# ASTM E837-13a

Designation: E837 − 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 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-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 measured 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 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 hole 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 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, it is possible for localyielding to occur due to the stress concentration around thedrilled hole. Satisfactory measurement results can be achievedproviding the residual stresses do not exceed about 80 % of thematerial yield stress for hole drilling in a “thick” material andabout 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 andoften does not significantly affect the usefulness 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 introduction 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 practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E251 Test Methods for Performance Characteristics of Me-tallic Bonded Resistance Strain Gages3. Terminology3.1 Symbols:a¯ = calibration constant for isotropic stressesb¯= calibration constant for shear stressesa¯jk= calibration matrix for isotropic stressesb¯jk= calibration matrix for shear stressesD = diameter of the gage circle, see Table 1.D0= diameter of the drilled holeE = Young’s modulus1This test method is under the jurisdiction of ASTM Committee E28 onMechanical Testing and is the direct responsibility of Subcommittee E28.13 onResidual Stress Measurement.Current edition approved Sept. 15, 2013. Published October 2013. Originallyapproved in 1981. Last previous edition approved in 2013 as E837 – 13 DOI:10.1520/E0837-13A.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1j = 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 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 = (superscript) matrix transposeαP= regularization factor for P stressesαQ= regularization factor for Q stressesαT= regularization factor for T stressesβ = clockwise angle from the x-axis (gage 1) to themaximum principal stress directionε = relieved strain for “uniform” stress caseεj= relieved strain measured after j hole depth stepshave been drilledν = Poisson’s ratioθ = angle of strain gage from the x-axisσmax= maximum (more tensile) principal stressαmin= minimum (more compressive) principal stressσx= uniform normal x-stress(σx)k= normal x-stress within hole depth step kσy= uniform normal y-stress(σy)k= normal y-stress within hole depth step kτxy= uniform shear xy-stress(τxy)k= shear xy-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 is to be drilled. Thesestresses are assumed to be uniform within the in-plane direc-tions x and y.NOTE 1—For 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 residual 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 measured 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 σx, σyand τxythroughout the thickness. 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 diameters.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 measure-ments. Within depth step k, the in-plane stresses are (σx)k,(σy)kand (τxy)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: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 residual 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.4.4 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(a)(b)FIG. 1 Hole Geometry and Residual Stresses, (a) UniformStresses, (b) Non-uniform StressesE837 − 13a2(1-5)).3The relieved strains depend 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:ε 511νEa¯σx1σy2(1)11Eb¯σx2 σy2cos2θ11Eb¯τxysin2θ4.4.3 The calibration constants a¯ and b¯indicate the relievedstrains 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-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 that existed in the materialoriginally contained in all the hole depth steps 1 ≤ k ≤ j:εj511νE(k51ja¯jk~~σx1σy!/2!k(2)11E(k51jb¯jk~~σx2 σy!/2!kcos2θ11E(k51jb¯jk~τxy!ksin2θ4.4.5 The calibration constants a¯jkand b¯jkindicate therelieved strains in a hole j steps deep, due to unit stresseswithin hole step k. 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 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 σx, σyand τxywithin each step. From these stresses, thecorresponding principal stresses σmaxand σminand theirorientation β can be found.3The boldface numbers in parentheses refer to the list of references at the end ofthis standard.(a)(b)FIG. 2 Schematic Geometry of a Typical Three-Element Clock-wise (CW) Hole-Drilling Rosette, (a) Rosette Layout, (b) Detail ofa Strain GageFIG. 3 Physical Interpretation of Coefficients a¯jkE837 − 13a34.4.7 The relieved strains are mostly influenced by thenear-surface residual stresses. Interior stresses have influencesthat diminish with their depth from the surface. Thus, hole-drilling 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. Satisfactorymeasurement results can be achieved providing the residualstresses do not exceed about 80 % of the material yield stressfor hole drilling in a “thick” material (6) and about 50% of thematerial yield stress in a “thin” material.5. Significance 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 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 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, where a through-hole is to beused, the workpiece thickness should not exceed 0.2D for atype A 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 thanthe workpiece thickness is to be used, the workpiece thicknessshould be at least D for a typeAor B rosette, or 1.2D for a typeC 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 mechanicalabrasion.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 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 used. The numbering scheme for the straingages follows a clockwise (CW) convention (7).NOTE 2—The 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 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 β defining the direction of themost tensile principal stress σmaxis reversed and is measured counter-clockwise from the new gage 1.NOTE 3—It is recommended that the gages be calibrated in accordancewith Test Methods E251.7.1.2 The gages shall be arranged in a circular pattern,equidistant from the center of the rosette.7.1.3 The gage axes shall be 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 needs. Theuse of standardized rosette designs greatly simplifies thecalculation of the residual stresses. Fig. 4 shows three differentrosette types and Table 1 lists their dimensions.7.2.2 The