# ASTM D7250D7250M-16

Designation: D7250/D7250M − 16Standard Practice forDetermining Sandwich Beam Flexural and Shear Stiffness1This standard is issued under the fixed designation D7250/D7250M; the number immediately following the designation indicates theyear of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of lastreapproval. A superscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers determination of the flexural andtransverse shear stiffness properties of flat sandwich construc-tions subjected to flexure in such a manner that the appliedmoments produce curvature of the sandwich facing planes.Permissible core material forms include those with continuousbonding surfaces (such as balsa wood and foams) as well asthose with discontinuous bonding surfaces (such as honey-comb). The calculation methods in this practice are limited tosandwich beams exhibiting linear force-deflection response.This practice uses test results obtained from Test MethodsC393/C393M and/or D7249/D7249M.1.2 The values stated in either SI units or inch-pound unitsare to be regarded separately as standard. The values stated ineach system may not be exact equivalents; therefore, eachsystem shall be used independently of the other. Combiningvalues from the two systems may result in non-conformancewith the standard.1.2.1 Within the text the inch-pound units are shown inbrackets.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2C273 Test Method for Shear Properties of Sandwich CoreMaterialsC393/C393M Test Method for Core Shear Properties ofSandwich Constructions by Beam FlexureD883 Terminology Relating to PlasticsD3878 Terminology for Composite MaterialsD7249/D7249M Test Method for Facing Properties of Sand-wich Constructions by Long Beam FlexureE6 Terminology Relating to Methods of Mechanical TestingE122 Practice for Calculating Sample Size to Estimate, WithSpecified Precision, the Average for a Characteristic of aLot or ProcessE177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE456 Terminology Relating to Quality and Statistics3. Terminology3.1 Definitions—Terminology D3878 defines terms relatingto high-modulus fibers and their composites, as well as termsrelating to sandwich constructions. Terminology D883 definesterms relating to plastics. Terminology E6 defines termsrelating to mechanical testing. Terminology E456 and PracticeE177 define terms relating to statistics. In the event of aconflict between terms, Terminology D3878 shall have prece-dence over the other terminologies.3.2 Symbols: b = sandwich width, mm [in.]c = core thickness, mm [in.]d = sandwich thickness, mm [in.]D = flexural stiffness, N-mm2[lb-in.2]∆ = beam mid-span deflection, mm [in.]G = core shear modulus, MPa [psi]S = support span length, mm [in.]L = load span length, mm [in.] (L = 0.0 for 3-point mid-spanloading configuration)n = number of specimensP = total applied force, N [lb]t = facing thickness, mm [in.]U = transverse shear rigidity, N [lb]4. Summary of Practice4.1 This practice consists of calculating the flexuralstiffness, transverse (through-thickness) shear rigidity and coreshear modulus of a sandwich beam using deflection and/orstrain data from two or more flexure tests of different loadingconfigurations conducted under Test Methods C393/C393Mand/or D7249/D7249M. This practice also includes equationsfor calculating the shear rigidity and core shear modulus of a1This practice is under the jurisdiction of ASTM Committee D30 on CompositeMaterials and is the direct responsibility of Subcommittee D30.09 on SandwichConstruction.Current edition approved April 1, 2016. Published April 2016. Originallyapproved in 2006. Last previous edition approved in 2012 as D7250/D7250M – 06(2012). DOI: 10.1520/D7250_D7250M-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1sandwich beam using deflection data from a single flexure testconducted under Test Method C393/C393M when the facingmodulus is known.5. Significance and Use5.1 Flexure tests on flat sandwich constructions may beconducted to determine the sandwich flexural stiffness, the coreshear strength and shear modulus, or the facings compressiveand tensile strengths. Tests to evaluate core shear strength mayalso be used to evaluate core-to-facing bonds.5.2 This practice provides a standard method of determiningsandwich flexural and shear stiffness and core shear modulususing calculations involving measured deflections of sandwichflexure specimens. Tests can be conducted on short specimensand on long specimens (or on one specimen loaded in twoways), and the flexural stiffness, shear rigidity and core shearmodulus can be determined by simultaneous solution of thecomplete deflection equations for each span or each