1、Designation: E 837 081Standard Test Method forDetermining Residual Stresses by the Hole-Drilling Strain-Gage Method1This standard is issued under the fixed designation E 837; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year
2、 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.1NOTEEquation 27 was editorially corrected in July 2009.INTRODUCTIONThe hole-drilling strain-gage method determines residual s
3、tresses near the surface of an isotropiclinear-elastic material. It involves attaching a strain rosette to the surface, drilling a hole at thegeometric center of the rosette, and measuring the resulting relieved strains. The residual stresseswithin the removed material are then determined from the m
4、easured strains using a series of equations.1. Scope1.1 Residual Stress Determination:1.1.1 This test method specifies a hole-drilling procedurefor determining residual stress profiles near the surface of anisotropic linearly elastic material. The test method is applicableto residual stress profile
5、determinations where in-plane stressgradients are small. The stresses may remain approximatelyconstant with depth (“uniform” stresses) or they may varysignificantly with depth (“non-uniform” stresses). The mea-sured workpiece may be “thin” with thickness much less thanthe diameter of the drilled hol
6、e or “thick” with thickness muchgreater than the diameter of the drilled hole. Only uniformstress measurements are specified for thin workpieces, whileboth uniform and non-uniform stress measurements are speci-fied for thick workpieces.1.2 Stress Measurement Range:1.2.1 The hole-drilling method can
7、identify in-plane re-sidual stresses near the measured surface of the workpiecematerial. The method gives localized measurements that indi-cate the residual stresses within the boundaries of the drilledhole.1.2.2 This test method applies in cases where materialbehavior is linear-elastic. In theory,
8、it is possible for localyielding to occur due to the stress concentration around thedrilled hole, for isotropic (equi-biaxial) residual stresses ex-ceeding 50 % of the yield stress, or for shear stresses in anydirection exceeding 25 % of the yield stress. However, inpractice it is found that satisfa
9、ctory results can be achievedproviding the residual stresses do not exceed about 60 % of thematerial yield stress.1.3 Workpiece Damage:1.3.1 The hole-drilling method is often described as “semi-destructive” because the damage that it causes is localized andoften does not significantly affect the use
10、fulness of the work-piece. In contrast, most other mechanical methods for measur-ing residual stresses substantially destroy the workpiece. Sincehole drilling does cause some damage, this test method shouldbe applied only in those cases either where the workpiece isexpendable, or where the introduct
11、ion of a small shallow holewill not significantly affect the usefulness of the workpiece.1.4 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 practice
12、s and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E 251 Test Methods for Performance Characteristics ofMetallic Bonded Resistance Strain Gages3. Terminology3.1 Symbols:1This test method is under the jurisdiction of ASTM Committee E28
13、 onMechanical Testing and is the direct responsibility of Subcommittee E28.13 onResidual Stress Measurement.Current edition approved Feb. 1, 2008. Published April 2008. Originallyapproved in 1981. Last previous edition approved in 2001 as E 837 011.2For referenced ASTM standards, visit the ASTM webs
14、ite, 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 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United Stat
15、es.a= calibration constant for isotropic stressesb= calibration constant for shear stressesajk= calibration matrix for isotropic stressesbjk= calibration matrix for shear stressesD = diameter of the gage circle, see Table 1.D0= diameter of the drilled holeE = Youngs modulusj = number of hole depth s
16、teps so fark = sequence number for hole depth stepsP = uniform isotropic (equi-biaxial) stressPk= isotropic stress within hole depth step kp = uniform isotropic (equi-biaxial) strainpk= isotropic strain after hole depth step kQ = uniform 45 shear stressQk= 45 shear stress within hole depth step kq =
17、 uniform 45 shear strainqk= 45 shear strain after hole depth step kT = uniform x-y shear stressTk= x-y shear stress within hole depth step kt = x-y shear straintk= x-y shear strain after hole depth step kT = (superscript) matrix transposeaP= regularization factor for P stressesaQ= regularization fac
