ASTM E111-17

Standard Test Method for Young’s Modulus, Tangent Modulus, and Chord Modulus

SIGNIFICANCE AND USE
5.1 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).  
5.2 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.  
5.3 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.  
5.4 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.  
5.5 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).  
5.6 When the modulus determination is made at strains in excess of 0.25 %, correction shall be made for changes in cross-sectional area and gauge length, by substituting the instantaneous cross section and instantaneous gauge length for the original values.  
5.7 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, see Fig. 1. 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.
FIG. 1 Stress-Strain Diagrams Showing Straight Lines Corresponding to (a) Young’s Modulus, (b) Tangent Modulus, and (c) Chord Modulus    
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, health, and environmental 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.

General Information

• Status: Published
• Publication Date: 14-Jul-2017
• ICS: 77.040.10 - Mechanical testing of metals
• Technical Committee: E28 - Mechanical Testing
• Drafting Committee: E28.04 - Uniaxial Testing

Relations

• Refers: ASTM E8/E8M-15 - Standard Test Methods for Tension Testing of Metallic Materials
• Effective Date: 01-Feb-2015
• Refers: ASTM E8/E8M-16 - Standard Test Methods for Tension Testing of Metallic Materials
• Effective Date: 15-Jul-2016

Standards Content (Sample)

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.
Designation: E111 − 17
Standard Test Method for
1
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* E9Test Methods of Compression Testing of Metallic Mate-
rials at Room Temperature
1.1 This test method covers the determination of Young’s
E21TestMethodsforElevatedTemperatureTensionTestsof
modulus, tangent modulus, and chord modulus of structural
Metallic Materials
materials,seeFig.1.Thistestmethodislimitedtomaterialsin
E83Practice for Verification and Classification of Exten-
which and to temperatures and stresses at which creep is
someter Systems
negligible compared to the strain produced immediately upon
E177Practice for Use of the Terms Precision and Bias in
loading and to elastic behavior.
ASTM Test Methods
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: Terms common to mechanical testing.
priate safety, health, and environmental practices and deter-
3.1.1 The definitions of mechanical testing terms that ap-
mine the applicability of regulatory limitations prior to use.
pear inTerminology E6 apply to this test method.These terms
1.5 This international standard was developed in accor-
include initial tangent modulus, secant modulus, gauge length,
dance with internationally recognized principles on standard-
yield strength, tensile strength, stress-strain diagram, and
ization established in the Decision on Principles for the
extensometer.
Development of International Standards, Guides and Recom-
3.1.2 The terms accuracy, precision, and bias are used as
mendations issued by the World Trade Organization Technical
defined in Practice E177.
Barriers to Trade (TBT) Committee.
3.1.3 In addition, the following common terms that appear
2. Referenced Documents in the Terminology E6 apply to this test method.
2
3.1.4 chord modulus—theslopeofthechorddrawnbetween
2.1 ASTM Standards:
any two specified points on the stress-strain curve below the
E6Terminology Relating to Methods of MechanicalTesting
elastic limit of the material.
E8/E8MTest Methods for Tension Testing of Metallic Ma-
2
terials
3.1.5 elastic limit [FL ], n—the greatest stress that a mate-
rial is capable of sustaining without any permanent strain
remaining upon complete release of the stress.
1
This test method is under the jurisdiction of ASTM Committee E28 on
3.1.5.1 Discussion—Due to practical considerations in de-
Mechanical Testing and is the direct responsibility of Subcommittee E28.04 on
Uniaxial Testing.
termining the elastic limit, measurements of strain using a
Current edition approved July 15, 2017. Published September 2017. Originally
small force, rather than zero force, are usually taken as the
approvedin1955.Lastpreviouseditionapprovedin2010asE111–04(2010).DOI:
initial and final reference.
10.1520/E0111-04R10
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
3.1.6 indicated temperature, n—the temperature indicated
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
by a temperature measuring device using good pyrometric
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. practice.
*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
1

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...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
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: E111 − 04 (Reapproved 2010) E111 − 17
Standard Test Method for
1
Young’s Modulus, Tangent Modulus, and Chord Modulus
This standard is issued under the fixed designation E111; 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.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope Scope*
1.1 This test method covers the determination of Young’s modulus, tangent modulus, and chord modulus of structural materials.
materials, see Fig. 1. 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 safety, health, and healthenvironmental practices and determine the
applicability of regulatory requirementslimitations 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
2.1 ASTM Standards:
E4 Practices for Force Verification of Testing Machines
E6 Terminology Relating to Methods of Mechanical Testing
E8E8/E8M Test Methods for Tension Testing of Metallic Materials
E9 Test Methods of Compression Testing of Metallic Materials at Room Temperature
E21 Test Methods for Elevated Temperature Tension Tests of Metallic Materials
E83 Practice for Verification and Classification of Extensometer Systems
E231E177 MethodPractice for Static Determination of Young’s Modulus of Metals at Low and Elevated TemperaturesUse of the
Terms Precision and Bias in ASTM Test Methods (Withdrawn 1985)
E1012 Practice for Verification of Testing Frame and Specimen Alignment Under Tensile and Compressive Axial Force
Application
2.2 General Considerations—While certain portions of the standards and practices listed are applicable and should be referred
to, the precision required in this test method is higher than that required in general testing.
3. Terminology
3.1 Definitions: Terms common to mechanical testing.
3.1.1 accuracy—the degree of agreement between an accepted standard value of Young’sThe definitions of mechanical testing
terms that appear in Terminology E6 modulus (the average of many observations made according to this method, preferably by
many observers) and the value determined.apply to this test method. These terms include initial tangent modulus, secant modulus,
gauge length, yield strength, tensile strength, stress-strain diagram, and extensometer.
1
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 Sept. 15, 2010July 15, 2017. Published January 2011September 2017. Originally approved in 1955. Last previous edition approved in 20042010
as E111 – 04.E111 – 04(2010). DOI: 10.1520/E0111-04R10
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. 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
1

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E111 − 17
3.1.1.1 Increased accuracy is associated with decreased bias relative to the accepted standard value; two methods with equal bias
relative to t
...