A12ev a2EEq

Table 2 Numerical values of dimensionless calibration coefficients a and b

D0/D

Through-the-thickness hole(a)

Blind hole(b), depth = 0.4 D

a

b

a

b

0.30

0.089

0.278

0.111

0.288

0.31

0.095

0.295

0.118

0.305

0.32

0.101

0.312

0.126

0.322

0.33

0.108

0.329

0.134

0.340

0.34

0.114

0.347

0.142

0.358

0.35

0.121

0.364

0.150

0.376

0.36

0.128

0.382

0.158

0.394

0.37

0.135

0.400

0.166

0.412

0.38

0.143

0.418

0.174

0.430

0.39

0.150

0.436

0.182

0.448

0.40

0.158

0.454

0.190

0.466

0.41

0.166

0.472

0.199

0.484

0.42

0.174

0.490

0.208

0.503

0.43

0.183

0.508

0.217

0.521

0.44

0.191

0.526

0.226

0.540

0.45

0.200

0.544

0.236

0.558

0.46

0.209

0.562

0.246

0.576

0.47

0.218

0.579

0.255

0.594

0.48

0.228

0.596

0.265

0.612

0.49

0.237

0.613

0.275

0.630

0.50

0.247

0.629

0.285

0.648

Source: ASTM E 837-92

Source: ASTM E 837-92

(b) In a thick material.

Residual stress measurements in coated materials create an additional complication because the combination of coating and substrate is no longer a homogeneous material. The calibration coefficients provided in ASTM E 837-92 no longer accurately apply. However, the above two equations are still valid for coated materials, if the coating has a uniform thickness. If the substrate is less than several times greater than the hole depth, then it is also necessary for the substrate thickness to be uniform.

The calibration coefficients A and B for hole drilling in a coated material differ from the standard values given in ASTM E 837-92. The actual values depend on the elastic properties of the coating and the substrate, the coating thickness, and the hole diameter and depth. These coefficients can be determined by either experimental calibrations (Ref 22) using known externally applied stresses or finite-element calculations (Ref 23).

Approximate values of A and B for thick coatings can be estimated from the values given in ASTM E 837-92. For this purpose, a "thick" coating is one that is at least 0.25 times the mean radius of the strain-gage rosette. For the smallest commercially available hole-drilling rosette, the mean radius is about 1.25 mm (0.050 in.). Therefore, the minimum acceptable coating thickness is about 0.3 mm (0.012 in.).

An approximate estimation of A and B for a coated material is based on the observation that the hole-drilling method is most sensitive to the stresses closest to the specimen surface. Almost all of the measured strain relief is due to the stresses in the material within a depth of about 0.25 times the mean radius of the hole-drilling rosette. Thus, a specimen coated to at least this depth is likely to behave similarly to a homogeneous thick specimen consisting only of coating material. Thus, the A and B calibration coefficients for a "thick" coating are approximately equal to the ASTM tabulated values for a homogeneous material with the elastic properties of the coating.

The A and B coefficients for coatings that are thinner than 0.25 times the mean radius of the hole-drilling rosette will deviate significantly from the ASTM tabulated values. The coefficients must be determined on an individual basis, either by experimental or computational means. The use of the hole-drilling method with such "thin" coatings is not generally recommended because the sensitivity of the resulting strain measurements is rather low. As a result, small absolute errors in the strain measurements can cause large relative errors in the computed residual stresses.

Stress Measurement. The following example illustrates a hole-drilling measurement on a detonation gun type of tungsten carbide-cobalt (WC-Co) coating deposited on an AISI 1018 steel substrate. The coating was approximately 0.75 mm (0.03 in.) thick and had a macroscopically homogeneous structure. The elastic properties of the coating were Ec = 172 GPa (25 x 106 psi) and u c = 0.3.

A 062-RE hole-drilling strain-gage rosette (5.13 mm, or 0.202 in., strain-gage mean diameter) was attached to the coated specimen. A 2.44 mm (0.096 in.) diameter hole was cut in the WC-Co coating by abrasive-jet drilling using 27 pm (1080 pin.) alumina particles. Drilling proceeded in four approximately equal depth increments, up to a final depth of 0.356 mm (0.014 in.). The strain measurements listed in Table 3 were made after each hole-depth increment. Using the A and B calibration coefficients from ASTM E 837-92, adjusted for the elastic properties of the coating material, the principal residual stresses in the coating were found to be -260 MPa (-38 ksi) and -286 MPa (-41 ksi), respectively. As might be anticipated, the residual stresses in the coating are approximately isotropic.

