1、Designation: E 1426 98 (Reapproved 2003)Standard Test Method forDetermining the Effective Elastic Parameter for X-RayDiffraction Measurements of Residual Stress1This standard is issued under the fixed designation E 1426; the number immediately following the designation indicates the year oforiginal
2、adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.INTRODUCTIONWhen a crystalline material is strained the spacings between parall
3、el planes of atoms, ions, ormolecules in the lattice change. X-ray diffraction techniques can measure these changes and, therefore,they constitute a powerful means for studying the residual stress state in a body. To calculatemacroscopic stresses from lattice strains requires a material constant, Ee
4、ff, called the effective elasticparameter, that must be empirically determined by X-ray diffraction techniques as described in this testmethod.1. Scope1.1 This test method covers a procedure for experimentallydetermining the effective elastic parameter, Eeff, for the evalu-ation of residual and appl
5、ied stresses by X-ray diffractiontechniques. The effective elastic parameter relates macroscopicstress to the strain measured in a particular crystallographicdirection in polycrystalline samples. Eeffshould not be con-fused with E, the modulus of elasticity. Rather, it is nominallyequivalent to E/(1
6、 + n) for the particular crystallographicdirection, where n is Poissons ratio. The effective elasticparameter is influenced by elastic anisotropy and preferredorientation of the sample material.1.2 This test method is applicable to all X-ray diffractioninstruments intended for measurements of macros
7、copic re-sidual stress that use measurements of the positions of thediffraction peaks in the high back-reflection region to deter-mine changes in lattice spacing.1.3 This test method is applicable to all X-ray diffractiontechniques for residual stress measurement, including single,double, and multip
8、le exposure techniques.1.4 The values stated in inch pound units are to be regardedas the standard. The SI units given in parentheses are forinformation only.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
9、of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:E 4 Practices for Force Verification of Testing Machines2E 6 Terminology Relating to Methods of Mechanical Test-ing
10、2E 7 Terminology Relating to Metallography2E 1237 Guide for Installing Bonded Resistance StrainGages23. Terminology3.1 Definitions:3.1.1 Many of the terms used in this test method are definedin Terminology E 6 and E 7.3.2 Definitions of Terms Specific to This Standard:3.2.1 interplanar spacingthe pe
11、rpendicular distance be-tween adjacent parallel lattice planes.3.2.2 macrostressan average stress acting over a region ofthe test specimen containing many crystals.3.3 Symbols:3.3.1 a = dummy parameter for Sum(a) and SD(a).3.3.2 c = ordinate intercept of a graph of Dd versus stress.3.3.3 d = interpl
12、anar spacing between crystallographicplanes; also called d-spacing.3.3.4 d0= interplanar spacing for unstressed material.3.3.5 Dd = change in interplanar spacing caused by stress.3.3.6 E = modulus of elasticity.3.3.7 Eeff= effective elastic parameter for X-ray measure-ments.3.3.8 i = measurement ind
13、ex, 1 # i # n.3.3.9 m = slope of a graph of Dd versus stress.3.3.10 n = number of measurements used to determineslope m.1This 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
14、 edition approved April 10, 2003. Published July 2003. Originallyapproved in 1991. Last previous edition approved in 1998 as E 1426 98.2Annual Book of ASTM Standards, Vol 03.01.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.3.11 S
15、D(a) = standard deviation of a set of quantities “a”.3.3.12 Sum(a) = sum of a set of quantities “a”.3.3.13 Ti=Ximinus mean of all Xivalues.3.3.14 Xi= i-th value of applied stress.3.3.15 Yi= measurement of Dd corresponding to Xi.3.3.16 n = Poissons ratio.3.3.17 c = angle between the specimen surface
16、normal andthe normal to the diffracting crystallographic planes.4. Summary of Test Method4.1 A test specimen is prepared from a material that isrepresentative of that of the object in which residual stressmeasurements are to be made.NOTE 1If a sample of the same material is available it should be us
17、ed.4.2 The test specimen is instrumented with an electricalresistance strain gage, mounted in a location that experiencesthe same stress as the region that will be subsequentlyirradiated with X-rays.4.3 The test specimen is calibrated by loading it in such amanner that the stress, where the strain g
18、age is mounted, isdirectly calculable, and a calibration curve relating the straingage reading to the stress is developed.4.4 The test specimen is mounted in a loading fixture in anX-ray diffraction apparatus, and sequentially loaded to severalload levels.4.4.1 The change in interplanar spacing is m
19、easured foreach load level and related to the corresponding stress that isdetermined from the strain gage reading and the calibrationcurve.4.5 The effective elastic parameter and its standard devia-tion are calculated from the test results.5. Significance and Use5.1 This test method provides standar
