ASTM E855-08(2013)

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

SIGNIFICANCE AND USE
4.1 Measurements of bending strength 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 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 and bending strength require due regard for numerous variables that may affect their determination. These include (1) 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- perature, temperature variations, condition of the test equipment and adherence to the recommended test procedure.
SCOPE
1.1 This standard describes three test methods2 for determining the modulus of elasticity in bending and the bending strength of metallic strips or sheets intended for the use in flat springs:  
1.1.1 Test Method A—a cantilever beam,  
1.1.2 Test Method B—a three-point loaded beam (that is, a beam resting on two supports and centrally loaded), and  
1.1.3 Test Method C—a four-point loaded beam (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 and health practices and determine the applicability of regulatory limitations prior to use.

General Information

• Status: Historical
• Publication Date: 31-Mar-2013
• ICS: 21.160 - Springs
• Technical Committee: E28 - Mechanical Testing
• Drafting Committee: E28.02 - Ductility and Formability

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E855 − 08 (Reapproved 2013)
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 E177 Practice for Use of the Terms Precision and Bias in
2 ASTM Test Methods
1.1 This standard describes three test methods for deter-
E691 Practice for Conducting an Interlaboratory Study to
mining the modulus of elasticity in bending and the bending
Determine the Precision of a Test Method
strength of metallic strips or sheets intended for the use in flat
springs:
3. Terminology
1.1.1 Test Method A—a cantilever beam,
1.1.2 Test Method B—a three-point loaded beam (that is, a 3.1 Definitions of Terms Specific to This Standard:
beam resting on two supports and centrally loaded), and
3.1.1 In addition to the terms in Terminology E6, the
1.1.3 Test Method C—a four-point loaded beam (that is, a
following descriptions of terms apply in connection with these
beam resting on two supports and loaded at two points equally
test methods for determining bend properties:
spaced from each support).
3.1.2 bend properties—those properties of a material that
1.2 The values stated in inch-pound units are to be regarded are associated with elastic and inelastic behavior when a
bending force is applied, or that involve the relationship
as standard. The values given in parentheses are mathematical
conversions to SI units that are provided for information only between bending stress and strain.
and are not considered standard. −2
3.1.3 bending stress at outer fiber (FL )—the nominal
1.3 This standard does not purport to address all of the
stressintheouterfibersofabeamresultingfromapplicationof
safety concerns, if any, associated with its use. It is the
a bending load.
responsibility of the user of this standard to establish appro-
−2
3.1.4 elastic limit in bending (FL )—the greatest bending
priate safety and health practices and determine the applica-
stress that a material is capable of sustaining without perma-
bility of regulatory limitations prior to use.
nent strain remaining after complete release of the bending
moment.
2. Referenced Documents
−2
3.1.5 modulus of elasticity in bending (FL )—the ratio of
2.1 The following documents of the issue in effect on date
bending stress to corresponding strain below the elastic limit in
of use of these test methods form a part of these test methods
bending.
to the extent referenced herein:
3.1.6 span length (L)—the distance between supports.
2.2 ASTM Standards:
E4 Practices for Force Verification of Testing Machines
3.1.7 uniform bending moment (FL)—a bending moment
E6 Terminology Relating to Methods of Mechanical Testing
that produces a uniform strain at the outer fibers throughout the
E111 Test Method for Young’s Modulus, Tangent Modulus,
gage length of the specimen.
and Chord Modulus
−2
3.1.8 bending proof strength (FL )—the nominal stress in
the outer fibers of a beam that results in a specific permanent
1 strain in the outer fibers upon unloading.
These test methods are under the jurisdiction of ASTM Committee E28 on
Mechanical Testing and are the direct responsibility of Subcommittee E28.02 on
−2
3.1.9 cyclic bending yield strength (FL )—the maximum
Ductility and Formability.
nominalstressinuniformcyclicbendingresultingfromagiven
Current edition approved April 1, 2013. Published April 2013. Originally
approved in 1981. Last previous edition approved in 2008 as E855 – 08. DOI:
plastic deformation in the outer fibers of a beam.
10.1520/E0855-08R13.
−2
3.1.10 offset yield strength in bending (FL )—thenominal
Method D, which appeared in the last previous edition, was dropped because of
