ASTM E855-21

Standard Test Methods for Bend Testing of Metallic Flat Materials for Spring Applications Involving Static Loading

SIGNIFICANCE AND USE
4.1 Measurements of bending proof strength, offset yield strength in bending, and modulus of elasticity in bending should be made for materials whose principal stressing mode is bending. For many materials, the tensile and compressive moduli are somewhat different. Since the modulus of elasticity in bending is a combination of the tensile and compressive moduli, it is often different from each of them.  
4.2 Precise measurements of the modulus of elasticity in bending offset yield strength in bending, and bending proof strength require due regard for numerous variables that can affect their determination. These include (1) material characteristics such as specimen orientation with respect to the rolling direction, grain size, residual stresses, previous strain history, dimensions and specimen preparation, orientation of deformed grains relative to the direction of the normal stress; and (2) test conditions, such as temperature, temperature variations, condition of the test equipment, and adherence to the test procedure.  
4.3 Fundamental Assumptions:  
4.3.1 The test section of the specimen is subjected to uniform bending moment, which produces a uniform strain at the outer fiber throughout the gauge length of the specimen (applies to Test Method C only).  
4.3.2 The neutral axis is located at the centerline of the thickness of the test specimen.  
4.3.3 Transverse cross sections of the beam remain plane and normal to the longitudinal fiber of the beam during bending.  
4.3.4 The effect of shear stresses is negligible.
SCOPE
1.1 This standard describes three test methods2 for determining the modulus of elasticity in bending, the bending proof strength, and the offset yield strength in bending of metallic strips or sheets intended for the use in flat springs:  
1.1.1 Test Method A—a cantilever beam test,  
1.1.2 Test Method B—a three-point beam test (that is, a beam resting on two supports and centrally loaded), and  
1.1.3 Test Method C—a four-point beam test (that is, a beam resting on two supports and loaded at two points equally spaced from each support).  
1.2 The values stated in inch-pound 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 standard.  
1.3 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.  
1.4 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: 31-Jan-2021
• ICS: 21.160 - Springs
• Technical Committee: E28 - Mechanical Testing
• Drafting Committee: E28.02 - Ductility and Formability

Relations

• Refers: ASTM E4-14 - Standard Practices for Force Verification of Testing Machines
• Effective Date: 01-Jun-2014
• Refers: ASTM E177-14 - Standard Practice for Use of the Terms Precision and Bias in ASTM Test Methods
• Effective Date: 01-May-2014
• Refers: ASTM E691-13 - Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method
• Effective Date: 01-May-2013
• Refers: ASTM E177-13 - Standard Practice for Use of the Terms Precision and Bias in ASTM Test Methods
• Effective Date: 01-May-2013
• Refers: ASTM E691-11 - Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method
• Effective Date: 01-Nov-2011
• Refers: ASTM E177-10 - Standard Practice for Use of the Terms Precision and Bias in ASTM Test Methods
• Effective Date: 01-Oct-2010
• Refers: ASTM E4-10 - Standard Practices for Force Verification of Testing Machines
• Effective Date: 01-Jun-2010
• Refers: ASTM E4-09a - Standard Practices for Force Verification of Testing Machines
• Effective Date: 01-Nov-2009
• Refers: ASTM E6-09be1 - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 15-May-2009
• Refers: ASTM E6-09b - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 15-May-2009
• Refers: ASTM E6-09a - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 01-Apr-2009
• Refers: ASTM E4-09 - Standard Practices for Force Verification of Testing Machines
• Effective Date: 01-Apr-2009
• Refers: ASTM E6-09 - Standard Terminology Relating to Methods of Mechanical Testing
• Effective Date: 01-Jan-2009
• Refers: ASTM E4-08 - Standard Practices for Force Verification of Testing Machines
• Effective Date: 01-Dec-2008
• Refers: ASTM E177-08 - Standard Practice for Use of the Terms Precision and Bias in ASTM Test Methods
• Effective Date: 01-Oct-2008

Overview

ASTM E855-21 is the internationally recognized standard for the bend testing of metallic flat materials specifically intended for spring applications under static loading. Developed by ASTM International, this standard provides methods to accurately determine key mechanical properties - such as the modulus of elasticity in bending, offset yield strength in bending, and bending proof strength - for metallic sheets and strips used in the manufacturing of flat springs. Bend testing is critical for understanding the behavior of spring materials subjected to bending loads, which directly correlates with performance and reliability in many engineering applications.

Key Topics

• Bend Testing Methods: ASTM E855-21 outlines three distinct bend testing methods:
  • Test Method A: Cantilever beam test for modulus of elasticity and offset yield strength in bending.
  • Test Method B: Three-point beam test for modulus of elasticity in bending and bending proof strength.
  • Test Method C: Four-point beam test, also for modulus of elasticity in bending and bending proof strength.
• Measured Properties:
  • Modulus of Elasticity in Bending: Indicates stiffness in response to bending, reflecting a combination of tensile and compressive properties.
  • Bending Proof Strength: Maximum stress a material can withstand without permanent deformation.
  • Offset Yield Strength in Bending: The stress at which a specified deviation from proportionality is observed in the stress-strain curve.
• Precision and Variables: The standard underscores the importance of precise measurement and consideration of variables such as specimen orientation, grain size, residual stresses, test temperature, and equipment calibration.
• Applicability: Intended for flat metallic strip or sheet materials used in spring manufacturing, with guidelines on specimen preparation, measurement, and reporting for reliable, reproducible results.

