1、Designation: E837 082E837 13Standard Test Method forDetermining Residual Stresses by the Hole-Drilling Strain-Gage Method1This standard is issued under the fixed designation E837; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the
2、 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 NOTEEq 27 was editorially corrected in July 2009.2 NOTEEq 21 was editorially corrected in March 2013.INTRODUCTIONThe ho
3、le-drilling strain-gage method determines residual stresses 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
4、 the removed material are then determined from the measured strains using a series of equations.1. Scope1.1 Residual Stress Determination:1.1.1 This test method specifies a hole-drilling procedure for determining residual stress profiles near the surface of an isotropiclinearly elastic material. The
5、 test method is applicable to residual stress profile determinations where in-plane stress gradients aresmall. The stresses may remain approximately constant with depth (“uniform” stresses) or they may vary significantly with depth(“non-uniform” stresses). The measured workpiece may be “thin” with t
6、hickness much less than the diameter of the drilled holeor “thick” with thickness much greater than the diameter of the drilled hole. Only uniform stress measurements are specified forthin workpieces, while both uniform and non-uniform stress measurements are specified for thick workpieces.1.2 Stres
7、s Measurement Range:1.2.1 The hole-drilling method can identify in-plane residual stresses near the measured surface of the workpiece material. Themethod gives localized measurements that indicate the residual stresses within the boundaries of the drilled hole.1.2.2 This test method applies in cases
8、 where material behavior is linear-elastic. In theory, it is possible for local yielding tooccur due to the stress concentration around the drilled hole, for isotropic (equi-biaxial) residual stresses exceeding 50 % of theyield stress, or for shear stresses in any direction exceeding 25 % of the yie
9、ld stress. However, in practice it is found thatsatisfactory results can be achieved providing the residual stresses do not exceed about 60 % of the material yield stress.hole.Satisfactory measurement results can be achieved providing the residual stresses do not exceed about 80 % of the material yi
10、eldstress for hole drilling in a “thick” material and about 50% of the material yield stress in a “thin” material.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 and oftendoes not significantly affect the use
11、fulness of the workpiece. In contrast, most other mechanical methods for measuring residualstresses substantially destroy the workpiece. Since hole drilling does cause some damage, this test method should be applied onlyin those cases either where the workpiece is expendable, or where the introducti
12、on of a small shallow hole will not significantlyaffect the usefulness of the workpiece.1.4 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 health practices
13、 and determine the applicability of regulatorylimitations prior to use.1 This test method is under the jurisdiction of ASTM Committee E28 on Mechanical Testing and is the direct responsibility of Subcommittee E28.13 on Residual StressMeasurement.Current edition approved July 23, 2009April 1, 2013. P
14、ublished April 2008October 2013. Originally approved in 1981. Last previous edition approved in 2001 asE837 01E837 081 . DOI: 10.1520/E0837-08E01.10.1520/E0837-13.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have bee
15、n 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 as published by ASTM is to be considered the official document
16、.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States12. Referenced Documents2.1 ASTM Standards:2E251 Test Methods for Performance Characteristics of Metallic Bonded Resistance Strain Gauges3. Terminology3.1 Symbols:a = calibration constan
17、t 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 steps so fark = sequen
18、ce 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 = uniform 45 shear
19、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 transposeP = regularization factor for P stressesQ = regularization factor for Q stres
20、sesT = regularization factor for T stresses = clockwise angle from the x-axis (gage 1) to the maximum principal stress direction = relieved strain for “uniform” stress casej = relieved strain measured after j hole depth steps have been drilled = Poissons ratio = angle of strain gage from the x-axism
21、ax = maximum (more tensile) principal stressmin = minimum (more compressive) principal stressx = uniform normal x-stress(x)k = normal x-stress within hole depth step ky = uniform normal y-stress(y)k = normal y-stress within hole depth step kxy = uniform shear xy-stress(xy)k = shear xy-stress within
22、hole depth step k4. Summary of Test Method4.1 Workpiece:4.1.1 A flat uniform surface area away from edges and other irregularities is chosen as the test location within the workpieceof interest. Fig. 1 schematically shows the residual stresses acting at the test location at which a hole is to be dri
23、lled. These stressesare assumed to be uniform within the in-plane directions x and y.NOTE 1For reasons of pictorial clarity in Fig. 1, the residual stresses are shown as uniformly acting over the entire in-plane region around the testlocation. In actuality, it is not necessary for the residual stres
24、ses to be uniform over such a large region. The surface strains that will be relieved by drillinga hole depend only on the stresses that originally existed at the boundaries of the hole. The stresses beyond the hole boundary do not affect the relievedstrains, even though the strains are measured bey
25、ond the hole boundary. Because of this, the hole-drilling method provides a very localized measurementof residual stresses.4.1.2 Fig. 1(a) shows the case where the residual stresses in the workpiece are uniform in the depth direction. The in-planestresses are x, y and xy throughout the thickness. Un
26、iform residual stress measurements can be made using this test method with2 For referencedASTM 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
27、ASTM website.E837 132“thin” workpieces whose material thickness is small compared with the hole and strain gage circle diameters, and with “thick”workpieces whose material thickness is large compared with the hole and strain gage circle diameters.4.1.3 Fig. 1(b) shows the case where the residual str
28、esses in the workpiece vary in the depth direction. The calculation methoddescribed in this test method represents the stress profile as a staircase shape, where the depth steps correspond to the depthincrements used during the hole-drilling measurements. Within depth step k, the in-plane stresses a
