1、Designation: E 1928 07Standard Practice forEstimating the Approximate Residual Circumferential Stressin Straight Thin-walled Tubing1This standard is issued under the fixed designation E 1928; the number immediately following the designation indicates the year oforiginal adoption or, in the case of r
2、evision, 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.1. Scope1.1 A qualitative estimate of the residual circumferentialstress in thin-walled tubing may be calcul
3、ated from the changein outside diameter that occurs upon splitting a length of thetubing. This practice assumes a linear stress distributionthrough the tube wall thickness and will not provide anestimate of local stress distributions such as surface stresses.(Very high local residual stress gradient
4、s are common at thesurface of metal tubing due to cold drawing, peening, grinding,etc.) The Hatfield and Thirkell formula, as later modified bySachs and Espey,2provides a simple method for calculating theapproximate circumferential stress from the change in diameterof straight, thin-walled, metal tu
5、bing.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. Referen
6、ced Documents2.1 ASTM Standards:3E6 Terminology Relating to Methods of Mechanical Test-ing3. 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 str
7、esses 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 pr
8、oduce 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
9、 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
10、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
11、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 th
12、is 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 (0.7
13、5-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,1This practice is under the jurisdiction of ASTM Committee E28 on MechanicalTesting and is the direct responsibility of Subcommittee E2
14、8.13 on Residual StressMeasurement.Current edition approved March 1, 2007. Published April 2007. Originallyapproved in 1998. Last previous edition approved in 1999 as E 1928 - 99.2Sachs, G. and Espey, G., “A New Method for Determination of StressDistribution in Thin-walled Tubing,” Transactions of t
15、he AIME, Vol 147, 1942.3For 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.1Copyright ASTM International, 100 Bar
16、r Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.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 eac
17、h lot orheat of material in the final size and heat treatment. The resultsof 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 midlen
18、gth 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 is
19、not 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 the diameter at 90 to the line where thesplit will be made, and at four equally spaced locations alongthe length, and avera
20、ging. Any measuring system may be usedprovided that the measurement uncertainty does not exceed0.013 mm (0.0005 in.) or 0.07 %, whichever is larger. See 5.6and Note 2.5.5 Split the sample longitudinally on one side over its fulllength along the preselected line. Care must be taken to avoidthe develo
21、pment 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.NOTE 1The tube may be split by electric discharge machining, bysawing on a milling machine
22、, or by any other gentle cutting method whichdoes not severely distort the stresses. On a milling machine the specimenshall be held by clamps which apply only longitudinal compressivestresses to the tube ends.5.6 After splitting, determine the average final outsidediameter, Df, of the sample by meas
23、uring the diameter at 90 tothe split and at four equally spaced locations along the length,and averaging. Use the same measuring system as that used in5.4.NOTE 2It is important not to deform the sample while measuring thediameter. After splitting, the diametral stiffness of the sample is very low.Fo
24、r this reason, a non-contact measurement method is preferred. If acontact measuring instrument, such as a micrometer or calipers, is used,special care or an electrical contact sensor must be used to minimize thecontact pressure applied.5.7 After splitting, determine the effective thickness, t,ofthe
25、tube wall by measuring the thickness to the nearest 0.013mm (0.0005 in.) at 180 to the split and at four equally spacedlocations along the length of the sample, and averaging. Ballpoints or pointed ends should be used with micrometers,calipers, or similar instruments in order to obtain correct wallt
26、hicknesses.NOTE 3The instrument used for the thickness measurements shouldbe calibrated 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
27、 length of tubing, thatis released by such a flexure is given as follows:M 5EI12F1Ro1R1G5EI123R1 RoRoR1(1)where:E = modulus of elasticity, = Poissons ratio,Ro= mean outside radius before splitting,R1= mean outside radius after splitting, andI = cross-sectional moment of inertia of unit length oftube
28、 wall.6.2.1 Standard reference book values of the modulus ofelasticity and Poissons 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 onesurf
29、ace to the other, then the minimum and maximum stressesoccur at the surfaces and are given as follows:S 5Mt2I56E123t23R1 RoRoR1(2)where:t = average thickness of tube wall.6.4 Rewriting the equation in terms of tube diameterS 56Et123Df DoDfDo(3)where:Do= mean outside diameter of tube before splitting
30、,Df= mean outside diameter of tube after splitting.NOTE 4If Df Do, the maximum tensile residual stresses are on theouter surface of the tube. If Df Do, the maximum tensile residual stressesare on the inner surface of the tube.6.5 Calculate and record the maximum residual circumfer-ential stress.7. R
31、eport7.1 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, lot, heat, and so forth, ofthe sample,TABLE 1 Residual Stresses in Successive Heats of TubingHeat No.Ferritic Cr-Mo-Ni Stainless Steel TitaniumkPa
32、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 5400E19280727.1.2 Length of the sample,7.1.3 Average outside diameter, Do, before splitting,7.1.4 Average o
33、utside diameter, Df, after splitting,7.1.5 Effective wall thickness, t, and7.1.6 Minimum and maximum residual circumferentialstress, S.8. Precision and Bias8.1 PrecisionSince this is a destructive practice, it isimpossible to conduct replicate tests on the same specimen toevaluate the precision of t
34、his 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 BiasThe bias
35、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.
36、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 relations
37、hipbetween 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
38、 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 g
39、ood 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
40、stress measurement; tubingASTM 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 infrin
41、gement 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
42、 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
43、 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. Individual reprints (single or multiple copies) of this standard may be obtained by contacting
44、 ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org).TABLE 2 Residual Stress Measurements on Austenitic StainlessSteel TubingDo3 t, mm (in.) Measurement Method Stress, kPa (psi)22 3 0.71 (78 3 0.028) This standard practice 154000 (22300)This standard practice 160000 (23200)Circumferential strain gages 165000 (24000)25 3 0.71 (1 3 0.028) This standard practice 160000 (23200)Circumferential strain gages 174000 (25300)E1928073
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