1、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 l
2、ast 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-t
3、ions 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). Th
4、e 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 standa
5、rd. 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
6、 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 Stand
7、ards: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 Cons
8、tructions 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 Termi
9、nology Relating to Quality and Statistics3. Terminology3.1 DefinitionsTerminology 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 m
10、echanical 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 =
11、flexural stiffness, N-mm2lb-in.2 = beam mid-span deflection, mm in.G = core shear modulus, MPa psiS = 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 lbt = facing thickness, mm in.U = transve
12、rse shear rigidity, N lb4. 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 c
13、onducted 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 o
14、n 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
15、 Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards 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
16、 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 t
17、ensile 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 specime
18、ns. 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 modul
19、us values are known, a short span beam can betested and the calculated bending deflection subtracted fromthe beams total deflection. This gives the shear deflection fromwhich the transverse shear modulus can be determined.NOTE 1Core shear strength and shear modulus are best determined inaccordance w
20、ith Test Method C273 provided bare core material isavailable.NOTE 2For 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 3To insure that simple sandwich beam the
21、ory 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 PreparationImportant aspectsof
22、 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 GeometrySpecific geometric factors that affect sand-wich facing stiffness and thereby the sandwich flexural stiff-
23、ness include facing thickness, core cell geometry, and facingsurface flatness (toolside or bagside surface in compression).6.3 EnvironmentResults are affected by the environmentalconditions under which specimens are conditioned, as well asthe conditions under which the tests are conducted. Specimens
24、tested 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 MaterialFor some core materia
25、ls, 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 SamplingTest at least five specimens per test condi-t
26、ion 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 GeometryThe test specimens shall be rect-angular in cross
27、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 sp
28、an length plus 50 mm 2 in. or plus one half thesandwich thickness whichever is the greater.7.3 Loading Configurations, Unknown Facing ModulusFor 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
29、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
30、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 ma
31、y 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 ModulusForcases where the facing modulus is known for sandwich beamswith identi
32、cal facings, a short support span loading configura-tion test should be conducted per Test Method C393/C393M.8. Procedure8.1 Unknown Facing ModulusConduct tests on sandwichbeam specimens per Test Methods C393/C393M and/orD7249/D7249M using two or more different loading configu-rations; Fig. 1. It is
33、 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 ModulusConduct tests on sandwichbeam specimen
34、s per Test Methods C393/C393M using a singleshort support span loading configuration.8.3 Data RecordingRecord force-deflection curves foreach test specimen using a transducer, deflectometer, or dialgage to measure the mid-span deflection.NOTE 4The use of crosshead or actuator displacement for the be
35、ammid-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
36、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 ModulusCalcu
37、lation 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 5The equat
38、ions 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/D7249
39、M 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 LinearityFor pur-poses
40、 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
41、than 10 % for the linearity assumption to bevalid.10.1.2 Results from Tests Using Two Loading Configura-tions on the Same Test SpecimenFor 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 m
42、aximum 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
43、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 individ
44、ual andaverage calculated stiffness values.10.1.3 Results from Tests Using Three or More LoadingConfigurations on the Same Test SpecimenFor 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 s
45、eries 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 forc
46、e 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 isline
47、ar, 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 SpecimensIn some cas
48、es 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 va
49、lue. 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
