1、Designation: E2860 12Standard Test Method forResidual Stress Measurement by X-Ray Diffraction forBearing Steels1This standard is issued under the fixed designation E2860; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of
2、last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.INTRODUCTIONThe measurement of residual stress using X-ray diffraction (XRD) techniques has gained muchpopularity in the materials
3、 testing field over the past half century and has become a mandatory test formany production and prototype bearing components. However, measurement practices have evolvedover this time period. With each evolutionary step, it was discovered that previous assumptions weresometimes erroneous, and as su
4、ch, results obtained were less reliable than those obtained usingstate-of-the-art XRD techniques. Equipment and procedures used today often reflect different periodsin this evolution; for example, systems that still use the single- and double-exposure techniques as wellas others that use more advanc
5、ed multiple exposure techniques can all currently be found inwidespread use. Moreover, many assumptions made, such as negligible shear components andnon-oscillatory sin2c distributions, cannot safely be made for bearing materials in which the demandfor measurement accuracy is high. The use of the mo
6、st current techniques is, therefore, mandatory toachieve not only the most reliable measurement results but also to enable identification and evaluationof potential measurement errors, thus paving the way for future developments.1. Scope1.1 This test method covers a procedure for experimentallydeter
7、mining macroscopic residual stress tensor components ofquasi-isotropic bearing steel materials by X-ray diffraction(XRD).1.2 This test method provides a guide for experimentallydetermining stress values, which play a significant role inbearing life.1.3 Examples of how tensor values are used are:1.3.
8、1 Detection of grinding type and abusive grinding;1.3.2 Determination of tool wear in turning operations;1.3.3 Monitoring of carburizing and nitriding residual stresseffects;1.3.4 Monitoring effects of surface treatments such as sandblasting, shot peening, and honing;1.3.5 Tracking of component life
9、 and rolling contact fatigueeffects;1.3.6 Failure analysis;1.3.7 Relaxation of residual stress; and1.3.8 Other residual-stress-related issues that potentiallyaffect bearings.1.4 UnitsThe values stated in SI units are to be regardedas standard. No other units of measurement are included in thisstanda
10、rd.1.5 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.2. Reference
11、d Documents2.1 ASTM Standards:2E6 Terminology Relating to Methods of Mechanical TestingE7 Terminology Relating to MetallographyE915 Test Method for Verifying the Alignment of X-RayDiffraction Instrumentation for Residual Stress Measure-mentE1426 Test Method for Determining the Effective ElasticParam
12、eter for X-Ray Diffraction Measurements of Re-sidual Stress2.2 ANSI Standards:31This test method is under the jurisdiction of ASTM Committee E28 onMechanical Testing and is the direct responsibility of Subcommittee E28.13 onResidual Stress Measurement.Current edition approved April 1, 2012. Publishe
13、d May 2012. DOI: 10.1520/E286012.2For 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 website.3Available from American Nat
14、ional Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http:/www.ansi.org.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.N43.2 Radiation Safety for X-ray Diffraction and Fluores-cence Analysis EquipmentN43.3
15、 For General Radiation SafetyInstallations UsingNon-Medical X-Ray and Sealed Gamma-Ray Sources,Energies Up to 10 MeV3. Terminology3.1 DefinitionsMany of the terms used in this test methodare defined in Terminologies E6 and E7.3.2 Definitions of Terms Specific to This Standard:3.2.1 interplanar spaci
16、ng, nperpendicular distance be-tween adjacent parallel atomic planes.3.2.2 macrostress, naverage stress acting over a region ofthe test specimen containing many gains/crystals/coherentdomains.3.3 Abbreviations:3.3.1 ALARAAs low as reasonably achievable3.3.2 FWHMFull width half maximum3.3.3 LPALorent
17、z-polarization-absorption3.3.4 MSDSMaterial safety data sheet3.3.5 XECX-ray elastic constant3.3.6 XRDX-ray diffraction3.4 Symbols:12 S2hkl= X-ray elastic constant of quasi-isotropic materialequal to1 1nEeff$hkl%aL= Linear thermal expansion coefficientb = Angle between the incident beam and s33or sur
18、facenormal on the s33s11planex = Angle between the sf+90direction and the normal to thediffracting planexm= Fixed x offset used in modified-chi moded = Interplanar spacing between crystallographic planes;also called d-spacingdo= Interplanar spacing for unstressed materiald= Perpendicular spacingDd =
19、 Change in interplanar spacing caused by stresseij= Strain component i, jE = Modulus of elasticity (Youngs modulus)Eeffhkl= Effective elastic modulus for X-ray measurements = Attenuation coefficienth = Rotation of the sample around the measuring directiongiven by f and c or x and bv or V = Angle bet
20、ween the specimen surface and incidentbeam when x =0f = Angle between the s11direction and measurementdirection azimuth, see Fig. 1“hkl” = Miller indicessij= Normal stress component i, js1hkl= X-ray elastic constant of quasi-isotropic materialequal to nEeff$hkl%tij= Shear stress component i, ju = Br
21、agg anglen = Poissons ratioxMode= Mode dependent depth of penetrationc = Angle between the specimen surface normal and thescattering vector, that is, normal to the diffracting plane, seeFig. 14. Summary of Test Method4.1 A test specimen is placed in a XRD goniometer alignedas per Test Method E915.4.
