1、Designation: E 143 02Standard 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. A number in parent
2、heses indicates the year of last reapproval. Asuperscript epsilon (e) 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 shearmodulus of structur
3、al 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 aregenerally not specifie
4、d in materials specifications. Precisionand bias statements for these test methods are therefore notavailable.1.2 Values stated in inch-pound units are to be regarded asthe standard. SI units are provided for information only.1.3 This standard may involve hazardous materials, opera-tions, and equipm
5、ent. 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 use.2. Referenced Do
6、cuments2.1 ASTM Standards:E6 Terminology Relating to Methods of Mechanical Test-ing2E8 Test Methods of Tension Testing of Metallic Materials2E 111 Test Method forYoungs Modulus, Tangent Modulus,and Chord Modulus2E 1012 Practice for Specimen Alignment Under TensileLoading23. Terminology3.1 Definition
7、s:3.1.1 shear modulus FL2the ratio of shear stress tocorresponding shear strain below the proportional limit, alsocalled 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,
8、 many plasticsand certain metals are markedly anisotropic. Deviations from isotropyshould be suspected if the shear 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 advis
9、able, in reporting values of shearmodulus to state the stress range over which it is measured.3.1.2 torque, FLa 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 theap
10、plication of torque.3.1.4 angle of twist (torsion test) the angle of relativerotation measured in a plane normal 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 cylin
11、drical or tubular test specimen is loaded eitherincrementally or continuously by applying an external torqueso as 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 appropria
12、te 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 pretorque).5. Significance and Use5.1 Shear modulus is a material property u
13、seful 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 rotating shafts and helical compression springs.NOTE 3For materials that foll
14、ow nonlinear elastic stress-strain behav-ior, the value of tangent or chord shear modulus is useful for estimating1This 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
15、 Nov. 10, 2002. Published January 2003. Originallyapproved in 1959. Last previous edition approved in 2001 as E 143 01.2Annual Book of ASTM Standards, Vol 03.01.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.the change in torsional
16、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 precision of the apparatus andthe test specimens should be appropriate to the shape and the
17、material 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 specimensuch as residual stress, concentricity, wall thic
18、kness 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 temperaturevariations, and maintenance of the apparatus.5.3.3 Interpretation of data also
19、 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 = polar moment of inertia of the section about its center,andu = angle of twist, in radian
20、s.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 isto be used for applying the required torque to the specimen,shall be calibrated for
21、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 within the required accuracy (see 12.3.1).7.2 GripsThe ends of the specimen shall b
22、e 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 (Metal Plugs for Testing TubularSpecimens) of Test Methods E8may be inserted in the
23、ends topermit tightening the grips without crushing the specimen. Thegrips shall 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 theapplication of axial forces.7.3 Twist GagesThe angle
24、 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 removedfrom the grips. The relative rotational displacement of the twosections may be measured
25、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 arms (3). Readingsshould be taken for both sets of arms and averaged to eliminateerrors due t
26、o 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 whichwould have negligible effect in determining Youngs modulus,may cause appreciable
27、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.3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.4See any standard text in Mechanics of Material
28、s.FIG. 1 Shear Stress-Strain Diagram Showing a Straight Line, Corresponding to the Shear Modulus, Between R , a Pretorque Stress,and P , the Proportional LimitE 143 0228.1.1.1 Specimens in the form of solid cylinders should bestraight and of uniform diameter for a length equal to the gagelength plus
29、 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 outside diameters (see12.2.1 and 12.3.2).8.2 LengthThe gage length should be at least four diam-eters. T
30、he 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 ratio of free length to diameter shall notbe so large that helical twisting of the axis of the spec
31、imentakes 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. In addition, in the case of tubularspecimens, determine the average wall thickness at each endto6
32、 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 axial alignment of thespecimen. Procedure
33、s 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 Torque and Angle of TwistMake simultaneous mea-surements of torque and angle of twist and record the da
34、ta.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 oftenhelpful to use a variation of the strain dev
35、iation 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,L = gage length,u = angle of twist, in radians per unit length,T = torque, andK = a constant chos
36、en 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 a straight line, for example, the leastcount of the twist gage, and examining the deviation graphw
37、ith 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 means of thedeviation graph by fitting graphically a straight line to theappropriate points. Fro
38、m 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 increment,DT = torque increment, andDu = increment in angle of twist, in radians per unit length.10
39、.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 variations in the angle of twist u.Indetermining the torque-range for which data should be used inthe
40、 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 first small increment of torque, thereadings at zero torque and the first small increme
41、nt of torqueare typically not included in the calculations and the line is notconstrained to pass through zero.11. Report11.1 Test Specimen Materialdescribe the specimen mate-rial, alloy, heat treatment, mill batch, number, grain direction,FIG. 2 Torque-Deviation GraphE 143 023as applicable, and any
42、 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 reference to the specimendrawing.11.3 Test Specimen Dimensions State the actual measureddimensions for each test
43、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 thetesting machine and twist gages.11.6 Speed of Testing Record the test rate and mode ofcontrol.11.7 Temperat
44、ure 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,specimen number, test data, rate and other p
45、ertinent 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 reproducibility) to expect. Furthermorethere are
46、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 eccentricity, the uniformity of its diameter, an
47、d, 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:DGG524DDD(7)12.2.2 According to Eqs 2 and Eqs 4 (see 6.1 and 6.1.2) thevariations in shear modulus DG due
48、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
49、, 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 DG due to errors in torque DT are given by:DGG5DTT(9)12.3.2 According to Eq 2 (see 6.1), the error in shearmodulus DG due to errors in angle of twist Du are given by:DGG52Duu (10)The least count of the twist gage should always be smallerthan the minimum acceptable value of Du. In general, theoverall precision that is required in twist data for the determi-nation of shear modulus is of a higher order
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