ASTM D7250/D7250M-06
(Practice)Standard Practice for Determining Sandwich Beam Flexural and Shear Stiffness
Standard Practice for Determining Sandwich Beam Flexural and Shear Stiffness
SIGNIFICANCE AND USE
Flexure tests on flat sandwich constructions may be conducted to determine the sandwich flexural stiffness, the core shear strength and shear modulus, or the facings compressive and tensile strengths. Tests to evaluate core shear strength may also be used to evaluate core-to-facing bonds.
This practice provides a standard method of determining sandwich flexural and shear stiffness and core shear modulus using calculations involving measured deflections of sandwich flexure specimens. Tests can be conducted on short specimens and on long specimens (or on one specimen loaded in two ways), and the flexural stiffness, shear rigidity and core shear modulus can be determined by simultaneous solution of the complete deflection equations for each span or each loading. If the facing modulus values are known, a short span beam can be tested and the calculated bending deflection subtracted from the beam’total deflection. This gives the shear deflection from which the transverse shear modulus can be determined.
Note 1—Core shear strength and shear modulus are best determined in accordance with Test Method C 273 provided bare core material is available.
Note 2—For cores with high shear modulus, the shear deflection will be quite small and ordinary errors in deflection measurements will cause considerable variations in the calculated shear modulus.
Note 3—To insure that simple sandwich beam theory is valid, a good rule of thumb for a four-point bending test is the span length divided by the sandwich thickness should be greater than 20 (L1/d > 20) with the ratio of facing thickness to core thickness less than 0.1 (t/c 0.1).
SCOPE
1.1 This practice covers determination of the flexural and transverse shear stiffness properties of flat sandwich constructions subjected to flexure in such a manner that the applied moments produce curvature of the sandwich facing planes. Permissible core material forms include those with continuous bonding surfaces (such as balsa wood and foams) as well as those with discontinuous bonding surfaces (such as honeycomb). The calculation methods in this practice are limited to sandwich beams exhibiting linear force-deflection response. This practice uses test results obtained from Test Methods C 393/C 393M and/or D 7249/D 7249M.
1.2 The values stated in either SI units or inch-pound units are to be regarded separately as standard. Within the text the inch-pound units are shown in brackets. The values stated in each system are not exact equivalents; therefore, each system must be used independently of the other. Combining values from the two systems may result in nonconformance with the standard.
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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Standards Content (Sample)
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Designation: D7250/D7250M – 06
Standard Practice for
Determining Sandwich Beam Flexural and Shear Stiffness
This standard is issued under the fixed designation D7250/D7250M; 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 D7249/D7249M Test Method for Facing Properties of
Sandwich Constructions by Long Beam Flexure
1.1 This practice covers determination of the flexural and
E6 TerminologyRelatingtoMethodsofMechanicalTesting
transverse shear stiffness properties of flat sandwich construc-
E122 Practice for Calculating Sample Size to Estimate,
tions subjected to flexure in such a manner that the applied
With Specified Precision, the Average for a Characteristic
moments produce curvature of the sandwich facing planes.
of a Lot or Process
Permissible core material forms include those with continuous
E177 Practice for Use of the Terms Precision and Bias in
bonding surfaces (such as balsa wood and foams) as well as
ASTM Test Methods
those with discontinuous bonding surfaces (such as honey-
E456 Terminology Relating to Quality and Statistics
comb). The calculation methods in this practice are limited to
E1309 Guide for Identification of Fiber-Reinforced
sandwich beams exhibiting linear force-deflection response.
Polymer-Matrix Composite Materials in Databases
This practice uses test results obtained from Test Methods
E1434 Guide for Recording Mechanical Test Data of Fiber-
C393/C393M and/or D7249/D7249M.
Reinforced Composite Materials in Databases
1.2 The values stated in either SI units or inch-pound units
are to be regarded separately as standard. Within the text the
3. Terminology
inch-pound units are shown in brackets. The values stated in
3.1 Definitions—Terminology D3878 defines terms relating
each system are not exact equivalents; therefore, each system
to high-modulus fibers and their composites. Terminology
must be used independently of the other. Combining values
C274 defines terms relating to structural sandwich construc-
from the two systems may result in nonconformance with the
tions. Terminology D883 defines terms relating to plastics.
standard.
Terminology E6 defines terms relating to mechanical testing.
1.3 This standard does not purport to address all of the
Terminology E456 and Practice E177 define terms relating to
safety concerns, if any, associated with its use. It is the
statistics.Intheeventofaconflictbetweenterms,Terminology
responsibility of the user of this standard to establish appro-
D3878 shall have precedence over the other terminologies.
priate safety and health practices and determine the applica-
3.2 Symbols:
bility of regulatory limitations prior to use.
b = sandwich width, mm [in.]
2. Referenced Documents c = core thickness, mm [in.]
d = sandwich thickness, mm [in.]
2.1 ASTM Standards:
2 2
D = flexural stiffness, N-mm [lb-in. ]
C273 Test Method for Shear Properties of Sandwich Core
D = beam mid-span deflection, mm [in.]
