D790 - 10 PDF
D790 - 10 PDF
D790 - 10 PDF
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1. Scope*
1.1 These test methods cover the determination of flexural
properties of unreinforced and reinforced plastics, including
high-modulus composites and electrical insulating materials in
the form of rectangular bars molded directly or cut from sheets,
plates, or molded shapes. These test methods are generally
applicable to both rigid and semirigid materials. However,
flexural strength cannot be determined for those materials that
do not break or that do not fail in the outer surface of the test
specimen within the 5.0 % strain limit of these test methods.
These test methods utilize a three-point loading system applied
to a simply supported beam. A four-point loading system
method can be found in Test Method D6272.
1.1.1 Procedure A, designed principally for materials that
break at comparatively small deflections.
1.1.2 Procedure B, designed particularly for those materials
that undergo large deflections during testing.
1.1.3 Procedure A shall be used for measurement of flexural
properties, particularly flexural modulus, unless the material
specification states otherwise. Procedure B may be used for
measurement of flexural strength only. Tangent modulus data
obtained by Procedure A tends to exhibit lower standard
deviations than comparable data obtained by means of Procedure B.
1.2 Comparative tests may be run in accordance with either
procedure, provided that the procedure is found satisfactory for
the material being tested.
1.3 The values stated in SI units are to be regarded as the
standard. The values provided in parentheses are for information only.
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 appro-
1
These test methods are under the jurisdiction of ASTM Committee D20 on
Plastics and are the direct responsibility of Subcommittee D20.10 on Mechanical
Properties.
Current edition approved April 1, 2010. Published April 2010. Originally
approved in 1970. Last previous edition approved in 2007 as D790 07 1. DOI:
10.1520/D0790-10.
priate safety and health practices and determine the applicability of regulatory limitations prior to use.
NOTE 1These test methods are not technically equivalent to ISO 178.
2. Referenced Documents
2.1 ASTM Standards:2
D618 Practice for Conditioning Plastics for Testing
D638 Test Method for Tensile Properties of Plastics
D883 Terminology Relating to Plastics
D4000 Classification System for Specifying Plastic Materials
D4101 Specification for Polypropylene Injection and Extrusion Materials
D5947 Test Methods for Physical Dimensions of Solid
Plastics Specimens
D6272 Test Method for Flexural Properties of Unreinforced
and Reinforced Plastics and Electrical Insulating Materials
by Four-Point Bending
E4 Practices for Force Verification of Testing Machines
E691 Practice for Conducting an Interlaboratory Study to
Determine the Precision of a Test Method
2.2 ISO Standard:3
ISO 178 PlasticsDetermination of Flexural Properties
3. Terminology
3.1 DefinitionsDefinitions of terms applying to these test
methods appear in Terminology D883 and Annex A1 of Test
Method D638.
4. Summary of Test Method
4.1 A bar of rectangular cross section rests on two supports
and is loaded by means of a loading nose midway between the
supports. A support span-to-depth ratio of 16:1 shall be used
unless there is reason to suspect that a larger span-to-depth
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standards Document Summary page on
the ASTM website.
3
Available from American National Standards Institute (ANSI), 25 W. 43rd St.,
4th Floor, New York, NY 10036, http://www.ansi.org.
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D790 10
V RB
rC
RD
1.59
6.58
1.67
1.43
5.16
4.76
6.05
6.58
11.3
2.14
6.05
7.19
4.44
18.6
4.73
4.05
14.6
13.5
17.2
18.6
32.0
6.08
17.1
20.4
A
Vr = within-laboratory coefficient of variation for the indicated material. It is
obtained by first pooling the within-laboratory standard deviations of the test
results from all of the participating laboratories: Sr = [[(s1)2 + (s2)2 . . . + ( sn)2]/n]
1/2 then Vr = (Sr divided by the overall average for the material) 3 100.
B
Vr = between-laboratory reproducibility, expressed as the coefficient of variation: SR = {Sr2 + SL2}1/2 where SL is the standard deviation of laboratory means.
Then: VR = (S R divided by the overall average for the material) 3 100.
C
r = within-laboratory critical interval between two test results = 2.8 3 Vr.
D
R = between-laboratory critical interval between two test results = 2.8 3 VR.
such that the total elastic deformation of the system does not
exceed 1 % of the total deflection of the test specimen during
testing, or appropriate corrections shall be made. The load
indicating mechanism shall be essentially free from inertial lag
at the crosshead rate used. The accuracy of the testing machine
shall be verified in accordance with Practices E4.
