An Enhanced Calibration Scheme for the EDM Hole-Drilling Strain Gage Method for the Measurement of Residual Stress in Ferrous Materials

Transcription

1 Materials Transactions, Vol. 49, No. 8 (2008) pp to 1910 #2008 The Japan Institute of Metals EXPRESS REGULAR ARTICLE An Enhanced Calibration Scheme for the EDM Hole-Drilling Strain Gage Method for the Measurement of Residual Stress in Ferrous Materials H. T. Lee, C. Liu*, F. C. Hsu* and J. M. Hsu* Department of Mechanical Engineering, National Cheng-Kung University, 701, Tainan, Taiwan, R. O. China Recent studies revealed that EDM hole-drilling strain gage method is applicable for the measurement of residual stress in materials with higher hardness and toughness. However, the metallurgical transformation layer formed on the wall of the hole induces an additional stress and therefore generates a measurement error. Usually this error can be calibrated by estimating and reducing the hole-drilling induced extra stress, IS. However, the value of IS is highly sensitive to the EDM parameters. Accordingly, the current study aimed at lowering IS by optimizing the working parameters of pulse current, pulse-on duration and pulse-off duration with experiments. An inverse power law relationship was constructed to predict the magnitude of the hole-drilling induced stress where was referred. A convenient calibration method was proposed where calibration factor can be easily determined. The calibrated results revealed good accuracy where deviation is no more than 10 MPa. The accuracy of the proposed calibration scheme was confirmed in study. [doi: /matertrans.mer ] (Received March 25, 2008; Accepted June 2, 2008; Published July 25, 2008) Keywords: electrical discharge machining, hole-drilling strain gage method, residual stress, transformation layer 1. Introduction In the measurement procedure of the hole-drilling strain gage method, a strain gage rosette is attached to the specimen surface, and a circular hole is drilled vertically into the specimen at the center of the gage circle in order to partially release the residual stress within the specimen. 1) The magnitude of the released strain is monitored continuously during the drilling process and once the depth of the measurement hole reaches the prescribed value, the strain values are substituted into the stress-strain equation provided within the ASTM E837 standard in order to derive the residual stress value. However, the drilling operation inevitably induces an additional stress within the component. This additional stress is mixed with residual stress detected and therefore leads to a corresponding error in computing the residual stress. 2) It has been reported that the additional stress induced by High-Speed (HS) drilling techniques is relatively lower than that generated by conventional hole-drilling methods such as low-speed end milling technique and abrasion jet machining technique, for example. 3) Furthermore, HS drilling techniques have the advantages of simple experimental setup, straightforward operation and improved precision. 4,5) Accordingly, the ASTM E837 standard explicitly recommends the use of HS drilling technique to accomplish the hole-drilling strain gage measurement of residual stress. However, hole drilling with high speed leaded to a severe wear on cutting tool when performed on specimens with high hardness and high toughness. This tool wear increased not only the induced stress and deviation, 6) but also might prompt a catastrophic failure. The completion of the measurement process became questionable. Consequently, alternative drilling method is required here. The electrical discharge machining (EDM) technique has the advantage that its applicability is not limited by the mechanical properties of the specimen. It can be applied to all ferrous materials, even by those with high hardness and high toughness. *Graduate Student, National Cheng-Kung University Previous studies 7 9) have shown that tensile residual stresses as high as 400 MPa can be induced within the region of the transformation layer extending from the machined surface to a depth of around 40 micrometers. However, at greater depths, the tensile stress gradually reduces toward zero and may even transform to a small compressive stress. By EDM hole-drilling strain-gage method, an extra strain introduced by this transformation layer is inevitably included within the released strain detected. Such measurement error should be calibrated if the accuracy of the residual stress measurement is aimed at. In previous studies by the current group, it was shown that the hole-drilling induced stress ( IS ) measured on stress-free specimens could be useful in compensating the measurement error ) However, it was also noted that the value of IS was highly sensitive to the working parameters such as pulse current and pulse-on duration. Thus it is required to specify the appropriate EDM working conditions in order to ensure the validity of the calibration. It is clear that the stress induced during the hole-drilling process should be minimized. Accordingly, the current study commences by finding suitable values of the pulse current, pulse-on duration and pulse-off duration. Good combination of those parameters can effectively suppress the occurrence of secondary discharges and therefore result in a lower induced stress. A series of experiments were performed using the various combination of parameter settings to check the hole-drilling induced stress generated. In this study, six different ferrous specimens with varying thermal conductivities were used. A mathematical correlation between the hole-drilling induced stress and the thermal conductivity coefficient of the specimen was derived on the base of the experimental data. This correlation was employed further to construct a calibration equation with which the measured stress value obtained using the EDM hole-drilling strain-gage method was compensated. Study results were further checked and discussed. 2. Experimental Procedure The residual stress measurements conducted in the present