22、2 The diffraction profile is collected over three or moreangles within the required angular range for a given hklplane, although at least seven or more are recommended.4.3 The XRD profile data are then corrected for LPA,background, and instrument-specific corrections.4.4 The peak position/Bragg angl
23、e is determined for eachXRD peak profile.4.5 The d-spacings are calculated from the peak positionsvia Braggs law.4.6 The d-spacing values are plotted versus their sin2c orsin2b values, and the residual stress is calculated using Eq 4 orEq 8, respectively.4.7 The error in measurement is evaluated as
24、per Section 14.4.8 The following additional corrections may be applied.The use of these corrections shall be clearly indicated with thereported results.4.8.1 Depth of penetration correction (see 12.12) and4.8.2 Relaxation as a result of material removal correction(see 12.14).5. Significance and Use5
25、.1 This test method covers a procedure for experimentallydetermining macroscopic residual stress tensor components ofquasi-isotropic bearing steel materials by XRD. Here the stresscomponents are represented by the tensor sijas shown in Eq 1(1,4p. 40). The stress strain relationship in any direction
26、of a4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.FIG. 1 Stress Tensor ComponentsE2860 122component is defined by Eq 2 with respect to the azimuthphi(f) and polar angle psi(c) defined in Fig. 1 (1, p. 132).sij5Fs11t21t31t12s22t32t13t23s33Gwhere tij5t
27、ji(1)efc$hkl%512s2$hkl%s11cos2fsin2c1s22sin2fsin2c1s33cos2c#112s2$hkl%t12sin2f!sin2c1t13cosfsin2c! 1t23sinfsin2c!#1 s1$hkl%s111s221s33# (2)5.1.1 Alternatively, Eq 2 may also be shown in the follow-ing arrangement (2, p. 126):efc$hkl%512s2$hkl%s11cos2f1t12sin2f! 1s22sin2f s33#sin2c112s2$hkl%s33 s1$hk
28、l%s111s221s33# 112s2$hkl%t13cosf1t23sinf#sin2c!5.2 Using XRD and Braggs law, interplanar strain measure-ments are performed for multiple orientations. The orientationsare selected based on a modified version of Eq 2, which isdictated by the mode used. Conflicting nomenclature may befound in literatu
29、re with regard to mode names. For example,what may be referred to as a c (psi) diffractometer in Europemay be called a x (chi) diffractometer in North America. Thethree modes considered here will be referred to as omega, chi,and modified-chi as described in 9.5.5.3 Omega Mode (Iso Inclination) and C
30、hi Mode (SideInclination)Interplanar strain measurements are performedat multiple c angles along one f azimuth (let f = 0) (Figs. 2and 3), reducing Eq 2 to Eq 3. Stress normal to the surface(s33) is assumed to be insignificant because of the shallowdepth of penetration of X-rays at the free surface,
31、 reducing Eq3 to Eq 4. Post-measurement corrections may be applied toaccount for possible s33influences (12.12). Since the sijvalueswill remain constant for a given azimuth, the s1hklterm isrenamed C.efc$hkl%512s2$hkl%s11sin2c1s33cos2c# 112s2$hkl%t13sin2c!# 1 s1$hkl%s111s221s33# (3)efc$hkl%512s2$hkl
32、%s11sin2c1t13sin2c!# 1 C (4)5.3.1 The measured interplanar spacing values are con-verted to strain using Eq 24, Eq 25, or Eq 26. Eq 4 is used tofit the strain versus sin2c data yielding the values s11, t13, andC. The measurement can then be repeated for multiple phiangles (for example 0, 45, and 90)
33、 to determine the fullstress/strain tensor. The value, s11, will influence the overallslope of the data, while t13is related to the direction and degreeof elliptical opening. Fig. 4 shows a simulated d versus sin2cprofile for the tensor shown. Here the positive 20-MPa t13stress results in an ellipti
34、cal opening in which the positive psirange opens upward and the negative psi range opens down-ward. A higher t13value will cause a larger elliptical opening.Anegative 20-MPa t13stress would result in the same ellipticalopening only the direction would be reversed with the positivepsi range opening d
35、ownwards and the negative psi rangeopening upwards as shown in Fig. 5.FIG. 2 Omega Mode Diagram for Measurement in s11DirectionE2860 1235.4 Modified Chi ModeInterplanar strain measurementsare performed at multiple b angles with a fixed x offset,xm(Fig. 6). Measurements at various b angles do not pro
36、videa constant f angle (Fig. 7), therefore, Eq 2 cannot be simplifiedin the same manner as for omega and chi mode.5.4.1 Eq 2 shall be rewritten in terms of b and xm.Eq5 and6 are obtained from the solution for a right-angled sphericaltriangle (3).c5arccoscosbcosxm! (5)f5arccosSsinbcosxmsincD(6)5.4.2
37、Substituting f and c in Eq 2 with Eq 5 and 6 (seeX1.1), we get:ebxm$hkl%512s2$hkl%s11sin2bcos2xm1s22sin2xm1s33cos2bcos2xm#112s2$hkl%t12sinbsin2xm! 1t13sin2b!cos2xm1t23cosbsin2xm!#1 s1$hkl%s111s221s33# (7)NOTEStress matrix is rotated 90 about the surface normal compared to Fig. 2 and Fig. 14.FIG. 3 C
38、hi Mode Diagram for Measurement in s11DirectionFIG. 4 Sample d (2u) Versus sin2c Dataset with s11= -500 MPa and t13= +20 MPaE2860 1245.4.3 Stress normal to the surface (s33) is assumed to beinsignificant because of the shallow depth of penetration ofX-rays at the free surface reducing Eq 7 to Eq 8.
