1、Designation: E143 13Standard Test Method forShear Modulus at Room Temperature1This standard is issued under the fixed designation E143; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parenthe
2、ses 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 shearmodulus of structural materials. This test method is limited tomaterials in which, and to stresses at
3、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 aregenerally not specified in materials specifications. Precisionand bias statements for these test methods
4、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 forinformation only and are not considered standard.1.3 This standard may involve hazardous materials,ope
5、rations, 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 appropriate safety and health practices and deter-mine the applicability of regulatory limitations prior to u
6、se.2. Referenced Documents2.1 ASTM Standards:2E6 Terminology Relating to Methods of Mechanical TestingE8/E8M Test Methods for Tension Testing of Metallic Ma-terialsE111 Test Method for Youngs Modulus, Tangent Modulus,and Chord ModulusE1012 Practice for Verification of Testing Frame and Speci-men Ali
7、gnment Under Tensile and Compressive AxialForce Application3. Terminology3.1 Definitions: Terms common to mechanical testing.3.1.1 angle of twist (torsion test) the angle of relativerotation measured in a plane normal to the torsion specimenslongitudinal axis over the gauge length.3.1.2 shear modulu
8、s, G, FL2,nthe ratio of shear stressto corresponding shear strain below the proportional limit, alsocalled torsional modulus and modulus of rigidity. (See Fig. 1.)3.1.2.1 DiscussionThe value of shear modulus may de-pend on the direction in which it is measured if the material isnot isotropic. Wood,
9、many plastics and certain metals aremarkedly anisotropic. Deviations from isotropy should besuspected if the shear modulus, G, differs from that determinedby substituting independently measured values of Youngsmodulus, E, and Poissons ratio, in the relationG 5E211!(1)3.1.2.2 DiscussionIn general, it
10、 is advisable, in reportingvalues of shear modulus to state the stress range over which itis measured.3.1.3 torque, FL,na moment (of forces) that produces ortends to produce rotation or torsion.3.1.4 torsional stress FL2,nthe shear stress in a body,in a plane normal to the axis or rotation, resultin
11、g from theapplication of torque.4. Summary of Test Method4.1 The cylindrical or tubular test specimen is loaded eitherincrementally or continuously by applying an external torqueso as to cause a uniform twist within the gauge length.4.1.1 Changes in torque and the corresponding changes inangle of tw
12、ist 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 increasing or decreasing torque (increasing from pre-torque to maximum torque or decreasing from maximumtorque to preto
13、rque).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 angle of twist is proportional tothe applied torque. Examples of the use of shear modulus arein the design of rotati
14、ng 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 E28.04 onUniaxial Testing.Current edition approved Nov. 1, 2013. Published May 2014. Originallyapproved in 1959. Last prev
15、ious edition approved in 2008 as E143 02(2008). DOI:10.1520/E0143-13.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM
16、website.*A Summary of Changes section appears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1NOTE 1For materials that follow nonlinear elastic stress-strainbehavior, the value of tangent or chord shear modu
17、lus is useful forestimating the change in torsional strain to corresponding stress for aspecified stress or stress-range, respectively. Such determinations are,however, outside the scope of this standard. (See for example Ref (1).)35.2 The procedural steps and precision of the apparatus andthe test
18、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 include characteristics of the speci
19、mensuch 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 includeaxial position of the specimen, temperature and temperaturevariations, and maintenance
20、 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/J (2)where:G = shear modulus of the specimen,T = torque,L = gauge length,J = polar moment of inertia of the sectio
21、n about its center,and = angle of twist, in radians.6.1.1 For a solid cylinder:J 5 D4/32 (3)where:D = diameter.6.1.2 For a tube:J 532D042 Di4! (4)where:D0= outside diameter, andDi= inside diameter.7. Apparatus7.1 Testing MachineThe torsion testing machine, which isto be used for applying the require
22、d 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 G in shear modulus, due to errors in torque T,well within the required accuracy (see 12
23、.3.1).7.2 GripsThe ends of the specimen shall be gripped firmlybetween the jaws of a testing machine that have been designedto produce a state of uniform twist within the gauge length. Inthe case of tubes, closely fitting rigid plugs, such as are shownin Fig. 11 (Metal Plugs for Testing Tubular Spec