2 1906 H. T. Lee, C. Liu, F. C. Hsu and J. M. Hsu Fig. 1 Schematic illustration of rosette strain gage. study were performed in accordance with the ASTM E837 standard using a TEA RE strain gage rosette and a P-3500 strain indicator (both manufactured by the Vishay Measurements Group Inc., USA). Figure 1 presents a schematic illustration of the strain gage, in which D is the diameter of the gage circle (5.13 mm in the present case) and D 0 is the diameter of the drilled hole. According to ASTM E837, the diameter of the measurement hole should be between 0.3D and 0.5D, while its maximum depth should be 0.4D. During the drilling process, the released strain was monitored continuously through the strain gage and indicator. When the measurement hole reached its maximum depth, the corresponding values of the strain, namely " 1, " 2, and " 3 (see Fig. 1) were read and substituted into eq. (1) shown below to obtain the corresponding value of the residual stress. Note that in eq. (1), m,min and m,max represent the minimum and maximum principal residual stress. (m,min),(m,max) ¼ð" 3 þ " 1 Þ=4A ½ð" 3 " 1 Þ 2 þð" 3 þ " 1 2" 2 Þ 2 Š 0:5 ð1þ =4B: A and B are material-dependent coefficients, whose values are derived directly from the tables presented in ASTM E837 depends on Young s modulus and Poisson s ratio of the specimen and the diameter of the measurement hole. The experiments were performed using a CNC die-sinking EDM machine (Yihawjet Inc., Taiwan) with an open circuit voltage of 120 V. Kerosene dielectric with a temperature of 25 C and solid CuW electrode with an external diameter of 1.5 mm were used. AISI 1045 mild steel was used to investigate the influence of the EDM parameters on the relative stability coefficient of the discharge duty ratio and the hole-drilling induced stress. In our experiments, the specimens with a diameter of 35 mm and a thickness of 6.2 mm were annealed to ensure a stressfree state (as confirmed via X-ray diffraction analysis). The specimens were then drilled in accordance with the ASTM E837 standard. Since the internal residual stress of a fully annealed specimen prior to the drilling is nearly zero and can be neglected. The values of the measured stress obtained from eq. (1) should thus be the principal stress, IS,min and IS,max, induced by the hole-drilling operation ) Further step required was to explore the correlation between the hole-drilling induced stress and the thermal conductivity coefficient of the sample. Derivation of a more robust calibration scheme was aimed at. Six different ferrous materials, namely AISI 1045, 4140, L6, H13, M2 and 304 were used in this experiment. They were deliberately chosen so as to provide a wide range of thermal conductivity coefficients. The values correspondingly are 50.2, 41.8, 36.4, 28.6, 21.3 and 16.3 W m 1 K 1, respectively. Finally, further checkup aimed at the validity and precision of the proposed calibration approach. Annealed AISI H13 tool steel specimen was used here. Specimens were made and pre-stressed with uniaxial loading equivalent to 20%, 35%, 50% and 65% of their yield strength, respectively, where the presence of residual stress was simulated. Note that the dimensions of the specimens and the grip used were designed in conformance with the guidelines stated in ASTM E8M tension testing standard. 13) The magnitude of the pre-stress was then measured using the EDM hole-drilling strain gage method. 3. Results and Discussions Figure 2 illustrated the variation of the measured stresses in AISI 1045 stress-free specimens drilled with a solid CuW electrode under different EDM conditions. It can be seen that the maximum ( IS,max ) and minimum ( IS,min ) principal stress induced by I P = on = off settings of 4A/23 ms/23 ms and 12A/23 ms/23 ms were 157:9 MPa/ 136:4 MPa and 170:2 MPa/ 155:6 MPa, respectively. These stress values were greater than 48% of the yield strength of AISI 1045 carbon steel ( ys ¼ 285 MPa) in magnitude, and thus these parameter combinations were obviously inappropriate for the EDM hole-drilling strain gage method. On the other hand, the hole-drilling induced stresses obtained by 4A/ 9 ms/9 ms and 12A/9 ms/9 ms were comparatively much lower, where those corresponding values were 40:4 MPa/ 30:2 MPa and 43:0 MPa/ 35:0 MPa, respectively. However, the discrepancy between the IS,max and IS,min was found to be around 12.2 MPa and 8.0 MPa, respectively. Theoretically, if the transformation layer formed on the hole surface is homogenous and has uniform properties, then the three strains (" 1, " 2, " 3 ) detected by the strain gage should be approximately equal, i.e. IS,max IS,min. However, for the Fig. 2 Hole-drilling induced stress generated under various combinations of I P = on = off parameters with solid CuW electrode in AISI 1045 stressfree specimens.

