1、Designation: D 747 08Standard Test Method forApparent Bending Modulus of Plastics by Means of aCantilever Beam1This standard is issued under the fixed designation D 747; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of l
2、ast revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope*1.1 This test method covers the determination of the appar-ent bending modulus2of plastics by means of a cantileverbeam. I
3、t is well suited for determining relative flexibility ofmaterials over a wide range. It is particularly useful formaterials too flexible to be tested by Test Methods D 790.1.2 The values stated in SI units are to be regarded as thestandard. The values given in parentheses are for informationonly.1.3
4、 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.NOTE 1There is no
5、known ISO equivalent to this standard.2. Referenced Documents2.1 ASTM Standards:3D 618 Practice for Conditioning Plastics for TestingD 790 Test Methods for Flexural Properties of Unreinforcedand Reinforced Plastics and Electrical Insulating MaterialsD 4000 Classification System for Specifying Plasti
6、c Mate-rialsD 4066 Classification System for Nylon Injection and Ex-trusion Materials (PA)D 5947 Test Methods for Physical Dimensions of SolidPlastics SpecimensE 177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE 691 Practice for Conducting an Interlaboratory Study toDetermine
7、 the Precision of a Test Method3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 apparent bending modulusan apparent modulus ofelasticity obtained in flexure, using a cantilever beam testingapparatus, where the deformation involved is not purely elasticbut contains both elastic
8、and plastic components.4. Significance and Use4.1 This test method provides a means of deriving theapparent bending modulus of a material by measuring forceand angle of bend of a cantilever beam. The mathematicalderivation assumes small deflections and purely elastic behav-ior. Under actual test con
9、ditions, the deformation has bothelastic and plastic components. This test method does notdistinguish or separate these, and hence a true elastic modulusis not calculable. Instead, an apparent value is obtained and isdefined as the apparent bending modulus of the material. Thetangent modulus obtaine
10、d by Test Methods D 790 is preferred,when the material can be tested by the Test Methods D 790 testprocedure.4.2 Because of deviations from purely elastic behavior,changes in span length, width, and depth of the specimen willaffect the value of the apparent bending modulus obtained;therefore, values
11、 obtained from specimens of different dimen-sions are not necessarily comparable.4.3 Rate of loading is controlled only to the extent that therate of angular change of the rotating jaw is fixed at 58 to66/min. Actual rate of stressing will be affected by spanlength, width, depth of the specimen, and
12、 weight of thependulum.4.4 For many materials, there are specifications that requirethe use of this test method, but with some procedural modifi-cations that take precedence when adhering to the specifica-tion. Therefore, it is advisable to refer to that material speci-fication before using this tes
13、t method. Table 1 of ClassificationSystem D 4000 lists the ASTM materials standards that cur-rently exist.NOTE 2A discussion of the theory of obtaining a purely elasticbending modulus, using a cantilever beam testing apparatus, can be found1This test method is under the jurisdiction of ASTM Committe
14、e D20 on Plasticsand is the direct responsibility of Subcommittee D20.10 on Mechanical Properties.Current edition approved Aug. 1, 2008. Published September 2008. Originallyapproved in 1943. Last previous edition approved in 2002 as D 747 - 02.2This property was designated stiffness in versions of t
15、his test method issuedprior to 1984.3For referenced 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.1*A Summary of Changes se
16、ction appears at the end of this standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.in Appendix X1. The results obtained under actual test conditions will bethe apparent bending modulus.5. Apparatus5.1 The apparatus for the appa
17、rent bending modulus test, asshown in Fig. 1, shall be the cantilever beam bending type,consisting essentially of the following:5.1.1 ViseA motor-driven specimen vise, V, with handcrank for initial loading, to which the pointer indicator I2isattached, and which is capable of uniform clockwise rotati
18、onabout the point O at a nominal rate of 60 of arc/min.5.1.2 Bending PlateA bending plate, Q, which is adjust-able to provide several different spans. The rotation of the visecauses the specimen to bend against this plate applying theload.5.1.3 Weighing SystemA pendulum weighing system, in-cluding a