24、imens) of TestMethods E8/E8M may be inserted in the ends to permittightening the grips without crushing the specimen. The gripsshall be such that axial alignment can be obtained andmaintained in order to prevent the application of bendingmoments. One grip shall be free to move axially to prevent the
25、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 gauge length and at least one diameter removedfrom the grips. The relative rotati
26、onal 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 light3The boldface numbers in parentheses refer to a list of references at the end ofthis
27、 standard.4See any standard text in Mechanics of Materials.FIG. 1 Shear Stress-Strain Diagram Showing a Straight Line, Corresponding to the Shear Modulus, Between R, a Pretorque Stress, andP, the Proportional LimitE143 132beam from mirrors or prisms attached to the arms (3). Readingsshould be taken
28、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 fissures thatwould have negligible e
29、ffect in determining Youngs modulus,may cause appreciable errors in shear modulus. In the case ofmachined specimens take care to prevent changing the prop-erties of the material at the surface of the specimen.8.1.1.1 Specimens in the form of solid cylinders should bestraight and of uniform diameter
30、for a length equal to the gaugelength 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 gauge length plus at least four outside diameters (see12.2.1 and 12.3.2).8.2 LengthThe gauge
31、length should be at least fourdiameters. The length of the specimen shall be sufficient for afree length between grips equal to the gauge length plus two tofour diameters, unless otherwise prescribed in the productspecification. However, the ratio of free length to diametershall not be so large that
32、 helical twisting of the axis of thespecimen takes 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 gauge length. In addition, in the case of tubularspecimens, determine
33、 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 with therequired accuracy.9.2 AlignmentTake care to ensure
34、 axial alignment of thespecimen. Procedures for alignment are described in detail inPractice E1012. Although E1012 is for a specimen underuniaxial loading, it provides guidance for machine setup andfixturing for other loading regimes.9.3 Torque and Angle of TwistMake simultaneous mea-surements of to
35、rque 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 Results10.1 For the determination of shear modulus it is oftenhel
36、pful to use a variation of the strain deviation method (4-6),frequently used for determining Youngs modulus. For thispurpose, a graph (Fig. 2) may be plotted of torque versus twistdeviation from the following equation: 5 L 2 T/K! (5)where: = twist deviation,L = gauge length, = angle of twist, in rad
37、ians per unit length,FIG. 2 Torque-Twist Deviation GraphE143 133T = torque, andK = a constant chosen so that 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 a
38、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 by
39、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 5 T/J 5 T/T/K1/L!J (6)where: = deviation increment,
40、T = torque increment, and = 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 (7-9). For this test method, random variations in thedata are considered as variations in
41、the angle of twist .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 during the f
42、irst 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.11. Report11.1 Test Specimen Materialdescribe the specimenmaterial, alloy, heat treatment, mill batch,
43、 number, graindirection, as applicable, and any relevant information regardingthe sample that may have an influenced on its mechanicalproperties.11.2 Test Specimen Configuration Include a sketch of thetest specimen configuration of reference to the specimendrawing.11.3 Test Specimen Dimensions State
44、 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 themanufacturer, make, model, serial number and load range ofthe testing machine and twist gages.11.6 Speed of Testing Record the
45、 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 deviationdiagram showing both torque and twist deviation, with scales,s
46、pecimen 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 presently no indication of what preci-sion (repeatability or reprod
47、ucibility) 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 uniformity of the specimen, for example, its straightnessand eccen
48、tricity, 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 G due to variations in diameterD are given by:GG524DD(7)12.2.2 According to Eq 2 and Eq 4 (see 6.1 and 6.1.2) t
49、hevariations in shear modulus G due to variations in wallthickness t are given by:GG52tt(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 shearmodulus G due to errors in torque T are gi
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