6.2 Loading Noses and SupportsThe loading nose and
supports shall have cylindrical surfaces. The default radii of the
loading nose and supports shall be 5.0 6 0.1 mm (0.197 6
0.004 in.) unless otherwise specified in an ASTM material
specification or as agreed upon between the interested parties.
When the use of an ASTM material specification, or an agreed
upon modification, results in a change to the radii of the
loading nose and supports, the results shall be clearly identified
as being obtained from a modified version of this test method
and shall include the specification (when available) from which
the modification was specified, for example, Test Method D790
in accordance with Specification D4101.
6.2.1 Other Radii for Loading Noses and SupportsWhen
other than default loading noses and supports are used, in order
to avoid excessive indentation, or failure due to stress concentration directly under the loading nose, they must comply with
the following requirements: they shall have a minimum radius
of 3.2 mm (18 in.) for all specimens. For specimens 3.2 mm or
greater in depth, the radius of the supports may be up to 1.6
times the specimen depth. They shall be this large if significant
indentation or compressive failure occurs. The arc of the
loading nose in contact with the specimen shall be sufficiently
large to prevent contact of the specimen with the sides of the
nose. The maximum radius of the loading nose shall be no
more than four times the specimen depth.
6.3 Micrometers Suitable micrometers for measuring the
width and thickness of the test specimen to an incremental
discrimination of at least 0.025 mm (0.001 in.) should be used.
All width and thickness measurements of rigid and semirigid
plastics may be measured with a hand micrometer with ratchet.
A suitable instrument for measuring the thickness of nonrigid
test specimens shall have: a contact measuring pressure of
25 6 2.5 kPa (3.6 6 0.36 psi), a movable circular contact foot
6.35 6 0.025 mm (0.250 6 0.001 in.) in diameter and a lower
fixed anvil large enough to extend beyond the contact foot in
all directions and being parallel to the contact foot within 0.005
mm (0.002 in.) over the entire foot area. Flatness of foot and
anvil shall conform to the portion of the Calibration section of
Test Methods D5947.
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7. Test Specimens
7.1 The specimens may be cut from sheets, plates, or
molded shapes, or may be molded to the desired finished
dimensions. The actual dimensions used in Section 4.2, Calculation, shall be measured in accordance with Test Methods
D5947.
NOTE 2Any necessary polishing of specimens shall be done only in
the lengthwise direction of the specimen.
7.2 Sheet Materials (Except Laminated Thermosetting Materials and Certain Materials Used for Electrical Insulation,
Including Vulcanized Fiber and Glass Bonded Mica):
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7.2.1 Materials 1.6 mm (116 in.) or Greater in Thickness
For flatwise tests, the depth of the specimen shall be the
thickness of the material. For edgewise tests, the width of the
specimen shall be the thickness of the sheet, and the depth shall
not exceed the width (see Notes 3 and 4). For all tests, the
support span shall be 16 (tolerance 61) times the depth of the
beam. Specimen width shall not exceed one fourth of the
support span for specimens greater than 3.2 mm (18 in.) in
depth. Specimens 3.2 mm or less in depth shall be 12.7 mm (12
in.) in width. The specimen shall be long enough to allow for
overhanging on each end of at least 10 % of the support span,
but in no case less than 6.4 mm (14 in.) on each end. Overhang
shall be sufficient to prevent the specimen from slipping
through the supports.
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D790 10
10.1.2 Determine the support span to be used as described in
Section 7 and set the support span to within 1 % of the
determined value.
10.1.3 For flexural fixtures that have continuously adjustable spans, measure the span accurately to the nearest 0.1 mm
(0.004 in.) for spans less than 63 mm (2.5 in.) and to the nearest
0.3 mm (0.012 in.) for spans greater than or equal to 63 mm
(2.5 in.). Use the actual measured span for all calculations. For
flexural fixtures that have fixed machined span positions, verify
the span distance the same as for adjustable spans at each
machined position. This distance becomes the span for that
position and is used for calculations applicable to all subsequent tests conducted at that position. See Annex A2 for
information on the determination of and setting of the span.
10.1.4 Calculate the rate of crosshead motion as follows and
set the machine for the rate of crosshead motion as calculated
by Eq 1:
R 5 ZL 2/6d
(1)
where:
R = rate of crosshead motion, mm (in.)/min,
L = support span, mm (in.),
d = depth of beam, mm (in.), and
Z = rate of straining of the outer fiber, mm/mm/min (in./
in./min). Z shall be equal to 0.01.
In no case shall the actual crosshead rate differ from that
calculated using Eq 1, by more than 610 %.