19、n angular deflection scale, pointer indicator I1, bend-ing plate Q for contacting the free end of the specimen, and aseries of detachable weights. This system shall be pivoted fornearly frictionless rotation about the point O. The total appliedbending moment, MW, consists of the effective moment of
20、thependulum and the bending plate, A1, plus the moments of theadded calibrated weights, A2. Thus,MW5 WL sin u (1)where:Mw= actual bending moment at the angle u,W = total applied load, N (or lbf),L = length of the pendulum arm, m (or in.), andu = angle through which the pendulum rotates.NOTE 3Auxilia
21、ry weights for the test apparatus are calibrated andmarked directly with the values for M, the bending moment at a loadreading of 100. Since Mwdepends on the geometry of the testing machine,these weights are not interchangeable between machines of differentcapacities.5.1.4 Load ScaleA fixed scale th
22、at measures the load as afunction of the deflection, u, of the load pendulum system. Itshall be calibrated such that:Load scale reading 5 100 WL sin u/ M (2)where:M = bending moment at a load scale reading of 100.Thus,Mw5 M 3 load scale reading!/100 (3)where:Mw= actual bending moment.5.1.5 Angular D
23、eflection ScaleThe angular deflectionscale shall be calibrated in degrees of arc and shall indicate theangle through which the rotating vise has been turned relativeto the pendulum system. This is the difference between theangle through which the vise has been turned and the anglethrough which the l
24、oad pendulum has been deflected, and isdesignated as angle f.5.1.6 Depth Measuring DevicesSuitable micrometers, orthickness gages, reading to 0.0025 mm (0.0001 in.) or less,shall be used for measuring the depth of the test specimens.The pressure exerted by the gage on the specimen beingmeasured shal
25、l be between 159 and 186 kPa (23 and 27 psi).MethodAof Test Methods D 5947 is suitable for measuring thespecimen depth. The apparatus and procedure of Method C ofTest Methods D 5947 is also suitable for measuring thespecimen depth, provided the load on the spindle is adjusted sothat the exerted pres
26、sure is between 159 and 186 kPa (23 and27 psi).5.1.7 Width-Measuring DevicesSuitable scales or otherwidth measuring devices reading to 0.025 mm (0.001 in.) orless shall be used for measuring the width of the test specimen.6. Test Specimens6.1 Test specimens shall either be molded or be cut frommolde
27、d, calendered, or cast sheets of the material to be tested.They shall have a rectangular cross section and shall be cutwith their longitudinal axes parallel to the direction of theprincipal axis of anisotropy, unless anisotropy effects arespecifically to be evaluated. The width and depth of thespeci
28、men to be tested, as well as the span length, will dependupon the apparent bending modulus of the material and thecapacity of the testing machine. Specimens shall have an evensurface. If they exhibit a surface tackiness, they shall be dustedlightly with talc before being tested.6.2 Specimen width sh
29、all be between 5.0 and 25.4 mm (0.20and 1.00 in.), provided the material does not extend over thewidth of the anvil. Width shall be measured to the nearest 0.025mm (0.001 in.).6.3 The minimum specimen depth shall be 0.5 mm (0.020in.) and shall be measured to the nearest 0.0025 mm (0.0001in.).NOTE 4A
30、 minimum specimen depth requirement is included since alarge percentage error can result in the final apparent bending modulusvalue because of small errors in the depth measurement. The reason forFIG. 1 Mechanical System of Test ApparatusD747082this large dependence of apparent bending modulus on de
31、pth errors isbecause the depth is to the third power in the formula.6.4 The span-to-depth ratio shall be greater than 15 to 1.NOTE 5Large span-to-depth ratios may be limited by the sensitivityof the load-measuring and deflectometer equipment. A span of 50 mm (2in.) is preferred, providing the span-t
32、o-depth ratio meets the abovecriterion.6.5 The number of specimens tested shall be at least five.7. Conditioning7.1 ConditioningCondition the test specimens at 23 62C (73.4 6 3.6F) and 50 6 10 % relative humidity for notless than 40 h prior to test in accordance with Procedure A ofPractice D 618 unl
33、ess otherwise specified by contract or therelevant ASTM material specification. Reference pre-test con-ditioning, to settle disagreements, shall apply tolerances of61C (1.8F) and 65 % relative humidity.7.2 Test ConditionsConduct the tests at 23 6 2C (73.4 63.6F) and 50 6 10 % relative humidity unles
34、s otherwisespecified by contract or the relevant ASTM material specifica-tion. Reference testing conditions, to settle disagreements,shall apply tolerances of 61C (1.8F) and 65 % relativehumidity.7.3 Specimens to be tested at temperatures above or belownormal shall be conditioned at the test tempera
