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: D7264/D7264M − 21

Standard Test Method for

Flexural Properties of Polymer Matrix Composite Materials1
This standard is issued under the fixed designation D7264/D7264M; 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. Referenced Documents

1.1 This test method determines the flexural stiffness and 2.1 ASTM Standards:2
strength properties of polymer matrix composites. D790 Test Methods for Flexural Properties of Unreinforced
1.1.1 Procedure A—A three-point loading system utilizing and Reinforced Plastics and Electrical Insulating Materi-
center loading on a simply supported beam. als
D792 Test Methods for Density and Specific Gravity (Rela-
1.1.2 Procedure B—A four-point loading system utilizing tive Density) of Plastics by Displacement
two load points equally spaced from their adjacent support D883 Terminology Relating to Plastics
points, with a distance between load points of one-half of the D2344/D2344M Test Method for Short-Beam Strength of
support span. Polymer Matrix Composite Materials and Their Laminates
NOTE 1—Unlike Test Method D6272, which allows loading at both D2584 Test Method for Ignition Loss of Cured Reinforced
one-third and one-half of the support span, in order to standardize Resins
geometry and simplify calculations, this standard permits loading at only D2734 Test Methods for Void Content of Reinforced Plastics
one-half the support span. D3171 Test Methods for Constituent Content of Composite
1.2 For comparison purposes, tests may be conducted ac- Materials
cording to either test procedure, provided that the same D3878 Terminology for Composite Materials
procedure is used for all tests, since the two procedures D5229/D5229M Test Method for Moisture Absorption Prop-
generally give slightly different property values. erties and Equilibrium Conditioning of Polymer Matrix
Composite Materials
1.3 Units—The values stated in either SI units or inch- D5687/D5687M Guide for Preparation of Flat Composite
pound units are to be regarded separately as standard. The Panels with Processing Guidelines for Specimen Prepara-
values stated in each system are not necessarily exact equiva- tion
lents; therefore, to ensure conformance with the standard, each D6272 Test Method for Flexural Properties of Unreinforced
system shall be used independently of the other, and values and Reinforced Plastics and Electrical Insulating Materi-
from the two systems shall not be combined. als by Four-Point Bending
1.4 This standard does not purport to address all of the D6856 Guide for Testing Fabric-Reinforced “Textile” Com-
safety concerns, if any, associated with its use. It is the posite Materials
responsibility of the user of this standard to establish appro- E4 Practices for Force Verification of Testing Machines
E6 Terminology Relating to Methods of Mechanical Testing
priate safety, health, and environmental practices and deter-
E122 Practice for Calculating Sample Size to Estimate, With
mine the applicability of regulatory limitations prior to use.
Specified Precision, the Average for a Characteristic of a
1.5 This international standard was developed in accor- Lot or Process
dance with internationally recognized principles on standard- E177 Practice for Use of the Terms Precision and Bias in
ization established in the Decision on Principles for the ASTM Test Methods
Development of International Standards, Guides and Recom- E456 Terminology Relating to Quality and Statistics
mendations issued by the World Trade Organization Technical 2.2 Other Documents:3
Barriers to Trade (TBT) Committee. ANSI Y14.5-1999 Dimensioning and Tolerancing—
Includes Inch and Metric

1 2
This test method is under the jurisdiction of ASTM Committee D30 on For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Composite Materials and is the direct responsibility of Subcommittee D30.04 on contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Lamina and Laminate Test Methods. Standards volume information, refer to the standard’s Document Summary page on
Current edition approved Jan. 1, 2021. Published February 2021. Originally the ASTM website.
3
approved in 2006. Last previous edition approved in 2015 as D7264/D7264M – 15. Available from American National Standards Institute (ANSI), 25 W. 43rd St.,
DOI: 10.1520/D7264_D7264M-21. 4th Floor, New York, NY 10036, http://www.ansi.org.

Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States

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ANSI B46.1-1995 Surface Texture (Surface Roughness,
Waviness and Lay)
3. Terminology
3.1 Definitions—Terminology D3878 defines the terms re-
lating to high-modulus fibers and their composites. Terminol-
ogy D883 defines terms relating to plastics. Terminology E6
defines terms relating to mechanical testing. Terminology E456
and Practice E177 define terms relating to statistics. In the
event of a conflict between terms, Terminology D3878 shall FIG. 2 Procedure B—Loading Diagram
have precedence over the other documents.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 flexural modulus, n—the ratio of stress range to
corresponding strain range for a test specimen loaded in 4.2 Force applied to the specimen and resulting specimen
flexure. deflection at the center of span are measured and recorded until
the failure occurs on either one of the outer surfaces, or the
3.2.2 flexural strength, n—the maximum stress at the outer deformation reaches some pre-determined value.
surface of a flexure test specimen corresponding to the peak
applied force prior to flexural failure. 4.3 The major difference between four-point and three-point
loading configurations is the location of maximum bending
3.3 Symbols: moment and maximum flexural stress. With the four-point
b = specimen width configuration, the bending moment is constant between the
CV = sample coefficient of variation, in percent central force application members. Consequently, the maxi-
Efchord = flexural chord modulus of elasticity mum flexural stress is uniform between the central force
Efsecant = flexural secant modulus of elasticity application members. In the three-point configuration, the
h = specimen thickness maximum flexural stress is located directly under the center
L = support span force application member. Another difference between the
m = slope of the secant of the load-deflection curve three-point and four-point configurations is the presence of
n = number of specimens resultant vertical shear force in the three-point configuration
P = applied force everywhere in the beam except right under the mid-point force
sn-1 = sample standard deviation application member whereas in the four-point configuration,
xi = measured or derived property the area between the central force application members has no
x̄5 sample mean
resultant vertical shear force. The distance between the outer
δ = mid-span deflection of the specimen support members is the same as in the equivalent three-point
ε = strain at the outer surface at mid-span of the specimen configuration.
σ = stress at the outer surface at mid-span of the specimen
4.4 The test geometry is chosen to limit out-of-plane shear
4. Summary of Test Method deformations and avoid the type of short beam failure modes
that are interrogated in Test Method D2344/D2344M.
4.1 A bar of rectangular cross section, supported as a beam,
is deflected at a constant rate as follows:
5. Significance and Use
4.1.1 Procedure A—The bar rests on two supports and is
loaded by means of a loading nose midway between the 5.1 This test method determines the flexural properties
supports (see Fig. 1). (including strength, stiffness, and load/deflection behavior) of
4.1.2 Procedure B—The bar rests on two supports and is polymer matrix composite materials under the conditions
loaded at two points (by means of two loading noses), each an defined. Procedure A is used for three-point loading and
equal distance from the adjacent support point. The distance Procedure B is used for four-point loading. This test method
between the loading noses (that is, the load span) is one-half of was developed for optimum use with continuous-fiber-
the support span (see Fig. 2). reinforced polymer matrix composites and differs in several
respects from other flexure methods, including the use of a
standard span-to-thickness ratio of 32:1 versus the 16:1 ratio
used by Test Methods D790 (a plastics-focused method cov-
ering three-point flexure) and D6272 (a plastics-focused
method covering four-point flexure).
5.2 This test method is intended to interrogate long-beam
strength in contrast to the short-beam strength evaluated by
Test Method D2344/D2344M.
5.3 Flexural properties determined by these procedures can
be used for quality control and specification purposes, and may
FIG. 1 Procedure A—Loading Diagram find design applications.