10.1.5 Align the loading nose and supports so that the axes
of the cylindrical surfaces are parallel and the loading nose is
midway between the supports. The parallelism of the apparatus
may be checked by means of a plate with parallel grooves into
which the loading nose and supports will fit when properly
aligned (see A2.3). Center the specimen on the supports, with
the long axis of the specimen perpendicular to the loading nose
and supports.
10.1.6 Apply the load to the specimen at the specified
crosshead rate, and take simultaneous load-deflection data.
Measure deflection either by a gage under the specimen in
contact with it at the center of the support span, the gage being
mounted stationary relative to the specimen supports, or by
measurement of the motion of the loading nose relative to the
supports. Load-deflection curves may be plotted to determine
the flexural strength, chord or secant modulus or the tangent
modulus of elasticity, and the total work as measured by the
area under the load-deflection curve. Perform the necessary toe
compensation (see Annex A1) to correct for seating and
indentation of the specimen and deflections in the machine.
10.1.7 Terminate the test when the maximum strain in the
outer surface of the test specimen has reached 0.05 mm/mm
(in./in.) or at break if break occurs prior to reaching the
maximum strain (Notes 8 and 9). The deflection at which this
strain will occur may be calculated by letting r equal 0.05
mm/mm (in./in.) in Eq 2:
D 5 rL2/6d
where:
D = midspan deflection, mm (in.),
r = strain, mm/mm (in./in.),
(2)
10.2 Procedure B:
10.2.1 Use an untested specimen for each measurement.
10.2.2 Test conditions shall be identical to those described
in 10.1, except that the rate of straining of the outer surface of
the test specimen shall be 0.10 mm/mm (in./in.)/min.
10.2.3 If no break has occurred in the specimen by the time
the maximum strain in the outer surface of the test specimen
has reached 0.05 mm/mm (in./in.), discontinue the test (see
Note 9).
11. Retests
11.1 Values for properties at rupture shall not be calculated
for any specimen that breaks at some obvious, fortuitous flaw,
unless such flaws constitute a variable being studied. Retests
shall be made for any specimen on which values are not
calculated.
12. Calculation
12.1 Toe compensation shall be made in accordance with
Annex A1 unless it can be shown that the toe region of the
curve is not due to the take-up of slack, seating of the
specimen, or other artifact, but rather is an authentic material
response.
12.2 Flexural Stress (sf)When a homogeneous elastic
material is tested in flexure as a simple beam supported at two
points and loaded at the midpoint, the maximum stress in the
outer surface of the test specimen occurs at the midpoint. This
stress may be calculated for any point on the load-deflection
curve by means of the following equation (see Notes 10-12):
sf 5 3PL/2bd2
where:
s = stress in the outer fibers at midpoint, MPa (psi),
P = load at a given point on the load-deflection curve, N
(lbf),
L = support span, mm (in.),
b = width of beam tested, mm (in.), and
d = depth of beam tested, mm (in.).
NOTE 10Eq 3 applies strictly to materials for which stress is linearly
proportional to strain up to the point of rupture and for which the strains
are small. Since this is not always the case, a slight error will be
introduced if Eq 3 is used to calculate stress for materials that are not true
Hookean materials. The equation is valid for obtaining comparison data
and for specification purposes, but only up to a maximum fiber strain of
5 % in the outer surface of the test specimen for specimens tested by the
procedures described herein.
NOTE 11When testing highly orthotropic laminates, the maximum
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(3)
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stress may not always occur in the outer surface of the test specimen.4
Laminated beam theory must be applied to determine the maximum
tensile stress at failure. If Eq 3 is used to calculate stress, it will yield an
apparent strength based on homogeneous beam theory. This apparent
strength is highly dependent on the ply-stacking sequence of highly
orthotropic laminates.
NOTE 12The preceding calculation is not valid if the specimen slips
excessively between the supports.
where:
sf, P, L, b, and d are the same as for Eq 3, and
D = deflection of the centerline of the specimen at the
middle of the support span, mm (in.).
NOTE 13When large support span-to-depth ratios are used, significant
end forces are developed at the support noses which will affect the
moment in a simple supported beam. Eq 4 includes additional terms that
are an approximate correction factor for the influence of these end forces
in large support span-to-depth ratio beams where relatively large deflections exist.
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(5)
where:
f = strain in the outer surface, mm/mm (in./in.),
D = maximum deflection of the center of the beam, mm
(in.),
L = support span, mm (in.), and
d = depth, mm (in.).
12.9 Modulus of Elasticity:
12.9.1 Tangent Modulus of ElasticityThe tangent modulus of elasticity, often called the modulus of elasticity, is the
ratio, within the elastic limit, of stress to corresponding strain.
