus, Tangent Modulus, and Chord Modulus
E1012 Practice for Verification of Testing Frame and Specimen Alignment Under Tensile and Compressive Axial Force
Application
E2624 Practice for Torque Calibration of Testing Machines
3. Terminology
3.1 Definitions:
This test method is under the jurisdiction of ASTM Committee E28 on Mechanical Testing and is the direct responsibility of Subcommittee E28.04 on Uniaxial Testing.
Current edition approved Nov. 1, 2013Dec. 1, 2020. Published May 2014January 2021. Originally approved in 1959. Last previous edition approved in 200820138 as
E143– 02(2008).13. DOI: 10.1520/E0143-13.10.1520/E0143-20.
The boldface numbers in parentheses refer to a list of references at the end of this standard.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E143 − 20
3.1.1 Definitions that appear in Terminology E6 apply to this test method, including accuracy, chord modulus, creep, eccentricity,
Poisson’s ratio, proportional limit, resolution, shear modulus, shear strain, stress-strain curve, stress-strain diagram, tangent
modulus, testing machine, torsional stress, yield strength, and Young’s modulus. Terms common to mechanical testing.
3.1.1 angle of twist (torsion test)— the angle of relative rotation measured in a plane normal to the torsion specimen’s longitudinal
axis over the gauge length.
−2
3.1.2 shear modulus, G, [FL ],n—the ratio of shear stress to corresponding shear strain below the proportional limit, also called
torsional modulus and modulus of rigidity. (See Fig. 1.)
3.1.2.1 Discussion—
The value of shear modulus maycan depend on the direction in which it is measured if the material is not isotropic. Wood, many
plastics, and certain metals are markedly anisotropic. Deviations from isotropy should be suspected if the shear modulus, G, differs
from that determined by substituting independently measured values of Young’s modulus, E, and Poisson’s ratio, μ, in the relation
E
G 5 (1)
2 11μ
~ !
3.1.2.2 Discussion—
In general, it is advisable, in When reporting values of shear modulus to state modulus, the stress range over which it is
measured.measured should be stated.
3.1.3 torque, [FL],n—a moment (of forces) that produces or tends to produce rotation or torsion.
−2
3.1.4 torsional stress [FL ],n—the shear stress in a body, in a plane normal to the axis or rotation, resulting from the application
of torque.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 angle of twist (torsion test)—the angle of relative rotation measured in a plane normal to the torsion specimen’s longitudinal
axis over the gauge length.
4. Summary of Test Method
4.1 The cylindrical or tubular test specimen is loaded either incrementally or continuously by applying an external torque so as
to cause a uniform twist within the gauge length.
4.1.1 Changes in torque and the corresponding changes in angle of twist are determined either incrementally or continuously. The
appropriate slope is then calculated from the shear stress-strain curve, which may be derived under conditions of either increasing
or decreasing torque (increasing from pretorque to maximum torque or decreasing from maximum torque to pretorque).
FIG. 1 Shear Stress-Strain Diagram Showing a Straight Line, Corresponding to the Shear Modulus, Between R, a Pretorque Stress, and
P, the Proportional Limit
E143 − 20
5. Significance and Use
5.1 Shear modulus is a material property useful in calculating compliance of structural materials in torsion provided they follow
Hooke’s law, that is, the angle of twist is proportional to the applied torque. Examples of the use of shear modulus are in the design
of rotating shafts and helical compression springs.
NOTE 1—For materials that follow nonlinear elastic stress-strain behavior, the value of tangent or chord shear modulus is useful for estimating the change
in torsional strain to corresponding stress for a specified stress or stress-range, respectively. Such determinations are, however, outside the scope of this
standard. (See for example Ref (1).)
5.2 The procedural steps and precision of the apparatus and the test specimens should be appropriate to the shape and the material
type, since the method applies to a wide variety of materials and sizes.
5.3 Precise determination of shear modulus depends on the numerous variables that may affect such determinations.
5.3.1 These factors include characteristics of the specimen such as residual stress, concentricity, wall thickness in the case of tubes,
deviation from nominal value, previous strain history, and specimen dimension.
