ASTM E855-90(1995)
(Test Method)Standard Test Methods for Bend Testing of Metallic Flat Materials for Spring Applications Involving Static Loading
Standard Test Methods for Bend Testing of Metallic Flat Materials for Spring Applications Involving Static Loading
SCOPE
1.1 This standard describes three test methods 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 Ca four-point loaded beam (that is, a beam resting on two supports and loaded at two points equally spaced from each support).
1.2 Values stated in inch-pound units are to be regarded as the standard. SI units are provided for information only.
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.
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Designation: E 855 – 90 (Reapproved 1995) An American National Standard
AMERICAN SOCIETY FOR TESTING AND MATERIALS
100 Barr Harbor Dr., West Conshohocken, PA 19428
Reprinted from the Annual Book of ASTM Standards. Copyright ASTM
Standard Test Methods for
Bend Testing of Metallic Flat Materials for Spring
Applications Involving Static Loading
This standard is issued under the fixed designation E 855; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope are associated with elastic and inelastic behavior when a
bending force is applied, or that involve the relationship
1.1 This standard describes three test methods for deter-
between bending stress and strain.
mining the modulus of elasticity in bending and the bending
−2
3.1.3 bending stress at outer fiber (FL )—the nominal
strength of metallic strips or sheets intended for the use in flat
stress in the outer fibers of a beam resulting from application of
springs:
a bending load.
1.1.1 Test Method A—a cantilever beam,
−2
3.1.4 elastic limit in bending (FL )—the greatest bending
1.1.2 Test Method B—a three-point loaded beam (that is, a
stress that a material is capable of sustaining without perma-
beam resting on two supports and centrally loaded), and
nent strain remaining after complete release of the bending
1.1.3 Test Method C—a four-point loaded beam (that is, a
moment.
beam resting on two supports and loaded at two points equally
−2
3.1.5 modulus of elasticity in bending (FL )—the ratio of
spaced from each support).
bending stress to corresponding strain below the elastic limit in
1.2 Values stated in inch-pound units are to be regarded as
bending.
the standard. SI units are provided for information only.
3.1.6 span length (L)—the distance between supports.
1.3 This standard does not purport to address all of the
3.1.7 uniform bending moment (FL)—a bending moment
safety concerns, if any, associated with its use. It is the
that produces a uniform strain at the outer fibers throughout the
responsibility of the user of this standard to establish appro-
gage length of the specimen.
priate safety and health practices and determine the applica-
−2
3.1.8 bending proof strength (FL )—the nominal stress in
bility of regulatory limitations prior to use.
the outer fibers of a beam that results in a specific permanent
2. Referenced Documents strain in the outer fibers upon unloading.
−2
3.1.9 cyclic bending yield strength (FL )—the maximum
2.1 The following documents of the issue in effect on date
nominal stress in uniform cyclic bending resulting from a given
of use of these test methods form a part of these test methods
plastic deformation in the outer fibers of a beam.
to the extent referenced herein:
−2
3.1.10 offset yield strength in bending (FL )—the nominal
2.2 ASTM Standards:
stress in the outer fibers of a beam in bending at which a
E 4 Practices for Force Verification of Testing Machines
specified limiting deviation from proportionality of bending
E 6 Terminology Relating to Methods of Mechanical Test-
stress to bending strain is exhibited. The deviation is expressed
ing
in terms of strain.
E 111 Test Method for Young’s Modulus, Tangent Modulus,
and Chord Modulus
4. Significance and Use
3. Terminology
4.1 Measurements of bending strength and modulus of
elasticity in bending should be made for materials whose
3.1 Definitions of Terms Specific to This Standard:
principal stressing mode is bending. For many materials, the
3.1.1 In addition to the terms in Terminology E 6, the
tensile and compressive moduli are somewhat different. Since
following descriptions of terms apply in connection with these
the bending modulus is a combination of the tensile and
test methods for determining bend properties:
compressive moduli, it is often different from each of them.
3.1.2 bend properties—those properties of a material that
4.2 Precise measurements of the modulus of elasticity in
bending and bending strength require due regard for numerous
These test methods are under the jurisdiction of ASTM Committee E-28 on
variables that may affect their determination. These include (1)
Mechanical Testing and are the direct responsibility of Subcommittee E28.02 on
characteristics such as specimen orientation with respect to the
Ductility and Flexure Testing.
Current edition approved March 30, 1990. Published May 1990. Originally
rolling direction, grain size, residual stresses, previous strain
published as E 855 – 81. Last previous edition E 855 – 84.
history, dimensions and specimen preparation, orientation of
Method D, which appeared in the last previous edition, was dropped because of
deformed grains relative to the direction of the normal stress;
the unavailability of commercial testing equipment.
and (2) test conditions, such as tem-
Annual Book of ASTM Standards, Vol 03.01.
E 855
perature, temperature variations, condition of the test equip- recommended that a deflection angle of 30° not be exceeded.
ment and adherence to the recommended test procedure. These approximations are explained in Appendix X1.
8.4 Rate of loading is controlled only to the extent that the
5. Fundamental Assumptions
rate of angular change of the rotating jaw is fixed at 58 to
5.1 The test section of the specimen is subjected to uniform
66°/min. Actual rate of stressing will depend on the specimen
bending moment (applies to Test Method C only).
width and thickness and the weight of the pendulum.
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
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
(Test Method A)
nonlinear elastic materials.