Materials
G = core shear modulus, MPa [psi]
C274 Terminology of Structural Sandwich Constructions
S = support span length, mm [in.]
C393/C393M Test Method for Core Shear Properties of
L = load span length, mm [in.] (L = 0.0 for 3-point mid-span
Sandwich Constructions by Beam Flexure
loading configuration)
D883 Terminology Relating to Plastics
n = number of specimens
D3878 Terminology for Composite Materials
P = total applied force, N [lb]
t = facing thickness, mm [in.]
U = transverse shear rigidity, N [lb]
This practice is under the jurisdiction ofASTM Committee D30 on Composite
Materials and is the direct responsibility of Subcommittee D30.09 on Sandwich
4. Summary of Practice
Construction.
4.1 This practice consists of calculating the flexural stiff-
Current edition approved Sept. 1, 2006. Published October 2006. DOI: 10.1520/
D7250_D7250M-06.
ness, transverse (through-thickness) shear rigidity and core
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
shear modulus of a sandwich beam using deflection and/or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
strain data from two or more flexure tests of different loading
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. configurations conducted under Test Methods C393/C393M
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D7250/D7250M – 06
and/or D7249/D7249M. This practice also includes equations specimens, as in the case of a designed experiment. For
for calculating the shear rigidity and core shear modulus of a statistically significant data, consult the procedures outlined in
sandwich beam using deflection data from a single flexure test Practice E122. Report the method of sampling.
conducted under Test Method C393/C393M when the facing 7.2 Specimen Geometry—The test specimens shall be rect-
modulus is known.
angular in cross section. The depth of the specimens shall be
equal to the thickness of the sandwich construction, and the
5. Significance and Use
width shall be not less than twice the total thickness, not less
5.1 Flexure tests on flat sandwich constructions may be
than three times the dimension of a core cell, nor greater than
conductedtodeterminethesandwichflexuralstiffness,thecore
one half the span length.The specimen length shall be equal to
shear strength and shear modulus, or the facings compressive
the span length plus 50 mm [2 in.] or plus one half the
and tensile strengths. Tests to evaluate core shear strength may
sandwich thickness whichever is the greater.
also be used to evaluate core-to-facing bonds.
7.3 Loading Configurations, Unknown Facing Modulus—
5.2 Thispracticeprovidesastandardmethodofdetermining
For cases where the facing modulus is not known, a minimum
sandwich flexural and shear stiffness and core shear modulus
of two loading configurations must be selected. Refer to Test
using calculations involving measured deflections of sandwich
Methods C393/C393M and D7249/D7249M for the equations
flexure specimens. Tests can be conducted on short specimens
usedtosizethespecimenlengthsandloadingconfigurationsso
and on long specimens (or on one specimen loaded in two
that facing failure and core shear failures do not occur below
ways), and the flexural stiffness, shear rigidity and core shear
the desired maximum applied force level. It is recommended
modulus can be determined by simultaneous solution of the
that one loading configuration use a short support span and
complete deflection equations for each span or each loading. If
specimen and the other loading configuration use a long
thefacingmodulusvaluesareknown,ashortspanbeamcanbe
support span and specimen. The purpose of this recommenda-
tested and the calculated bending deflection subtracted from
tion is to obtain force-deflection data for one test with
thebeam’stotaldeflection.Thisgivesthesheardeflectionfrom
relativelyhighsheardeflectionandonetestwithrelativelyhigh
which the transverse shear modulus can be determined.
flexural deformation. If two short configurations or two long
configurations are tested, measurement errors may be large
NOTE 1—Core shear strength and shear modulus are best determined in
relative to the difference in shear and flexural deflections
accordance with Test Method C273 provided bare core material is
available.
between the two tests and may lead to significant errors in the
NOTE 2—For cores with high shear modulus, the shear deflection will
calculated flexural and shear stiffness values.
be quite small and ordinary errors in deflection measurements will cause
7.4 Loading Configurations, Known Facing Modulus—For
considerable variations in the calculated shear modulus.
cases where the facing modulus is known for sandwich beams
NOTE 3—To insure that simple sandwich beam theory is valid, a good
with identical facings, a short support span loading configura-
rule of thumb for a four-point bending test is the span length divided by
tion test should be conducted per Test Method C393/C393M.
thesandwichthicknessshouldbegreaterthan20(L /d>20)withtheratio
of facing thickness to core thickness less than 0.1 (t/c < 0.1).
8. Procedure
6. Interferences
8.1 Unknown Facing Modulus—Conduct tests on sandwich
6.1 Material and Specimen Preparation—Important aspects
beam specimens per Test Methods C393/C393M and/or
of sandwich core specimen preparation that contribute to data
D7249/D7249M using two or more different loading configu-
scatter include the existence of joints, voids or other core
rations; Fig. 1. It is preferable to conduct each of the loading
discontinuities, out-of-plane curvature, and surface roughness.
conditionsoneachtestspecimen.Thisrequiresthattheapplied
6.2 Geometry—Specific geometric factors that affect sand-
forces for all but the last loading condition to be kept
wich facing stiffness and thereby the sandwich flexural stiff-
sufficientlylowtoavoidfailureandpermanentdeformationsof
ness include facing thickness, core cell geometry, and facing
the specimen.
surface flatness (toolside or bagside surface in compression).