3 An Enhanced Calibration Scheme for the EDM Hole-Drilling Strain Gage Method for the Measurement of Residual Stress 1907 (a) (b) Fig. 3 (a) Ten successive discharge sparks are randomly on machined surface; (b) occurrence of secondary discharge phenomenon during third to eighth discharge events. parameter settings of 12A/9 ms/9 ms and 4A/9 ms/9 ms, the discrepancies between IS,max and IS,min were more than 20% of the average of the two principal stresses in each case. It means that the properties of the transformation layer were far from uniform. However, by parameter setting of 12A/ 6 ms/30 ms as shown in Fig. 2, the data for IS,max and IS,min were found to be 25:8 MPa and 23:7 MPa, respectively. The discrepancy between these two values was reduced to just 2.1 MPa. According to ASTM E837 regulation, the resolution of the strain indicator used in the measurement process requires less than 2 m". This resolution corresponds to a stress of approximately 2.5 MPa. Comparing the discrepancy of the principal induced stresses mentioned above (2.1 MPa) with the strain indicator resolution (2.5 MPa), it can be concluded that the discrepancy between the IS,max and IS,min under this working condition was sufficiently small which can be ignored. By EDM process, the electrical energy of each single discharge (E) is contributed by the product of the pulse current (I P ), the voltage (V g ) between the electrode and the workpiece, and the pulse-on duration ( on ), i.e. E ¼ I P V g on. Theoretically, it seems reasonable to expect that a lower discharge energy will also result in a lower holedrilling induced stress. However, this is found not to be the case in practice. Under the five EDM parameter settings as shown in Fig. 2, V g voltage was restricted to the range V. And thus five sets of EDM conditions can be ranked according to energy level as follows: 12A/23 ms/23 ms > 12A/9 ms/9 ms > 4A/23 ms/23 ms > 12A/6 ms/30 ms > 4A/ 9 ms/9 ms, where the energy values were 12.4, 4.9, 4.1, 3.2 and 1.6 mj, respectively. However, experimental results showed that the magnitude of induced stresses was in the order as: 12A/23 ms/23 ms > 4A/23 ms/23 ms > 12A/9 ms/ 9 ms > 4A/9 ms/9 ms > 12A/6 ms/30 ms. The two ordered sequences are clearly different, and thus it is apparent that there must be some other factors affecting the magnitude of the induced stress besides of I P and on. Numerous experiments were performed in this study, we found that the holedrilling induced stress is basically affected by the occurrence of the secondary discharge. Theoretically, if the dielectric fluid can be kept its good function as an effective insulation layer between the electrode and the workpiece, the successive discharge sparks are randomly distributed over the machined surface, as shown schematically in Fig. 3(a). The craters shown in this schematic figure were pasted from SEM micrograph symbolized spark results of a single discharge on surface. If there is no secondary discharge happened during discharging process, the morphology of EDMed surface will take the form similar to that shown in Fig. 3(a) where individual spark craters are separately dispersed on surface. However, as the insulation property of the dielectric fluid after the discharge is not fully restored before the next discharge event. The secondary discharges would occur during the process, and some sparks would hit the same site that caused overlapped craters formed on surface. Schematic figure is shown in Fig. 3(b) where the third to the eighth discharge hit the same place for example. Under these circumstances, a significant amount of discharge heat can be accumulated on site of the place where secondary discharge occurred, and thus an increased induced stress is generated. Hence we assumed that the magnitude of the hole-drilling induced stress was fundamentally related to the occurrence of secondary discharge events during the drilling process. However, it is practically quite difficult to detect the occurrence of secondary discharges so far nowadays our techniques attainable. As alternative parameter designated as the relative stability coefficient of the discharge duty ratio (C sta ) was introduced here in order to detect the occurrence of the secondary discharge. Figure 4 presented a schematic illustration showing several scope patterns of working voltage in one discharge duty cycle. As shown, the pattern of normal duty comprised delay duration ( d ), pulse-on duration ( on ), and pulse-off duration ( off ). 