EVALUATION OF NONUNIFORM RESIDUAL STRESSUSING BLIND-HOLE DRILLING TECHNIQUE

Blind-hole drilling is a semi-destructive method forevaluating the residual stress in a structure by dril-ling a small hole into it to a depth that is equal to itsdiameter at the geometric center of a specialized

three-element strain gage rosette.1 Themeasured strain reliefin the surrounding material is made use of for establishingthe residual stress. The hole that is made is so small (whencompared to the structural thickness) that it will not signifi-cantly impair the integrity of the structure. The hole drillingmethod can assess the residual stress that is either uniform orvarying with depth.2–10 For the stress that is uniform withdepth, the relieved strains are measured at the end of thedrilling operation. For a stress that is nonuniform with depth,an incremental technique is used in which relieved strains aremeasured during a series of small hole-depth increments. Theconstants relating the principal stresses to the measuredstrains are established using a calibration experiment.

Calibration constants define the sensitivity of the hole drillingmethod. Numerical values of the calibration constants dependon measurement conditions such as strain gage rosette geom-etry, specimen material properties, hole diameter, and depth.Calibration procedure accounts for the procedural influencesand the material dependent effects on the measured strain. Itimproves the calculation accuracy and eliminates the effect ofinitial residual stresses and machining stresses. In addition,in order to assess the validity of the hole drilling method asa means of measuring stress, the method must be tested by itsapplication to known stress conditions.11 Though cumber-some, experimental calibration method is direct when com-pared to finite-element method. Furthermore, experimentaldetermination of calibration coefficients is not feasible fornonuniform residual stress.

A good comparison of experimental calibration constants withthe manufacturer supplied constants confirms that the holegeometry, the hole diameter, and depth are acceptable for thestress measurement. The material properties (Young’s modu-lus and Poisson’s ratio) should be independently evaluated sothat it is possible to make a comparison between the manu-facturer supplied and the experimentally determined calibra-tion constants. Once the blind-hole drilling system issuccessfully calibrated, it is applied to measure the residualstress in a structure.

This article brings out the experimental calibration of theblind-hole drilling system and its application for evaluatingthe nonuniform residual stress.

THEORETICAL OVERVIEW

The introduction of a hole into a residually stressed bodyrelaxes the stresses at that location. Since the perpendicularto the hole surface is a principal axis on which the shear and

normal stresses are zero, the elimination of these stresseson the hole surface changes the stress in the immediatesurrounding region, causing the local strains on the surfaceof the structure change correspondingly. For a biaxial loa-ding, the radial strain is given as follows1:

er 5 Aðsx1syÞ1Bðsx2syÞcos 2a ð1Þ

where a is the angle of local area on the plate from the direc-tion of residual stress. The unknowns sx, sy, and a are solvedfor by measuring the strains in three directions simulta-neously and substituting them into Eq.1 as follows:

smax 5e31 e14A

21

4B

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðe32 e1Þ21 ðe322e21 e1Þ2

qð2aÞ

smin 5e31 e14A

11

4B

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðe32 e1Þ21 ðe322e21 e1Þ2

qð2bÞ

tan 2a5ðe122e21 e3Þ

ðe32 e1Þð2cÞ

The coefficients A and B are more accurately obtained by inte-grating the strain over the areas of respective grid lengthsand designated as �A and �B. The material independent dimen-sionless �a and �b are given as follows10:

�a5 22E �A

11nð3aÞ

�b5 22E �B ð3bÞ

where E is the Young’s modulus and n is the Poisson’s ratio.