29、re (x)k, (y)k and (xy)k.Non-uniform residual stress measurements can be made using this test method only with “thick” workpieces whose materialthickness is large compared with the hole and strain gage circle diameters.4.2 Strain Gage Rosette:4.2.1 A strain gage rosette with three or more elements of
30、 the general type schematically illustrated in Fig. 2 is attached to theworkpiece at the location under consideration.4.3 Hole-Drilling:4.3.1 A hole is drilled in a series of steps at the geometric center of the strain gage rosette.4.3.2 The residual stresses in the material surrounding the drilled
31、hole are partially relieved as the hole is drilled. The associatedrelieved strains are measured at a specified sequence of steps of hole depth using a suitable strain-recording instrument.4.4 Residual Stress Calculation Method:4.4.1 The residual stresses originally existing at the hole location are
32、evaluated from the strains relieved by hole-drilling usingmathematical relations based on linear elasticity theory (1-5).3 The relieved strains depend on the residual stresses that existed inthe material originally within the hole.4.4.2 For the uniform stress case shown in Fig. 1 (a), the surface st
33、rain relief measured after hole-drilling is:3 The boldface numbers in parentheses refer to the list of references at the end of this standard.(a)(b)FIG. 1 Hole Geometry and Residual Stresses, (a) Uniform Stresses, (b) Non-uniform StressesE837 133511E a x1y2 (1)11E b x 2y2 cos211E b xysin24.4.3 The c
34、alibration constants a and b indicate the relieved strains due to unit stresses within the hole depth. They aredimensionless, almost material-independent constants. Slightly different values of these constants apply for a through-thicknesshole made in a thin workpiece and for a blind hole made in a
35、thick workpiece. Numerical values of these calibration constants havebeen determined from finite element calculations (4) for standard rosette patterns, and are tabulated in this test method.4.4.4 For the non-uniform stress case shown in Fig. 1(b), the surface strain relief measured after completing
36、 hole depth step jdepends on the residual stresses that existed in the material originally contained in all the hole depth steps 1 k j:(a)(b)FIG. 2 Schematic Geometry of a Typical Three-Element Clockwise (CW) Hole-Drilling Rosette, (a) Rosette Layout, (b) Detail of a StrainGageE837 134j 511E (k51jaj
37、k x1y!/2!k (2)11E (k51jbjk x 2y!/2!kcos211E (k51jbjk xy!ksin24.4.5 The calibration constants ajk and bjk indicate the relieved strains in a hole j steps deep, due to unit stresses within holestep k.Fig. 3 shows cross-sections of drilled holes for an example sequence where a hole is drilled in four d
38、epth steps. Within thissequence, calibration constant represents an intermediate stage where the hole has reached 3 steps deep, and has a unit stress actingwithin depth step 2. Numerical values of the calibration constants have been determined by finite element calculations (4) forstandard rosette p
39、atterns, and are tabulated in this test method.4.4.6 Measurement of the relieved strains after a series of hole depth steps provides sufficient information to calculate thestresses x, y and xy within each step. From these stresses, the corresponding principal stresses max and min and their orientati
40、on can be found.4.4.7 The relieved strains are mostly influenced by the near-surface residual stresses. Interior stresses have influences thatdiminish with their depth from the surface. Thus, hole-drilling measurements can evaluate only near-surface stresses. Deep interiorstresses cannot be identifi
41、ed reliably, see Note 7.4.4.8 In theory, it is possible for local yielding to occur due to the stress concentration around the drilled hole. Such yieldingcan occur with isotropic residual stresses exceeding 50 % of the yield stress, and for shear stresses exceeding 25 % of the yieldstress. However,
42、in practice it is found that satisfactory Satisfactory measurement results can be achieved providing the residualstresses do not exceed about 60 %80 % of the material yield stress for hole drilling in a “thick” material (6).) and about 50% ofthe material yield stress in a “thin” material.5. Signific
43、ance and Use5.1 Summary:5.1.1 Residual stresses are present in almost all materials. They may be created during the manufacture or during the life of thematerial. If not recognized and accounted for in the design process, residual stresses can be a major factor in the failure of amaterial, particula
44、rly one subjected to alternating service loads or corrosive environments. Residual stress may also be beneficial,for example, the compressive stresses produced by shot peening. The hole-drilling strain-gage technique is a practical method fordetermining residual stresses.6. Workpiece Preparation6.1
45、Requirements:6.1.1 For a “thin” workpiece, where a through-hole is to be used, the workpiece thickness should not exceed 0.4D0.2D for atype A or B rosette, or 0.48D0.24D for a type C rosette (see Fig. 4).FIG. 3 Physical Interpretation of Coefficients ajkE837 1356.1.2 For a “thick” workpiece, where a
46、 hole depth less than the workpiece thickness is to be used, the workpiece thicknessshould be at least 1.2D0.8D for a type A or B rosette, or 1.44D40.96D for a type C rosette (see Fig. 4).6.1.3 A smooth surface is usually necessary for strain gage application. However, abrading or grinding that coul
47、d appreciablyalter the surface stresses must be avoided. Chemical etching could be used, thus avoiding the need for mechanical abrasion.6.1.4 The surface preparation prior to bonding the strain gages shall conform to the recommendations of the manufacturer ofthe adhesive used to attach the strain ga
48、ges.Athorough cleaning and degreasing is required. In general, surface preparation shouldbe restricted to those methods that have been demonstrated to induce no significant residual surface stresses. This is particularlyimportant for workpieces that contain sharp near-surface stress gradients.7. Str
49、ain Gages and Instrumentation7.1 Rosette Geometry:7.1.1 A rosette comprising three single or pairs of strain gage grids shall be used. The numbering scheme for the strain gagesfollows a clockwise (CW) convention (7).NOTE 2The gage numbering scheme used for the rosette illustrated in Fig. 2 differs from the counter-clockwise (CCW) convention often used forgeneral-purpose strain gage rosettes and for some other types of residual stress rosette. If a strain gage rosette with CCW gage numberi