14) The ratio of the pulse-on duration to the total duration of the cycle was referred to as the discharge duty ratio, R on (see eq. (2a)). R on ¼ on =ð d þ on þ off Þ ð2aþ In the current study, an electronic monitoring system was designed to detect the R on values 100 times every 350 ms. The R on data were then used to compute its mean (R on ) and standard deviation (s R ) in accordance with eqs. (2b) and (2c), respectively. From a statistical perspective, the standard deviations of data obtained from different experiments can not directly be compared unless their means are close to equal. 15) Therefore, the s R should be converted into an equivalent relative variability coefficient, designated as CV R,

4 1908 H. T. Lee, C. Liu, F. C. Hsu and J. M. Hsu Fig. 4 Scope patterns of discharge duty cycle: (A) profile of normal duty cycle; (B), (C) and (D) profiles of abnormal duty cycle. Fig. 5 Relative stability coefficient of discharge duty ratio for various combinations of I P = on = off parameters. (material: AISI 1045). Fig. 6 SEM micrograph of recast layer and heat affected zone. (material: AISI 1045; EDM condition: 4A/23 ms/23 ms). where CV R = standard deviation/mean (see eq. (2d)). The relative stability coefficient of the discharge duty ratio (C sta ) was then defined as 1 CV R (see eq. (2e)). R on ¼ X100 ðr on,i =100Þ i¼1 X 100 i¼1 ð2bþ " s R ¼ ðr on,i R on Þ!=ð100 # 0:5 2 1Þ ð2cþ CV R ¼ s R =R on ð2dþ C sta ¼ 1 CV R ð2eþ When the scope pattern of each discharge duty conforms exactly to the EDM parameter settings, the C sta coefficient can be maintained at (or very close to) a value of 1. The occurrence of secondary discharge events yields abnormal scope patterns such as those labeled as B, C and D in Fig. 4. The corresponding changes in d and on prompt a significant reduction in the value of C sta. Figure 5 illustrated the C sta value when using the five sets of EDM conditions shown in Fig. 2. From the experimental results presented in Figs. 2 and 5, it can be seen that the hole-drilling induced stress decreased as the C sta value increased. When the drilling operation was performed using parameter setting of 12A/6 ms/30 ms, the value of C sta lain between 0.99 and 1. Accordingly, it was reasonable to infer that the occurrence of secondary discharges was suppressed in drilling process, and therefore, the hole-drilling induced stress could be efficiently decreased. Furthermore, Fig. 5 showed that when the hole-drilling process was performed using EDM conditions of 4A/9 ms/9 ms, 12A/9 ms/9 ms, 4A/23 ms/23 ms and 12A/23 ms/23 ms, the corresponding C sta coefficient had a value of 0.93, 0.91, 0.62 and 0.56, respectively. In other words, it was significant to infer that the secondary discharge events took place in these drilling processes, which not only decreased the C sta value, but also increased the induced stress. Figure 6 presented a SEM micrograph showing the crosssection of the transformation layer by AISI 1045 specimen. Two distinguishable layers, namely the recast layer and the heat affected zone, were readily identified via their distinctive microstructures. Similar SEM images were obtained for AISI 1045 specimens machined using each of the five parameter settings shown in Fig. 2 and were used to measure the thickness of the recast layer in each case. The corresponding results were presented in Fig. 7. Significantly, the results showed that the thickness of the recast layer was not directly related to the discharge energy. For example, the EDM condition of 12A/9 ms/9 ms had a higher value of discharge energy than the condition of 4A/23 ms/23 ms, however, the thickness of the corresponding recast layer was

