Nonuniform Rs Using Blind Hole Drilling

TECHNIQUES

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

EVALUATION OF NONUNIFORM RESIDUAL STRESS USING BLIND-HOLE DRILLING TECHNIQUE

B

lind-hole drilling is a semi-destructive method for evaluating the residual stress in a structure by drilling a small hole into it to a depth that is equal to its diameter at the geometric center of a specialized three-element strain gage rosette.1 The measured strain relief in the surrounding material is made use of for establishing the residual stress. The hole that is made is so small (when compared to the structural thickness) that it will not significantly impair the integrity of the structure. The hole drilling method can assess the residual stress that is either uniform or varying with depth.2–10 For the stress that is uniform with depth, the relieved strains are measured at the end of the drilling operation. For a stress that is nonuniform with depth, an incremental technique is used in which relieved strains are measured during a series of small hole-depth increments. The constants relating the principal stresses to the measured strains are established using a calibration experiment. Calibration constants define the sensitivity of the hole drilling method. Numerical values of the calibration constants depend on measurement conditions such as strain gage rosette geometry, specimen material properties, hole diameter, and depth. Calibration procedure accounts for the procedural influences and the material dependent effects on the measured strain. It improves the calculation accuracy and eliminates the effect of initial residual stresses and machining stresses. In addition, in order to assess the validity of the hole drilling method as a means of measuring stress, the method must be tested by its application to known stress conditions.11 Though cumbersome, experimental calibration method is direct when compared to finite-element method. Furthermore, experimental determination of calibration coefficients is not feasible for nonuniform residual stress. A good comparison of experimental calibration constants with the manufacturer supplied constants confirms that the hole geometry, the hole diameter, and depth are acceptable for the stress measurement. The material properties (Young’s modulus and Poisson’s ratio) should be independently evaluated so that it is possible to make a comparison between the manufacturer supplied and the experimentally determined calibration constants. Once the blind-hole drilling system is successfully calibrated, it is applied to measure the residual stress in a structure. This article brings out the experimental calibration of the blind-hole drilling system and its application for evaluating the nonuniform residual stress.

THEORETICAL OVERVIEW The introduction of a hole into a residually stressed body relaxes the stresses at that location. Since the perpendicular to the hole surface is a principal axis on which the shear and R.Rajendran, P.Baksi, and S.Bhattacharya are Scientific Officers and S.Basu is a Director affiliated with the BARC Facilities, Kalpakkam, India.

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EXPERIMENTAL TECHNIQUES May/June 2008

normal stresses are zero, the elimination of these stresses on the hole surface changes the stress in the immediate surrounding region, causing the local strains on the surface of the structure change correspondingly. For a biaxial loading, the radial strain is given as follows1: er 5 Aðsx 1 sy Þ 1 Bðsx 2 sy Þcos 2a

ð1Þ

where a is the angle of local area on the plate from the direction of residual stress. The unknowns sx, sy, and a are solved for by measuring the strains in three directions simultaneously and substituting them into Eq.1 as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e3 1 e1 1 ðe3 2 e1 Þ2 1 ðe3 2 2e2 1 e1 Þ2 2 4B 4A

ð2aÞ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e3 1 e1 1 ðe3 2 e1 Þ2 1 ðe3 2 2e2 1 e1 Þ2 1 smin 5 4B 4A

ð2bÞ

smax 5

tan 2a 5

ðe1 2 2e2 1 e3 Þ ðe3 2 e1 Þ

ð2cÞ

The coefficients A and B are more accurately obtained by integrating the strain over the areas of respective grid lengths  The material independent dimenand designated as A and B. sionless a and b are given as follows10: 2EA 11n

ð3aÞ

b 5 2 2EB

ð3bÞ

a 5 2

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

EXPERIMENTAL CALIBRATION Experimental method eliminates errors due to integration effects of the strain gage and to any imperfect geometry of the hole.10 Two tension test specimens12 of the structural material were prepared as per ASTM E-8, one for obtaining the yield stress and the other for performing the calibration test. The specimen dimensions adhered to the guidelines given by ASTM E 837. Calibration is accomplished by installing13 a Vishay CEA-06-062UM-120 residual stress rosette (Vishay micro-measurements, Malvern, PA) on a tensile test specimen12 as shown in Fig. 1. The rosette is oriented such that grid no. 3 is aligned parallel to the direction of loading and grid no. 1 along transverse axis. The gage rosette was checked for gage resistance and installation resistance. Approved soldering process was used. The rosette was coated with a transparent protective coating to prevent shorting of doi: 10.1111/j.1747-1567.2007.00224.x Ó 2007, Society for Experimental Mechanics

