1、Designation: E 143 02 (Reapproved 2008)Standard Test Method forShear Modulus at Room Temperature1This standard is issued under the fixed designation E 143; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision.
2、A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.This standard has been approved for use by agencies of the Department of Defense.1. Scope1.1 This test method covers the determination of shearmo
3、dulus of structural materials. This test method is limited tomaterials in which, and to stresses at which, creep is negligiblecompared to the strain produced immediately upon loading.Elastic properties such as shear modulus, Youngs modulus,and Poissons ratio are not determined routinely and aregener
4、ally not specified in materials specifications. Precisionand bias statements for these test methods are therefore notavailable.1.2 UnitsThe values stated in inch-pound units are to beregarded as standard. The values given in parentheses aremathematical conversions to SI units that are provided forin
5、formation only and are not considered standard.1.3 This standard may involve hazardous materials, opera-tions, and equipment. This standard does not purport toaddress all of the safety concerns, if any, associated with itsuse. It is the responsibility of the user of this standard toestablish appropr
6、iate safety and health practices and deter-mine the applicability of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E6 Terminology Relating to Methods of Mechanical Test-ingE 8/E 8M Test Methods for Tension Testing of MetallicMaterialsE 111 Test Method forYoungs Modul
7、us, Tangent Modulus,and Chord ModulusE 1012 Practice for Verification of Test Frame and Speci-men Alignment Under Tensile and Compressive AxialForce Application3. Terminology3.1 Definitions:3.1.1 shear modulus FL2the ratio of shear stress tocorresponding shear strain below the proportional limit, al
8、socalled torsional modulus and modulus of rigidity. (See Fig. 1.)NOTE 1The value of shear modulus may depend on the direction inwhich it is measured if the material is not isotropic. Wood, many plasticsand certain metals are markedly anisotropic. Deviations from isotropyshould be suspected if the sh
9、ear modulus, G, differs from that determinedby substituting independently measured values of Youngs modulus, E,and Poissons ratio, in the relationG 5E21 1 !(1)NOTE 2In general, it is advisable, in reporting values of shearmodulus to state the stress range over which it is measured.3.1.2 torque, FLa
10、moment (of forces) that produces ortends to produce rotation or torsion.3.1.3 torsional stress FL2the shear stress in a body, ina plane normal to the axis or rotation, resulting from theapplication of torque.3.1.4 angle of twist (torsion test) the angle of relativerotation measured in a plane normal
11、 to the torsion specimenslongitudinal axis over the gage length.3.1.5 For definitions of other terms used in this test method,refer to Terminology E6.4. Summary of Test Method4.1 The cylindrical or tubular test specimen is loaded eitherincrementally or continuously by applying an external torqueso a
12、s to cause a uniform twist within the gage length.4.1.1 Changes in torque and the corresponding changes inangle of twist are determined either incrementally or continu-ously. The appropriate slope is then calculated from the shearstress-strain curve, which may be derived under conditions ofeither in
13、creasing or decreasing torque (increasing from pre-torque to maximum torque or decreasing from maximumtorque to pretorque).5. Significance and Use5.1 Shear modulus is a material property useful in calculat-ing compliance of structural materials in torsion provided theyfollow Hookes law, that is, the
14、 angle of twist is proportional tothe applied torque. Examples of the use of shear modulus arein the design of rotating shafts and helical compression springs.1This test method is under the jurisdiction of ASTM Committee E28 onMechanical Testing and is the direct responsibility of Subcommittee E28.0
15、4 onUniaxial Testing.Current edition approved May 1, 2008. Published December 2008. Originallyapproved in 1959. Last previous edition approved in 2002 as E 143 02.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book
16、 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 Conshohocken, PA 19428-2959, United States.NOTE 3For materials that follow nonlinear elastic stress-strain behav-ior, the valu
17、e of tangent or chord shear modulus is useful for estimatingthe change in torsional strain to corresponding stress for a specified stressor stress-range, respectively. Such determinations are, however, outsidethe scope of this standard. (See for example Ref (1).)35.2 The procedural steps and precisi