EXPERIMENTAL CALIBRATION

Experimental method eliminates errors due to integrationeffects of the strain gage and to any imperfect geometryof the hole.10 Two tension test specimens12 of the structuralmaterial were prepared as per ASTM E-8, one for obtainingthe yield stress and the other for performing the calibrationtest. The specimen dimensions adhered to the guidelinesgiven by ASTM E 837. Calibration is accomplished by install-ing13 a Vishay CEA-06-062UM-120 residual stress rosette(Vishay micro-measurements, Malvern, PA) on a tensile testspecimen12 as shown in Fig. 1. The rosette is oriented suchthat grid no. 3 is aligned parallel to the direction of loadingand grid no. 1 along transverse axis. The gage rosette waschecked for gage resistance and installation resistance.Approved soldering process was used. The rosette was coatedwith a transparent protective coating to prevent shorting of

TECHNIQUES by R. Rajendran, P. Baksi, S. Bhattacharya, and S. Basu

R.Rajendran, P.Baksi, and S.Bhattacharya are Scientific Officers and S.Basu isa Director affiliated with the BARC Facilities, Kalpakkam, India.

58 EXPERIMENTAL TECHNIQUES May/June 2008doi: 10.1111/j.1747-1567.2007.00224.x

� 2007, Society for Experimental Mechanics

the exposed leads by metal chips. A three lead wire configu-ration was adapted to connect the rosette elements to P-3strain indicator and SB-10 channel switching unit. Bridgebalancing was carried out for the third and first gage elementsto make the initial reading zero. The gage factor was set to 2.0.

A 100-ton universal testing machine (Fuel Instruments andEngineers Pvt., Ltd., Kolapur, Maharashtra, India) was usedfor the experiments. Tension test was carried out on the firstspecimen to obtain the yield strength as 560MPa. Calibrationstress was kept less than 1/3 the yield stress on the secondspecimen. Calibration load was applied before and after theblind-hole drilling in steps of 19,620 N up to 117,720 N. Ateach step, the strain indicated by the meter was recorded.After reaching 117,720 N, the process of unloading was donein steps of 19,620 N and the strains were recorded. Uniformstress acting on the specimen is obtained as the load applieddivided by the gage area of cross section of the specimen.Young’s modulus E and Poisson’s ratio n of the structuralmaterial is given as follows:

E5sa

eað4aÞ

n5 2etea

ð4bÞ

where sa is the axial stress, ea is the axial strain, and et is thetransverse strain.

The specimen was removed from the machine to drill a blindhole at the center of the rosette using RS200 milling guide.The process of tension test was repeated. For every load-step,the strain recorded before the hole drilling was subtractedfrom the strain recorded after the hole drilling to give calibra-tion strains (e3)cal and (e1)cal from which calibration constantswere established as follows:

�A5ðe3Þcal1 ðe1Þcal

2scalð5aÞ

�B5ðe3Þcal2 ðe1Þcal

2scalð5bÞ

The variation of axial stress with axial strain is shown inFig. 2. The Young’s modulus is obtained from the slope of thecurve as 197GPa (the maker supplied value is 198GPa). Thevariation of transverse strain as a function of the axial strain isshown in Fig. 3. The slope of the curve yields the Poisson’s ratioas 0.280 (the maker supplied value is 0.275). Substitution ofthe experimentally derived Young’s modulus and Poisson’s

0 200 400 600 800

Axial strain (micro strain)

0

40

80

120

160

Axi

al s

tres

s (M

Pa)

Fig. 2: Variation of axial stress as a function of axial strain onthe tension test specimen during the calibration test

Fig. 1: Schematic of the tensile test specimen used for thecalibration test

0 200 400 600 800

Axial strain (micro strain)

-250

-200

-150

-100

-50

0

Tra

nsve

rse

stra

in (

mic

ro s

trai

n)

Fig. 3: Variation of the transverse strain as a function ofthe axial strain on the tension test specimen during thecalibration test

EVALUATION OF NONUNIFORMRESIDUAL STRESS

May/June 2008 EXPERIMENTAL TECHNIQUES 59

ratio into Eq. 3 along with the rosette maker supplied materialindependent calibration constants �a and �b yield maker sup-plied material dependent calibration constants �A and �B. Thevariation of the calibration constants with the maker suppliedreference values is shown in Fig. 4. The deviation of the cali-bration constants is within 5%. This ensures the validity of theresidual stress measurement system.

