1、Designation: E1426 98 (Reapproved 2009)1E1426 14Standard Test Method forDetermining the EffectiveX-Ray Elastic Parameter for X-RayDiffraction Measurements Constants for Use in theMeasurement of Residual Stress Using X-Ray DiffractionTechniques1This standard is issued under the fixed designation E142
2、6; 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 parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapprova
3、l.1 NOTE9.7 was editorially revised in September 2009.INTRODUCTIONWhen a crystalline material is strained, the spacingsspacing between parallel planes of atoms, ions,or molecules in the lattice change. X-raychanges. X-Ray diffraction techniques can measure thesechanges and, therefore, they constitut
4、e a powerful means for studying the residual stress state in abody. To calculate The calculation of macroscopic stresses fromusing lattice strains requires a materialconstant,the use of Ex-ray elasticeff, called theconstants (XEC effective elastic parameter, that ) whichmust be empirically determine
5、d by X-rayx-ray diffraction techniques as described in this test method.1. Scope1.1 This test method covers a procedure for experimentally determining the effectivex-ray elastic parameter,constants E(XEC)eff,for the evaluation of residual and applied stresses by X-rayx-ray diffraction techniques. Th
6、e effectiveXEC elastic parameter relatesrelate macroscopic stress to the strain measured in a particular crystallographic direction in polycrystalline samples. The EXECeffshould not be confused withare a function of the E,elastic modulus, Poissons ratio of the material and the hkl the modulus ofelas
7、ticity. Rather, it is nominally equivalent to plane selected for the measurement. There are two EXEC/(1 + ) for the particularcrystallographic direction, where that are referred to as 12 S2hkl is Poissons ratio. The effective elastic parameter is influencedby elastic anisotropy and preferred S1hklor
8、ientation .of the sample material.1.2 This test method is applicable to all X-rayx-ray diffraction instruments intended for measurements of macroscopic residualstress that use measurements of the positions of the diffraction peaks in the high back-reflection region to determine changes inlattice spa
9、cing.1.3 This test method is applicable to all X-rayx-ray diffraction techniques for residual stress measurement, including single,double, and multiple exposure techniques.1.4 The values stated in inch-poundSI units are to be regarded as standard. The values given in parentheses are mathematicalconv
10、ersions to SIinch-pound units that are provided for information only and are not considered standard.1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety and hea
11、lth practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E4 Practices for Force Verification of Testing Machines1 This test method is under the jurisdiction of ASTM Committee E28 on Mechanical Testing and is the direct responsibil
12、ity of Subcommittee E28.13 on Residual StressMeasurement.Current edition approved June 1, 2009Dec. 1, 2014. Published September 2009March 2015. Originally approved in 1991. Last previous edition approved in 20032009as E1426 98(2003).(2009)1. DOI: 10.1520/E1426-98R09E01.10.1520/E1426-14.2 For referen
13、cedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.This document is not an ASTM standard and is intended only to provide the
14、user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard
15、 as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1E6 Terminology Relating to Methods of Mechanical TestingE7 Terminology Relating to MetallographyE1237 Guide for Installing
16、 Bonded Resistance Strain Gages3. Terminology3.1 Definitions:3.1.1 Many of the terms used in this test method are defined in Terminology E6 and Terminology E7.3.2 Definitions of Terms Specific to This Standard:3.2.1 interplanar spacingthe perpendicular distance between adjacent parallel lattice plan
17、es.3.2.2 macrostressan average stress acting over a region of the test specimen containing many crystals.3.3 Symbols:3.3.1 ax = dummy = dummy parameter for Sum(a)Sum(x) and SD(a).SD(x).3.3.2 c = ordinate = ordinate intercept of a graph of d versus stress.3.3.3 d = interplanar = interplanar spacing b
18、etween crystallographic planes; also called d-spacing.d-spacing.3.3.4 d0 = interplanar = interplanar spacing for unstressed material.3.3.5 d = change= change in interplanar spacing caused by stress.3.3.6 E = modulus = modulus of elasticity.3.3.7 = Poissons ratio.3.3.8 EXECeff = effective = x-ray ela
19、stic parameter for X-ray measurements.constants for residual stress measurements usingx-ray diffraction.3.3.9 hkl = Miller indices.3.3.10 12 S2hkl= (1+v)/E for an elastically isotropic body.3.3.11 S1hkl= v/E for an elastically isotropic body.3.3.12 i = measurement = measurement index, 1 i n.3.3.13 m