Applications

The practical value of ASTM E855-21 is most evident in industries and applications where metallic flat springs are essential, such as:

• Spring Design and Manufacturing: Manufacturers use the test results for selecting materials, designing springs, and validating performance criteria including maximum deflection and spring constants.
• Quality Control: Routine bend testing as per ASTM E855-21 can verify consistency in material mechanical properties, ensuring that only suitable materials enter production.
• Research and Development: Engineers and researchers use bending test data to study the impact of alloy composition, heat treatments, and fabrication methods on bend properties, informing material selection and spring design improvements.
• Standard Compliance and Specifications: Provides a standardized framework for specifying and accepting material performance in contract requirements and technical datasheets.

Related Standards

ASTM E855-21 references and complements several other ASTM standards related to mechanical testing and terminology, including:

• ASTM E4: Practices for Force Verification of Testing Machines.
• ASTM E6: Terminology Relating to Methods of Mechanical Testing.
• ASTM E111: Test Method for Young’s Modulus, Tangent Modulus, and Chord Modulus.
• ASTM E177: Practice for Use of the Terms Precision and Bias in ASTM Test Methods.
• ASTM E691: Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method.

These related standards ensure that bend testing for metallic flat springs is performed with consistent terminology, measurement precision, and data analysis methods, supporting high-quality outcomes in both manufacturing and research environments.

By adhering to ASTM E855-21, professionals ensure that metallic flat materials for spring applications are rigorously evaluated for their bending strength and elasticity, contributing to safer, more reliable, and high-performing finished products.