RESIDUAL STRESS MEASUREMENT

An incremental blind hole was made on a stress-free plate ofthe same structural steel recording strains at every step. The

recorded zero strain values at all depths ascertained that theresidual stress system functions without error, and the dril-ling method was satisfactory.

A summary of the strain data and the evaluated stresses onthe structure is shown in Table 1. The variation of e1 1 e3 ande12 e3 as a function of the hole depth Z to the hole diameterDo

is shown in Fig. 5. This trend, in comparison with ASTME-837, clearly shows that there is variation of stress alongthe depth. Calibration constants for different incrementalhole depths are estimated as a function of strain gage rosettemean diameter D, hole diameter Do, and hole depth Z,14,15

from which the biaxial principal stresses and their directionwith reference to the first element of the rosette are esti-mated. For the complete hole depth, experimental calibrationconstants are applied. A plot of the maximum principal stressand the minimum principal stress as a function of the ratio ofthe hole depth (Z) to the hole diameter (Do) is shown in Fig. 6.For the full depth, the residual stresses have stabilized.

CONCLUSIONS

A comprehensive methodology was evolved to estimate theresidual stress undergone by a structure. A tension test wasperformed to arrive at the yield stress of the structural mate-rial, which forms the basis for the estimation of the incremen-tal load for calibration. The rosette along with the structuralmaterial and the hole drilling system was calibrated as perASTM E 837 to ensure that the hole geometry, the hole diam-eter, and depth are acceptable for the stress measurement.The isotropic elastic homogeneous properties of the structuralmaterial were obtained as an auxiliary product of the calibra-tion experiment. These properties help arriving at the mate-rial independent calibration coefficients. In order to calibratethe system for field application, incremental hole drilling wasemployed on a stress-free plate of the same structural steelthat showed zero strain on all the three arms at all the time.

0 40 80 120 160

Stress (MPa)

-6

-4

-2

0

2

4

Dev

iatio

n (%

)

Abar

Bbar

Fig. 4: Deviation of the experimental calibration constantsfrom the gage supplier constants

Table 1—A summary of the relieved strain data

Z Z/Do Z/D e1 e2 e3 �a �b2�A

(3 10213)2�B

(3 10213)smax

(MPa)smin

(MPa) a (º)

0 0 0 0 0 0 0 0 0 0 0 0 0

0.2 0.1 0.03898 0 0 0 — — — — 0 0 0

0.4 0.2 0.07797 21 10 19 0.080 0.160 2.575 4.061 25.0 229.9 25.7

0.6 0.3 0.11695 240 15 93 0.120 0.240 3.863 6.091 21.4 289.9 9.7

0.8 0.4 0.15594 284 41 195 0.150 0.300 4.829 7.575 35.3 2151.8 5.7

1.0 0.5 0.19493 2124 55 267 0.170 0.360 5.634 9.090 44.5 2171.4 4.8

1.2 0.6 0.23391 2162 70 330 0.180 0.400 5.795 10.010 49.5 2194.4 3.2

1.4 0.7 0.27290 2198 77 379 — — — — — — —

1.6 0.8 0.31890 2224 77 408 — — — — — — —

1.8 0.9 0.35088 2245 76 427 — — — — — — —

2.0 1.0 0.38986 2258 73 436 0.210 0.540 6.439 13.636 58.2 2196.5 2.6

2.2 1.1 0.42884 2267 71 441 — — — — — — —

2.4 1.2 0.46783 2271 70 446 — — — — — — —

Do 5 2.0 mm; D 5 5.13 mm.

EVALUATION OF NONUNIFORMRESIDUAL STRESS

60 EXPERIMENTAL TECHNIQUES May/June 2008

Incremental blind-hole drilling was employed on the struc-ture for which residual stress was to be evaluated. The cali-bration constants for incremental depths were employed toarrive at the biaxial principal stresses. The residual stress

on the structure varied with the depth from the surface butgot almost stabilized at its full depth.

ACKNOWLEDGMENTS

Acknowledgments are due to Mr. M.A.K. Iyer, Cental workshop, Indira Gandhi Center for Atomic Research, for thehelp in tension test and Mr. B. Chandrasekar for strainmeasurement.