5 An Enhanced Calibration Scheme for the EDM Hole-Drilling Strain Gage Method for the Measurement of Residual Stress 1909 Fig. 7 Recast layer thickness for various combinations of I P = on = off parameters. Note that C sta values for 12A/9 ms/9 ms and 4A/23 ms/23 ms are 0.91 and 0.62, respectively. (material: AISI 1045). far less than that produced in the latter case. From the experimental results presented in Figs. 2 and 7, it can be seen that greater C sta (e.g by 12A/6 ms/30 ms setting) value prompted a significant reduction in the thickness of the recast layer. Accordingly, it was reasonably confirmed that the occurrence of secondary discharge was an important factor in enhancing the accumulation of discharge heat. Because the EDM condition of 12A/6 ms/30 ms ensured that the C sta coefficient is kept within throughout the drilling operation, we suggest that this condition is optimal for EDM hole-drilling strain gage method. In previous studies 10 12) performed by the current group demonstrated that the hole-drilling induced stress ( IS ) was insensitive to the magnitude of the original residual stress within the specimens. Therefore, the IS value obtained from stress-free sample could be used to calibrate the value of the measured stress. As shown in eq. (3), the calibration procedure simply involves subtracting the IS value from the measured value of the residual stress, i.e. (cal,min),(cal,max) ¼ (m,min),(m,max) IS : ð3þ However, the application of this calibration scheme requires the use of a extra measurement in order to determine the value of calibration factor ( IS ). Accordingly, the objective of the current study is to enhance this correction scheme such that the calibration factor can be predicted directly by the properties of the specimen without the need for any auxiliary measurement. In a previous study by the current group, 12) it was shown that of the various properties of a specimen, its thermal conductivity has the greatest effect on the EDM hole-drilling induced stress. In order to establish the relationship of the induced stress and thermal conductivity, a series of measurement experiments was performed using the optimal parameter setting of 12A/6 ms/30 ms in six different ferrous materials, namely AISI 1045, 4140, L6, H13, M2 and 304, respectively. From Fig. 8, it was found that this relationship, calculated by regression, had the form IS ¼ 325:9k 0:65, where R 2 ¼ 0:998. Substituting this expression into eq. (3) yielded the enhanced EDM hole-drilling strain gage calibration equation shown in eq. (4). Fig. 8 Regression correlation between hole-drilling induced stress and thermal conductivity. (EDM conditions: 12A/6 ms/30 ms). (cal,min),(cal,max) ¼ (m,min),(m,max) þ 325:9k 0:65 ¼½ð" 3 þ " 1 Þ=4A ðð" 3 " 1 Þ 2 þð" 3 þ " 1 2" 2 Þ 2 Þ 0:5 =4BŠ þ 325:9k 0:65 ð4þ Since the thermal conductivity coefficient of various ferrous materials is readily available in the literature, and thus eq. (4) provides a highly convenient means to calibrate the measurement results obtained using the EDM hole-drilling strain gage method. In order to evaluate the accuracy of the calibration equation given in eq. (4), various uniaxial pre-stress loadings were applied to stress-free AISI H13 specimens to simulate the presence of residual stress. In applying the pre-stress loading, the minimum stress was specified as P,min ¼ 0, while the maximum stress ( P,max ) was assigned values of approximately 20%, 35%, 50% and 65%, respectively, of the yield stress of AISI H13 tool steel ( ys ¼ 350 MPa). The residual stress (i.e. the pre-stress) within each sample was then evaluated by conducting an EDM hole-drilling measurement process using the optimal parameter settings of 12A/ 6 ms/30 ms. Figure 9 illustrated the un-calibrated and calibrated results of the measured stress. It can be seen that the measured stress ( m,min, m,max ) obtained from eq. (1) was lower than the original pre-stress. The thermal conductivity coefficient of AISI H13 tool steel is 28.6 W m 1 K 1. Substituting this value into eq. (4), together with the strain data measured in the corresponding EDM hole-drilling process, yielded the calibrated residual stress values ( cal,max, cal,min ). Plotting these calibrated values in Fig. 9, it was found that the maximum discrepancy between the calibrated results and the original pre-stress values was less than 10 MPa in every case. This deviation was well within the limit of 20 MPa recommended in the Handbook of Measurement of Residual Stresses, 16) and therefore confirmed the precision of the calibration scheme. In this study, the ideal C sta value of was obtained only using parameter setting of 12A/6 ms/30 ms. In other words, it can be inferred that when drilling employed this EDM condition, pulse-off duration of 30 ms was sufficient to allow the insulating properties of the dielectric fluid to be restored. By contrast, in the other four parameter settings, the