Table 3 Hole-drilling residual stress measurements on a detonation gun WC-Co coating

Depth

Strains, ^e

Average stress

a

«x

«y

t xy

«max

«min

t max

mm

in.

£1

£2

£3

MPa

ksi

MPa

ksi

MPa

ksi

MPa

ksi

MPa

ksi

MPa

ksi

0.00

0.000

0

0

0

-271

-39.3

-275

-39.9

-13

-1.9

-260

-37.7

-286

-41.5

13

1.9

41°

0.10

0.004

56

52

52

0.20

0.008

116

107

109

0.28

0.011

163

155

168

0.36

0.014

210

200

218

Note: Rosette type, EA-XX-062RE; Young's modulus, 172.0 GPa (25 x 106 psi); Poisson's ratio, 0.3; hole diameter, 2.440 mm

Practical considerations for the use of the hole-drilling method are:

• A high-speed drilling technique using carbide drills is recommended for producing a hole in a ductile coating. Abrasive-jet drilling is recommended for a brittle, hard coating (Ref 24).

• The use of specially made hole-drilling strain-gage rosettes is essential. The application of the strain-gage should follow the procedure recommended by the manufacturer.

• A smooth coating surface less than 0.41 pm Ra (16 pin. Ra) is desirable for secure strain-gage adhesion. An abrading or grinding process that does not induce significant residual surface stress should be used for surface preparation.

• The selection of an appropriately sized strain gage should be based on coating thickness, as well as on the depth and diameter of the hole to be drilled. The diameter of the drilled hole, D0, should be related to the diameter of the gage circle, D, where 0.3 < (D/D0) < 0.5.

• A depth microscope with a resolution better than 12.7 pm (0.0005 in.) should be used to measure the depth of the drilled hole at each depth increment.

• The center of the drilled hole should coincide with the center of the strain-gage circle within ±0.015 D0. A measurement microscope should be used to align the drill holder or abrasive-jet nozzle with the center of the rosette.

• Precautions should be taken to ensure that the walls of the drilled hole are square to the coating surface on which the rosette is cemented. It is important to protect the strain gage from abrasive-particle erosion or mechanical damage during the drilling operation.

• Values for the Young's modulus and Poisson's ratio of the coating should be independently measured in order to determine the residual stress from strain relaxations.

Significance and Use. The hole-drilling strain-gage method is a semidestructive technique for measuring residual stress on a coating with a thickness of at least 0.1 mm (0.004 in.). The method, which is quite versatile, can apply to test samples as well as to actual components with complex geometries. Furthermore, it can be used for on-site measurements.

References cited in this section

21. "Determining Residual Stresses by the Hole-Drilling Strain-Gage Method," E 837-92, Annual Book of ASTM Standards, ASTM

22. "Measurements of Residual Stresses by Hole-Drilling Strain Gage Method," TN503-4, Measurements Group, Wendell, NC, 1993

23. G.S. Schajer, J. Eng. Mater. Technol. (Trans. ASME), Vol 103 (No. 2), 1981, p 157

24. M.T. Flaman and J.A. Herring, Exp. Tech., Vol 9 (No. 8), 1985, p 30 Method Comparison

The mechanical-deflection method is capable of measuring the average stress throughout the coating thickness, but requires the stress to be uniform over large distances in the in-plane directions. In contrast, the x-ray diffraction and holedrilling methods can make a much more localized measurement in-plane, but they have a significantly more limited depth capability. A good agreement in stress measurements between the deflection and x-ray diffraction methods has been demonstrated (Ref 13). With the extrapolation of blind-hole measurements to the near surface, the stress measurement is in good agreement with that measured by x-ray diffraction (Ref 25). A user can select the most suitable method based on economics, environment, coating microstructures, and the geometry of the component to be measured.

References cited in this section

13. J.A. Sue, Surf Coat. Technol., Vol 54/55, 1992, p 154

25. C O. Ruud, P S. DiMascio and J.J. Yavelak, Exp. Mech, Vol 25 (No. 4), 1985, p 338

Testing of Stability and Thermal Properties of Thermal Barrier Coatings

Thomas A. Taylor, Praxair Surface Technologies, Inc.; Ray E. Taylor, Purdue University

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