Designation: E1928 − 13Standard Practice forEstimating the Approximate Residual Circumferential Stressin Straight Thin-walled Tubing1This standard is issued under the fixed designation E1928; 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.1. Scope*1.1 A qualitative estimate of the residual circumferentialstress in thin-walled tubing may be calculated from the changein outside diameter that occurs upon splitting a length ofthin-walled tubing. This practice assumes a linear stressdistribution through the tube wall thickness and will notprovide an estimate of local stress distributions such as surfacestresses. (Very high local residual stress gradients are commonat the surface of metal tubing due to cold drawing, peening,grinding, etc.) The Hatfield and Thirkell formula, as latermodified by Sachs and Espey,2provides a simple method forcalculating the approximate circumferential stress from thechange in diameter of straight, thin-walled, metal tubing.1.2 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:3E6 Terminology Relating to Methods of Mechanical Testing3. Terminology3.1 The definitions in this practice are in accordance withTerminology E6.4. Significance and Use4.1 Residual stresses in tubing may be detrimental to thefuture performance of the tubing. Such stresses may, forexample, influence the susceptibility of a tube to stress corro-sion cracking when the tube is exposed to certain environ-ments.4.2 Residual stresses in new thin-walled tubing are verysensitive to the parameters of the fabrication process, and smallvariations in these parameters can produce significant changesin the residual stresses. See, for example, Table 1, which showsthe residual stresses measured by this practice in samples fromsuccessive heats of a ferritic Cr-Mo-Ni stainless steel tube anda titanium condenser tube. This practice provides a means forestimating the residual stresses in samples from each and everyheat.4.2.1 This practice may also be used to estimate the residualstresses that remain in tubes after removal from service indifferent environments and operating conditions.4.3 This practice assumes a linear stress distribution throughthe wall thickness. This assumption is usually reasonable forthin-walled tubes, that is, for tubes in which the wall thicknessdoes not exceed one tenth of the outside diameter. Even incases where the assumption is not strictly justified, experiencehas shown that the approximate stresses estimated by thispractice frequently serve as useful indicators of the suscepti-bility to stress corrosion cracking of the tubing of certain metalalloys when exposed to specific environments.4.3.1 Because of this questionable assumption regarding thestress distribution in the tubing, the user is cautioned againstusing the results of this practice for design, manufacturingcontrol, localized surface residual stress evaluation, or otherpurposes without supplementary information that supports theapplication.4.4 This practice has primarily been used to estimate re-sidual fabrication stresses in new thin-walled tubing between19-mm (0.75-in.) and 25-mm (1-in.) outside diameter and1.3-mm (0.05-in.) or less wall thickness. While measurementdifficulties may be encountered with smaller or larger tubes,there does not appear to be any theoretical size limitation onthe applicability of this practice.5. Procedure5.1 On new material, the stress determination shall be madeon at least one representative sample obtained from each lot orheat of material in the final size and heat treatment. The results1This practice is under the jurisdiction of ASTM Committee E28 on MechanicalTesting and is the direct responsibility of Subcommittee E28.13 on Residual StressMeasurement.Current edition approved Nov. 1, 2013. Published January 2014. Originallyapproved in 1998. Last previous edition approved in 2007 as E1928–07. DOI:10.1520/E1928-13.2Sachs, G. and Espey, G., “A New Method for Determination of StressDistribution in Thin-walled Tubing,” Transactions of the AIME, Vol 147, 1942.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1of tests on brass and steel tubes, reported by Sachs and Espey,2indicate that the length of the sample piece of tube should beat least three times the outside diameter in order to avoidsignificant end effects.5.2 At the midlength of the tube sample, measure theoutside diameter at four locations (every 45°) around the tubecircumference in order to verify that the cross section isreasonably circular.5.3 Select and mark a straight line lengthwise on the sample,indicating where the split will be made. If the tube thickness isnot uniform around the periphery, some practitioners prefer thesplit to be made at the thinnest location.5.4 Determine the average outside diameter, Do,ofthesample by measuring and averaging the diameter at four pointsalong a line that is 90° from where the split will be made. Anymeasurement method may be used provided that the associatedmeasurement uncertainty does not exceed 0.013 mm (0.0005in.) or 0.07 %, whichever is larger. See 5.6 and Note 1.5.5 Split the sample longitudinally on one side over its fulllength along the preselected line. Take care to avoid thedevelopment of additional residual stresses in the splittingoperation. Monitoring the specimen temperatures during thesplitting operation may help to ensure that new stresses areconfined to the vicinity of the split.5.5.1 The tube may be split by electric discharge machining,by sawing, or by any other gentle cutting method that does notsignificantly distort the stresses. On a milling machine it ispreferable to hold the specimen by clamps that apply onlylongitudinal compressive stresses to the tube ends.5.6 After splitting, determine the average final outsidediameter, Df, of the sample by measuring the diameter at 90° tothe split and averaging the readings taken at four equallyspaced locations along the length of the sample. Use the samemeasurement method that was used in 5.4.NOTE 1—It is