EVALUATION OF NONUNIFORM RESIDUAL STRESS

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

160

the exposed leads by metal chips. A three lead wire configuration was adapted to connect the rosette elements to P-3 strain indicator and SB-10 channel switching unit. Bridge balancing was carried out for the third and first gage elements to make the initial reading zero. The gage factor was set to 2.0. A 100-ton universal testing machine (Fuel Instruments and Engineers Pvt., Ltd., Kolapur, Maharashtra, India) was used for the experiments. Tension test was carried out on the first specimen to obtain the yield strength as 560 MPa. Calibration stress was kept less than 1/3 the yield stress on the second specimen. Calibration load was applied before and after the blind-hole drilling in steps of 19,620 N up to 117,720 N. At each step, the strain indicated by the meter was recorded. After reaching 117,720 N, the process of unloading was done in steps of 19,620 N and the strains were recorded. Uniform stress acting on the specimen is obtained as the load applied divided by the gage area of cross section of the specimen. Young’s modulus E and Poisson’s ratio n of the structural material is given as follows: E5

sa ea

ð4aÞ

et ea

ð4bÞ

n5 2

where sa is the axial stress, ea is the axial strain, and et is the transverse strain. The specimen was removed from the machine to drill a blind hole 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 subtracted from the strain recorded after the hole drilling to give calibration strains (e3)cal and (e1)cal from which calibration constants were established as follows:

80

40

0 0

ð5aÞ

ðe3 Þcal 2 ðe1 Þcal B 5 2scal

ð5bÞ

400

600

800

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

0

-50

-100

-150

-200

-250 0

ðe3 Þcal 1 ðe1 Þcal A 5 2scal

200

Axial strain (micro strain)

Transverse strain (micro strain)

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

Axial stress (MPa)

120

200

400

600

800

Axial strain (micro strain)

Fig. 3: Variation of the transverse strain as a function of the axial strain on the tension test specimen during the calibration test May/June 2008 EXPERIMENTAL TECHNIQUES

59

EVALUATION OF NONUNIFORM RESIDUAL STRESS

recorded zero strain values at all depths ascertained that the residual stress system functions without error, and the drilling method was satisfactory.

4

A summary of the strain data and the evaluated stresses on the structure is shown in Table 1. The variation of e1 1 e3 and e1 2 e3 as a function of the hole depth Z to the hole diameter Do is shown in Fig. 5. This trend, in comparison with ASTM E-837, clearly shows that there is variation of stress along the depth. Calibration constants for different incremental hole depths are estimated as a function of strain gage rosette mean diameter D, hole diameter Do, and hole depth Z,14,15 from which the biaxial principal stresses and their direction with reference to the first element of the rosette are estimated. For the complete hole depth, experimental calibration constants are applied. A plot of the maximum principal stress and the minimum principal stress as a function of the ratio of the hole depth (Z) to the hole diameter (Do) is shown in Fig. 6. For the full depth, the residual stresses have stabilized.

Deviation (%)

2

0 0

40

80

120

160

Stress (MPa) -2

Abar

-4

Bbar

-6

CONCLUSIONS

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

A comprehensive methodology was evolved to estimate the residual stress undergone by a structure. A tension test was performed to arrive at the yield stress of the structural material, which forms the basis for the estimation of the incremental load for calibration. The rosette along with the structural material and the hole drilling system was calibrated as per ASTM E 837 to ensure that the hole geometry, the hole diameter, and depth are acceptable for the stress measurement. The isotropic elastic homogeneous properties of the structural material were obtained as an auxiliary product of the calibration experiment. These properties help arriving at the material independent calibration coefficients. In order to calibrate the system for field application, incremental hole drilling was employed on a stress-free plate of the same structural steel that showed zero strain on all the three arms at all the time.

ratio into Eq. 3 along with the rosette maker supplied material independent calibration constants a and b yield maker sup The plied material dependent calibration constants A and B. variation of the calibration constants with the maker supplied reference values is shown in Fig. 4. The deviation of the calibration constants is within 5%. This ensures the validity of the residual stress measurement system.