8.2 Known Facing Modulus—Conduct tests on sandwich
6.3 Environment—Results are affected by the environmen-
beam specimens perTest Methods C393/C393M using a single
tal conditions under which specimens are conditioned, as well
short support span loading configuration.
as the conditions under which the tests are conducted. Speci-
8.3 Data Recording—Record force-deflection curves for
mens tested in various environments can exhibit significant
each test specimen using a transducer, deflectometer, or dial
differences in stiffness. Critical environments must be assessed
gage to measure the mid-span deflection.
independently for each specific combination of core material,
facing material, and core-to-facing interfacial adhesive (if
NOTE 4—The use of crosshead or actuator displacement for the beam
used) that is tested. mid-span deflection produces inaccurate results; the direct measurement
of the deflection of the mid-span of the beam must be made by a suitable
6.4 Core Material—For some core materials, the core shear
instrument.
modulus is a function of the direction that the core is oriented
relative to the length of the specimen. Another material factor
9. Validation
thataffectssandwichcorestiffnessisvariabilityincoredensity.
9.1 Values for stiffness properties shall not be calculated at
7. Sampling and Test Specimens
any applied force level above or beyond the point of initial
7.1 Sampling—Test at least five specimens per test condi- specimen failure, or above a point where the specimen exhibits
tion unless valid results can be gained through the use of fewer obvious non-linear deflection response due to excessive local
D7250/D7250M – 06
(a) 3-Point Loading (C393/C393M Standard Configuration)
(b) 4-Point Loading (D7249/D7249MLong Beam Flexure Standard Configu-
ration)
(c) 4-Point Loading (C393/C393M and D7249/D7249M Non-Standard Con-
figuration)
FIG. 1 Loading Configurations
or overall deflection. Retests shall be performed for any shearrigidityforcaseswherethefacingmodulusvaluesarenot
specimen on which values are not calculated. known are given in 10.1-10.2. Calculation procedures for
transverse shear rigidity and core shear modulus for cases
10. Calculation
where the facing modulus is known are given in 10.3.
10.1 General Instructions, Unknown Facing Modulus—
Calculation procedures for flexural stiffness and transverse
D7250/D7250M – 06
NOTE 5—The equations in this section assume linear force-deflection
loading configurations for a series of applied forces up to the
response for both the facing and core materials. If the force-deflection
lowest maximum applied force of the loading configurations.
response is non-linear, the extraction of non-linear flexural and shear
Values should be calculated for a minimum of ten (10) force
stiffnesses is significantly more complicated and is beyond the scope of
levels evenly spaced over the force range. Next, calculate the
this standard practice.
average value of flexural stiffness, shear rigidity and core shear
10.1.1 Criteria for Force-Deflection Linearity—For pur-
modulusforeachforcelevelforeachspecimen.Thencalculate
poses of validating the force-displacement linearity assump-
the average values of the flexural stiffness, shear rigidity and
tion, determine the maximum offset from a linear force-
core shear modulus using the values calculated at each force
displacement curve over the range of applied forces to be used
level for each specimen replicate.The result is a set of stiffness
to calculate the stiffnesses. Determine the offset from linearity
values as a function of force level. If the sandwich response is
usingthemethodshowninFig.2.Themaximumoffsetshallbe
linear, then calculate an overall average flexural stiffness, shear
less than 10 % for the linearity assumption to be valid.
rigidity and core shear modulus using the values from all force
10.1.2 Results from Tests Using Two Loading Configura-
levels. Report all of the individual and average calculated
tions on the Same Test Specimen—For each specimen, calcu-
stiffness values.
late the flexural stiffness, shear rigidity and core shear modulus
using the equations in 10.2 for a series of applied forces up to
10.1.4 Results from Tests Using Two Loading Configura-
the lowest maximum applied force of the two loading configu-
tions on Different Test Specimens—In some cases it may not be
rations. Values should be calculated for a minimum of ten (10)
possible or desired to conduct tests using two or more loading
force levels evenly spaced over the force range. Calculate the
conditions on the same specimen. In this case, a continuous
average value and statistics of the flexural stiffness, shear
force-displacement curve must be calculated for each loading
rigidity and core shear modulus using the values calculated at
configuration so that displacement values for the two speci-
each force level for each specimen replicate. The result is a set
mens can be determined at the same force value. To calculate
of stiffness values as a function of force level. If the sandwich
the continuous force-displacement curve, perform a linear
response is linear, then calculate an overall average flexural
regression analysis on the force-displacement data for each
stiffness, shear rigidity and core shear modulus using the
loading condition for each specimenusing a linear function in
values from all force levels. Report all of the individual and
displacement for th
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