39、Post-measurement corrections may be applied to account for pos-sible s33influences (see 12.12). Since the sijvalues and xmwill remain constant for a given azimuth, the s1hklterm isrenamed C, and the s22term is renamed D.ebxm$hkl%512s2$hkl%s11sin2bcos2xm1 D# 112s2$hkl%t12sinbsin2xm!1t13sin2b!cos2xm1t
40、23cosbsin2xm!# 1 C (8)5.4.4 The s11influence on the d versus sin2b plot is similarto omega and chi mode (Fig. 8) with the exception that theslope shall be divided by cos2xm. This increases the effective12s2hklby a factor of 1/cos2xmfor s11.FIG. 5 Sample d (2u) Versus sin2c Dataset with s11= -500 MPa
41、 and t13= -20 MPaFIG. 6 Modified Chi Mode Diagram for Measurement in s11DirectionE2860 1255.4.5 The tijinfluences on the d versus sin2b plot are morecomplex and are often assumed to be zero (3). However, thismay not be true and significant errors in the calculated stressmay result. Figs. 9-13 show t
42、he d versus sin2b influences ofindividual shear components for modified chi mode consider-ing two detector positions (xm= +12 and xm= -12). Com-ponents t12and t13cause a symmetrical opening about the s11slope influence for either detector position (Figs. 9-11); there-fore, s11can still be determined
43、 by simply averaging thepositive and negative b data. Fitting the opening to the t12andt13terms may be possible, although distinguishing between thetwo influences through regression is not normally possible.FIG. 7 c and f Angles Versus b Angle for Modified Chi Mode with xm= 12FIG. 8 Sample d (2u) Ve
44、rsus sin2b Dataset with s11= -500 MPaFIG. 9 Sample d (2u) versus sin2b Dataset with xm= +12, s11= -500 MPa, and t12= -100 MPaE2860 1265.4.6 The t23value affects the d versus sin2b slope in asimilar fashion to s11for each detector position (Figs. 12 and13). This is an unwanted effect since the s11and
45、 t23influencecannot be resolved for one xmposition. In this instance, the t23shear stress of -100 MPa results in a calculated s11value of-472.5 MPa for xm= +12 or -527.5 MPa for xm= -12, whilethe actual value is -500 MPa. The value, s11can still bedetermined by averaging the b data for both xmpositi
46、ons.5.4.7 The use of the modified chi mode may be used todetermine s11but shall be approached with caution using onexmposition because of the possible presence of a t23stress.The combination of multiple shear stresses including t23FIG. 10 Sample d (2u) Versus sin2b Dataset with xm= -12, s11= -500 MP
47、a, and t12= -100 MPaFIG. 11 Sample d (2u) Versus sin2b Dataset with xm= +12 or -12, s11= -500 MPa, and t13= -100 MPaFIG. 12 Sample d (2u) Versus sin2b Dataset with xm= +12, s11= -500 MPa, t23= -100 MPa, and Measured s11= -472.5 MPaE2860 127results in increasingly complex shear influences. Chi andome
48、ga mode are preferred over modified chi for these reasons.6. Apparatus6.1 A typical X-ray diffractometer is composed of thefollowing main components:6.1.1 GoniometerAn angle-measuring device responsiblefor the positioning of the source, detectors, and sample relativeto each other.6.1.2 X-Ray SourceT
49、here are generally three X-raysources used for XRD.6.1.2.1 Conventional Sealed TubeThis is by far the mostcommon found in XRD equipment. It is identified by its anodetarget element such as chromium (Cr), manganese (Mn), orcopper (Cu). The anode is bombarded by electrons to producespecific X-ray wavelengths unique to the target element.6.1.2.2 Rotating Anode TubeThis style of tube offers ahigher intensity than a conventional sealed tube.6.1.2.3 SynchrotronParticle accelerator that is cap