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: E855 − 21
Standard Test Methods for
Bend Testing of Metallic Flat Materials for Spring
Applications Involving Static Loading
This standard is issued under the fixed designation E855; 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 2.2 ASTM Standards:
E4 Practices for Force Verification of Testing Machines
1.1 This standard describes three test methods for deter-
E6 Terminology Relating to Methods of Mechanical Testing
mining the modulus of elasticity in bending, the bending proof
E177 Practice for Use of the Terms Precision and Bias in
strength, and the offset yield strength in bending of metallic
ASTM Test Methods
strips or sheets intended for the use in flat springs:
E691 Practice for Conducting an Interlaboratory Study to
1.1.1 Test Method A—a cantilever beam test,
Determine the Precision of a Test Method
1.1.2 Test Method B—a three-point beam test (that is, a
beam resting on two supports and centrally loaded), and 3. Terminology
1.1.3 Test Method C—a four-point beam test (that is, a beam
3.1 Definitions of terms common to mechanical testing:
resting on two supports and loaded at two points equally
3.1.1 The terms bend test, chord modulus, gauge length,
spaced from each support).
modulus of elasticity, proportional limit, springback, stress-
strain curve, tangent modulus, testing machine, yield strength,
1.2 The values stated in inch-pound units are to be regarded
and Young’s modulus are used as defined in Terminology E6.
as standard. The values given in parentheses are mathematical
conversions to SI units that are provided for information only
3.2 Definitions of Terms Specific to This Standard:
and are not considered standard. 3.2.1 In addition to the terms in Terminology E6, the
following descriptions of terms apply in connection with these
1.3 This standard does not purport to address all of the
test methods for determining bend properties:
safety concerns, if any, associated with its use. It is the
−2
3.2.2 bending stress at the outer fiber, σ [FL ]—the nomi-
b
responsibility of the user of this standard to establish appro-
nalstressintheouterfiberofabeamresultingfromapplication
priate safety, health, and environmental practices and deter-
of a bending moment.
mine the applicability of regulatory limitations prior to use.
−2
3.2.3 elastic limit in bending [FL ]—the greatest bending
1.4 This international standard was developed in accor-
stress that a material is capable of sustaining without perma-
dance with internationally recognized principles on standard-
nent strain remaining after complete release of the bending
ization established in the Decision on Principles for the
moment.
Development of International Standards, Guides and Recom-
−2
3.2.4 modulus of elasticity in bending, E [FL ]—the ratio
mendations issued by the World Trade Organization Technical
b
of bending stress at the outer fiber to corresponding strain
Barriers to Trade (TBT) Committee.
below the elastic limit in bending.
2. Referenced Documents
3.2.5 span length, L [L]—the distance between supports.
−2
3.2.6 bending proof strength, σ [FL ]—the nominal bend-
2.1 The following documents of the issue in effect on date
p
ing stress at the outer fiber of a beam that results in a specific
of use of these test methods form a part of these test methods
permanent strain in the outer fibers upon unloading.
to the extent referenced herein:
−2
3.2.7 cyclic bending yield strength [FL ]—the maximum
nominalstressinuniformcyclicbendingresultingfromagiven
plastic deformation in the outer fibers of a beam.
These test methods are under the jurisdiction of ASTM Committee E28 on
Mechanical Testing and are the direct responsibility of Subcommittee E28.02 on
Ductility and Formability.
Current edition approved Feb. 1, 2021. Published March 2021. Originally
approvedin1981.Lastpreviouseditionapprovedin2013asE855 – 08(2013).DOI: For referenced ASTM standards, visit the ASTM website, www.astm.org, or
10.1520/E0855-21. contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
Method D, which appeared in the last previous edition, was dropped because of Standards volume information, refer to the standard’s Document Summary page on
the unavailability of commercial testing equipment. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E855 − 21
−2
3.2.8 offset yield strength in bending [FL ]—the nominal and deflection data obtained are normalized with regard to
stress in the outer fibers of a beam in bending at which a specimengeometry.Thesenormalizedtermsarethenplottedto
specified limiting deviation from proportionality of bending produce a stress-strain curve for cantilever bending that is
stress at the outer fiber to bending strain is exhibited. similar to a stress-strain curve for tension or compression. The
3.2.8.1 Discussion—The deviation is expressed in terms of modulus of elasticity in bending and the offset yield strength in
strain. bending are determined from the bending stress-strain curve
using a procedure similar to that used for tensile stress-strain
4. Significance and Use
curves.
4.1 Measurements of bending proof strength, offset yield
7. Significance and Use
strength in bending, and modulus of elasticity in bending
7.1 Values of offset yield strength in bending and modulus
shouldbemadeformaterialswhoseprincipalstressingmodeis
bending. For many materials, the tensile and compressive of elasticity in bending are useful to spring designers to
determine spring constants and permissible maximum deflec-
moduli are somewhat different. Since the modulus of elasticity
in bending is a combination of the tensile and compressive tion of flat springs. The offset yield strength in bending as
determinedbythistestmethodisnotnecessarilyequaltoeither
moduli, it is often different from each of them.
the yield strength in tension, the cyclic bending yield strength,
4.2 Precise measurements of the modulus of elasticity in
or to bending proof strengths determined by other methods.
bending offset yield strength in bending, and bending proof
strength require due regard for numerous variables that can 7.2 The test method can also serve the following purposes:
7.2.1 For research and development to study the effects of
affect their determination. These include (1) material charac-
teristicssuchasspecimenorientationwithrespecttotherolling metallurgical variables, such as composition, heat treatment,
fabrication operations, and alloy development.