18、tor for Q stressesaT= regularization factor for T stressesb = clockwise angle from the x-axis (gage 1) to themaximum principal stress direction = relieved strain for “uniform” stress casej= relieved strain measured after j hole depth stepshave been drilledn = Poissons ratiou = angle of strain gage f
19、rom the x-axissmax= maximum (more tensile) principal stressamin= minimum (more compressive) principal stresssx= uniform normal x-stress(sx)k= normal x-stress within hole depth step ksy= uniform normal y-stress(sy)k= normal y-stress within hole depth step ktxy= uniform shear xy-stress(txy)k= shear xy
20、-stress within hole depth step k4. Summary of Test Method4.1 Workpiece:4.1.1 Aflat uniform surface area away from edges and otherirregularities is chosen as the test location within the workpieceof interest. Fig. 1 schematically shows the residual stressesacting at the test location at which a hole
21、is to be drilled. Thesestresses are assumed to be uniform within the in-plane direc-tions x and y.NOTE 1For reasons of pictorial clarity in Fig. 1, the residual stressesare shown as uniformly acting over the entire in-plane region around thetest location. In actuality, it is not necessary for the re
22、sidual stresses to beuniform over such a large region. The surface strains that will be relievedby drilling a hole depend only on the stresses that originally existed at theboundaries of the hole. The stresses beyond the hole boundary do notaffect the relieved strains, even though the strains are me
23、asured beyond thehole boundary. Because of this, the hole-drilling method provides a verylocalized measurement of residual stresses.4.1.2 Fig. 1(a) shows the case where the residual stresses inthe workpiece are uniform in the depth direction. The in-planestresses are sx, syand txythroughout the thic
24、kness. Uniformresidual stress measurements can be made using this testmethod with “thin” workpieces whose material thickness issmall compared with the hole and strain gage circle diameters,and with “thick” workpieces whose material thickness is largecompared with the hole and strain gage circle diam
25、eters.4.1.3 Fig. 1(b) shows the case where the residual stresses inthe workpiece vary in the depth direction. The calculationmethod described in this test method represents the stressprofile as a staircase shape, where the depth steps correspond tothe depth increments used during the hole-drilling m
26、easure-ments. Within depth step k, the in-plane stresses are (sx)k,(sy)kand (txy)k. Non-uniform residual stress measurements can bemade using this test method only with “thick” workpieceswhose material thickness is large compared with the hole andstrain gage circle diameters.4.2 Strain Gage Rosette:
27、4.2.1 A strain gage rosette with three or more elements ofthe general type schematically illustrated in Fig. 2 is attachedto the workpiece at the location under consideration.4.3 Hole-Drilling:4.3.1 A hole is drilled in a series of steps at the geometriccenter of the strain gage rosette.4.3.2 The re
28、sidual stresses in the material surrounding thedrilled hole are partially relieved as the hole is drilled. Theassociated relieved strains are measured at a specified sequenceof steps of hole depth using a suitable strain-recording instru-ment.(a)(b)FIG. 1 Hole Geometry and Residual Stresses, (a) Uni
29、formStresses, (b) Non-uniform StressesE83708124.4 Residual Stress Calculation Method:4.4.1 The residual stresses originally existing at the holelocation are evaluated from the strains relieved by hole-drillingusing mathematical relations based on linear elasticity theory(1-5).3The relieved strains d
30、epend on the residual stresses thatexisted in the material originally within the hole.4.4.2 For the uniform stress case shown in Fig. 1(a), thesurface strain relief measured after hole-drilling is:51 1nEasx1sy2(1)11Ebsx sy2cos 2u11Eb txysin 2u4.4.3 The calibration constants aand bindicate the reliev
31、edstrains due to unit stresses within the hole depth. They aredimensionless, almost material-independent constants. Slightlydifferent values of these constants apply for a through-thickness hole made in a thin workpiece and for a blind holemade in a thick workpiece. Numerical values of these calibra
32、-tion constants have been determined from finite elementcalculations (4) for standard rosette patterns, and are tabulatedin this test method.4.4.4 For the non-uniform stress case shown in Fig. 1(b), thesurface strain relief measured after completing hole depth stepj depends on the residual stresses
33、that existed in the materialoriginally contained in all the hole depth steps 1 # k # j:j51 1nE(k51jajksx1sy! /2!k(2)11E(k51jbjksx sy! /2!kcos 2u11E(k51jbjktxy!ksin 2u4.4.5 The calibration constants ajkand bjkindicate therelieved strains in a hole j steps deep, due to unit stresseswithin hole step k.