20、d procedures forexperimentally determining the effective elastic parameter forX-ray diffraction measurement of residual and applied stresses.It also provides a standard means of reporting the precision ofthe parameter.5.2 This test method is applicable to any crystalline materialwhich exhibits a lin
21、ear relationship between stress and strain inthe elastic range.5.3 This test method should be used whenever residualstresses are to be evaluated by an X-ray diffraction techniqueand the effective elastic parameter of the material is unknown.6. Apparatus6.1 Any X-ray diffraction instrument intended f
22、or measure-ments of residual macrostress that employs measurements ofthe diffraction peaks in the high back-reflection region may beused, including film camera types, diffractometers, and por-table systems.6.2 A loading fixture is required to apply loads to the testspecimen while it is being irradia
23、ted in the X-ray diffractioninstrument.6.2.1 The fixture shall be designed such that the surfacestress applied by the fixture shall be uniform over the irradiatedarea of the specimen.6.2.2 The fixture shall maintain the irradiated surface of thespecimen at the exact center of rotation of the X-ray d
24、iffractioninstrument throughout the test with sufficient precision toprovide the desired levels of precision and bias in the mea-surements to be made.6.2.3 The fixture may be designed to apply tensile orbending loads. A four-point bending technique such as thatdescribed by Prevey3is most commonly us
25、ed.6.3 Electrical resistance strain gages are mounted upon thetest specimen to enable it to be accurately stressed to knownlevels.7. Test Specimens7.1 Test specimens should be fabricated from material withmicrostructure as nearly the same as possible as that in thematerial in which residual stresses
26、 are to be evaluated.7.2 For use in tensile or four-point bending fixtures, speci-mens should be rectangular in shape.7.2.1 The length of tensile specimens, between grips, shallbe not less than four times the width, and the width-to-thickness ratio shall not exceed eight.7.2.2 For use in four-point
27、bending fixtures, specimensshould have a length-to-width ratio of at least four. Thespecimen width should be sufficient to accommodate straingages (see 7.5) and the width-to-thickness ratio should begreater than one and consistent with the method used tocalculate the applied stresses in 8.1.NOTE 2No
28、minal dimensions often used for specimens for four-pointbending fixtures are 4.0 3 0.75 3 0.06 in. (10.2 3 1.9 3 0.15 cm).7.3 Tapered specimens for use in cantilever bending fix-tures, and split-ring samples, are also acceptable.7.4 Specimen surfaces may be electropolished or as-rolledsheet or plate
29、.7.5 One or more electrical resistance strain gages is affixedto the test specimen in accordance with Guide E 1237. Thegage(s) should be aligned parallel to the longitudinal axis of thespecimen, and should be mounted on a region of the specimenthat experiences the same strain as the region that is t
30、o beirradiated. The gage(s) should be applied to the irradiatedsurface of the beam either adjacent to, or on either side of, theirradiated area in order to minimize errors due to the absenceof a pure tensile or bending load.NOTE 3In the case of four-point bending fixtures the gage(s) shouldbe placed
31、 well inside the inner span of the specimen in order to minimizethe stress concentration effects associated with the inner knife edges.8. Calibration8.1 Calibrate the instrumented specimen using loads appliedby dead weights or by a testing machine that has been verifiedaccording to Practices E 4. Th
32、e loading configuration is suchthat the applied stresses, in the region where the strain gagesare mounted and where X-ray diffraction measurements will be3Prevey, P. S., “A Method of Determining the Elastic Properties of Alloys inSelected Crystallographic Directions for X-Ray Diffraction Residual St
33、ress Mea-surement,” Advances in X-Ray Analysis 20, 1977, pp. 345354.E 1426 98 (2003)2made, are statically determinate (that is, may be calculatedfrom the applied loads and the dimensions of the specimen andthe fixture).8.2 Prestress the specimen by loading to a level of approxi-mately 75 % of the lo
34、ad that is calculated to produce amaximum applied stress equal to the nominal yield strength ofthe material, then unload. This will minimize drift in the gagesand creep in the strain gage adhesive during the subsequenttesting procedure.8.3 Apply loads in increasing sequence at levels of approxi-mate
35、ly 5, 15, and 25 % of the load that would produce amaximum applied stress equal to the nominal yield strength ofthe material.8.4 At each load level calculate the applied stress and takestrain gage readings.8.5 Apply loads in decreasing sequence at levels of approxi-mately 15 and 5 %, calculating the
36、 applied stress and takingstrain gage readings at each level.8.6 Repeat 8.3-8.5.8.7 Examine the data for repeatability and linearity. Devia-tions from either may indicate the failure of a strain gage bond,stressing beyond the proportional limit of the material, or animperfect loading configuration.