direction, grain size, residual stresses, previous strain history,
7.2.2 For information or specification purposes, to provide a
dimensions and specimen preparation, orientation of deformed
grains relative to the direction of the normal stress; and (2) test manufacturing quality control where suitable correlations have
been established with service behavior.
conditions, such as temperature, temperature variations, con-
dition of the test equipment, and adherence to the test proce-
7.3 Due to necessary approximations in this test method
dure.
regarding the specimen’s deflection, D, and span length, L, the
4.3 Fundamental Assumptions: maximum deflection angle is 30°. These approximations are
explained in Appendix X1.
4.3.1 The test section of the specimen is subjected to
uniform bending moment, which produces a uniform strain at
7.4 Rate of loading is controlled only to the extent that the
the outer fiber throughout the gauge length of the specimen
rate of angular change of the rotating jaw is fixed at 58°/min to
(applies to Test Method C only).
66°/min. Actual rate of stressing will depend on the specimen
4.3.2 The neutral axis is located at the centerline of the
width and thickness and the weight of the pendulum.
thickness of the test specimen.
4.3.3 Transverse cross sections of the beam remain plane
and normal to the longitudinal fiber of the beam during
bending.
4.3.4 The effect of shear stresses is negligible.
TEST METHOD A—CANTILEVER BEAM TEST
5. Scope
5.1 This test method covers the determination of the modu-
lus of elasticity in bending and the offset yield strength in
bending of flat metallic strips or sheets for spring applications.
The test procedure involves measurements of the applied
moment and the corresponding deflection angle of a cantilever
beam. The thickness range covered is 0.015 in. to 0.130 in.
(0.38 mm to 3.30 mm).This test method should not be used for
nonlinear elastic materials.
(Test Method A)
FIG. 1 Cantilever Beam Test Apparatus
6. Summary of Test Method
6.1 The test specimen is loaded as a simple cantilever beam,
and the bending moment is measured at predetermined incre-
8. Apparatus
ments of angular deflection. When the maximum desired
8.1 The cantilever beam test apparatus shown in Fig. 1
deflection is reached, the bending moment is removed and the
consists of the following components:
permanent set angle resulting from the bend is recorded. All
testing is performed under conditions of plane strain (that is,
ratio of specimen width/thickness >10). The bending moment The Olsen Stiffness Tester meets the requirements of this test method.
E855 − 21
8.1.1 Specimen Holder, A vise, V, to which an angular 9. Test Specimens
deflection indicator, I , is attached. The specimen holder is
9.1 Rectangular test specimens shall be used. Specimen
rotates about point O.
orientation relative to the rolling direction shall be identified.
8.1.2 Pendulum Weighing System, composed of a set of
Specimens with curvature due to coil set may be used if the
detachable weights, an angular deflection scale, A, with a
ratio of the radius of curvature to thickness exceeds 500.
moment indicator, I , a bending pin that transmits the bending
However, the specimen shall not be twisted or wavy. No
force of the pendulum weighing system to the free end of the
attemptshallbemadetoflattenorstraightenspecimenspriorto
testspecimen,andaweighttocounter-balancethebendingpin.
testing. Care shall be exercised not to alter the microstructure
The pendulum weighing system pivots about point O. For a
duringspecimenpreparation.Allburrsshallberemovedbefore
pendulum weighing system (Fig. 2) having no internal
testing.
moments, the total bending moment, M, is:
NOTE 1—Testing machine capacity will determine the maximum
M 5wdsinθ (1)
allowable specimen size.
where:
9.2 The minimum specimen thickness should be 0.015 in.
(0.38 mm).The thickness shall be measured at the four corners
M = bending moment at angle θ, lbf·in (N·m),
w = total force applied by pendulum weighing system, lbf and the center of the specimen. Specimens having thickness
variations in excess of 2 % of the average (of these five
(N),
d = length of the pendulum arm, in (m), and measured thicknesses) shall not be tested. The instrument used
θ = angle through which the pendulum weighing system
to measure the thickness shall have a precision within 2 % of
rotates, rad.
the average thickness.
8.1.3 Angular Deflection Scale, A,isgraduatedindegreesof
NOTE 2—Eq 3 in 10.1 shows that the value of the modulus of elasticity
arc and indicates the angle through which the vise has been
in bending varies as the third power of thickness. Hence, thickness is by
farthemostcriticalmeasurementinthedeterminationofthemodulus.For
turned relative to the pendulum weighing system. This is the
example, an error in the thickness measurement of 60.0001 in.
difference between the angle through which the vise has been
(60.0025 mm) for a specimen having the minimum recommended thick-
turned and the angle through which the pendulum weighing
ness of 0.015 in. (0.38 mm), the measurement is reproducible to within
system has been deflected, and is designated as angle φ. The
0.67 % and the error in modulus of elasticity in bending attributable to the
bending pin has a diameter of 0.25 in. (6.35 mm), and the
reproducibility of the thickness measurement is 2 %. Further, if the
thickness actually varies by 2 % over the gauge section or by 0.0003 in.
distance between the clamping point (that is, center of rotation
(0.0075 mm), the error in modulus of elasticity in bending attributable to
of the pendulum weighing system) and the center of the
actual thickness variation is 6 %, and the total error attributable to both
bending pin is 2.0 in. (50.8 mm). The reason for specifying the
measurement and actual variation is 8 %. Additional sources of uncer-
diameter and location of the bending pin is explained in
tainty are the precisions of determining the span length, the specimen
width, and the beam deflection.
Appendix X1.
8.1.4 Moment Scale—This stationary moment scale mea-
9.3 The ratio of the specimen span length to thickness shall
sures the applied moment as a function of the pendulum
begreaterthan15;consequently,sincethespanlengthis2.0in.
weighing system’s rotation θ. A full scale reading of 100
(50.8 mm), the specimen thickness cannot exceed 0.13 in.
corresponds to the pendulum weighing system’s maximum
(3.30 mm).
bending moment, M .This system shall be calibrated such that
m
