1、Designation: E837 13E837 13aStandard 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.INTRODUCTIONThe hole-drilling strain-gage method determines residual stresses near the surface of an isotropiclinear-elas
3、tic 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 measured strains using a series of equations.1. Scop
4、e1.1 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 test method is applicable to residual stress profile determinations where in-plane stress gradients ar
5、esmall. 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 thickness much less than the diameter of the drilled holeor “thick” with thickness much greater than the
6、 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 Stress Measurement Range:1.2.1 The hole-drilling method can identify in-plane residual stresses near the mea
7、sured 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 where material behavior is linear-elastic. In theory, it is possible for local yielding tooccur due to
8、 the stress concentration around the drilled hole. Satisfactory measurement results can be achieved providing theresidual stresses do not exceed about 80 % of the material yield stress for hole drilling in a “thick” material and about 50% of thematerial yield stress in a “thin” material.1.3 Workpiec
9、e 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 usefulness of the workpiece. In contrast, most other mechanical methods for measuring residualstresses substantially destroy the
10、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 introduction of a small shallow hole will not significantlyaffect the usefulness of the workpiece.1.4 This standard does not purport to
11、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 and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E251 Test Me
12、thods for Performance Characteristics of Metallic Bonded Resistance Strain Gauges1 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 April 1, 2013Sept.
13、15, 2013. Published October 2013. Originally approved in 1981. Last previous edition approved in 20012013 asE837 08E837 131 . DOI: 10.1520/E0837-13.10.1520/E0837-13A.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Bo
14、ok of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.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 been made to the previous version. Becauseit may not be techn
15、ically 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.Copyright ASTM International, 100 Barr Harbor Drive, PO B
16、ox C700, West Conshohocken, PA 19428-2959. United States13. Terminology3.1 Symbols: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
17、Table 1.D0 = diameter of the drilled holeE = Youngs modulusj = number of hole depth steps 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
18、 depth step kQ = uniform 45 shear stressQk = 45 shear stress within hole depth step kq = 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 = (
19、superscript) matrix transposeP = regularization factor for P stressesQ = regularization factor for Q stressesT = 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 me
20、asured after j hole depth steps have been drilled = Poissons ratio = angle of strain gage from the x-axismax = 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
21、(y)k = normal y-stress within hole depth step kxy = uniform shear xy-stress(xy)k = shear xy-stress within 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.
22、 Fig. 1 schematically shows the residual stresses acting at the test location at which a hole is to be drilled. 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 th
23、e entire in-plane region around the testlocation. In actuality, it is not necessary for the residual stresses 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 str
24、esses beyond the hole boundary do not affect the relievedstrains, even though the strains are measured beyond 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 workp
25、iece are uniform in the depth direction. The in-planestresses are x, y and xy throughout the thickness. Uniform residual stress measurements can be made using this test method with“thin” workpieces whose material thickness is small compared with the hole and strain gage circle diameters, and with “t
26、hick”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 stresses in the workpiece vary in the depth direction. The calculation methoddescribed in this test method represents the stress profile as a st
27、aircase shape, where the depth steps correspond to the depthincrements used during the hole-drilling measurements. Within depth step k, the in-plane stresses are (x)k, (y)k and (xy)k.Non-uniform residual stress measurements can be made using this test method only with “thick” workpieces whose materi
28、althickness is large compared with the hole and strain gage circle diameters.E837 13a24.2 Strain Gage Rosette:4.2.1 A strain gage rosette with three or more elements of the general type schematically illustrated in Fig. 2 is attached to theworkpiece at the location under consideration.4.3 Hole-Drill
29、ing: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 hole are partially relieved as the hole is drilled. The associatedrelieved strains are measured at a specified sequence of steps of
30、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 evaluated from the strains relieved by hole-drilling usingmathematical relations based on linear elasticity theory (1-5).3 The relie
31、ved 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 strain relief measured after hole-drilling is:511E a x1y2 (1)11E b x 2y2 cos211E b xysin24.4.3 The calibration constants a and b indic
32、ate 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 thick workpiece. Numerical values
33、of these calibration constants havebeen determined from finite element calculations (4) for standard rosette patterns, and are tabulated in this test method.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 Stres
34、ses, (a) Uniform Stresses, (b) Non-uniform StressesE837 13a34.4.4 For the non-uniform stress case shown in Fig. 1(b), the surface strain relief measured after completing hole depth step jdepends on the residual stresses that existed in the material originally contained in all the hole depth steps 1
35、k j:j 511E (k51jajk 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
36、 drilled in four depth 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) for
37、standard rosette patterns, 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 a
38、nd their orientation can be found.(a)(b)FIG. 2 Schematic Geometry of a Typical Three-Element Clockwise (CW) Hole-Drilling Rosette, (a) Rosette Layout, (b) Detail of a StrainGageE837 13a44.4.7 The relieved strains are mostly influenced by the near-surface residual stresses. Interior stresses have inf
39、luences thatdiminish with their depth from the surface. Thus, hole-drilling measurements can evaluate only near-surface stresses. Deep interiorstresses cannot be identified reliably, see Note 7.4.4.8 In theory, it is possible for local yielding to occur due to the stress concentration around the dri
40、lled hole. Satisfactorymeasurement results can be achieved providing the residual stresses do not exceed about 80 % of the material yield stress for holedrilling in a “thick” material (6) and about 50% of the material yield stress in a “thin” material.5. Significance and Use5.1 Summary:5.1.1 Residua
41、l 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, particularly one subjected to alternating serv
42、ice 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 Requirements:6.1.1 For a “thin” workp
43、iece, where a through-hole is to be used, the workpiece thickness should not exceed 0.2D for a typeA or B rosette, or 0.24D for a type C rosette (see Fig. 4).6.1.2 For a “thick” workpiece, where a hole depth less than the workpiece thickness is to be used, the workpiece thicknessshould be at least 0
44、.8DD for a type A or B rosette, or 40.96D1.2D 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 could appreciablyalter the surface stresses must be avoided. Chemical etching could be used, thus avoiding the n
45、eed 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 gages.Athorough cleaning and degreasing is required. In general, surface preparation shouldbe restricted to th
46、ose 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. Strain Gages and Instrumentation7.1 Rosette Geometry:7.1.1 A rosette comprising three single or pairs of strain
47、 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 o
48、ther types of residual stress rosette. If a strain gage rosette with CCW gage numbering is used, theresidual stress calculation procedure described in this test method still applies. The only changes are that the numbering of gages 1 and 3 are interchangedand that the angle defining the direction of
49、 the most tensile principal stress max is reversed and is measured counter-clockwise from the new gage 1.NOTE 3It is recommended that the gages be calibrated in accordance with Test Methods E251.FIG. 3 Physical Interpretation of Coefficients ajkE837 13a57.1.2 The gages shall be arranged in a circular pattern, equidistant from the center of the rosette.7.1.3 The gage axes shall be oriented in each of three directions, (1) a reference direction, (2) 45 or 135 to the referencedirection, and
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