loading. Ifthe facing modulus values are known, a short span beam can betested and the calculated bending deflection subtracted fromthe beam’s total deflection. This gives the shear deflection fromwhich the transverse shear modulus can be determined.NOTE 1—Core shear strength and shear modulus are best determined inaccordance with Test Method C273 provided bare core material isavailable.NOTE 2—For cores with high shear modulus, the shear deflection willbe quite small and ordinary errors in deflection measurements will causeconsiderable variations in the calculated shear modulus.NOTE 3—To insure that simple sandwich beam theory is valid, a goodrule of thumb for a four-point bending test is the span length divided bythe sandwich thickness should be greater than 20 (L1/d 20) with the ratioof facing thickness to core thickness less than 0.1 (t/c 0.1).6. Interferences6.1 Material and Specimen Preparation—Important aspectsof sandwich core specimen preparation that contribute to datascatter include the existence of joints, voids or other corediscontinuities, out-of-plane curvature, and surface roughness.6.2 Geometry—Specific geometric factors that affect sand-wich facing stiffness and thereby the sandwich flexural stiff-ness include facing thickness, core cell geometry, and facingsurface flatness (toolside or bagside surface in compression).6.3 Environment—Results are affected by the environmentalconditions under which specimens are conditioned, as well asthe conditions under which the tests are conducted. Specimenstested in various environments can exhibit significant differ-ences in stiffness. Critical environments must be assessedindependently for each specific combination of core material,facing material, and core-to-facing interfacial adhesive (ifused) that is tested.6.4 Core Material—For some core materials, the core shearmodulus is a function of the direction that the core is orientedrelative to the length of the specimen. Another material factorthat affects sandwich core stiffness is variability in core density.7. Sampling and Test Specimens7.1 Sampling—Test at least five specimens per test condi-tion unless valid results can be gained through the use of fewerspecimens, as in the case of a designed experiment. Forstatistically significant data, consult the procedures outlined inPractice E122. Report the method of sampling.7.2 Specimen Geometry—The test specimens shall be rect-angular in cross section. The depth of the specimens shall beequal to the thickness of the sandwich construction, and thewidth shall be not less than twice the total thickness, not lessthan three times the dimension of a core cell, nor greater thanone half the span length. The specimen length shall be equal tothe span length plus 50 mm [2 in.] or plus one half thesandwich thickness whichever is the greater.7.3 Loading Configurations, Unknown Facing Modulus—For cases where the facing modulus is not known, a minimumof two loading configurations must be selected. Refer to TestMethods C393/C393M and D7249/D7249M for the equationsused to size the specimen lengths and loading configurations sothat facing failure and core shear failures do not occur belowthe desired maximum applied force level. It is recommendedthat one loading configuration use a short support span andspecimen and the other loading configuration use a longsupport span and specimen. The purpose of this recommenda-tion is to obtain force-deflection data for one test withrelatively high shear deflection and one test with relatively highflexural deformation. If two short configurations or two longconfigurations are tested, measurement errors may be largerelative to the difference in shear and flexural deflectionsbetween the two tests and may lead to significant errors in thecalculated flexural and shear stiffness values.7.4 Loading Configurations, Known Facing Modulus—Forcases where the facing modulus is known for sandwich beamswith identical facings, a short support span loading configura-tion test should be conducted per Test Method C393/C393M.8. Procedure8.1 Unknown Facing Modulus—Conduct tests on sandwichbeam specimens per Test Methods C393/C393M and/orD7249/D7249M using two or more different loading configu-rations; Fig. 1. It is preferable to conduct each of the loadingconditions on each test specimen. This requires that the appliedforces for all but the last loading condition to be keptsufficiently low to avoid failure and permanent deformations ofthe specimen.8.2 Known Facing Modulus—Conduct tests on sandwichbeam specimens per Test Methods C393/C393M using a singleshort support span loading configuration.8.3 Data Recording—Record force-deflection curves foreach test specimen using a