20、 = slope = slope of a graphplot of d versus stress.3.3.14 n = number = number of measurements used to determine slope m.3.3.15 SD(a)SD(x) = standard= standard deviation of a set of quantities “a”. “x”.3.3.16 Sum(a)Sum(x) = sum= sum of a set of quantities “a”.“x”.3.3.17 Ti = X = Xi minus mean of all
21、Xi values.3.3.18 Xi = = i-th value of applied stress.3.3.19 Yi = measurement = measurement of d corresponding to Xi.3.3.16 = Poissons ratio.3.3.20 = angle= angle between the specimen surface normal and the normal to the diffracting crystallographic planes.3.3.21 = the in-plane direction of stress me
22、asurement.3.3.22 ij = in-plane directions of the sample reference frame.3.3.23 ij = calculated stress tensor terms.3.3.24 hkl = measured lattice strain tensor terms at a given tilt angle.3.3.25 A = applied stress.3.3.26 max = maximum strain.3.3.27 max = maximum deflection.3.3.28 h = specimen thickne
23、ss.3.3.29 b = width of specimen.3.3.30 AX = cross sectional area of specimen.3.3.31 L = distance between outer rollers on four-point bend fixture.3.3.32 a = distance between inner and outer rollers on four-point bend fixture.3.3.33 F = known force applied to specimen.3.3.34 0 = the intercept value f
24、or each applied force necessary for S1 calculation.4. Theory4.1 The sin2 method is widely used to measure stresses in materials using x-ray diffraction techniques. The governing equationcan be written as follows:3,43 Evenschor P.D., Hauk V. Z., Metallkunde, 1975, 66 pp. 167168.4 Dlle H., J. Appl. Cr
25、yst, 1979, 12, pp. 489-501.E1426 142hkl 512S2hkl11 cos2 112 sin 2 122 sin2 2 33!sin21 (1)12S2hkl331S1hkl11 122 133!112S2hkl13 cos 123 sin !sin2where:12 S2hkl and S1hkl = are the XEC.For a body that is elastically isotropic on the microscopic scale, 12 S2hkl= (1+ v)/E and S1hkl= (v/E) where E and v a
26、re themodulus of elasticity and Poissons ratio respectively for the material for all hkl.4.2 When a uniaxial force is applied along e.g. = 0, Eq 1 becomes:hkl 512S2hklAsin21S1hklA (2)where:A = the applied stress due to the uniaxial force.Therefore:12S2hkl 5 2hklsin2 !A (3)S1hkl is embedded in the in
27、tersection term for each applied force increment and is necessary when performing triaxial mea-surements.5. Summary of Test Method5.1 Atest specimen is prepared from a material that is representative of that of the object in which residual stress measurementsare to be made.performed.NOTE 1If a sampl
28、e of the same material is available it should be used.5.2 The test specimen is instrumented with an electrical resistance strain gage,gauge, mounted in a location that experiences thesame stress as the region that will be subsequently irradiated with X-rays.x-rays.5.3 The test specimen is calibrated
29、 by loading it in such a manner that the stress, where the strain gagegauge is mounted, isdirectly calculable, and a calibration curve relating the strain gagegauge reading to the applied stress is developed.5.4 The test specimen is mounted in a loading fixture in an X-rayx-ray diffraction apparatus
30、,instrument and sequentially loadedto several loadforce levels.5.4.1 The change in interplanar spacing is measured for each loadforce level and related to the corresponding stress that isdetermined from the strain gagegauge reading and the calibration curve.5.5 The effectiveXEC elastic parameter and
31、 its standard deviationdeviations are calculated from the test results.6. Significance and Use6.1 This test method provides standard procedures for experimentally determining the effectiveXEC elastic parameter for X-raydiffraction for use in the measurement of residual and applied stresses. stresses
32、 using x-ray diffraction techniques. It also providesa standard means of reporting the precision of the parameter.XEC.6.2 This test method is applicable to any crystalline material whichthat exhibits a linear relationship between stress and strainin the elastic range.range, that is, only applicable
33、to elastic loading.6.3 This test method should be used whenever residual stresses are to be evaluated by an X-ray x-ray diffractiontechniquetechniques and the effectiveXEC elastic parameter of the material isare unknown.7. Apparatus7.1 Any X-rayx-ray diffraction instrument intended for measurements
34、the measurement of residual macrostress that employsmeasurements of the diffraction peaks that are, ideally and for best accuracy, in the high back-reflection region may be used,including film camera types, diffractometers, and portable systems.7.2 A loading fixture is required to apply loads a forc