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 D7264/D7264M − 21
5.4 These procedures can be useful in the evaluation of 6.4 Loading noses shall be fixed, rotatable, or rolling.
multiple environmental conditions to determine which are Typically, for testing composites, fixed or rotatable loading
design drivers and may require further testing. noses are used. The type of loading nose can affect results,
5.5 These procedures may also be used to determine flexural since non-rolling paired supports on either the tension or
properties of structures. compression side of the specimen introduce slight longitudinal
forces and resisting moments on the beam, which superpose
6. Interferences with the intended loading. The type of supports used is to be
reported as described in Section 14. The loading noses shall
6.1 Flexural properties may vary depending on which sur- uniformly contact the specimen across its width. Lack of
face of the specimen is in compression, as no laminate is uniform contact can affect flexural properties by initiating
perfectly symmetric (even when full symmetry is intended); damage by crushing and by non-uniformly loading the beam.
such differences will shift the neutral axis and will be further Formulas used in this standard assume a uniform line loading
affected by even modest asymmetry in the laminate. Flexural at the specimen supports across the entire specimen width;
properties may also vary with specimen thickness, condition- deviations from this type of loading is beyond the scope of this
ing or testing environments, or both, and rate of straining. standard.
When evaluating several datasets, these parameters shall be
equivalent for all data in the comparison. 7. Apparatus
6.2 For multidirectional laminates with a small or moderate 7.1 Testing Machine—The testing machine shall be properly
number of laminae, flexural modulus and flexural strength may calibrated and operate at a constant rate of crosshead motion
be affected by the ply-stacking sequence and will not neces- with the error in the force application system not exceeding
sarily correlate with extensional modulus, which is not 61 % of the full scale. The force indicating mechanism shall
stacking-sequence dependent. be essentially free of inertia lag at the crosshead rate used.
6.3 The calculation of the flexural properties in Section 13 Inertia lag shall not exceed 1 % of the measured force. The
of this standard is based on beam theory, while the specimens accuracy of the testing machine shall be verified in accordance
in general may be described as plates. The differences may in with Practices E4.
some cases be significant, particularly for laminates containing 7.2 Loading Noses and Supports—The loading noses and
a large number of plies in the 645° direction. The deviations supports shall have cylindrical contact surfaces with a hardness
from beam theory decrease with decreasing width. ≥55 HRC and shall have finely ground surfaces free of

FIG. 3 Example Loading Nose and Supports for Procedures A (top) and B (bottom)

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 D7264/D7264M − 21
indentation and burrs, with all sharp edges relieved. The radii D5229M. Chamber conditions shall be monitored either on an
of the loading nose and supports shall be 5.0 6 0.1 mm [0.197 automated continuous basis or on a manual basis at regular
6 0.004 in.], as shown in Fig. 3, unless otherwise specified or intervals.
agreed upon between the interested parties. Loading noses and
supports shall be arranged in a fixed, rotatable, or rolling 7.6 Environmental Test Chamber—An environmental test
arrangement. Typically, with composites, rotatable or fixed chamber is required for test environments other than ambient
arrangements are used. testing laboratory conditions. This chamber shall be capable of
maintaining the test specimen at the required temperature
7.3 Micrometers and Calipers—For width and thickness within 63 °C [65 °F] and the required vapor level to within
measurements, the micrometers shall use a 4 to 8 mm [0.16 to 65 % relative humidity.
0.32 in.] nominal diameter ball-interface on an irregular
surface such as the bag side of a laminate, and a flat anvil 8. Test Specimens
interface on machined edges or very smooth tooled surfaces. A
micrometer or caliper with flat anvil faces shall be used to 8.1 Specimen Preparation—Guide D5687/D5687M pro-
measure the length of the specimen. The use of alternative vides recommended specimen preparation practices and shall
measurement devices is permitted if specified (or agreed to) by be followed when practical.
the test requestor and reported by the testing laboratory. The
8.2 Specimen Size is chosen such that the flexural properties
accuracy of the instrument(s) shall be suitable for reading to
are determined accurately from the tests. For flexural strength,
within 1 % or better of the specimen dimensions. For typical
the standard support span-to-thickness ratio is chosen such that
section geometries, an instrument with an accuracy of
failure occurs at the outer surface of the specimens, due only to
60.02 mm [60.001 in.] is adequate for thickness and width
the bending moment (see Notes 2 and 3). The standard
measurement, while an instrument with an accuracy of
60.1 mm [60.004 in.] is adequate for length measurement. span-to-thickness ratio is 32:1, the standard specimen thickness
is 4 mm [0.16 in.], and the standard specimen width is 13 mm
7.4 Deflection Measurement—Specimen deflection at the [0.5 in.] with the specimen length being about 20 % longer
common center of the loading span shall be measured by a than the support span. See Figs. 4 and 5 for a drawing of the
properly calibrated device having an accuracy of 61 % or standard test specimen in SI and inch-pound units, respectively.
better of the expected maximum displacement. The device For fabric-reinforced textile composite materials, the width of
shall automatically and continuously record the deflection the specimen shall be at least two unit cells, as defined in Guide
during the test. D6856. If the standard specimen thickness cannot be obtained
7.5 Conditioning Chamber—When conditioning materials in a given material system, an alternate specimen thickness
at non-laboratory environments, a temperature/vapor-level- shall be used while maintaining the support span-to-thickness
controlled environmental conditioning chamber is required that ratio [32:1] and specimen width. Optional support span-to-
shall be capable of maintaining the required temperature to thickness ratios of 16:1, 20:1, 40:1, and 60:1 may also be used,
within 63 °C [65 °F] and the required vapor level to within provided it is so noted in the report. Also, the data obtained
63 % relative humidity, as outlined in Test Method D5229/ from a test using one support span-to-thickness ratio shall not