5.3.2 Testing conditions that influence the results include axial position of the specimen, temperature and temperature variations,
and maintenance of the apparatus.
5.3.3 Interpretation of data also influences results.
6. General Considerations
6.1 Shear modulus for a specimen of circular cross-section is given by the equation
G 5 TL/Jθ (2)
TL
G 5 (2)
Jθ
where:
G = shear modulus of the specimen,
T = torque,
L = gauge length,
J = polar moment of inertia of the section about its center, and
θ = angle of twist, in radians.
6.1.1 For a solid cylinder:
J 5πD /32 (3)
πD
J 5 (3)
where:
D = diameter.
6.1.2 For a tube:
π
4 4
J 5 ~D 2 D ! (4)
0 i
π
4 4
J 5 ~D 2 D ! (4)
o i
See any standard text in Mechanics of Materials.
E143 − 20
where:
D = outside diameter, and
D = outside diameter, and
o
D = inside diameter.
i
7. Apparatus
7.1 Testing Machine—The torsion testing machine, which is to be used for applying the required torque to the specimen, shall be
calibrated for the range of torques used in the determination. Corrections may be applied for demonstrated systematic errors. The
torques should be chosen such as to bring the error Δmachine shall conform to the requirements ofG inPractice E2624shear
modulus, due to errors in torque Δ.T, well within the required accuracy (see 12.3.1).
7.2 Grips—The ends of the specimen shall be gripped firmly between the jaws of a testing machine that have been designed to
produce a state of uniform twist within the gauge length. In the case of tubes, closely fitting rigid plugs, such as are shown in Fig.
11 (Metal Plugs for Testing Tubular Specimens) of Test Methods E8/E8M, may be inserted in the ends to permit tightening the
grips without crushing the specimen. The grips shall be such that axial alignment can be obtained and maintained in order to
prevent the application of bending moments. One grip shall be free to move axially to prevent the application of axial forces.
7.3 Twist Gages—Gauges—The angle of twist may be measured by two pairs of lightweight but rigid arms, each pair fastened
diametrically to a ring attached at three points to the section at an end of the gauge length and at least one diameter removed from
the grips. The relative rotational displacement of the two sections may be measured by mechanical, optical, or electrical means;
for example, the displacement of a pointer on one arm relative to a scale on the other (2), or the reflection of a light beam from
mirrors or prisms attached to the arms (3). Readings should be taken for both sets of arms and averaged to eliminate errors due
to bending of the specimen (see 12.3.2).
8. Test Specimens
8.1 Selection and Preparation of Specimens:
8.1.1 Specimens shall be chosen from sound, clean material.
NOTE 1—Slight imperfections near the surface, such as fissures that would have negligible effect in determining Young’s modulus, can cause appreciable
errors in shear modulus.
8.1.2 In the case of machined specimens take care to prevent changing the properties of the material at the surface of the specimen.
8.1.3 Specimens in the form of solid cylinders should be straight and of uniform diameter for a length equal to the gauge length
plus two to four diameters (see 12.2.1).
8.1.4 Specimens shall be chosen from sound, clean material. Slight imperfections near the surface, such as fissures that would have
negligible effect in determining Young’s modulus, may cause appreciable errors in shear modulus. In the case of machined
specimens take care to prevent changing the properties of the material at the surface of the specimen.tubes, the specimen should
be straight and of uniform diameter and wall thickness for a length equal to the gauge length plus at least four outside diameters
(see 12.2.1 and 12.3.2).
8.1.1.1 Specimens in the form of solid cylinders should be straight and of uniform diameter for a length equal to the gauge length
plus two to four diameters (see 12.2.1).
8.1.1.2 In the case of tubes, the specimen should be straight and of uniform diameter and wall thickness for a length equal to the
gauge length plus at least four outside diameters (see 12.2.1 and 12.3.2).
8.2 Length—The gauge length should be at least four diameters. T
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