1、Designation: D 747 02Standard 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 (e) 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.
3、It 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.
4、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.NOTE 1There is no
5、 known ISO equivalent for this standard.2. Referenced Documents2.1 ASTM Standards:D 374 Test Methods for Thickness of Solid Electrical Insu-lation3D 618 Practice for Conditioning Plastics for Testing4D 790 Test Methods for Flexural Properties of Unreinforcedand Reinforced Plastics and Electrical Ins
6、ulating Materi-als4D 4000 Classification System for Specifying Plastic Mate-rials5D 4066 Classification System for Nylon Injection and Ex-trusion Materials5E 177 Practice for Use of the Terms Precision and Bias inASTM Test Methods6E 691 Practice for Conducting an Interlaboratory Study toDetermine th
7、e Precision of a Test Method63. 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 an
8、d 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 condi
9、tions, 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 obtained
10、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 o
11、btained from specimens of different dimen-sions may not necessarily be 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, an
12、d weight of thependulum.4.4 For many materials, there may be a specification thatrequires the use of this test method, but with some proceduralmodifications that take precedence when adhering to thespecification. Therefore, it is advisable to refer to that materialspecification before using this tes
13、t method. Table 1 of Classi-fication System D 4000 lists theASTM materials standards thatcurrently exist.NOTE 2A discussion of the theory of obtaining a purely elastic1This test method is under the jurisdiction of ASTM Committee D20 on Plasticsand is the direct responsibility of Subcommittee D20.10
14、on Mechanical Properties.Current edition approved April 10, 2002. Published June 2002. Originallypublished as D 747 43 T. Last previous edition D 747 99.2This property was designated stiffness in versions of this test method issuedprior to 1984.3Annual Book of ASTM Standards, Vol 10.01.4Annual Book
15、of ASTM Standards, Vol 08.01.5Annual Book of ASTM Standards, Vol 08.02.6Annual Book of ASTM Standards, Vol 14.02.1*A Summary of Changes section appears at the end of this standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.bendin
16、g modulus, using a cantilever beam testing apparatus, can be foundin Appendix X1. The results obtained under actual test conditions will bethe apparent bending modulus.5. Apparatus5.1 The apparatus for the apparent bending modulus test, asshown in Fig. 1, shall be the cantilever beam bending type,co
17、nsisting essentially of the following:5.1.1 ViseA specimen vise, V, to which the pointerindicator I2is attached, and which is capable of uniformclockwise rotation about the point O at a nominal rate of 60 ofarc/min.5.1.2 Weighing SystemA pendulum weighing system, in-cluding an angular deflection sca
18、le, 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 thependulum and the bend
19、ing 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 3Auxiliary weights for the test
20、apparatus7are 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.5.1.3 Load ScaleA fixed scale that measures the load as
21、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.5.1.4 Angular Deflection ScaleThe angul
22、ar 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 load pendulum has been de
23、flected, and isdesignated as angle f.5.1.5 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 shall be between 159 and 186
24、 kPa (23 and 27 psi).Method A of Test Methods D 374 may be used. Alternatively,the apparatus and procedure of Method C of Test MethodsD 374 may be used provided the load on the spindle isincreased so that the exerted pressure is between 159 and 186kPa (23 and 27 psi).5.1.6 Width-Measuring DevicesSui
25、table 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 may be molded or cut from molded,calendered, or cast sheets of the material to be tested. Theyshall have a rectangular cr
26、oss section and shall be cut with theirlongitudinal axes parallel to the direction of the principal axisof anisotropy, unless anisotropy effects are specifically to beevaluated. The width and depth of the specimen to be tested, aswell as the span length, will depend upon the apparent bendingmodulus
27、of the material and the capacity of the testingmachine. Specimens shall have an even surface. If they exhibita surface tackiness, they shall be dusted lightly with talc beforebeing tested.6.2 Specimen width shall be between 5.0 and 25.4 mm (0.25and 1.00 in.), provided the material does not extend ov
28、er 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 cm (0.0001in.).NOTE 4A minimum specimen depth requirement is included since alarge percentage error can result in
29、 the final apparent bending modulusvalue because of small errors in the depth measurement. The reason forthis large dependence of apparent bending modulus on depth errors is7This apparatus can be obtained from Tinius Olsen Testing Machine Co., Inc.,Easton Road, Willow Grove, PA 19090.FIG. 1 Mechanic
30、al System of Test ApparatusD747022because the depth is to the third power in the formula.6.4 The span-to-depth ratio shall be greater than 15 to 1.Large span-to-depth ratios may be limited by the sensitivity ofthe load-measuring and deflectometer equipment.6.5 The number of specimens tested shall be
31、 at least five.7. Conditioning7.1 ConditioningCondition the test specimens at 23 62C (73.4 6 3.6F) and 50 6 5 % relative humidity for not lessthan 40 h prior to test in accordance with Procedure A ofPractice D 618 unless otherwise specified by contract or therelevant ASTM material specification. Ref
32、erence pre-test con-ditioning, to settle disagreements, shall apply tolerances of61C (1.8F) and 62 % relative humidity.7.2 Test ConditionsConduct the tests at 23 6 2C (73.4 63.6F) and 50 6 5 % relative humidity unless otherwisespecified by contract or the relevant ASTM material specifica-tion. Refer
33、ence testing conditions, to settle disagreements,shall apply tolerances of 61C (1.8F) and 62 % relativehumidity.7.3 Specimens to be tested at temperatures above or belownormal shall be conditioned at the test temperature at least 2 hprior to testing, unless shorter equilibration time has beenproven.
