1、Designation: D7250/D7250M 06 (Reapproved 2012)Standard 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 revis
2、ion, 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 s
3、andwich 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
4、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 se
5、parately 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
6、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 Docum
7、ents2.1 ASTM Standards:2C273 Test Method for Shear Properties of Sandwich CoreMaterialsC274 Terminology of Structural Sandwich ConstructionsC393/C393M Test Method for Core Shear Properties ofSandwich Constructions by Beam FlexureD883 Terminology Relating to PlasticsD3878 Terminology for Composite Ma
8、terialsD7249/D7249M Test Method for Facing Properties ofSandwich Constructions by Long Beam FlexureE6 Terminology Relating to Methods of Mechanical TestingE122 Practice for Calculating Sample Size to Estimate,With Specified Precision, the Average for a Characteristicof a Lot or ProcessE177 Practice
9、for Use of the Terms Precision and Bias inASTM Test MethodsE456 Terminology Relating to Quality and StatisticsE1309 Guide for Identification of Fiber-ReinforcedPolymer-Matrix Composite Materials in DatabasesE1434 Guide for Recording Mechanical Test Data of Fiber-Reinforced Composite Materials in Dat
10、abases3. Terminology3.1 DefinitionsTerminology D3878 defines terms relatingto high-modulus fibers and their composites. TerminologyC274 defines terms relating to structural sandwich construc-tions. Terminology D883 defines terms relating to plastics.Terminology E6 defines terms relating to mechanica
11、l testing.Terminology E456 and Practice E177 define terms relating tostatistics. In the event of a conflict between terms, TerminologyD3878 shall have precedence over the other terminologies.3.2 Symbols:b = sandwich width, mm in.c = core thickness, mm in.d = sandwich thickness, mm in.D = flexural st
12、iffness, N-mm2lb-in.2D = 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 = transverse shear
13、rigidity, N lb4. Summary of Practice4.1 This practice consists of calculating the flexural stiff-ness, 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
14、 under Test Methods C393/C393M1This 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 Feb. 1, 2012. Published March 2012. DOI: 10.1520/D7250_D7250M-06R12.2For referen
15、ced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West C
16、onshohocken, PA 19428-2959, United States.and/or D7249/D7249M. This practice also includes equationsfor calculating the shear rigidity and core shear modulus of asandwich beam using deflection data from a single flexure testconducted under Test Method C393/C393M when the facingmodulus is known.5. Si
17、gnificance 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
18、 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 t
19、woways), 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 subtract
20、ed 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 with Test Method C273 provided bare core material isavailable.NOTE 2For cores with high shear modul
21、us, 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 theory is valid, a goodrule of thumb for a four-point bending test is the span length divided bythe s
22、andwich 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 sandwich core specimen preparation that contribute to datascatter include the existence of joints
23、, 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-ness include facing thickness, core cell geometry, and facingsurface flatness (toolside or bagside
24、 surface in compression).6.3 EnvironmentResults are affected by the environmen-tal conditions under which specimens are conditioned, as wellas the conditions under which the tests are conducted. Speci-mens tested in various environments can exhibit significantdifferences in stiffness. Critical envir
25、onments 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 materials, the core shearmodulus is a function of the direction that the core is orientedrelative to th
26、e 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-tion unless valid results can be gained through the use of fewerspecimens, as in the case of a de
27、signed 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 section. The depth of the specimens shall beequal to the thickness of the sandwich construction,
28、 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 L
29、oading 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 the equationsused to size the specimen lengths and loading configurations sothat facing failure
30、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-defl
31、ection 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
32、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 identical facings, a short support span loading configura-tion test should be conducted per Test Metho
33、d 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 preferable to conduct each of the loadingconditions on each test specimen. This requires that t
34、he 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 specimens per Test Methods C393/C393M using a singleshort support span loading configuration.8.3 Data Re
35、cordingRecord 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 beammid-span deflection produces inaccurate results; the direct measurementof the deflection of th
36、e 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
37、to excessive localD7250/D7250M 06 (2012)2or overall deflection. Retests shall be performed for anyspecimen on which values are not calculated.10. Calculation10.1 General Instructions, Unknown Facing ModulusCalculation procedures for flexural stiffness and transverseshear rigidity for cases where the
38、 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.(a) 3-Point Loading (C393/C393M Standard Configuration)(b) 4-Point Loading (D7249/D7249MLong Beam Flexur
39、e Standard Configu-ration)(c) 4-Point Loading (C393/C393M and D7249/D7249M Non-Standard Con-figuration)FIG. 1 Loading ConfigurationsD7250/D7250M 06 (2012)3NOTE 5The equations in this section assume linear force-deflectionresponse for both the facing and core materials. If the force-deflectionrespons
40、e 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 of validating the force-displacement linearity assump-tion, determine the maximum
41、 offset from a linear force-displacement curve over the range of applied forces to be usedto calculate the stiffnesses. Determine the offset from linearityusing the method shown in Fig. 2. The maximum offset shall beless than 10 % for the linearity assumption to be valid.10.1.2 Results from Tests Us
42、ing Two Loading Configura-tions on the Same Test SpecimenFor each specimen, calcu-late the 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 ca
43、lculated 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 val
44、ues 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 T
45、hree 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 series of applied forces up to thelowest maximum applied force of the loading
46、 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
47、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
48、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 cases it may not bepossible or desired to conduct tests using two or more loadi
49、ngconditions 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 specimenusing a linear function indisplacement for the regression analysis. If the linear curvegives a poor fit to the data, the regression and stiffnesscalcu
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