1、Designation: D 7250/D 7250M 06Standard Practice forDetermining Sandwich Beam Flexural and Shear Stiffness1This standard is issued under the fixed designation D 7250/D 7250M; the number immediately following the designation indicates theyear of original adoption or, in the case of revision, the year
2、of last revision. A number in parentheses indicates the year of lastreapproval. A superscript epsilon (e) 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 const
3、ruc-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
4、). The calculation methods in this practice are limited tosandwich beams exhibiting linear force-deflection response.This practice uses test results obtained from Test MethodsC 393/C 393M and/or D 7249/D 7249M.1.2 The values stated in either SI units or inch-pound unitsare to be regarded separately
5、as standard. Within the text theinch-pound units are shown in brackets. The values stated ineach system are not exact equivalents; therefore, each systemmust be used independently of the other. Combining valuesfrom the two systems may result in nonconformance with thestandard.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 Standa
7、rds:2C 273 Test Method for Shear Properties of Sandwich CoreMaterialsC 274 Terminology of Structural Sandwich ConstructionsC 393 Test Method for Flexural Properties of SandwichConstructionsD 883 Terminology Relating to PlasticsD 3878 Terminology for Composite MaterialsD 7249/D 7249M Test Method for
8、Facing Properties ofSandwich Constructions by Long Beam FlexureE6 Terminology Relating to Methods of Mechanical Test-ingE 122 Practice for Calculating Sample Size to Estimate,With a Specified Tolerable Error, the Average for aCharacteristic of a Lot or ProcessE 177 Practice for Use of the Terms Prec
9、ision and Bias inASTM Test MethodsE 456 Terminology Relating to Quality and StatisticsE 1309 Guide for Identification of Fiber-ReinforcedPolymer-Matrix Composite Materials in DatabasesE 1434 Guide for Recording Mechanical Test Data of Fiber-Reinforced Composite Materials in Databases3. Terminology3.
10、1 DefinitionsTerminology D 3878 defines terms relatingto high-modulus fibers and their composites. TerminologyC 274 defines terms relating to structural sandwich construc-tions. Terminology D 883 defines terms relating to plastics.Terminology E6defines terms relating to mechanical testing.Terminolog
11、y E 456 and Practice E 177 define terms relating tostatistics. In the event of a conflict between terms, TerminologyD 3878 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 stiffness, N-mm2lb-
12、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 rigidity, N lb4.
13、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/or1This practice is under the jurisdiction of ASTM Committee D30 on CompositeMaterials and is the direct r
14、esponsibility of Subcommittee D30.09 on SandwichConstruction.Current edition approved Sept. 1, 2006. Published October 2006.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, r
15、efer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.strain data from two or more flexure tests of different loadingconfigurations conducted under Test Methods C 393/C 393Mand
16、/or D 7249/D 7249M. 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 C 393/C 393M when the facingmodulus is known.5. Significance and Use5.1 Flexure tests on fl
17、at 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 stand
18、ard 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, shea
19、r 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 beams total deflection. This g
20、ives 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 C 273 provided bare core material isavailable.NOTE 2For cores with high shear modulus, the shear deflection willbe quite sm
21、all 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 sandwich thickness should be greater than
22、 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, voids or other corediscontinuities, ou
23、t-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 surface in compression).6.3 Environment
24、Results 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 environments must be assessedindependently fo
25、r 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 the length of the specimen. Another materi
26、al 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 designed experiment. Forstatistically sign
27、ificant data, consult the procedures outlined inPractice E 122. 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, and thewidth shall be not less than tw
28、ice 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 M
29、odulusFor cases where the facing modulus is not known, a minimumof two loading configurations must be selected. Refer to TestMethods C 393/C 393M and D 7249/D 7249M for the equa-tions used to size the specimen lengths and loading configu-rations so that facing failure and core shear failures do noto
30、ccur below the desired maximum applied force level. It isrecommended that one loading configuration use a shortsupport span and specimen and the other loading configurationuse a long support span and specimen. The purpose of thisrecommendation is to obtain force-deflection data for one testwith rela
31、tively high shear deflection and one test with relativelyhigh flexural deformation. If two short configurations or twolong configurations are tested, measurement errors may belarge relative to the difference in shear and flexural deflectionsbetween the two tests and may lead to significant errors in
32、 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 Method C 393/C 393M.8. Procedure8.1 Un
33、known Facing ModulusConduct tests on sandwichbeam specimens per Test Methods C 393/C 393M and/orD 7249/D 7249M 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 bu
34、t 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 C 393/C 393M using asingle short support span loading configuration.8.3 Data RecordingRecord force-defle
35、ction 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 the mid-span of the beam mu
36、st 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 initialD 7250/D 7250M 062specimen failure, or above a point where the specimen exhibitsobvious non-linear deflection response due to exce
37、ssive localor 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 facing modulus values are not
38、known 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 equations in this section assume linear force-deflectionresponse for both the facing and core materials. If the force-deflec
39、tion(a) 3-Point Loading (C 393/C 393M Standard Configuration)(b) 4-Point Loading (D 7249/D 7249M Long Beam Flexure Standard Con-figuration)(c) 4-Point Loading (C 393/C 393M and D 7249/D 7249M Non-Standard Con-figuration)FIG. 1 Loading ConfigurationsD 7250/D 7250M 063response is non-linear, the extra
40、ction 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 offset from a linear forc
41、e-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 Using Two Loading Configura-
42、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 calculated for a minimum of
43、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
44、 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 LoadingConfig
45、urations 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 configurations.Values sho
46、uld 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
47、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 t
48、he 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 loadingconditions on the same s
49、pecimen. 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 stiffnesscalculations should only be perf
