ASTM_E_1426_-_14.pdf

Designation:E142614Standard Test Method forDetermining the X-Ray Elastic Constants for Use in theMeasurement of Residual Stress Using X-Ray DiffractionTechniques1This standard is issued under the fixed designation E1426;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 reapproval.INTRODUCTIONWhen a crystalline material is strained,the spacing between parallel planes of atoms,ions,ormolecules in the lattice changes.X-Ray diffraction techniques can measure these changes and,therefore,they constitute a powerful means for studying the residual stress state in a body.Thecalculation of macroscopic stresses using lattice strains requires the use of x-ray elastic constants(XEC)which 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 x-ray elastic constants(XEC)for the evalua-tion of residual and applied stresses by x-ray diffractiontechniques.The XEC relate macroscopic stress to the strainmeasured in a particular crystallographic direction in polycrys-talline samples.The XEC are a function of the elastic modulus,Poissons ratio of the material and the hkl plane selected for themeasurement.There are two XEC that are referred to as12S2hkland S1hkl.1.2 This test method is applicable to all x-ray diffractioninstruments intended for measurements of macroscopic 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 multiple exposure techniques.1.4 The values stated in SI units are to be regarded asstandard.The values given in parentheses are mathematicalconversions to inch-pound units that are provided for informa-tion only and are not considered standard.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.Referenced Documents2.1 ASTM Standards:2E4 Practices for Force Verification of Testing MachinesE6 Terminology Relating to Methods of Mechanical TestingE7 Terminology Relating to MetallographyE1237 Guide for Installing Bonded Resistance Strain Gages3.Terminology3.1 Definitions:3.1.1 Many of the terms used in this test method are definedin Terminology E6 and Terminology E7.3.2 Definitions of Terms Specific to This Standard:3.2.1 interplanar spacingthe perpendicular 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 x=dummy parameter for Sum(x)and SD(x).3.3.2 c=ordinate intercept of a graph of d versus stress.3.3.3 d=interplanar spacing between crystallographicplanes;also called d-spacing.3.3.4 d0=interplanar spacing for unstressed material.3.3.5 d=change in interplanar spacing caused by stress.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 edition approved Dec.1,2014.Published March 2015.Originallyapproved in 1991.Last previous edition approved in 2009 as E1426 98(2009)1.DOI:10.1520/E1426-14.2For 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.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United States1 3.3.6 E=modulus of elasticity.3.3.7 =Poissons ratio.3.3.8 XEC=x-ray elastic constants for residual stressmeasurements using x-ray diffraction.3.3.9 hkl=Miller indices.3.3.1012S2hkl=(1+v)/E for an elastically isotropic body.3.3.11 S1hkl=v/E for an elastically isotropic body.3.3.12 i=measurement index,1 i n.3.3.13 m=slope of a plot of d versus stress.3.3.14 n=number of measurements used to determine slopem.3.3.15 SD(x)=standard deviation of a set of quantities“x”.3.3.16 Sum(x)=sum of a set of quantities“x”.3.3.17 Ti=Ximinus mean of all Xivalues.3.3.18 Xi=i-th value of applied stress.3.3.19 Yi=measurement of d corresponding to Xi.3.3.20 =angle between the specimen surface normal andthe normal to the diffracting crystallographic planes.3.3.21 =the in-plane direction of stress measurement.3.3.22 ij=in-plane directions of the sample referenceframe.3.3.23 ij=calculated stress tensor terms.3.3.24 hkl=measured lattice strain tensor terms at agiven tilt a