18、on of the apparatus andthe test specimens should be appropriate to the shape and thematerial type, since the method applies to a wide variety ofmaterials and sizes.5.3 Precise determination of shear modulus depends on thenumerous variables that may affect such determinations.5.3.1 These factors incl
19、ude characteristics of the specimensuch as residual stress, concentricity, wall thickness in the caseof tubes, deviation from nominal value, previous strain historyand specimen dimension.5.3.2 Testing conditions that influence the results include:axial position of the specimen, temperature and tempe
20、raturevariations, and maintenance of the apparatus.5.3.3 Interpretation of data also influences results.6. General Considerations6.1 Shear modulus for a specimen of circular cross-sectionis given by the equation4G 5 TL/Ju (2)where:G = shear modulus of the specimen,T = torque,L = gage length,J = pola
21、r moment of inertia of the section about its center,andu = angle of twist, in radians.6.1.1 For a solid cylinder:J 5pD4/32 (3)where:D = diameter.6.1.2 For a tube:J 5p32D042 Di4! (4)where:D0= outside diameter, andDi= inside diameter.7. Apparatus7.1 Testing MachineThe torsion testing machine, which is
22、to be used for applying the required torque to the specimen,shall be calibrated for the range of torques used in thedetermination. Corrections may be applied for demonstratedsystematic errors. The torques should be chosen such as tobring the error DG in shear modulus, due to errors in torqueDT, well
23、 within the required accuracy (see 12.3.1).7.2 GripsThe ends of the specimen shall be grippedfirmly between the jaws of a testing machine which have beendesigned to produce a state of uniform twist within the gagelength. In the case of tubes, closely fitting rigid plugs, such asare shown in Fig. 11
24、(Metal Plugs for Testing TubularSpecimens) of Test Methods E 8/E 8M may be inserted in theends to permit tightening the grips without crushing thespecimen. The grips shall be such that axial alignment can beobtained and maintained in order to prevent the application ofbending moments. One grip shall
25、 be free to move axially toprevent the application of axial forces.7.3 Twist GagesThe angle of twist may be measured bytwo pairs of lightweight but rigid arms, each pair fasteneddiametrically to a ring attached at three points to the section atan end of the gage length and at least one diameter remo
26、vedfrom the grips. The relative rotational displacement of the twosections may be measured by mechanical, optical, or electricalmeans; for example, the displacement of a pointer on one armrelative to a scale on the other (2), or the reflection of a lightbeam from mirrors or prisms attached to the ar
27、ms (3). Readingsshould be taken for both sets of arms and averaged to eliminateerrors due to bending of the specimen (see 12.3.2).8. Test Specimens8.1 Selection and Preparation of Specimens:8.1.1 Specimens shall be chosen from sound, clean material.Slight imperfections near the surface, such as fiss
28、ures whichwould have negligible effect in determining Youngs modulus,3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.4See any standard text in Mechanics of Materials.FIG. 1 Shear Stress-Strain Diagram Showing a Straight Line, Corresponding to the Shear M
29、odulus, Between R , a Pretorque Stress,and P , the Proportional LimitE 143 02 (2008)2may cause appreciable errors in shear modulus. In the case ofmachined specimens care shall be taken to prevent changingthe properties of the material at the surface of the specimen.8.1.1.1 Specimens in the form of s
30、olid cylinders should bestraight and of uniform diameter for a length equal to the gagelength plus two to four diameters (see 12.2.1).8.1.1.2 In the case of tubes, the specimen should be straightand of uniform diameter and wall thickness for a length equalto the gage length plus at least four outsid
31、e diameters (see12.2.1 and 12.3.2).8.2 LengthThe gage length should be at least four diam-eters. The length of the specimen shall be sufficient for a freelength between grips equal to the gage length plus two to fourdiameters, unless otherwise prescribed in the product specifi-cation. However, the r
32、atio of free length to diameter shall notbe so large that helical twisting of the axis of the specimentakes place before the determination is completed.9. Procedure9.1 Measurement of SpecimensMeasure diameter to givean accurate determination of average polar moment of inertia,J, for the gage length.