37、If the deviations exceed theacceptable degree of uncertainty in the subsequent measure-ments of residual stress, the source of the deviations should belocated and corrected before proceeding further.8.8 If the repeatability and the linearity of the data areacceptable, plot a graph of applied stress
38、versus strain gagereading, draw a straight line through the data, and extrapolateit down to zero applied stress and up to 75 % of the nominalyield strength of the material. This is the calibration curve. (SeeFig. 1.)NOTE 4For bending specimens, the strain indicated by the straingage(s) differs in ma
39、gnitude from the strain in the specimen surfacebecause of the elevation of the strain gage grid above the surface. Thisdoes not affect the accuracy of the procedure.9. Procedure9.1 The X-ray diffraction technique, the crystallographicplanes, the c angle, and the instrumentation that are used todeter
40、mine the effective elastic parameter of the material shouldbe the same as those to be used subsequently to measureresidual stresses in objects of the same material.9.2 Mount the calibrated specimen in the loading fixture andmount the fixture in the X-ray diffraction instrument.9.2.1 When using a ben
41、ding fixture the arrangement shouldbe such that the irradiated surface of the specimen is stressedin tension.9.3 Load the specimen with the loading fixture whilemonitoring the strain gage readings. Using the calibrationcurve to convert strain gage readings to applied stresses, applystresses in incre
42、asing sequence at levels of approximately 5,20, 40, 60, and 70 % of the nominal yield strength of thematerial. The prestress level, 75 %, must not be exceeded.9.4 At each stress level calculate the change in interplanarspacing, Dd, between the c = 0 and c = c orientations for theparticular crystallo
43、graphic planes and c angles used.9.5 Apply stresses in decreasing sequence at levels ofapproximately 60, 40, 20, and 5 %, measuring the change inthe interplanar spacing at each level.9.6 Repeat 9.3-9.5.9.7 Examine the data for repeatability and linearity. Devia-tions from either may indicate the fai
44、lure of a strain gage bond,failure of the fixture to apply the correct loading, or deviationfrom the proper X-ray geometry. The latter source of error,when present, is often caused by failure to maintain theirradiated area of the specimen surface at the exact center of thediffractometer while the sp
45、ecimen is under load. If the devia-tions exceed the acceptable degree of uncertainty in thesubsequent measurements of residual stress, the source of thedeviations should be located and corrected before proceedingfurther.10. Calculation10.1 For each measurement described in Sections 9.3-9.6 ofthis te
46、st method, calculate the change in interplanar spacingand the corresponding applied stress.10.2 Plot the data on a graph of change in interplanarspacing vs. applied stress, and check for apparent errors. (SeeFig. 2.)10.3 Calculate the slope, m, of the best-fit straight line usingleast-squares linear
47、 regression. The following formulas4maybe used:4Press, W. H., et al., “Numerical Recipes: The Art of Scientific Computing.”Cambridge, 1986, Art. 14.2.FIG. 1 Calibration Curve for Instrumented Test SpecimenNOTE 1For clarity, only one point is shown for each applied stresslevelFIG. 2 Change in Interpl
48、anar Spacing Versus Applied StressE 1426 98 (2003)3SumX!5(i51nXiTi5 Xi2SumX!n(1)SumT2!5(i 51nTi2SumTY!5(TiYim 5SumTY!SumT2!In these equations, Xirepresents the i-th value of the appliedstress, and Yirepresents the measured value of Dd thatcorresponds to Xi.10.4 For the procedure described in 9.3-9.6
49、 of this testmethod,n=18intheabove equations. This number corre-sponds to 2 repetitions of a sequence of 5 measurements atascending loads and 4 measurements at descending loads.NOTE 5There is no particular significance to using 18 data points.Any number equal to or greater than 14 (4 ascending, 3 descending) wouldbe acceptable.10.5 Calculate the X-ray effective elastic constant using thefollowing equation:Eeff51mdosin2c (2)where:do= the interplanar spacing for unstressed material, isusually approximated by the interplanar spacing for c=0.11. Precision and Bias11.1 Pr