FIG. 1 Cantilever Bend Test Apparatus
7. Summary of Test Method
7.1 The test specimen is loaded as a simple cantilever beam,
9. Apparatus
and the bending moment is measured at predetermined incre-
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
specimen geometry. These normalized terms are then plotted to
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
pendulum weighing system pivots about point O. For a
using a procedure similar to that used for tensile stress-strain
pendulum system (Fig. 2) having no internal moments, the total
curves.
bending moment, M, is:
M 5 wd sinu (1)
8. Significance and Use
8.1 This test method may be used for obtaining values of
where:
offset yield strength in bending and modulus of elasticity in
M 5 bending moment at angle u, lbf·in (N·m),
bending. These values are useful to spring designers to
w 5 total load applied by pendulum system, lbf (N),
determine spring constants and permissible maximum deflec-
d 5 length of the pendulum arm, in (m), and
tion of flat springs. It should be recognized that the offset yield
u5 angle through which the pendulum system rotates, rad.
strength in bending as determined by this test method is not
necessarily equal to either the yield strength in tension, the
9.1.3 Angular Deflection Scale, A, is graduated in degrees of
cyclic yield strength in bending, or to bending proof strengths
arc and indicates the angle through which the rotating vise has
determined by other methods.
been turned relative to the pendulum system. This is the
8.2 The test method can also serve the following purposes:
difference between the angle through which the vise has been
8.2.1 For research and development to study the effects of
turned and the angle through which the load pendulum has
metallurgical variables, such as composition, heat treatment,
been deflected, and is designated as angle f. The loading pin
fabrication operations and alloy development.
has a diameter of 0.25 in. (6.35 mm), and the distance between
8.2.2 For information or specification purposes, to provide a
the clamping point (that is, center of rotation of the pendulum
manufacturing quality control where suitable correlations have
system) and the center of the loading pin is 2.0 in. (50.8 mm).
been established with service behavior.
8.3 Due to necessary approximations in this test method
regarding the specimen’s deflection, D, and span, L,itis The Olsen Stiffness Tester meets the requirements of this test method.
E 855
sions of determining the span length, the specimen width, and the beam
The reason for specifying the pin diameter and pin location is
deflection.
explained in Appendix X1.
9.1.4 Moment Scale—This stationary scale measures the
10.4 The ratio of the specimen span to thickness shall be
applied moment as a function of the pendulum’s rotation u.A
greater than 15; consequently, since the span is 2.0 in. (50.8
full scale reading of 100 corresponds to the pendulum’s
mm), the specimen thickness cannot exceed 0.13 in. (3.30
maximum bending moment, M . This system shall be cali-
mm).
m
brated such that the moment scale reading, f, is:
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
f 5 100 wd sinu/M (2)
m
specimen. Specimens having width variations greater than
0.5 % of the average width are not acceptable. The minimum
specimen width shall be 0.5 in. (12.7 mm). The specimen width
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 f/fL (3)
m b
where:
M 5 pendulum’s maximum bending moment, in·lbf (N·
m
(Test Method A)
m),
E 5 modulus of elasticity in bending (can be approxi-
b
FIG. 2 Schematic of Pendulum System 2
mated by Young’s modulus) lbf/in. (Pa),
b 5 specimen width, in. (m),
h 5 specimen thickness, in. (m),
10. Test Specimens
f5 angular deflection, rad (0.052 rad (3°) specified
10.1 Rectangular test specimens shall be used. Specimen
here),
orientation relative to the rolling direction must be identified.
f 5 moment scale reading (select 7.5 in this case), and
Specimen curvature due to coil set is permitted if the ratio of
L 5 span, 2 in. (50.8 mm).
the radius of curvature to thickness exceeds 500. However, the
11.2 Clamp the specimen firmly in the vise with its long
specimen cannot be twisted or wavy. No attempt shall be made
edges approximately parallel to the face of the dial plate.
to flatten or straighten specimens prior to testing. Care shall be
11.3 Manually rotate the vise to bring the specimen against
exercised not to alter the microstructure during specimen
the loading pin. When contact is made, the angular deflection
preparation. All burrs shall be removed before testing. Testing
indicator shall be set to indicate zero angle.
machine capacity will determine the maximum allowable
11.4 Hold down the motor engaging lever and record the
specimen size.
moment scale readings at increments of 2° angular deflection
10.2 The recommended minimum specimen thickness is
(f) until the desired deflection, not exceeding 30°, is reached.
0.015 in. (0.38 mm). The thickness shall be measured at the
The specimen then shall be unloaded. The permanent set angle
four corners and the center of the specimen. Specimens having
resulting from the bend shall be read on the angular deflection
thickness variations in excess of 2 % of the average (of these
scale with the specimen contacting the loading pin at zero load.
five measured thicknesses) shall not be tested. The instrument
11.5 A minimum of six specimens shall be tested from each
used to measure the thickness shall have a precision within 2 %
sample. For specimens having an initial residual curvature, half
of the average thickness.
of the specimens shall be tested with the concave surface
10.3 In Eq 3 in 11.1 it is shown that the value of the
facing upwards and half with the convex surface facing
modulus of elasticity in bending varies as the third power of
upwards. All specimens shall be deflected to the same maxi-
thickness. Hence, thickness is by far the most critical measure-
mum angle. The allowable maximum deflection angle is 30°.
ment in the determination of the modulus.
11.6 Replication required for evaluating material variability
within either the same sample or among several suppliers shall
NOTE 1—For example, an error in the thickness measurement of
60.0001 in. (0.0025 mm) for a specimen having the minimum recom-
be covered in product specifications or upon agreement be-
mended thickness of 0.015 in. (0.28 mm), the measurement is reproduc-
tween supplier and user.
ible to within 0.67 % and the error in modulus attributable to the
reproducibility of the thickness measurement is 2 %. Further, if the
12. Calculation
thickness actually varies by 2 % over the gage section or by 0.0003 in.
12.1 The bending moment-deflection data are normalized
(0.0075 mm), the error in modulus attributable to actual thickness
with regard
...
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