9.4 Thewidthtothicknessratioshallbegreaterthan10.The
the moment scale reading, f, is:
width shall be measured at both ends and the center of the
f 5 100wdsinθ/M (2)
m
specimen. The maximum variation in width shall be less than
orequalto0.5 %oftheaveragewidth.Theminimumspecimen
width shall be 0.5 in. (12.7 mm). The specimen width shall not
extend beyond the vise or the bending pin.
10. Procedure
10.1 Place the machine on a level surface. Set the bending
span length to 2.0 in. (50.8 mm) and adjust the moment
indicator to zero. For the best precision the maximum bending
moment, M , should be chosen so that the moment scale
m
reading is between 5 and 10 for an angular deflection of 3°. If
this value is not known, estimated it as follows:
φ
M 5 25 E bh (3)
m b
fL
where:
M = pendulum’s maximum bending moment, in·lbf (N·
m
m),
(Test Method A)
E = modulus of elasticity in bending (can be approxi-
b
FIG. 2 Schematic of Pendulum Weighing System
mated by Young’s modulus) lbf/in. (Pa),
E855 − 21
0.10 % should be determined, provided this does not require
b = specimen width, in. (m),
that the maximum allowable deflection angle of 30° be
h = specimen thickness, in. (m),
exceeded.
φ = angular deflection, rad (0.052 rad (3°) specified here),
NOTE 3—These values of offset yield strengths in bending are not
f = moment scale reading (select 7.5 in this case), and
necessarily equal to either the yield strengths in tension, the cyclic
L = span length, 2 in. (50.8 mm).
bending yield strength, or to bending proof strengths determined by other
methods.
10.2 Clamp the specimen firmly in the vise with its long
edges approximately parallel to the face of the dial plate.
12. Report
10.3 Manually rotate the vise to bring the specimen against
12.1 The following shall be included in the report.
the bending pin. When contact is made, set the angular
12.1.1 Complete description of the material tested, includ-
deflection indicator to indicate zero angle.
ing alloy, temper, and manufacturer’s identification number,
12.1.2 Specimen dimensions and orientation relative to the
10.4 Hold down the motor engaging lever and record the
rolling direction,
moment scale readings at increments of 2° angular deflection
12.1.3 Test temperature, and
(φ) until the desired deflection, not exceeding 30°, is reached.
12.1.4 The modulus of elasticity in bending and an estimate
unload the specimen. Read the permanent set angle resulting
of the precision of the value reported.
from the bend on the angular deflection scale with the
12.1.5 Offset yield strengths in bending, for strains of
specimen contacting the bending pin at zero force.
0.01 %, 0.05 %, and 0.10 % within the limitation of a maxi-
10.5 Test a minimum of six specimens from each sample.
mum deflection angle of 30°, plus an estimate of the precision
For specimens having an initial residual curvature, test half of
of the values reported.
the specimens with the concave surface facing upwards and
12.1.6 Estimate of the precision of the values reported.
half with the convex surface facing upwards. Deflect all
13. Precision and Bias
specimens to the same maximum deflection angle, which shall
be less than or equal to 30°.
13.1 Precision:
13.1.1 The precision of the values of the modulus of
10.6 Replication required for evaluating material variability
elasticity in bending and the offset yield strength in bending
within either the same sample or among several suppliers shall
will depend on the precision of each of the values used in the
be covered in product specifications or upon agreement be-
calculations, as well as the mean and standard deviation of the
tween supplier and user.
values determined for each of the replicate tests. The report
shall include an estimate of the precision of the values
11. Calculation
reported.
11.1 Normalize the bending moment-deflection data with
13.1.2 The following parameters will affect the results and
regardtospecimengeometryandplotoncoordinatepaperwith
can be quantified: precision of the applied forces, precision of
the bending stress at the outer fiber having (3M f/50bh )asthe
m the span length measurement, deviation of width measure-
ordinate and the bending strain [(3/2) (φ h/L)] as the abscissa
ments from the average value, deviation of thickness measure-
(see Appendix X1). These symbols are defined in 10.1. The
ments from the average value, and precision of the deflection
resulting bending stress-strain curve is similar to a tension or
measurements.
compression stress-strain curve.
13.2 Bias—Astatementofbiasrequiresareferencestandard
11.2 Determine the value of the modulus of elasticity in
or a true property value based on many measurements of the
bending, E , from the slope of a straight line extending from
propertyofthesamematerial.Suchstandardsortruevaluesare
b
the maximum deflection datum point (max) to the permanent
presently not available for bending properties of metallic flat
set point (p.s.), that is:
spring materials. Therefore, the bias of the test method is
unknown.
M f
m
S D
25bh
TEST METHOD B: THREE-POINT BEAM TEST
E 5 (4)
b
~φh/L!max2~φh/L!p.s.
TEST METHOD C: FOUR-POINT BEAM TEST
11.3 The first step in constructing the bending stress-strain
14. Scope
curve is to draw a straight line having slope E such that it
b
passes through the origin. The actual data points for elastic
14.1 These test methods cover the determination of the
loading may be slightly displaced from this line. Construct the
modulusofelasticityinbendingandthebendingproofstrength
non-linear portion of the bending stress-strain curve by draw-
of flat metallic strips or sheets for spring applications. The test
ing a curve through the remaining data points and connecting
methods consist of deflection tests of a simple beam configu-
it with the modulus of elasticity in bending line.
ration subjected to either three- or four-point symmetrical
loading. The thickness range covered is 0.010 in. to 0.050 in.
11.4 Calculate offset yield strengths in bending from the
(0.25 mm to 1.3 mm).
bending stress-strain curve using a procedure analogous to that
used for tensile or compressive stress-strain curves. The offset 14.2 Thickness ranges outside of those specified may be
yield strengths in bending for strains of 0.01 %, 0.05 %, and agreed upon between suppliers and users.
E855 − 21
15. Summary of Test Methods the problems mentioned in 16.3, the secant modulus or initial
tangent modulus should not be used.
15.1 The test specimen is loaded as a simple beam in either
three- or four-poi
...