References1. American Society for Testing of Materials, Determining

Residual Stress by the Hole-Drilling Strain-Gage Method, ASTME 837-01e1 (2001).

2. Rendler, N.J., and Vigness, I., ‘‘Hole-Drilling Strain-GageMethod of Measuring Residual Stress,’’ Experimental Mechanics6(12): 577–586 (1966).

3. Flaman, M.T., ‘‘Brief Investigation of Induced Drilling Stressin the Centre Hole Method of Residual Stress Measurement,’’Exper-imental Mechanics 22(1): 26–30 (1982).

4. Anderson, L.F., ‘‘Experimental Method for Residual StressEvaluation through the Thickness of the Plate, Transactions ofthe ASME,’’ Journal of Engineering Materials and Technology124:428–433 (2002).

5. Schajer, G.S., and Altus, E., ‘‘Stress Calculation Error Anal-ysis for Incremental Hole-Drilling Residual Stress Measurements,Transactions of the ASME,’’ Journal of Engineering Materials andTechnology 118:120–126 (1996).

6. Alvarez-Caldas, C., San Romain, J.L., Rodriguez-Fernandez,S., and Olmeda, E., ‘‘Methodology to Determine Stresses Due to OwnWeight by Using Residual Stresses Techniques,’’ ExperimentalTechniques 30(4): 29–32 (2006).

7. Niku-Lari, Lu, J., and Flavenot, J.F., ‘‘Measurement of Resid-ual Stress Distribution by the Incremental Hole Drilling Method,’’Experimental Mechanics 25(2): 175–185 (1985).

8. Flaman, M.T., and Manning, B.J., ‘‘Determination of Resid-ual Stress Variation with Depth by the Hole-drilling Method,’’Experimental Mechanics 25(9): 205–207 (1985).

9. Schajer, G.S., ‘‘Strain Data Averaging for the Hole-DrillingMethod,’’ Experimental Techniques 15(2): 25–28 (1991).

10. Schajer, G.S., and Tootoonian, M., ‘‘A New Rosette Design forMore Reliable Hole Drilling Residual Stress Measurements,’’ Exper-imental Mechanics 37(3): 299–306 (1977).

11. Tech Note TN503-6, Measurement of Residual Stresses byHole-Drilling Strain Gage Method, Vishay Measurements, Raleigh,NC (2003).

12. American Society for Testing of Materials, Standard TestMethods for Tension Testing of Metallic Materials, ASTM E 8-01,Philadelphia (2001).

13. American Society for Testing of Materials, Test Method forPerformance Characteristics of Bonded Resistance Strain Gages,ASTM E 251-89, Philadelphia (1989).

14. Schajer, G., ‘‘Measurement of Non-Uniform Residual Stressesby Hole-Drilling Method, Part-I—stress Calculation Procedures,’’ASME Journal of Engineering Materials Technology 110:338–343(1988).

15. Schajer, G., ‘‘Measurement of Non-Uniform Residual Stressesby Hole-Drilling Method, Part-II—practical Application of theMethod,’’ ASME Journal of Engineering Materials Technology110:344–349 (1988). n

0.00 0.40 0.80 1.20

Hole depth/Hole diameter

0.00

0.20

0.40

0.60

0.80

1.00

Nor

mal

ised

rel

ieve

d st

rain

epsilon3+epsilon1

epsilon3-epsilon1

Fig. 5: Variation of normalized relieved strain as a functionof the ratio of the hole depth to the hole diameter

0.00 0.20 0.40 0.60 0.80 1.00

Hole depth/ Hole diameter

-200

-100

0

100

Str

ess

(MP

a)

Sigma max

Sigma min

Fig. 6: Variation of maximum and minimum principalstresses as a function of the ratio of the hole depth to thehole diameter

EVALUATION OF NONUNIFORMRESIDUAL STRESS

May/June 2008 EXPERIMENTAL TECHNIQUES 61