important not to deform the sample while measuring thediameter. After splitting, the diametral stiffness of the sample is very low.For this reason, a non-contact measurement method is preferred. If acontact measurment instrument, such as a micrometer or caliper, is used,special care or an electrical contact sensor is needed to minimize thecontact pressure applied.5.7 After splitting, determine the effective thickness, t,ofthe tube wall by measuring the thickness to the nearest 0.013mm (0.0005 in.) at 180° to the split and averaging the readingstaken at four equally spaced locations along the length of thesample. Ball points or pointed ends should be used withmicrometers, calipers, or similar instruments in order to obtainreliable wall thickness measurements.NOTE 2—It can be useful to calibrate the instrument used for thethickness measurements against a standard test block prior to use.6. Calculation6.1 The circumferential stress is estimated from the changein outside diameter occurring on splitting a length of tubing.6.2 The bending moment M, per unit length of tubing, thatis released by such a flexure is given as follows:M 5EI1 2 µ2 F1Ro21R1G5EI1 2 µ23R12 RoRoR1(1)where:E = modulus of elasticity,µ = Poisson’s ratio,Ro= average outside radius before splitting, andR1= average outside radius after splitting6.2.1 Standard reference book values of the modulus ofelasticity and Poisson’s ratio may be used for this purpose.6.3 The release of this bending moment corresponds to arelease of the bending stresses in the section. If the stressdistribution is such that the stresses vary linearly from onesurface to the other, then the minimum and maximum stressesoccur at the surfaces and are given as follows:S 5Mt2I56E1 2 µ23t23R12 RoRoR1(2)where:S = surface circumferential stress,t = effective thickness of tube wall, andI = second moment of area per unit length of tube wall.6.4 Rewriting the equation in terms of tube diameterS 56Et1 2 µ23D12 DoD1Do(3)where:Do= mean outside diameter of tube before splitting,D1= mean outside diameter of tube after splitting.NOTE 3—If D1 Do, the maximum tensile residual circumferentialstresses are on the outer surface of the tube. If D1 Do, the maximumtensile residual stresses are on the inner surface of the tube.6.5 Calculate and record the maximum residual circumfer-ential stress.7. Report7.1 If a report is required, it should contain, as a minimum,the following information for each sample tested:7.1.1 Identification of the material, including details rel-evant to the test,7.1.2 Length of the sample,7.1.3 Average outside diameter, Do, before splitting,7.1.4 Average outside diameter, D1, after splitting,7.1.5 Effective wall thickness, t, and7.1.6 Minimum and maximum residual circumferentialstress, S.TABLE 1 Residual Stresses in Successive Heats of TubingHeat No.Ferritic Cr-Mo-Ni Stainless Steel TitaniumkPa psi kPa psi1 234000 34000 37000 54002 272000 39400 52000 76003 217000 31500 30000 43004 183000 26500 52000 75005 241000 34900 59000 86006 30000 43007 59000 86008 30000 43009 52000 750010 37000 5400E1928 − 1328. Precision and Bias8.1 Precision—Since this is a destructive practice, it isimpossible to conduct replicate tests on the same specimen toevaluate the precision of this practice.8.1.1 Users are encouraged to conduct tests on a series ofnominally identical specimens cut from adjacent sections of asingle tube in order to estimate the approximate repeatabilityachieved with alternate splitting techniques as applied to thetube materials of interest.8.2 Bias—The bias of this practice depends upon the actualstress distribution through the thickness of the tube and itsdeparture from the linear stress distribution that this practiceassumes. The actual stress distribution depends, in turn, uponthe fabrication processes, the service history, and the tubematerial.8.2.1 While the bias of this practice in any specific instancecould be evaluated by mounting strain gages on the specimenprior to splitting, this may not be especially useful since themerit of this practice lies not in the actual value of theestimated residual circumferential stress but in the relationshipbetween the estimated stress determined by this simple practiceand the subsequent performance of the tube. In this sense, usersare encouraged to develop and maintain comprehensive his-torical records to assess, for specific tube materials, fabricationprocesses, and environments, the relationships between theestimated stresses and subsequent performance.8.3 Some residual stress measurement results obtained with6-% Mo austentic stainless steel tubing of two sizes aresummarized in Table 2. For each tubing size the samples weretaken adjacent to each other from a single tube. These resultsshow good agreement between measurements made on adja-cent samples. The results also show good agreement betweenmeasurements made by this standard practice and measure-ments made using resistance strain gages with the gridsoriented parallel to the residual circumferential stresses.9. Keywords9.1 residual stress measurement; tubingSUMMARY OF CHANGESCommittee E28 has identified the location of selected changes to this standard since the last issue (E1928–07)that may impact the use of this standard.(1) Revisions were made to the following sections: 1.1, 5.4,5.5, 5.6, Note 1, 5.7, Section 6, Section 7, and 8.3.ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. 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[email protected] (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standard may also be secured from the ASTM website (www.astm.org/COPYRIGHT/).TABLE 2 Residual Stress Measurements on Austenitic StainlessSteel TubingDo× t, mm (in.) Measurement Method Stress, kPa (psi)22×0.71(7⁄8 × 0.028) This standard practice 154000 (22300)This standard practice 160000 (23200)Circumferential strain gages 165000 (24000)25 × 0.71 (1 × 0.028) This standard practice 160000 (23200)Circumferential strain gages 174000 (25300)E1928 − 133