It is calculated by drawing a tangent to the steepest initial
straight-line portion of the load-deflection curve and using Eq
6 (for highly anisotropic composites, see Note 15).
EB 5 L3m/4bd 3
where:
EB = modulus of elasticity in bending, MPa (psi),
L = support span, mm (in.),
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(6)
D790 10
= width of beam tested, mm (in.),
= depth of beam tested, mm (in.), and
= slope of the tangent to the initial straight-line portion
of the load-deflection curve, N/mm (lbf/in.) of deflection.
(7)
where:
sf2 and sf1 are the flexural stresses, calculated from Eq 3 or
Eq 4 and measured at the predefined points on the load
deflection curve, and f2 and
f1 are the flexural strain values, calculated from Eq 5 and
measured at the predetermined points on the load deflection
curve.
TABLE 2 Flexural Modulus
Material
ABS
DAP thermoset
Cast acrylic
GR polyester
GR polycarbonate
SMC
V RB
rC
RD
4.79
2.89
13.7
3.49
5.52
10.9
7.69
7.18
16.1
4.20
5.52
13.8
13.6
8.15
38.8
9.91
15.6
30.8
21.8
20.4
45.4
11.9
15.6
39.1
A
Vr = within-laboratory coefficient of variation for the indicated material. It is
obtained by first pooling the within-laboratory standard deviations of the test
results from all of the participating laboratories: Sr = [[(s1)2 + ( s2)2 . . . + (sn)2]/n]
1/2 then Vr = (Sr divided by the overall average for the material) 3 100.
B
Vr = between-laboratory reproducibility, expressed as the coefficient of variation: SR = {Sr2 + SL2}1/2 where SL is the standard deviation of laboratory means.
Then: VR = (SR divided by the overall average for the material) 3 100.
C
r = within-laboratory critical interval between two test results = 2.8 3 Vr.
D
R = between-laboratory critical interval between two test results = 2.8 3 VR.
(8)
where:
s = estimated standard deviation,
X = value of single observation,
n = number of observations, and
X = arithmetic mean of the set of observations.
13. Report
13.1 Report the following information:
13.1.1 Complete identification of the material tested, including type, source, manufacturers code number, form, principal
dimensions, and previous history (for laminated materials,
ply-stacking sequence shall be reported),
13.1.2 Direction of cutting and loading specimens, when
appropriate,
13.1.3 Conditioning procedure,
13.1.4 Depth and width of specimen,
13.1.5 Procedure used (A or B),
13.1.6 Support span length,
13.1.7 Support span-to-depth ratio if different than 16:1,
13.1.8 Radius of supports and loading noses, if different
than 5 mm. When support and/or loading nose radii other than
5 mm are used, the results shall be identified as being generated
by a modified version of this test method and the referring
specification referenced as to the geometry used.
13.1.9 Rate of crosshead motion,
13.1.10 Flexural strain at any given stress, average value
and standard deviation,
13.1.11 If a specimen is rejected, reason(s) for rejection,
13.1.12 Tangent, secant, or chord modulus in bending,
average value, standard deviation, and the strain level(s) used
if secant or chord modulus,
13.1.13 Flexural strength (if desired), average value, and
standard deviation,
13.1.14 Stress at any given strain up to and including 5 % (if
desired), with strain used, average value, and standard deviation,
13.1.15 Flexural stress at break (if desired), average value,
and standard deviation,
13.1.16 Type of behavior, whether yielding or rupture, or
both, or other observations, occurring within the 5 % strain
limit, and
13.1.17 Date of specific version of test used.
14. Precision and Bias
14.1 Tables 1 and 2 are based on a round-robin test
conducted in 1984, in accordance with Practice E691, involving six materials tested by six laboratories using Procedure A.
For each material, all the specimens were prepared at one
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b
d
m
D790 10
source. Each test result was the average of five individual
determinations. Each laboratory obtained two test results for
each material.
NOTE 16Caution: The following explanations of r and R (14.214.2.3) are intended only to present a meaningful way of considering the
approximate precision of these test methods. The data given in Tables 2
and 3 should not be applied rigorously to the acceptance or rejection of
materials, as those data are specific to the round robin and may not be
representative of other lots, conditions, materials, or laboratories. Users of
these test methods should apply the principles outlined in Practice E691 to
generate data specific to their laboratory and materials, or between specific
laboratories. The principles of 14.2-14.2.3 would then be valid for such
data.