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: E855 − 08 (Reapproved 2013) E855 − 21
Standard Test Methods for
Bend Testing of Metallic Flat Materials for Spring
Applications Involving Static Loading
This standard is issued under the fixed designation E855; 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 standard describes three test methods for determining the modulus of elasticity in bending bending, the bending proof
strength, and the bending strength offset yield strength in bending of metallic strips or sheets intended for the use in flat springs:
1.1.1 Test Method A—a cantilever beam,beam test,
1.1.2 Test Method B—a three-point loaded beam test (that is, a beam resting on two supports and centrally loaded), and
1.1.3 Test Method C—a four-point loaded beam test (that is, a beam resting on two supports and loaded at two points equally
spaced from each support).
1.2 The values stated in inch-pound 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 standard.
1.3 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.
1.4 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 The following documents of the issue in effect on date of use of these test methods form a part of these test methods to the
extent referenced herein:
2.2 ASTM Standards:
E4 Practices for Force Verification of Testing Machines
E6 Terminology Relating to Methods of Mechanical Testing
E111 Test Method for Young’s Modulus, Tangent Modulus, and Chord Modulus
These test methods are under the jurisdiction of ASTM Committee E28 on Mechanical Testing and are the direct responsibility of Subcommittee E28.02 on Ductility
and Formability.
Current edition approved April 1, 2013Feb. 1, 2021. Published April 2013March 2021. Originally approved in 1981. Last previous edition approved in 20082013 as
E855 – 08.E855 – 08(2013). DOI: 10.1520/E0855-08R13.10.1520/E0855-21.
Method D, which appeared in the last previous edition, was dropped because of the unavailability of commercial testing equipment.
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.
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E177 Practice for Use of the Terms Precision and Bias in ASTM Test Methods
E691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method
3. Terminology
3.1 Definitions of terms common to mechanical testing:
3.1.1 The terms bend test, chord modulus, gauge length, modulus of elasticity, proportional limit, springback, stress-strain curve,
tangent modulus, testing machine, yield strength, and Young’s modulus are used as defined in Terminology E6.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 In addition to the terms in Terminology E6, the following descriptions of terms apply in connection with these test methods
for determining bend properties:
3.1.2 bend properties—those properties of a material that are associated with elastic and inelastic behavior when a bending force
is applied, or that involve the relationship between bending stress and strain.
− −22
3.2.2 bending stress at the outer fiber, (FLσ [FL )—]—the nominal stress in the outer fibersfiber of a beam resulting from
b
application of a bending load.moment.
− −22
3.2.3 elastic limit in bending (FL[FL )—]—the greatest bending stress that a material is capable of sustaining without
permanent strain remaining after complete release of the bending moment.
− −22
3.2.4 modulus of elasticity in bending (FLbending, E [FL ) ]—the ratio of bending stress at the outer fiber to corresponding
b
strain below the elastic limit in bending.
3.2.5 span length (L)—length, L [L]—the distance between supports.
3.1.7 uniform bending moment (FL)—a bending moment that produces a uniform strain at the outer fibers throughout the gage
length of the specimen.
− −22
3.2.6 bending proof strength, (FLσ [FL )—]—the nominal bending stress inat the outer fibersfiber of a beam that results in
p
a specific permanent strain in the outer fibers upon unloading.
− −22
3.2.7 cyclic bending yield strength (FL[FL )—]—the maximum nominal stress in uniform cyclic bending resulting from a
given plastic deformation in the outer fibers of a beam.
− −22
3.2.8 offset yield strength in bending (FL[FL ) ]—the nominal stress in the outer fibers of a beam in bending at which a
specified limiting deviation from proportionality of bending stress at the outer fiber to bending strain is exhibited. The deviation
is expressed in terms of strain.
3.2.8.1 Discussion—
The deviation is expressed in terms of strain.
4. Significance and Use
4.1 Measurements of bending strength proof strength, offset yield strength in bending, and modulus of elasticity in bending should
be made for materials whose principal stressing mode is bending. For many materials, the tensile and compressive moduli are
somewhat different. Since the bending modulus modulus of elasticity in bending is a combination of the tensile and compressive
moduli, it is often different from each of them.
4.2 Precise measurements of the modulus of elasticity in bending offset yield strength in bending, and bending proof strength
require due regard for numerous variables that maycan affect their determination. These include (1) material characteristics such
as specimen orientation with respect to the rolling direction, grain size, residual stresses, previous strain history, dimensions and
specimen preparation, orientation of deformed grains relative to the direction of the normal stress; and (2) test conditions, such
as tem-temperature,
perature, temperature variations, condition of the test equipment, and adherence to the recommended test procedure.
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4.3 Fundamental Assumptions:
4.3.1 The test section of the specimen is subjected to uniform bending moment, which produces a uniform strain at the outer fiber
throughout the gauge length of the specimen (applies to Test Method C only).
4.3.2 The neutral axis is located at the centerline of the thickness of the test specimen.
4.3.3 Transverse cross sections of the beam remain plane and normal to the longitudinal fiber of the beam during bending.
4.3.4 The effect of shear stresses is negligible.
5. Fundamental Assumptions
5.1 The test section of the specimen is subjected to uniform bending moment (applies to Test Method C only).
5.2 The neutral axis is located at the centerline of the thickness of the test specimen.
5.3 Transverse cross sections of the beam remain plane and normal to the longitudinal fibers of the beam during bending.
5.4 The effect of shear stresses is negligible.
TEST METHOD A—CANTILEVER BEAM TEST
5. Scope
5.1 This test method covers the determination of the modulus of elasticity in bending and the offset yield strength in bending of
flat metallic strips or sheets for spring applications. The test procedure involves measurements of the applied moment and the
corresponding deflection angle of deflection of a cantilever beam. The thickness range covered is 0.015 in. to 0.130 in. (0.38 mm
to 3.30 mm). This test method isshould not applicable be used for nonlinear elastic materials.
6. Summary of Test Method
6.1 The test specimen is loaded as a simple cantilever beam, and the bending moment is measured at predetermined increments
of angular deflection. When the maximum desired deflection is reached, the bending moment is removed and the permanent set