FIG. 4 Standard Flexural Test Specimen Drawing (SI)

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 D7264/D7264M − 21

FIG. 5 Standard Flexural Test Specimen Drawing (Inch-Pound)

be compared with the data from another test using a different 9. Number of Test Specimens
support span-to-thickness ratio. 9.1 Test at least five specimens per test condition unless
8.2.1 Shear deformations can significantly reduce the appar- valid results can be gained through the use of fewer specimens,
ent modulus of highly orthotropic laminates when they are such as in the case of a designed experiment. For statistically
tested at low support span-to-thickness ratios. For this reason, significant data, the procedures outlined in Practice E122 shall
a high support span-to-thickness ratio is recommended for be consulted. Report the method of sampling.
flexural modulus determinations. In some cases, separate sets
of specimens may have to be used for modulus and strength 10. Conditioning
determination.
NOTE 2—A support span-to-thickness ratio of less than 32:1 may be 10.1 The recommended pre-test specimen condition is ef-
acceptable for obtaining the desired flexural failure mode when the ratio fective moisture equilibrium at a specific relative humidity as
of the lower of the compressive and tensile strength to out-of-plane shear established by Test Method D5229/D5229M; however, if the
strength is less than 8, but the support span-to-thickness ratio must be
test requester does not explicitly specify a pre-test conditioning
increased for composite laminates having relatively low out-of-plane
shear strength and relatively high in-plane tensile or compressive strength environment, conditioning is not required and the test speci-
parallel to the support span. mens shall be tested as prepared.
NOTE 3—While laminate stacking sequence is not limited by this test NOTE 4—The term moisture, as used in Test Method D5229/D5229M,
method, significant deviations from a lay-up of nominal balance and includes not only the vapor of a liquid and its condensate, but the liquid
symmetry may induce unusual test behaviors and a shift in the neutral itself in large quantities, as for immersion.
axis.
10.2 The pre-test specimen conditioning process, to include
8.3 If specific gravity, density, reinforcement volume, or specified environmental exposure levels and resulting moisture
void volume are to be reported, then obtain these samples from content, shall be reported with the data.
the same panels as the test samples. Specific gravity and
10.3 If there is no explicit conditioning process, the condi-
density may be evaluated by means of Test Methods D792.
tioning process shall be reported as “unconditioned” and the
Volume percent of the constituents may be evaluated by one of
moisture content as “unknown.”
the matrix digestion procedures of Test Method D3171, or, for
certain reinforcement materials such as glass and ceramics, by
the matrix burn-off technique of Test Method D2584. Void 11. Procedure
content may be evaluated from the equations of Test Method 11.1 Condition the specimens as required. Store the speci-
D2734 and is applicable to both Test Methods D2584 and mens in the conditioned environment until test time.
D3171. 11.2 Following final specimen machining and any
8.4 Labeling—Label the specimens so that they will be conditioning, but before testing, measure and record the
distinct from each other and traceable back to the raw material specimen width, b, and thickness, h, at the specimen mid-
and in a manner that will both be unaffected by the test and not section, and the specimen length, to the accuracy specified in
influence the test. 7.3.