RESIDUAL STRESS MEASUREMENT An incremental blind hole was made on a stress-free plate of the same structural steel recording strains at every step. The

Table 1—A summary of the relieved strain data Z

Z/Do

Z/D

e1

e2

0

0

0

 b

 a

e3

0

0

 2A (3 10213)

0

 2B (3 10213)

0

smax (MPa)

0

0

0

0

0.2

0.1

0.03898

0

0

0

—

—

—

—

0

0.4

0.2

0.07797

21

10

19

0.080

0.160

2.575

4.061

25.0

0.6

0.3

0.11695

240

15

93

0.120

0.240

3.863

6.091

0.8

0.4

0.15594

284

41

195

0.150

0.300

4.829

7.575

smin (MPa)

0 0

a (º)

0 0

229.9

25.7

21.4

289.9

9.7

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

2.2

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.

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EXPERIMENTAL TECHNIQUES May/June 2008

2.6

EVALUATION OF NONUNIFORM RESIDUAL STRESS

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

1.00

ACKNOWLEDGMENTS

Normalised relieved strain

0.80

Acknowledgments are due to Mr. M.A.K. Iyer, Cental work shop, Indira Gandhi Center for Atomic Research, for the help in tension test and Mr. B. Chandrasekar for strain measurement.

0.60

References 0.40

0.20

epsilon3+epsilon1 epsilon3-epsilon1

0.00 0.00

0.40

0.80

1.20

Hole depth/Hole diameter

Fig. 5: Variation of normalized relieved strain as a function of the ratio of the hole depth to the hole diameter Incremental blind-hole drilling was employed on the structure for which residual stress was to be evaluated. The calibration constants for incremental depths were employed to arrive at the biaxial principal stresses. The residual stress

100

Stress (MPa)

0 Sigma max Sigma min

-100

-200 0.00

0.20

0.40

0.60

0.80

Hole depth/ Hole diameter

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

1.00

1. American Society for Testing of Materials, Determining Residual Stress by the Hole-Drilling Strain-Gage Method, ASTM E 837-01e1 (2001). 2. Rendler, N.J., and Vigness, I., ‘‘Hole-Drilling Strain-Gage Method of Measuring Residual Stress,’’ Experimental Mechanics 6(12): 577–586 (1966). 3. Flaman, M.T., ‘‘Brief Investigation of Induced Drilling Stress in the Centre Hole Method of Residual Stress Measurement,’’ Experimental Mechanics 22(1): 26–30 (1982). 4. Anderson, L.F., ‘‘Experimental Method for Residual Stress Evaluation through the Thickness of the Plate, Transactions of the ASME,’’ Journal of Engineering Materials and Technology 124:428–433 (2002). 5. Schajer, G.S., and Altus, E., ‘‘Stress Calculation Error Analysis for Incremental Hole-Drilling Residual Stress Measurements, Transactions of the ASME,’’ Journal of Engineering Materials and Technology 118:120–126 (1996). 6. Alvarez-Caldas, C., San Romain, J.L., Rodriguez-Fernandez, S., and Olmeda, E., ‘‘Methodology to Determine Stresses Due to Own Weight by Using Residual Stresses Techniques,’’ Experimental Techniques 30(4): 29–32 (2006). 7. Niku-Lari, Lu, J., and Flavenot, J.F., ‘‘Measurement of Residual 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 Residual 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-Drilling Method,’’ Experimental Techniques 15(2): 25–28 (1991). 10. Schajer, G.S., and Tootoonian, M., ‘‘A New Rosette Design for More Reliable Hole Drilling Residual Stress Measurements,’’ Experimental Mechanics 37(3): 299–306 (1977). 11. Tech Note TN503-6, Measurement of Residual Stresses by Hole-Drilling Strain Gage Method, Vishay Measurements, Raleigh, NC (2003). 12. American Society for Testing of Materials, Standard Test Methods for Tension Testing of Metallic Materials, ASTM E 8-01, Philadelphia (2001). 13. American Society for Testing of Materials, Test Method for Performance Characteristics of Bonded Resistance Strain Gages, ASTM E 251-89, Philadelphia (1989). 14. Schajer, G., ‘‘Measurement of Non-Uniform Residual Stresses by 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 Stresses by Hole-Drilling Method, Part-II—practical Application of the Method,’’ ASME Journal of Engineering Materials Technology 110:344–349 (1988). n

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