angle resulting from the bend is recorded. All testing is performed under conditions of plane strain (that is, ratio of specimen
width/thickness >10). The bending moment and deflection data obtained are normalized with regard to specimen geometry. These
normalized terms are then plotted to produce a stress-strain curve for cantilever bending that is similar to a stress-strain curve for
tension or compression. The modulus of elasticity in bending and the offset yield strength in bending are determined from the
bending stress-strain curve using a procedure similar to that used for tensile stress-strain curves.
7. Significance and Use
7.1 This test method may be used for obtaining values Values of offset yield strength in bending and modulus of elasticity in
bending. These values bending are useful to spring designers to determine spring constants and permissible maximum deflection
of flat springs. It should be recognized that the The offset yield strength in bending as determined by this test method is not
necessarily equal to either the yield strength in tension, the cyclic yield strength in bending, bending yield strength, or to bending
proof strengths determined by other methods.
7.2 The test method can also serve the following purposes:
7.2.1 For research and development to study the effects of metallurgical variables, such as composition, heat treatment, fabrication
operations, and alloy development.
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7.2.2 For information or specification purposes, to provide a manufacturing quality control where suitable correlations have been
established with service behavior.
7.3 Due to necessary approximations in this test method regarding the specimen’s deflection, D, and span, span length, L, it is
recommended that a deflection angle of 30° not be exceeded. the maximum deflection angle is 30°. These approximations are
explained in Appendix X1.
7.4 Rate of loading is controlled only to the extent that the rate of angular change of the rotating jaw is fixed at 5858°/min to
66°/min. Actual rate of stressing will depend on the specimen width and thickness and the weight of the pendulum.
(Test Method A)
FIG. 1 Cantilever BendBeam Test Apparatus
8. Apparatus
8.1 The cantilever bendbeam test apparatus shown in Fig. 1 consists of the following components:
8.1.1 Specimen Holder, A vise, V, to which an angular deflection indicator, I , is attached. The specimen holder is rotatedrotates
about point O.
8.1.2 Pendulum Weighing System, composed of a set of detachable weights, an angular deflection scale scale, A, with a moment
pointer indicator, I , a loadingbending pin that transmits the bending force of the pendulum weighing system to the free end of
the cantilevertest specimen, and a weight to counter-balance the loadingbending pin. The pendulum weighing system pivots about
point O. For a pendulum weighing system (Fig. 2) having no internal moments, the total bending moment, M, is:
M 5 w dsinθ (1)
where:
M = bending moment at angle θ, lbf·in (N·m),
w = total load applied by pendulum system, lbf (N),
w = total force applied by pendulum weighing system, lbf (N),
d = length of the pendulum arm, in (m), and
θ = angle through which the pendulum weighing system rotates, rad.
8.1.3 Angular Deflection Scale, A, is graduated in degrees of arc and indicates the angle through which the rotating vise has been
turned relative to the pendulum weighing system. This is the difference between the angle through which the vise has been turned
and the angle through which the load pendulum weighing system has been deflected, and is designated as angle φ. The
loadingbending pin has a diameter of 0.25 in. (6.35 mm), and the distance between the clamping point (that is, center of rotation
The Olsen Stiffness Tester meets the requirements of this test method.
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of the pendulum weighing system) and the center of the loadingbending pin is 2.0 in. (50.8 mm). The reason for specifying the
pin diameter and pin location location of the bending pin is explained in Appendix X1.
8.1.4 Moment Scale—This stationary moment scale measures the applied moment as a function of the pendulum’s pendulum
weighing system’s rotation θ. A full scale reading of 100 corresponds to the pendulum’s pendulum weighing system’s maximum
bending moment, M . This system shall be calibrated such that the moment scale reading, f, is:
m
f 5 100 w dsinθ/M (2)
m
(Test Method A)
FIG. 2 Schematic of Pendulum Weighing System
9. Test Specimens
9.1 Rectangular test specimens shall be used. Specimen orientation relative to the rolling direction mustshall be identified.
Specimen Specimens with curvature due to coil set is permitted may be used if the ratio of the radius of curvature to thickness
exceeds 500. However, the specimen cannot shall not be twisted or wavy. No attempt shall be made to flatten or straighten
specimens prior to testing. Care shall be exercised not to alter the microstructure during specimen preparation. All burrs shall be
removed before testing. Testing machine capacity will determine the maximum allowable specimen size.
NOTE 1—Testing machine capacity will determine the maximum allowable specimen size.
10.2 The recommended minimum specimen thickness is 0.015 in. (0.38 mm). The thickness shall be measured at the four corners
and the center of the specimen. Specimens having thickness variations in excess of 2 % of the average (of these five measured
thicknesses) shall not be tested. The instrument used to measure the thickness shall have a precision within 2 % of the average
thickness.
9.2 InThe Eq 3 inminimum specimen 11.1 it is shown that the value of the modulus of elasticity in bending varies as the third
power of thickness. Hence, thickness is by far the most critical measurement in the determination of the modulus.thickness should
be 0.015 in. (0.38 mm). The thickness shall be measured at the four corners and the center of the specimen. Specimens having
thickness variations in excess of 2 % of the average (of these five measured thicknesses) shall not be tested. The instrument used
to measure the thickness shall have a precision within 2 % of the average thickness.
NOTE 2—Eq 3 in 10.1 shows that the value of the modulus of elasticity in bending varies as the third power of thickness. Hence, thickness is by far the
most critical measurement in the determination of the modulus. For example, an error in the thickness measurement of 60.0001 in. (0.0025 mm)
(60.0025 mm) for a specimen having the minimum recommended thickness of 0.015 in. (0.28(0.38 mm), the measurement is reproducible to within
0.67 % and the error in modulus of elasticity in bending attributable to the reproducibility of the thickness measurement is 2 %. Further, if the thickness
actually varies by 2 % over the gagegauge section or by 0.0003 in. (0.0075 mm), the error in modulus of elasticity in bending attributable to actual
thickness variation is 6 %, and the total error attributable to both measurement and actual variation is 8 %. Additional sources of uncertainty are the
precisions of determining the span length, the specimen width, and the beam deflection.