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11.3 Measure the span, L, accurately to the nearest 0.1 mm manifested as fiber micro-buckling or ply-level buckling.
[0.004 in.] for spans less than 63 mm [2.5 in.] and the nearest Ply-level buckling may result in, or be preceded by, delamina-
0.3 mm [0.012 in.] for spans greater than or equal to 63 mm tion of the outer ply.
[2.5 in.]. Use the measured span for all calculations. See Annex 11.7.1 Failure Identification Codes—Record the mode, area,
A1 for information on the determination of and setting of the and location of failure for each specimen. Choose a standard
span. failure identification code based on the three-part code shown
11.4 Speed of Testing—Set the speed of testing at a rate of in Fig. 6. A multimode failure can be described by including
crosshead movement of 1.0 mm/min [0.05 in./min] for a each of the appropriate failure-mode codes between the paren-
specimen with standard dimensions. For specimens with di- theses of the M failure mode.
mensions that vary greatly from the standard dimensions, a
12. Validation
crosshead rate that will give a similar rate of straining at the
outer surface can be obtained via the method outlined in Test 12.1 Values for properties at failure shall not be calculated
Methods D790 for Procedure A and Test Method D6272 for for any specimen that breaks at some obvious, fortuitous flaw,
Procedure B. The use of an alternative test rate is permitted if unless such flaws constitute a variable being studied. Speci-
specified (or agreed to) by the test requestor and reported by mens that fail in an unacceptable failure mode shall not be
the testing laboratory. included in the flexural property calculations. Retests shall be
made for any specimen for which values are not calculated. If
11.5 Align the loading nose(s) and supports so that the axes
a significant fraction (>50 %) of the specimens fail in an
of the cylindrical surfaces are parallel. For Procedure A, the
unacceptable failure mode, then the span-to-thickness ratio (for
loading nose shall be midway between the supports. For
excessive shear failures) or the loading nose diameter (crushing
Procedure B, the load span shall be one-half of the support
under the loading nose) shall be reexamined.
span and symmetrically placed between the supports. The
parallelism may be checked by means of plates with parallel 13. Calculation
grooves into which the loading nose(s) and supports will fit NOTE 5—In determination of the calculated value of some of the
when properly aligned. Center the specimen on the supports, properties listed in this section, it is necessary to determine if the toe
with the long axis of the specimen perpendicular to the loading compensation (see Annex A2) adjustment must be made. This toe
noses and supports. See Annex A1 for setting and measuring compensation correction shall be made only when it has been shown that
span. the toe region of the curve is due to take up of the slack, alignment, or
seating of the specimen and is not an authentic material response.
11.6 Apply the force to the specimen at the specified 13.1 Maximum Flexural Stress, Procedure A—When a beam
crosshead rate. Measure and record force-deflection data at a of homogenous, elastic material is tested in flexure as a beam
rate such that a minimum of 50 data points comprise the force simply supported at two points and loaded at the midpoint, the
deflection curve. (A higher sampling rate may be required to maximum stress at the outer surface occurs at mid-span. The
properly capture any nonlinearities or progressive failure of the stress shall be calculated for any point on the load-deflection
specimen.) Measure deflection by a transducer under the curve by the following equation (Note 6):
specimen in contact with it at the center of the support span, the
transducer being mounted stationary relative to the specimen 3PL
σ5 (1)
supports. Do not use the measurement of the motion of the 2bh2
loading nose relative to the supports as this will not take into where:
account the rotation of the specimen about the load and support σ = stress at the outer surface at mid-span, MPa [psi],
noses, nor account for the compliance in the loading nose or P = applied force, N [lbf],
crosshead. L = support span, mm [in.],
11.7 Failure Modes—To obtain valid flexural strength, it is b = width of beam, mm [in.], and
necessary that the specimen failure occurs on either one of its h = thickness of beam, mm [in.].
outer surfaces, without a preceding interlaminar shear failure NOTE 6—Eq 1 applies strictly to materials for which the stress is
linearly proportional to strain up to the point of rupture and for which the
or a crushing failure under a support or loading nose. Failure strains are small. Since this is not always the case, a slight error will be
on the tension surface may be a crack while that on the introduced in the use of this equation. The equation will however, be valid
compression surface may be local buckling. Buckling may be for comparison data and specification values up to the maximum fiber