35、e to the test specimen while it is being irradiated in the X-rayx-raydiffraction instrument.7.2.1 The fixture shall be designed such that the surface stress applied by the fixture shall be uniform over the irradiated areaof the specimen.7.2.2 The fixture shall maintain the irradiated surface of the
36、specimen at the exact center of rotation of the X-rayx-ray diffractioninstrument throughout the test with sufficient precision to provide the desired levels of precision and bias in the measurements tobe made.performed.E1426 1437.2.3 The fixture may be designed to apply tensile or bending loads.forc
37、es. A four-point bending technique such as thatdescribed by Prevey5 is most commonly used.7.3 Electrical resistance strain gagesgauges are mounted upon the test specimen to enable it to be accurately stressed to knownlevels.8. Test Specimens8.1 Test specimens should be fabricated from material with
38、microstructure as nearly the same as possible as that in the materialin which residual stresses are to be evaluated. It is preferred for superior results to use the same material with a fine grain structureand minimum cold work on the surface to minimize measurement errors.8.2 For use in tensile or
39、four-point bending fixtures, specimens should be rectangular in shape.8.2.1 The length of tensile specimens, between grips, shall be not less than four times the width, and the width-to-thickness ratioshall not exceed eight.8.2.2 For use in four-point bending fixtures, specimens should have a length
40、-to-width ratio of at least four. The specimen widthshould be sufficient to accommodate strain gagesgauges (see 7.58.5) and the width-to-thickness ratio should be greater than oneand consistent with the method used to calculate the applied stresses in 8.19.1.NOTE 2Nominal dimensions often used for s
41、pecimens for four-point bending fixtures are 4.0 0.75 0.06 in. (10.2 1.9 0.15cm).10.2 1.9 0.15 cm (4.0 0.75 0.06 in.).8.3 Tapered specimens for use in cantilever bending fixtures, and split-ring samples, are also acceptable.8.4 Specimen surfaces may be electropolished or as-rolled sheet or plate.8.5
42、 One or more electrical resistance strain gages isgauges are affixed to the test specimen in accordance with Guide E1237.The gage(s) shouldgauge(s) shall be aligned parallel to the longitudinal axis of the specimen, and should be mounted on a regionof the specimen that experiences the same strain as
43、 the region that is to be irradiated. The gage(s)gauge(s) should be applied tothe irradiated surface of the beam either adjacent to, or on either side of, the irradiated area in order to minimize errors due to theabsence of a pure tensile or bending load.force.NOTE 3In the case of four-point bending
44、 fixtures the gage(s)gauge(s) should be placed well inside the inner span of the specimen in order to minimizethe stress concentration effects associated with the inner knife edges.edges of the fixture.9. Calibration9.1 Calibrate the instrumented specimen using loadsforces applied by dead weights or
45、 by a testing machine that has beenverified according to Practices E4. The Use a loading configuration is such that the applied stresses,that produces statisticallydeterminate applied stresses in the region where the strain gagesgauges are mounted and where X-rayx-ray diffractionmeasurements will be
46、 made, are statically determinate (that is,performed (that is, such that stresses may be calculated from theapplied loadsforces and the dimensions of the specimen and the fixture). In the case of pure bending using a four-point bendingapparatus, the strain gauge may be calibrated by measurement of a
47、pplied strains via deflection of the specimen and calculated usingthe following equation:max5 max 12h3L224a2 (4)where:max = maximum applied strain to the strain gaugemax = maximum applied deflectionh = specimen thicknessL = distance between outer rollers on four-point bend fixturea = distance betwee
48、n inner and outer rollers on each side of the four-point bend fixtureIf the modulus of elasticity E for the material being tested is known, the applied stress on the specimen may then be calculatedusing Hookes law.A 5Emax (5)If the modulus of elasticity E for the material being tested is not known,
49、the applied stress on the specimen may be calculatedusing known applied forces in the case where bending is being used:A 53Fabh2 (6)where:5 Prevey, P. S., “A Method of Determining the Elastic Properties of Alloys in Selected Crystallographic Directions for X-Ray Diffraction Residual Stress Measurement,”Advances in X-Ray Analysis 20, 1977, pp. 345354.E1426 144b = the width of the specimen, andF = known total force applied by the rollers to the specimenFo
