ASTM E111-04(2010)
(Test Method)Standard Test Method for Young's Modulus, Tangent Modulus, and Chord Modulus
Standard Test Method for Young's Modulus, Tangent Modulus, and Chord Modulus
SIGNIFICANCE AND USE
The value of Young's modulus is a material property useful in design for calculating compliance of structural materials that follow Hooke's law when subjected to uniaxial loading (that is, the strain is proportional to the applied force).
For materials that follow nonlinear elastic stress-strain behavior, the value of tangent or chord modulus is useful in estimating the change in strain for a specified range in stress.
Since for many materials, Young's modulus in tension is different from Young's modulus in compression, it shall be derived from test data obtained in the stress mode of interest.
The accuracy and precision of apparatus, test specimens, and procedural steps should be such as to conform to the material being tested and to a reference standard, if available.
Precise determination of Young's modulus requires due regard for the numerous variables that may affect such determinations. These include (1) characteristics of the specimen such as orientation of grains relative to the direction of the stress, grain size, residual stress, previous strain history, dimensions, and eccentricity; (2) testing conditions, such as alignment of the specimen, speed of testing, temperature, temperature variations, condition of test equipment, ratio of error in applied force to the range in force values, and ratio of error in extension measurement to the range in extension values used in the determination; and (3) interpretation of data (see Section 9).
When the modulus determination is made at strains in excess of 0.25 %, correction should be made for changes in cross-sectional area and gage length, by substituting the instantaneous cross section and instantaneous gage length for the original values.
Compression results may be affected by barreling (see Test Methods E9). Strain measurements should therefore be made in the specimen region where such effects are minimal.
SCOPE
1.1 This test method covers the determination of Young's modulus, tangent modulus, and chord modulus of structural materials. This test method is limited to materials in which and to temperatures and stresses at which creep is negligible compared to the strain produced immediately upon loading and to elastic behavior.
1.2 Because of experimental problems associated with the establishment of the origin of the stress-strain curve described in 8.1, the determination of the initial tangent modulus (that is, the slope of the stress-strain curve at the origin) and the secant modulus are outside the scope of this test method.
1.3 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory requirements prior to use.
General Information
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Standards Content (Sample)
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Designation: E111 − 04 (Reapproved 2010)
Standard Test Method for
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Young’s Modulus, Tangent Modulus, and Chord Modulus
ThisstandardisissuedunderthefixeddesignationE111;thenumberimmediatelyfollowingthedesignationindicatestheyearoforiginal
adoptionor,inthecaseofrevision,theyearoflastrevision.Anumberinparenthesesindicatestheyearoflastreapproval.Asuperscript
epsilon (´) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope rials at Room Temperature
2 E21TestMethodsforElevatedTemperatureTensionTestsof
1.1 This test method covers the determination of Young’s
Metallic Materials
modulus, tangent modulus, and chord modulus of structural
E83Practice for Verification and Classification of Exten-
materials.Thistestmethodislimitedtomaterialsinwhichand
someter Systems
to temperatures and stresses at which creep is negligible
E231Method for Static Determination of Young’s Modulus
comparedtothestrainproducedimmediatelyuponloadingand
of Metals at Low and Elevated Temperatures (Withdrawn
to elastic behavior.
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1985)
1.2 Because of experimental problems associated with the
E1012Practice for Verification of Testing Frame and Speci-
establishment of the origin of the stress-strain curve described
men Alignment Under Tensile and Compressive Axial
in 8.1, the determination of the initial tangent modulus (that is,
Force Application
the slope of the stress-strain curve at the origin) and the secant
2.2 General Considerations—While certain portions of the
modulus are outside the scope of this test method.
standards and practices listed are applicable and should be
1.3 The values stated in SI units are to be regarded as
referred to, the precision required in this test method is higher
standard. No other units of measurement are included in this
than that required in general testing.
standard.
1.4 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
3. Terminology
responsibility of the user of this standard to establish appro-
3.1 Definitions:
priate safety and health practices and determine the applica-
3.1.1 accuracy—the degree of agreement between an ac-
bility of regulatory requirements prior to use.
cepted standard value of Young’s modulus (the average of
many observations made according to this method, preferably
2. Referenced Documents
by many observers) and the value determined.
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2.1 ASTM Standards:
3.1.1.1 Increasedaccuracyisassociatedwithdecreasedbias
E4Practices for Force Verification of Testing Machines
relativetotheacceptedstandardvalue;twomethodswithequal
E6Terminology Relating to Methods of MechanicalTesting
bias relative to the accepted standard value have equal accu-
E8Test Methods for Tension Testing of Metallic Materials
racyevenifonemethodismoreprecisethantheother.Seealso
E9Test Methods of Compression Testing of Metallic Mate-
bias and precision.
3.1.1.2 The accepted standard value is the value ofYoung’s
modulus for the statistical universe being sampled using this
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This test method is under the jurisdiction of ASTM Committee E28 on
method. When an accepted standard value is not available,
Mechanical Testing and is the direct responsibility of Subcommittee E28.04 on
Uniaxial Testing. accuracy cannot be established.
Current edition approved Sept. 15, 2010. Published January 2011. Originally
3.1.2 bias, statistical—a constant or systematic error in test
approved in 1955. Last previous edition approved in 2004 as E111–04. DOI:
results.
10.1520/E0111-04R10
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3.1.2.1 Bias can exist between the accepted standard value
ThistestmethodisarevisionofE111–61(1978),“Young’sModulusatRoom
Temperature” and includes appropriate requirements of E231–69(1975), “Static
andatestresultobtainedfromthistestmethod,orbetweentwo
Determination of Young’s Modulus of Metals at Low and Elevated Temperatures”
test results obtained from this test method, for example,
to permit the eventual withdrawal of the latter method. Method E231 is under the
between operators or between laboratories.
jurisdiction of ASTM-ASME Joint Committee on Effect of Temperature on the
Property of Metals.
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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
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Standards volume information, refer to the standard’s Document Summary page on The last approved version of this historical standard is referenced on
the ASTM website. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E111 − 04 (2010)
3.1.3 precision—the degree of mutual agreement among 5. Significance and Use
individual measurements made under prescribed like c
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