FIG. 6 Flexure Test Specimen Three-Part Failure Identification Code

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 D7264/D7264M − 21
strain of 2 % for specimens tested by the procedure herein described. It where:
should be noted that the maximum ply stress may not occur at the outer
surface of a multidirectional laminate.4 Laminated beam theory must be
δ = mid-span deflection, mm [in.],
applied to determine the maximum tensile stress at failure. Thus, Eq 1 ε = maximum strain at the outer surface, mm/mm [in./in.],
yields an apparent strength based on homogeneous beam theory. This L = support span, mm [in.], and
apparent strength is highly dependent on the ply-stacking sequence for h = thickness of beam, mm [in.].
multidirectional laminates.
13.7 Flexural Modulus of Elasticity:
13.2 Maximum Flexural Stress, Procedure B—When a 13.7.1 Flexural Chord Modulus of Elasticity—The flexural
beam of homogeneous, elastic material is tested in flexure as a chord modulus of elasticity is the ratio of stress range and
beam simply supported at two outer points and loaded at two corresponding strain range. For calculation of flexural chord
central points separated by a distance equal to 1⁄2 the support modulus, the recommended strain range is 0.002 with a start
span and at equal distance from the adjacent support point, the point of 0.001 and an end point 0.003. If the data is not
maximum stress at the outer surface occurs between the two available at the exact strain range end points (as often occurs
central loading points that define the load span (Fig. 2). The with digital data), use the closest available data point. Calculate
stress shall be calculated for any point on the load-deflection the flexural chord modulus of elasticity from the stress-strain
curve by the following equation (Note 7): data using Eq 5 (for multidirectional or highly orthotropic
3PL composites, see Note 8).
σ5 (2)
4bh2
∆σ
E fchord 5 (5)
where: ∆ε
σ = stress at the outer surface in the load span region, MPa where:
[psi], Efchord = flexural chord modulus of elasticity, MPa [psi],
P = applied force, N [lbf], ∆σ = difference in flexural stress between the two se-
L = support span, mm [in.],
lected strain points, MPa [psi], and
b = width of beam, mm [in.], and
∆ε = difference between the two selected strain points
h = thickness of beam, mm [in.].
NOTE 7—The limitations defined for Eq 1 in Note 6 apply also to Eq 2.
(nominally 0.002).
13.3 Flexural Strength—The flexural strength is equal to the 13.7.1.1 Report the chord modulus of elasticity in MPa [psi]
maximum stress at the outer surface corresponding to the peak for the strain range 0.001 to 0.003. If a different strain range is
applied force prior to failure (for multidirectional laminates, used in the calculations, also report the strain range used.
see Note 6). It is calculated in accordance with Eq 1 and 2 by NOTE 8—Shear deformation can seriously reduce the apparent flexural
letting P equal the peak applied force. modulus of highly orthotropic laminates when they are tested at low
span-to-thickness ratios.5 For this reason, a high span-to-thickness ratio is
13.4 Flexural Stress at a Given Strain—The maximum recommended for flexural modulus determinations. In some cases, sepa-
flexural stress at any given strain shall be calculated in rate sets of specimens may have to be used for modulus and strength
accordance with Eq 1 and 2 by letting P equal the applied force determination.
read from the force-deflection curve at the deflection corre- 13.7.2 Flexural Secant Modulus of Elasticity—The flexural
sponding to the desired strain (for multidirectional laminates, secant modulus of elasticity is the ratio of stress to correspond-
see Note 6). Equations for calculating strains from the mea- ing strain at any given point on the stress-strain curve. The
sured deflection are given in 13.5 and 13.6. flexural secant modulus is same as the flexural chord modulus
13.5 Maximum Strain, Procedure A—The maximum strain in which the initial strain point is zero. It shall be expressed in
at the outer surface also occurs at mid-span, and it shall be MPa [psi]. It is calculated as follows (for multidirectional or
calculated as follows: highly orthotropic composites, see Note 8):
6δh 13.7.2.1 For Procedure A:
ε5 (3)
L2 L 3m
E fsecant 5 (6)
where: 4bh3

ε = maximum strain at the outer surface, mm/mm [in./in.], where:

δ = mid-span deflection, mm [in.], Efsecant = flexural secant modulus of elasticity, MPa [psi],
L = support span, mm [in.], and L = support span, mm [in.],
h = thickness of beam, mm [in.]. b = width of beam, mm [in.],
13.6 Maximum Strain, Procedure B—The maximum strain h = thickness of beam, mm [in.] and
at the outer surface also occurs at mid-span, and it shall be m = slope of the secant of the force-deflection curve.
calculated as follows: 13.7.2.2 For Procedure B:
48δh
ε5 (4)
11L 2
5
For discussion of these effects, see Zweben C., Smith, W. S., and Wardle, M.
4
For the theoretical details, see Whitney, J. M., Browning, C. E., and Mair, A., W., “Test Methods for Fiber Tensile Strength, Composite Flexural Modulus, and
“Analysis of the Flexure Test for Laminated Composite Materials,” Composite Properties of Fabric-Reinforced Laminates,” Composite Materials: Testing and
Materials: Testing and Design (Third Conference), ASTM STP 546, 1974, pp. 30-45. Design (Fifth Conference), ASTM STP 674, 1979, pp. 228-262.