9.3 The ratio of the specimen span length to thickness shall be greater than 15; consequently, since the span length is 2.0 in. (50.8
mm), the specimen thickness cannot exceed 0.13 in. (3.30 mm).
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9.4 The width to thickness ratio shall be greater than 10. The width shall be measured at both ends and the center of the specimen.
Specimens having width variations greater than The maximum variation in width shall be less than or equal to 0.5 % of the average
width are not acceptable. width. The minimum specimen width shall be 0.5 in. (12.7 mm). The specimen width shall not extend
beyond the vise or the loadingbending pin.
10. Procedure
10.1 Place the machine on a level surface. Set the bending span length to 2.0 in. (50.8 mm) and adjust the moment indicator to
zero. For the best precision the maximum bending moment, M , should be chosen so that the moment scale reading is between
m
5 and 10 for an angular deflection of 3°. If this value is not known, it can be estimated estimated it as follows:
M 5 25 E bh φ/fL (3)
m b
φ
M 5 25 E bh (3)
m b
fL
where:
M = pendulum’s maximum bending moment, in·lbf (N· m),
m
E = modulus of elasticity in bending (can be approximated by Young’s modulus) lbf/in. (Pa),
b
b = specimen width, in. (m),
h = specimen thickness, in. (m),
φ = angular deflection, rad (0.052 rad (3°) specified here),
f = moment scale reading (select 7.5 in this case), and
L = span, 2 in. (50.8 mm).
L = span length, 2 in. (50.8 mm).
10.2 Clamp the specimen firmly in the vise with its long edges approximately parallel to the face of the dial plate.
10.3 Manually rotate the vise to bring the specimen against the loadingbending pin. When contact is made, set the angular
deflection indicator shall be set to indicate zero angle.
10.4 Hold down the motor engaging lever and record the moment scale readings at increments of 2° angular deflection (φ) until
the desired deflection, not exceeding 30°, is reached. The specimen then shall be unloaded. The unload the specimen. Read the
permanent set angle resulting from the bend shall be read on the angular deflection scale with the specimen contacting the
loadingbending pin at zero load.force.
10.5 A Test a minimum of six specimens shall be tested from each sample. For specimens having an initial residual curvature, test
half of the specimens shall be tested with the concave surface facing upwards and half with the convex surface facing upwards.
All specimens shall be deflected Deflect all specimens to the same maximum angle. The allowable maximum deflection angle is
deflection angle, which shall be less than or equal to 30°.
10.6 Replication required for evaluating material variability within either the same sample or among several suppliers shall be
covered in product specifications or upon agreement between supplier and user.
11. Calculation
11.1 The Normalize the bending moment-deflection data are normalized with regard to specimen geometry and plottedplot on
coordinate paper with the bending stress at the outer fiber having (3M f/50bh ) as the ordinate and the bending strain [(3/2) (φ
m
h/L)] as the abscissa (see Appendix X1). These symbols are defined in 11.110.1. The resulting bending stress-strain curve is similar
to a tension or compression stress-strain curve.
11.2 The Determine the value of the modulus of elasticity in bending, E , shall be determined by from the slope of a straight line
b
extending from the maximum deflection datum point (max) to the permanent set point (p.s.), that is:
E 5 M f/25bh / φh/L max2 φh/L p.s. (4)
~ ! @~ ! ~ ! #
b m
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M f
m
S D
25bh
E 5 (4)
b
φh/L max2 φh/L p.s.
~ ! ~ !
11.3 The first step in constructing the bending stress-strain curve is to draw a straight line having slope E such that it passes
b
through the origin. The actual data points for elastic loading may be slightly displaced from this line. The Construct the non-linear
portion of the bending stress-strain curve is constructed by drawing a curve through the remaining data points and connecting it
with the modulus of elasticity in bending line.
11.4 Offset Calculate offset yield strengths in bending can be obtained from the bending stress-strain curve using a procedure
analogous to that used for tensile or compressive stress-strain curves. The offset yield strengths in bending for strains of 0.01,
0.05,0.01 %, 0.05 %, and 0.10 % should be determined, provided this does not require that the maximum allowable deflection
angle of 30° be exceeded.
NOTE 3—These values of offset yield strengths in bending are not necessarily equal to either the yield strengths in tension, the cyclic bending yield
strength, or to bending proof strengths determined by other methods.
12. Report
12.1 The following shall be included in the report.
12.1.1 Complete description of the material tested, including alloy, temper, and manufacturer’s identification number,
12.1.2 Specimen dimensions and orientation relative to the rolling direction,
12.1.3 Test temperature, and
12.1.4 The modulus of elasticity in bending and an estimate of the precision of the value reported.
12.1.5 Offset yield strengths in bending, for strains of 0.01, 0.05,0.01 %, 0.05 %, and 0.10 % within the limitation of a maximum
deflection angle of 30°, plus an estimate of the precision of the values reported.
12.1.6 Estimate of the precision of the values reported.
13. Precision and Bias
13.1 Precision:
13.1.1 The precision of the values of the modulus of elasticity in bending and the offset yield strength in bending will depend on
the precision of each of the values used in the calculations, as well as the mean and standard deviation of the values determined
for each of the replicate tests. It is suggested that the report The report shall include an estimate of the precision of the values
reported.
13.1.2 The following parameters will affect the results and can be quantified as quantified: precision of the applied weights,forces,
precision of the span length measurement, deviation of width measurements from the average value, deviation of thickness
measurements from the average value, and precision of the deflection measurements.
13.2 Bias—A statement of bias requires a reference standard or a true property value based on many measurements of the property
of the same material. Such standards or true values are presently not available for bending properties of metallic flat spring
materials. Therefore, the bias of the test method is unknown.
TEST METHOD B: THREE-POINT BEAM TEST
TEST METHOD C: FOUR-POINT BEAM TEST
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14. Scope
14.1 These test methods cover the determination of the modulus of elasticity in bending and the bending proof strength of flat
metallic strips or sheets for spring applications. The test methods consist of deflection tests of a simple beam configuration
subjected to either three- or four-point symmetrical loading. The thickness range covered is 0.010 in. to 0.050 in. (0.25(0.25 mm
to 1.3 mm). 1.3 mm).
NOTE 3—Thickness ranges outside of those specified may be agreed upon between suppliers and users.
14.2 Thickness ranges outside of those specified may be agreed upon between suppliers and users.
15. Summary of Test Methods
...