34、 The test apparatus itself should be conditioned 2 hbefore testing.7.4 Lubrication of Test Apparatus For operations at tem-peratures below 0C (32F) it may be necessary to remove allthe lubricant from the gear box, bearings, etc., of the apparatusand replace it with kerosine or silicone oil.8. Proced
35、ure8.1 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 the motor and keep it running throughout the teststo min
36、imize 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 procedure. After obtaining M, test five specimens.8.3 Firml
37、y clamp the test specimen in the vise with thecenterline approximately parallel to the face of the dial plate.By turning the hand crank, apply sufficient load to thespecimen to show a 1 % load reading and then set the anglepointer to zero. Record this point and plot it as part of the data.8.4 Hold d
38、own the motor engaging lever and take subse-quent load scale readings at 3, 6, 9, 12, and 15. Do not retestany specimen.9. Calculation9.1 Plot the data on coordinate paper with the load scalereading as ordinate and the angular deflection as abscissa.9.2 Draw the steepest straight line through at lea
39、st threeconsecutive points on the plot (see Fig. 2, Fig. 3, and Fig. 4).If this line does not pass through 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 thr
40、ee signifi-cant figures, as follows:Eb5 4S/wd3! 3 M 3 load scale reading!/100 f (4)where:Eb= apparent bending 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
41、 = specimen width, m (or in.),d = specimen depth, m (or in.),M = total bending moment value of the pendulum 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 conver
42、ted toradians (Table 1).10. Report10.1 Report the following information:FIG. 2 Ideal CurveFIG. 3 Typical Curve for Nonrigid MaterialD74702310.1.1 Complete identification of the material tested, includ-ing type, source, manufacturers code number, form, surface,width of the test specimens, span, and d
43、irectionality,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 Test temperature, and10.1.5 Date of test.11. Precision and Bias811.1 Table 2 is based on a round-robin test conducted in1981, in
44、accordance with Practice E 691, involving fourmaterials tested by seven laboratories. Each “test result” wasthe average of five individual determinations. Each laboratoryobtained two test results for each material.NOTE 5Caution: The following explanations of r and R (11.2-11.2.3)are intended only to
45、 present a meaningful way of considering theapproximate precision of this test method. The data given in Table 2should not be applied rigorously to the acceptance or rejection ofmaterials, as those data are specific to the round robin and may not berepresentative of other lots, conditions, materials
46、, or laboratories. Users ofthis test method should apply the principles outlined in Practice E 691 togenerate data specific to their laboratory and materials, or between specificlaboratories. 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 SR
47、have beencalculated from a large enough body of data, and for test resultsthat were averages from testing five specimens for each testresult, then:11.2.1 RepeatabilityTwo test results obtained within onelaboratory shall be judged not equivalent if they differ by morethan the r value for that materia
48、l. 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 no
49、t equivalent if they differ bymore than the R value for that material. The R value is theinterval representing the critical difference between two testresults for the same material, obtained by different operatorsusing different equipment in different laboratories.11.2.3 The judgments in 11.2.1 and 11.2.2 will have anapproximately 95 % (0.95) probability of being correct.11.3 BiasNo statement may be made about the bias of thistest method, as there is no standard reference material orreference test method that is applicable.12. Keywords12.1 app