ANNEXES
(Mandatory Information)
A1. TOE COMPENSATION
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D790 10
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FIG. A2.3 Fixture Used to Set Loading Nose and Support Spacing and Alignment
APPENDIX
(Nonmandatory Information)
X1. DEVELOPMENT OF A FLEXURAL MACHINE COMPLIANCE CORRECTION
X1.1 Introduction
X1.1.1 Universal Testing instrument drive systems always
exhibit a certain level of compliance that is characterized by a
variance between the reported crosshead displacement and the
displacement actually imparted to the specimen. This variance
is a function of load frame stiffness, drive system wind-up, load
cell compliance and fixture compliance. To accurately measure
the flexural modulus of a material, this compliance should be
measured and empirically subtracted from test data. Flexural
modulus results without the corrections are lower than if the
correction is applied. The greater the stiffness of the material
the more influence the system compliance has on results.
X1.1.2 It is not necessary to make the machine compliance
correction when a deflectometer/extensometer is used to measure the actual deflection occurring in the specimen as it is
deflected.
X1.2 Terminology
X1.2.1 ComplianceThe displacement difference between
test machine drive system displacement values and actual
specimen displacement
X1.2.2 Compliance CorrectionAn analytical method of
modifying test instrument displacement values to eliminate the
amount of that measurement attributed to test instrument
compliance.
X1.3 Apparatus
X1.3.1 Universal Testing machine
X1.3.2 Load cell
X1.3.3 Flexure fixture including loading nose and specimen
supports
X1.3.4 Computer Software to make corrections to the displacements
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X1.5.1.4 Increase load to a point exceeding the highest load
expected during specimen testing. Stop the crosshead and
return to the pre-test location.
X1.5.1.5 The recorded load-deflection curve, starting when
the loading nose contacts the steel bar to the time that the
highest load expected is defined as test system compliance.
X1.5.2 Procedure to apply compliance correction is as
follows:
X1.5.2.1 Run the flexural test method on the material at the
crosshead required for the measurement.
X1.5.2.2 It is preferable that computer software be used to
make the displacement corrections, but if it is not available
compliance corrections can be made manually in the following
manner. Determine the range of displacement (D) on the load
versus displacement curve for the material, over which the
modulus is to be calculated. For Youngs Modulus that would
steepest region of the curve below the proportional limit. For
Secant and Chord Modulii that would be at specified level of
strain or specified levels of strain, respectively. Draw two
vertical lines up from the displacement axis for the two chosen
displacements (D1, D2) to the load versus displacement curve
for the material. In some cases one of these points maybe at
zero displacement after the toe compensation correction is
made. Draw two horizontal lines from these points on the load
displacement curve to the Load (P) axis. Determine the loads
(L1, L2).
X1.5.2.3 Using the Compliance Correction load displacement curve for the steel bar, mark off L1 and L2 on the Load
(P) axis. From these two points draw horizontal lines across till
they contact the load versus displacement curve for the steel
bar. From these two points on the load deflection curve draw
two vertical lines downwards to the displacement axis. These
two points on the displacement axis determine the corrections
(c1, c2) that need to be made to the displacements measurements for the test material.
X1.5.2.4 Subtract the corrections (c1, c2) from the measured displacements (D1, D2), so that a true measures of test
specimen deflection (D1-c1, D2-c2) are obtained.
X1.6 Calculations
X1.6.1 Calculation of Chord Modulus
X1.6.1.1 Calculate the stresses (sf1, sf2) for load points L1
and L2 from Fig. X1.1 using the equation in 12.2 3.
X1.6.1.2 Calculate the strains (f1, f2) for displacements
D1-c1 and D2-c2 from Fig. X1.3 using the equation in 12.8 Eq.
5.
X1.6.1.3 Calculate the flexural chord modulus in accordance with 12.9.3 Eq. 7.
X1.6.2 Calculation of Secant Modulus
X1.6.2.1 Calculation of the Secant Modulus at any strain
along the curve would be the same as conducting a chord
modulus measurement, except that sf1 = 0, L1= 0, and D1-c1
= 0.
X1.6.3 Calculation of Youngs Modulus
X1.6.3.1 Determine the steepest slope m along the curve,
below the proportional limit, using the selected loads L1 and
L2 from Fig. X1.1 and the displacements D1-c1 and D2-c2
from Fig. X1.3.
X1.6.3.2 Calculate the Youngs modulus in accordance with
12.9.1 Eq. 6.
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D790 10
SUMMARY OF CHANGES
Committee D20 has identified the location of selected changes to this standard since the last issue
(D790 - 071) that may impact the use of this standard. (April 1, 2010)
(1) Revised Section 9.
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