the unavailability of commercial testing equipment.
stress in the outer fibers of a beam in bending at which a
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
specified limiting deviation from proportionality of bending
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
stress to bending strain is exhibited.The deviation is expressed
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. in terms of strain.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E855 − 08 (2013)
4. Significance and Use 8. Significance and Use
8.1 This test method may be used for obtaining values of
4.1 Measurements of bending strength and modulus of
offset yield strength in bending and modulus of elasticity in
elasticity in bending should be made for materials whose
bending. These values are useful to spring designers to
principal stressing mode is bending. For many materials, the
determine spring constants and permissible maximum deflec-
tensile and compressive moduli are somewhat different. Since
tion of flat springs. It should be recognized that the offset yield
the bending modulus is a combination of the tensile and
strength in bending as determined by this test method is not
compressive moduli, it is often different from each of them.
necessarily equal to either the yield strength in tension, the
4.2 Precise measurements of the modulus of elasticity in
cyclic yield strength in bending, or to bending proof strengths
bending and bending strength require due regard for numerous
determined by other methods.
variables that may affect their determination. These include (1)
8.2 The test method can also serve the following purposes:
characteristics such as specimen orientation with respect to the
8.2.1 For research and development to study the effects of
rolling direction, grain size, residual stresses, previous strain
metallurgical variables, such as composition, heat treatment,
history, dimensions and specimen preparation, orientation of
fabrication operations and alloy development.
deformed grains relative to the direction of the normal stress;
8.2.2 For information or specification purposes, to provide a
and (2) test conditions, such as tem-
manufacturing quality control where suitable correlations have
perature, temperature variations, condition of the test equip-
been established with service behavior.
ment and adherence to the recommended test procedure.
8.3 Due to necessary approximations in this test method
5. Fundamental Assumptions regarding the specimen’s deflection, D, and span, L,itis
recommended that a deflection angle of 30° not be exceeded.
5.1 The test section of the specimen is subjected to uniform
These approximations are explained in Appendix X1.
bending moment (applies to Test Method C only).
8.4 Rate of loading is controlled only to the extent that the
5.2 The neutral axis is located at the centerline of the
rate of angular change of the rotating jaw is fixed at 58 to
thickness of the test specimen.
66°/min. Actual rate of stressing will depend on the specimen
width and thickness and the weight of the pendulum.
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
6. Scope
6.1 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 angle of deflection of a
cantilever beam.The thickness range covered is 0.015 to 0.130
in. (0.38 to 3.30 mm). This test method is not applicable for
nonlinear elastic materials.
(Test Method A)
7. Summary of Test Method
FIG. 1 Cantilever Bend Test Apparatus
7.1 The test specimen is loaded as a simple cantilever beam,
and the bending moment is measured at predetermined incre-
9. Apparatus
ments of angular deflection. When the maximum desired
9.1 The cantilever bend 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
9.1.1 Specimen Holder, A vise, V, to which an angular
testing is performed under conditions of plane strain (that is,
deflection indicator, I , is attached. The specimen holder is
ratio of specimen width/thickness >10). The bending moment
rotated about point O.
and deflection data obtained are normalized with regard to
9.1.2 Pendulum Weighing System, composed of a set of
specimengeometry.Thesenormalizedtermsarethenplottedto
detachable weights, an angular deflection scale with a moment
produce a stress-strain curve for cantilever bending that is
pointer indicator, I , a loading pin that transmits the bending
similar to a stress-strain curve for tension or compression. The
force of the pendulum system to the free end of the cantilever
modulus of elasticity in bending and the offset yield strength in
specimen, and a weight to counter-balance the loading pin.The
bending are determined from the bending stress-strain curve
using a procedure similar to that used for tensile stress-strain
curves. The Olsen Stiffness Tester meets the requirements of this test method.
E855 − 08 (2013)
pendulum weighing system pivots about point O. For a preparation. All burrs shall be removed before testing. Testing