35、ture at least 2 hprior to testing, unless shorter equilibration time has beenproven. The test apparatus itself should be conditioned 2 hbefore testing.NOTE 6For operations at temperatures below 0C (32F) it may benecessary to remove all the lubricant from the gear box, bearings, etc., ofthe apparatus
36、 and replace it with kerosene or silicone oil.8. Procedure8.1 Place the test apparatus on an approximately levelsurface. Add necessary weights to the pendulum and, ifnecessary, adjust the load scale to indicate zero. Set thebending pin or plate to the proper bending span as determinedin 6.4. Start t
37、he motor and keep it running throughout the teststo minimize friction effects in the weighing system.8.2 For maximum precision choose the value of M so that,at an angle of 3, the load scale reading is between 5 and 10.If this value is not known, determine it by trial and error usingthe standard proc
38、edure. After obtaining M, test five specimens.8.3 Insert one end of the specimen at least34 of the way intothe vise to ensure that the specimen is held securely and evenly.Firmly clamp the test specimen in the vise with the centerlineapproximately parallel to the face of the dial plate. By turningth
39、e hand crank, apply sufficient load to the specimen to showa 1 % load reading and then set the angle pointer to zero.Record this point and plot it as part of the data.8.4 Hold down the motor engaging lever and take subse-quent load scale readings at 3, 6, 9, 12, and 15. Do not retestany specimen.9.
40、Calculation9.1 Plot the data on coordinate paper with the load scalereading as ordinate (y axis) and the angular deflection asabscissa (x axis).9.2 Draw the steepest straight line through at least threeconsecutive points on the plot (see Fig. 2, Fig. 3, and Fig. 4).If this line does not pass through
41、 the origin, translate it parallelto itself until it passes through the origin. Use the data obtainedfrom this line in the equation given in 9.3.9.3 Calculate the apparent bending modulus to three signifi-cant figures, as follows:Eb5 4S/wd3! 3 M 3 load scale reading!/100 f (4)where:Eb= apparent bend
42、ing modulus, Pa (or psi),S = span length, length measured from the center ofrotation of the pendulum weighing system and thespecimen vise to the contacting edge of the bendingplate, m (or in.),w = specimen width, m (or in.),d = specimen depth, m (or in.),M = total bending moment value of the pendulu
43、m system,Nm (or lbfin.), based on the moment of the basicpendulum system, a1, plus the moments indicated onthe calibrated weight or weights, a2, andf = reading on angular deflection scale converted toradians (Table 1).10. Report10.1 Report the following information:10.1.1 Complete identification of
44、the material tested, includ-ing type, source, manufacturers code number, form, surface,width of the test specimens, span, and directionality,10.1.2 Average apparent bending modulus and the nominalspecimen depth used,10.1.3 All observed and recorded data on which the calcu-lations are based,10.1.4 Te
45、st temperature, and10.1.5 Date of test.FIG. 2 Ideal CurveD74708311. Precision and Bias411.1 Table 2 is based on a round-robin test conducted in1981, in accordance with Practice E 691, involving fourmaterials tested by seven laboratories. Each “test result” wasthe average of five individual determina
46、tions. Each laboratoryobtained two test results for each material. (WarningThefollowing explanations of r and R (11.2-11.2.3) are intendedonly to present a meaningful way of considering the approxi-mate precision of this test method. The data given in Table 2should not be applied rigorously to the a
47、cceptance or rejectionof materials, as those data are specific to the round robin andmay not be representative of other lots, conditions, materials,or laboratories. Users of this test method should apply theprinciples outlined in Practice E 691 to generate data specificto their laboratory and materi
48、als, or between specific laborato-ries. The principles of 11.2-11.2.3 would then be valid for suchdata.)11.2 Concept of r and R in Table 1If Srand SRhave beencalculated from a large enough body of data, and for test resultsthat were averages from testing five specimens for each testresult, then:11.2
49、.1 RepeatabilityTwo test results obtained within onelaboratory shall be judged not equivalent if they differ by morethan the r value for that material. The r value is the intervalrepresenting the critical difference between two test results forthe same material, obtained by the same operator using thesame equipment on the same day in the same laboratory.11.2.2 ReproducibilityTwo test results obtained by differ-ent laboratories shall be judged not equivalent if they differ bymore than the R value for that material. The R value is theinterval r