transducer, deflectometer, or dialgage to measure the mid-span deflection.NOTE 4—The use of crosshead or actuator displacement for the beammid-span deflection produces inaccurate results; the direct measurementof the deflection of the mid-span of the beam must be made by a suitableinstrument.9. Validation9.1 Values for stiffness properties shall not be calculated atany applied force level above or beyond the point of initialspecimen failure, or above a point where the specimen exhibitsobvious non-linear deflection response due to excessive localD7250/D7250M − 162or overall deflection. Retests shall be performed for anyspecimen on which values are not calculated.10. Calculation10.1 General Instructions, Unknown Facing Modulus—Calculation procedures for flexural stiffness and transverseshear rigidity for cases where the facing modulus values are notknown are given in 10.1 – 10.2. Calculation procedures fortransverse shear rigidity and core shear modulus for caseswhere the facing modulus is known are given in 10.3.NOTE 5—The equations in this section assume linear force-deflectionresponse for both the facing and core materials. If the force-deflection(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 ConfigurationsD7250/D7250M − 163response is non-linear, the extraction of non-linear flexural and shearstiffnesses is significantly more complicated and is beyond the scope ofthis standard practice.10.1.1 Criteria for Force-Deflection Linearity—For pur-poses of validating the force-displacement linearityassumption, determine the maximum offset from a linearforce-displacement curve over the range of applied forces to beused to calculate the stiffnesses. Determine the offset fromlinearity using the method shown in Fig. 2. The maximumoffset shall be less than 10 % for the linearity assumption to bevalid.10.1.2 Results from Tests Using Two Loading Configura-tions on the Same Test Specimen—For each specimen, calculatethe flexural stiffness, shear rigidity and core shear modulususing the equations in 10.2 for a series of applied forces up tothe lowest maximum applied force of the two loading configu-rations. Values should be calculated for a minimum of ten (10)force levels evenly spaced over the force range. Calculate theaverage value and statistics of the flexural stiffness, shearrigidity and core shear modulus using the values calculated ateach force level for each specimen replicate. The result is a setof stiffness values as a function of force level. If the sandwichresponse is linear, then calculate an overall average flexuralstiffness, shear rigidity and core shear modulus using thevalues from all force levels. Report all of the individual andaverage calculated stiffness values.10.1.3 Results from Tests Using Three or More LoadingConfigurations on the Same Test Specimen—For each speci-men calculate the flexural stiffness, shear rigidity and coreshear modulus using the equations in 10.2 for each pair ofloading configurations for a series of applied forces up to thelowest maximum applied force of the loading configurations.Values should be calculated for a minimum of ten (10) forcelevels evenly spaced over the force range. Next, calculate theaverage value of flexural stiffness, shear rigidity and core shearmodulus for each force level for each specimen. Then calculatethe average values of the flexural stiffness, shear rigidity andcore shear modulus using the values calculated at each forcelevel for each specimen replicate. The result is a set of stiffnessvalues as a function of force level. If the sandwich response islinear, then calculate an overall average flexural stiffness, shearrigidity and core shear modulus using the values from all forcelevels. Report all of the individual and average calculatedstiffness values.10.1.4 Results from Tests Using Two Loading Configura-tions on Different Test Specimens—In some cases it may not bepossible or desired to conduct tests using two or more loadingconditions on the same specimen. In this case, a continuousforce-displacement curve must be calculated for each loadingconfiguration so that displacement values for the two speci-mens can be determined at the same force value. To calculatethe continuous force-displacement curve, perform a linearregression analysis on the force-displacement data for eachloading condition for each specimen using a linear function indisplacement for the regression analysis. If the linear curvegives a poor fit to the data, the regression and stiffnesscalculations should only be performed over the linear range ofthe force-deflection curve. Once the force-displacement curvesare calculated for each loading condition, use the curves andthe procedure of 10.1.1 to calculate t