pendulumsystem(Fig.2)havingnointernalmoments,thetotal machine capacity will determine the maximum allowable
bending moment, M, is: specimen size.
M 5wdsinθ (1)
10.2 The recommended minimum specimen thickness is
0.015 in. (0.38 mm). The thickness shall be measured at the
where:
four corners and the center of the specimen. Specimens having
M = bending moment at angle θ, lbf·in (N·m),
thickness variations in excess of 2 % of the average (of these
w = total load applied by pendulum system, lbf (N),
five measured thicknesses) shall not be tested. The instrument
d = length of the pendulum arm, in (m), and
usedtomeasurethethicknessshallhaveaprecisionwithin2 %
θ = angle through which the pendulum system rotates, rad.
of the average thickness.
10.3 In Eq 3 in 11.1 it is shown that the value of the
9.1.3 Angular Deflection Scale, A,isgraduatedindegreesof
modulus of elasticity in bending varies as the third power of
arc and indicates the angle through which the rotating vise has
thickness. Hence, thickness is by far the most critical measure-
been turned relative to the pendulum system. This is the
ment in the determination of the modulus.
difference between the angle through which the vise has been
turned and the angle through which the load pendulum has
NOTE 1—For example, an error in the thickness measurement of
been deflected, and is designated as angle φ. The loading pin
60.0001 in. (0.0025 mm) for a specimen having the minimum recom-
mended thickness of 0.015 in. (0.28 mm), the measurement is reproduc-
has a diameter of 0.25 in. (6.35 mm), and the distance between
ible to within 0.67 % and the error in modulus attributable to the
the clamping point (that is, center of rotation of the pendulum
reproducibility of the thickness measurement is 2 %. Further, if the
system) and the center of the loading pin is 2.0 in. (50.8 mm).
thickness actually varies by 2 % over the gage section or by 0.0003 in.
The reason for specifying the pin diameter and pin location is
(0.0075 mm), the error in modulus attributable to actual thickness
explained in Appendix X1.
variation is 6 %, and the total error attributable to both measurement and
actual variation is 8 %. Additional sources of uncertainty are the preci-
9.1.4 Moment Scale—This stationary scale measures the
sions of determining the span length, the specimen width, and the beam
applied moment as a function of the pendulum’s rotation θ.A
deflection.
full scale reading of 100 corresponds to the pendulum’s
10.4 The ratio of the specimen span to thickness shall be
maximum bending moment, M . This system shall be cali-
m
greater than 15; consequently, since the span is 2.0 in. (50.8
brated such that the moment scale reading, f, is:
mm), the specimen thickness cannot exceed 0.13 in. (3.30
f 5 100wdsinθ/M (2)
m
mm).
10.5 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
0.5 % of the average width are not acceptable. The minimum
specimenwidthshallbe0.5in.(12.7mm).Thespecimenwidth
shall not extend beyond the vise or the loading pin.
11. Procedure
11.1 Place the machine on a level surface. Set the bending
span 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
m
between 5 and 10 for an angular deflection of 3°. If this value
is not known, it can be estimated as follows:
M 5 25 E bh φ/fL (3)
m b
(Test Method A)
where:
M = pendulum’s maximum bending moment, in·lbf (N·
m
FIG. 2 Schematic of Pendulum System
m),
E = modulus of elasticity in bending (can be approxi-
b
mated by Young’s modulus) lbf/in. (Pa),
10. Test Specimens
b = specimen width, in. (m),
h = specimen thickness, in. (m),
10.1 Rectangular test specimens shall be used. Specimen
φ = angular deflection, rad (0.052 rad (3°) specified here),
orientation relative to the rolling direction must be identified.
Specimen curvature due to coil set is permitted if the ratio of
f = moment scale reading (select 7.5 in this case), and
the radius of curvature to thickness exceeds 500. However, the
L = span, 2 in. (50.8 mm).
specimen cannot be twisted or wavy. No attempt shall be made
to flatten or straighten specimens prior to testing. Care shall be 11.2 Clamp the specimen firmly in the vise with its long
exercised not to alter the microstructure during specimen edges approximately parallel to the face of the dial plate.
E855 − 08 (2013)
11.3 Manually rotate the vise to bring the specimen against 13.1.2 Specimen dimensions and orientation relative to the
the loading pin. When contact is made, the angular deflection rolling direction,
indicator shall be set to indicate zero angle. 13.1.3 Test temperature, and
13.1.4 The modulus of elasticity in bending and an estimate
11.4 Hold down the motor engaging lever and record the
of the precision of the value reported.
moment scale readings at increments of 2° angular deflection
13.1.5 Offset yield strengths in bending, for strains of 0.01,
(φ) until the desired
...