34、 Fig. 3 shows cross-sections of drilled holesfor an example sequence where a hole is drilled in four depthsteps. Within this sequence, calibration constant represents anintermediate stage where the hole has reached 3 steps deep, andhas a unit stress acting within depth step 2. Numerical valuesof the
35、 calibration constants have been determined by finiteelement calculations (4) for standard rosette patterns, and aretabulated in this test method.4.4.6 Measurement of the relieved strains after a series ofhole depth steps provides sufficient information to calculate thestresses sx, syand txywithin e
36、ach step. From these stresses,the corresponding principal stresses smaxand sminand theirorientation b can be found.4.4.7 The relieved strains are mostly influenced by thenear-surface residual stresses. Interior stresses have influences3The boldface numbers in parentheses refer to the list of referen
37、ces at the end ofthis standard.(a)(b)FIG. 2 Schematic Geometry of a Typical Three-ElementClockwise (CW) Hole-Drilling Rosette, (a) Rosette Layout, (b)Detail of a Strain GageFIG. 3 Physical Interpretation of Coefficients ajkE8370813that diminish with their depth from the surface. Thus, hole-drilling
38、measurements can evaluate only near-surface stresses.Deep interior stresses cannot be identified reliably, see Note 7.4.4.8 In theory, it is possible for local yielding to occur dueto the stress concentration around the drilled hole. Suchyielding can occur with isotropic residual stresses exceeding5
39、0 % of the yield stress, and for shear stresses exceeding 25 %of the yield stress. However, in practice it is found thatsatisfactory results can be achieved providing the residualstresses do not exceed about 60 % of the material yield stress(6).5. Significance and Use5.1 Summary:5.1.1 Residual stres
40、ses are present in almost all materials.They may be created during the manufacture or during the lifeof the material. If not recognized and accounted for in thedesign process, residual stresses can be a major factor in thefailure of a material, particularly one subjected to alternatingservice loads
41、or corrosive environments. Residual stress mayalso be beneficial, for example, the compressive stressesproduced by shot peening. The hole-drilling strain-gage tech-nique is a practical method for determining residual stresses.6. Workpiece Preparation6.1 Requirements:6.1.1 For a “thin” workpiece, whe
42、re a through-hole is to beused, the workpiece thickness should not exceed 0.4D for atype A or B rosette, or 0.48D for a type C rosette (see Fig. 4).6.1.2 For a “thick” workpiece, where a hole depth less thanthe workpiece thickness is to be used, the workpiece thicknessshould be at least 1.2D for a t
43、ype A or B rosette, or 1.44D fora type C rosette (see Fig. 4).6.1.3 A smooth surface is usually necessary for strain gageapplication. However, abrading or grinding that could appre-ciably alter the surface stresses must be avoided. Chemicaletching could be used, thus avoiding the need for mechanical
44、abrasion.6.1.4 The surface preparation prior to bonding the straingages shall conform to the recommendations of the manufac-turer of the adhesive used to attach the strain gages.Athoroughcleaning and degreasing is required. In general, surface prepa-ration should be restricted to those methods that
45、have beendemonstrated to induce no significant residual surface stresses.This is particularly important for workpieces that contain sharpnear-surface stress gradients.7. Strain Gages and Instrumentation7.1 Rosette Geometry:7.1.1 A rosette comprising three single or pairs of straingage grids shall be
46、 used. The numbering scheme for the straingages follows a clockwise (CW) convention (7).NOTE 2The gage numbering scheme used for the rosette illustrated inFig. 2 differs from the counter-clockwise (CCW) convention often usedfor general-purpose strain gage rosettes and for some other types ofresidual
47、 stress rosette. If a strain gage rosette with CCW gage numberingis used, the residual stress calculation procedure described in this testmethod still applies. The only changes are that the numbering of gages 1and 3 are interchanged and that the angle b defining the direction of themost tensile prin
48、cipal stress smaxis reversed and is measured counter-clockwise from the new gage 1.NOTE 3It is recommended that the gages be calibrated in accordancewith Test Methods E 251.7.1.2 The gages shall be arranged in a circular pattern,equidistant from the center of the rosette.7.1.3 The gage axes shall be
49、 oriented in each of threedirections, (1) a reference direction, (2) 45 or 135 to thereference direction, and (3) perpendicular to the referencedirection. Direction (2) bisects directions (1) and (3), as shownin Fig. 2.7.1.4 The measurement direction of gage 1 in Fig. 1 isidentified as the x-axis. The y-axis is 90 counterclockwise ofthe x-axis.7.1.5 The center of the gage circle shall be clearly identifi-able.7.2 Standardized Rosettes:7.2.1 Several different standardized rosettes are available tomeet a wide range of residual stress measurement