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11L 3 m 14.1.12 Method of preparing the test specimens, including
E fsecant 5 (7)
64bh3 specimen labeling scheme and method, specimen geometry,
where Efsecant, m, L, b, and h are the same as defined for Eq 6. sampling method, and specimen cutting method.
13.7.3 Chord modulus of elasticity shall be reported, al- 14.1.13 Calibration dates and methods for all measurement
though other definitions of moduli may also be used. However, and test equipment.
when other definitions of moduli are used, it shall be clearly 14.1.14 Type of test machine, grips, jaws, alignment data,
indicated in the report. and data acquisition sampling rate and equipment type.
14.1.15 Dimensions of each specimen to at least three
13.8 Statistics—For each series of tests, calculate the aver- significant figures, including specimen width, thickness, and
age value, standard deviation, and coefficient of variation for overall length.
each property determined:
14.1.16 Conditioning parameters and results, and the proce-
x̄ 5S( D
1
n i51
n

xi (8)
dure used if other than that specified in this test method.
14.1.17 Relative humidity and temperature of the testing
laboratory.

!S ( D
n

x i2 2 nx̄ 2
14.1.18 Environment of the test machine environmental
s n21 5
i51 chamber (if used) and soak time at environment.
n21 14.1.19 Number of specimens tested.
s n21
14.1.20 Load-span length, support-span length, and support
CV 5 100·
x̄
span-to-thickness ratio.
14.1.21 Loading and support nose type and dimensions.
where: 14.1.22 Speed of testing.
x̄ = average value or sample mean, 14.1.23 Transducer placement on the specimen, transducer
xi = value of single measured or derived property, type, and calibration data for each transducer used.
n = number of specimens, 14.1.24 Force-deflection curves for each specimen. Note
sn-1 = estimated standard deviation,
method and offset value if toe compensation was applied to
CV = coefficient of variation in percentage.
force-deflection curve.
14. Report 14.1.25 Tabulated data of flexural stress versus strain for
each specimen.
14.1 Report the following information, or references point- 14.1.26 Individual flexural strengths and average value,
ing to other documentation containing this information, to the standard deviation, and coefficient of variation (in percent) for
maximum extent applicable. (Reporting of items beyond the the population. Note if the failure load was less than the
control of a given testing laboratory, such as might occur with maximum load prior to failure.
material details of panel fabrication parameters, shall be the 14.1.27 Individual strains at failure and the average value,
responsibility of the requestor): standard deviation, and coefficient of variation (in percent) for
14.1.1 The revision level or date of issue of the test method the population.
used.
14.1.28 Strain range used for the flexural chord modulus of
14.1.2 The date(s) and location(s) of the testing.
elasticity determination.
14.1.3 The name(s) of the test operator(s).
14.1.4 The test Procedure used (A or B). 14.1.29 Individual values of flexural chord modulus of
14.1.5 Any variations to this test method, anomalies noticed elasticity, and the average value, standard deviation, and
during testing, or equipment problems occurring during testing. coefficient of variation (in percent) for the population.
14.1.6 Identification of the material tested, including: mate- 14.1.30 If an alternate definition of flexural modulus of
rial specification, material type, material designation, elasticity is used in addition to chord modulus, describe the
manufacturer, manufacturer’s lot or batch number, source (if method used, the resulting correlation coefficient (if
not from the manufacturer), date of certification, expiration of applicable), and the strain range used for the evaluation.
certification, filament diameter, tow or yarn filament count and 14.1.31 Individual values of the alternate (see above) flex-
twist, sizing, form or weave, fiber areal weight, matrix type, ural modulus of elasticity, and the average value, standard
prepreg matrix content, and prepreg volatiles content. deviation, and coefficient of variation (in percent) for the
14.1.7 Description of the fabrication steps used to prepare population.
the laminate, including: fabrication start date, fabrication end 14.1.32 Individual maximum flexural stresses, and the
date, process specification, cure cycle, consolidation method, average, standard deviation, and coefficient of variation (in
and a description of the equipment used. percent) values for the population. Note any test in which the
14.1.8 Ply orientation stacking sequence of the laminate. failure load was less than the maximum load before failure.
14.1.9 If requested, report density, reinforcement volume 14.1.33 For flexural modulus only tests: maximum load
fraction, and void content test methods, specimen sampling applied, strain at maximum applied load, and calculated
method and geometries, test parameters, and test data. flexural modulus of elasticity (Ef).
14.1.10 Average ply thickness of the material. 14.1.34 Individual maximum flexural strains and the
14.1.11 Results of any nondestructive evaluation tests. average, standard deviation, and coefficient of variation (in