33、 In addition, in the case of tubularspecimens, determine the average wall thickness at each endto6 0.0001 in. 6 (0.0025 mm).9.1.1 In the case of thin-walled tubes, a survey of thicknessvariation by more sensitive devices, such as a pneumatic orelectric gage, may be needed to determine thicknesses wi
34、th therequired accuracy.9.2 AlignmentTake care to ensure axial alignment of thespecimen. Procedures for alignment are described in detail inPractice E 1012. Although E 1012 is for a specimen undertensile loading, it provides guidance for machine setup andfixturing for other loading regimes.9.3 Torqu
35、e and Angle of TwistMake simultaneous mea-surements of torque and angle of twist and record the data.9.4 Speed of TestingMaintain the speed of testing highenough to make creep negligible.9.5 TemperatureRecord the temperature. Avoid changesin temperature during the test.10. Interpretation of Results1
36、0.1 For the determination of shear modulus it is oftenhelpful to use a variation of the strain deviation method (46),frequently used for determining Youngs modulus. For thispurpose, a graph (Fig. 2) may be plotted of torque versusdeviation from the following equation:d5Lu2T/K! (5)where:d = deviation
37、,L = gage length,u = angle of twist, in radians per unit length,T = torque, andK = a constant chosen so that u T/K is nearly constantbelow the proportional limit.The range for which data are used for obtaining the shearmodulus may be determined by applying some suitable crite-rion of departure from
38、a straight line, for example, the leastcount of the twist gage, and examining the deviation graphwith the aid of a sheet of transparent paper on which threeparallel lines are drawn with the spacing between themequivalent to the least count of the twist gage.10.2 The shear modulus may be determined b
39、y means of thedeviation graph by fitting graphically a straight line to theappropriate points. From this line the deviation incrementcorresponding to a given torque increment can be read andsubstituted in the following equation (from Eq 2 and Eq 5):G 5DT/JDu5DT/DT/K 1Dd/L!J (6)where:Dd = deviation i
40、ncrement,DT = torque increment, andDu = increment in angle of twist, in radians per unit length.10.3 The best fit of a straight line for the initial linearportion of the curve can be obtained by the method of leastsquares (79). For this test method, random variations in thedata are considered as var
41、iations in the angle of twist u.Indetermining the torque-range for which data should be used inthe calculations it is helpful to examine the data using thedeviation graph described in 10.1. Due to possible small offsetsat zero torque and small variations in establishing the load pathin the specimen
42、during the first small increment of torque, thereadings at zero torque and the first small increment of torqueare typically not included in the calculations and the line is notconstrained to pass through zero.FIG. 2 Torque-Deviation GraphE 143 02 (2008)311. Report11.1 Test Specimen Materialdescribe
43、the specimen mate-rial, alloy, heat treatment, mill batch, number, grain direction,as applicable, and any relevant information regarding thesample that may have an influenced on its mechanical proper-ties.11.2 Test Specimen Configuration Include a sketch of thetest specimen configuration of referenc
44、e to the specimendrawing.11.3 Test Specimen Dimensions State the actual measureddimensions for each test specimen.11.4 Test Fixture Describe the test fixture or refer tofixture drawings.11.5 Testing Machine and Twist Gages Include the manu-facturer, make, model, serial number and load range of thete
45、sting machine and twist gages.11.6 Speed of Testing Record the test rate and mode ofcontrol.11.7 Temperature Record the temperature.11.8 Stress-Strain DiagramTorque-Twist DeviationDiagram Include either the stress-strain diagram showingboth shear stress and shear strain or the torque-twist deviation
46、diagram showing both torque and twist deviation, with scales,specimen number, test data, rate and other pertinent informa-tion.11.9 Shear Modulusreport the value as described in Sec-tion 8 or 10.12. Precision and Bias12.1 No interlaboratory test program is currently beingconducted and there is prese
47、ntly no indication of what preci-sion (repeatability or reproducibility) to expect. Furthermorethere are no reference standards. Therefore no estimate of biascan be obtained.12.2 Many parameters may be expected to influence theaccuracy of this test method. Some of these parameters pertainto the unif
48、ormity of the specimen, for example, its straightnessand eccentricity, the uniformity of its diameter, and, in the caseof tubes, the uniformity of its wall thickness.12.2.1 According to Eq 2 and Eq 3 (see 6.1 and 6.1.1), thevariation in shear modulus DG due to variations in diameterDD are given by:D
49、GG524DDD(7)12.2.2 According to Eqs 2 and Eqs 4 (see 6.1 and 6.1.2) thevariations in shear modulus DG due to variations in wallthickness Dt are given by:DGG52Dtt(8)for a thin-walled tube for which t/D is small compared withunity where t=(DoDi)/2.12.3 Other parameters that may be expected to influence theaccuracy of this test method pertain to the testing conditions,for example, alignment of the specimen, speed of testing,temperature, and errors in torque and twist values.12.3.1 According to Eq 2 (see 6.1), the error in shearmod
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