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 D7264/D7264M − 21
percent) values for the population. Note any test that was 15.2 Bias—Bias cannot be determined for this test method
truncated to 2 % strain. as no acceptable reference standard exists.
14.1.35 Failure mode and location of failure for each
specimen. 16. Keywords
15. Precision and Bias 16.1 fiber-reinforced composites; flexural properties; stiff-
ness; strength
15.1 Precision—The data required for the development of
precision is not currently available for this test method.

ANNEXES

(Mandatory Information)

A1. MEASURING AND SETTING SPAN

A1.1 For flexural fixtures that have adjustable spans, it is

important that the span between the supports is maintained
constant or the actual measured span is used in the calculation
of flexural stress, flexural modulus and strain, and the loading
noses are positioned and aligned properly with respect to the
supports. Some simple steps as follows can improve the
repeatability of results when using adjustable span fixtures.
FIG. A1.1 Markings on Fixed Specimen Supports
A1.2 Measurement of Span:
A1.2.1 This technique is needed to ensure that the correct
span, not an estimated span, is used in calculation of results.
A1.2.2 Scribe a permanent line or mark at the exact center
of the support where the specimen makes complete contact.
The type of mark depends on whether the supports are fixed or
rotatable (see Figs. A1.1 and A1.2).
A1.2.3 Using a vernier caliper with pointed tips that is FIG. A1.2 Markings on Rotatable Specimen Supports
readable to at least 0.1 mm [0.004 in.], measure the distance
between the supports, and use this measurement of span in the
calculations.
A1.3 Setting the Span and Alignment of Loading
Nose(s)—To ensure a constant day-to-day setup of the
span and ensure the alignment and proper positioning of the
loading nose(s), simple jigs should be manufactured for each of
the standard setups used. An example of a jig found to be
useful is shown in Fig. A1.3. FIG. A1.3 Fixture Used to Align Loading Noses and Supports

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 D7264/D7264M − 21

A2. TOE COMPENSATION

A2.1 In a typical force-deflection curve (see Fig. A2.1) there determined by dividing the change in force between any two
is a toe region, AC, which does not represent a property of the points along the line CD (or its extension) by the change in
material. It is an artifact caused by a take-up of slack and deflection at the same two points (measured from Point B,
alignment, or seating of the specimen. In order to obtain correct defined as zero-deflection).
values of such parameters as flexural modulus, and deflection
at failure, this artifact must be compensated for to give the A2.3 In the case of a material that does not exhibit any
corrected zero point on the deflection, or extension axis. linear region (see Fig. A2.2), the same kind of toe correction of
zero-deflection point can be made by constructing a tangent to
A2.2 In the case of a material exhibiting a region of the maximum slope at the inflection Point H’. This is extended
Hookean (linear) behavior (see Fig. A2.1), a continuation of to intersect the deflection axis at Point B’, the corrected
the linear (CD) region is constructed through the zero axis. zero-deflection point. Using Point B’ as zero deflection, the
This intersection (B) is the corrected zero deflection point from force at any point (G’) on the curve can be divided by the
which all deflections must be measured. The slope can be deflection at that point to obtain a flexural chord modulus
(slope of Line B’G’).

FIG. A2.1 Material with a Hookean Region FIG. A2.2 Material without a Hookean Region

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