6 1910 H. T. Lee, C. Liu, F. C. Hsu and J. M. Hsu Fig. 9 Calibrated ( cal,max, cal,min ) and un-calibrated ( m,min, m,max ) results for principal measurement stress. pulse-off duration was too short to restore the insulating properties, and thus the secondary discharge phenomenon occurred and yielded a lower C sta value. In order to further investigate the influence of pulse-off duration on C sta coefficient, a series of experiments was performed where I P = on parameters were 12A/23 ms, 12A/ 9 ms, 4A/23 ms, and 4A/9 ms, respectively. The experimental results showed that when the pulse-off duration exceeded 45 ms, the value of C sta was generally close to 0.99 in every case. However, it was found that on occasions, the value of C sta suddenly dropped to a very low value and then oscillated in an unstable state. The duration of each unstable state was around 3 5 seconds. It was conjectured that this phenomenon was a result of a poor removal of debris from the machining area during the drilling process. Accordingly, in a future study, the effects of the debris removal efficiency on the induced stress will be examined in order to enhance the robustness of the proposed measurement of residual stress. 4. Conclusions The experimental results presented in this study support the following major conclusions: (1) When the relative stability coefficient of the discharge duty ratio is kept within , the secondary discharge phenomenon is effectively suppressed with the result that the hole-drilling induced stress is reduced. (2) For the ferrous materials employed in the present study, the suggested optimal drilling parameters for the EDM hole-drilling strain gage method are as follows: a pulse current of 12A, a pulse-on duration of 6 ms, and a pulseoff duration of 30 ms. (3) When performing the hole-drilling operation using the suggested parameter setting of 12A/6 ms/30 ms, the value of the hole-drilling induced stress ( IS ) is related to the thermal conductivity coefficient (k) of the specimen via the following inverse power law relationship: IS ¼ 325:9k 0:65. (4) When using EDM hole-drilling strain gage method to measure the residual stress, the measurement error caused by metallurgical transformation layer can be calibrated by applying the following calibration equation: (cal,min),(cal,max) ¼½ð" 3 þ " 1 Þ=4A ðð" 3 " 1 Þ 2 þð" 3 þ " 1 2" 2 Þ 2 Þ 0:5 =4BŠþ325:9k 0:65 : (5) The calibrated values of the residual stress deviate from the true values by no more than 10 MPa. Consequently, the calibration scheme presented in this study provides a highly precise and convenient means of obtaining a significant improvement in the accuracy of the EDM hole-drilling strain gage method. REFERENCES 1) ASTM Standard E837-95, Standard Test Method for Determining Residual Stresses by Hole-Drilling Strain Gage Method, (ASTM, Philadelphia, PA, USA, 1995). 2) H. T. Lee, F. C. Hsu and T. Y. Tai: Mater. Sci. Eng. A 364 (2004) ) M. T. Flaman and J. A. Herring: Exp. Tech. 9 (1985) ) M. Tootoonian and G. S. Schajer: Exp. Mech. 35 (1995) ) G. S. Schajer: Transactions of the ASME 110 (1988) ) M. T. Flaman and J. A. Herring: Exp. Tech. 10 (1986) ) B. Ekmekci: Appl. Surf. Sci. 253 (2007) ) J. C. Rebelo, A. M. Dias, D. Kremer and J. L. Lebrun: J. Mater. Process. Technol. 84 (1998) ) B. Ekmekci, A. E. Tekkaya and A. Erden: Int. J. Mach. Tools Manuf. 46 (2006) ) H. T. Lee and F. C. Hsu: Mater. Sci. Technol. 19 (2003) ) H. T. Lee, W. P. Rehbach, F. C. Hsu, T. Y. Tai and E. Hsu: J. Mater. Process. Technol. 149 (2004) ) H. T. Lee, J. Mayer and F. C. Hsu: Transactions of the ASME 128 (2006) ) ASTM Standard E8M, Standard Test Methods for Tension Testing of Metallic Material (metric), (ASTM, Philadelphia, PA, USA, 1999). 14) S. Kher and A. Dua: SICE Annual, Proceedings of 38th Annual conference, (1999) pp ) R. L. Ott and M. Longnecker: Statistical Methods and Data Analysis, fifth ed., (Duxbury, CA, USA, 2001) pp ) J. Lu: Handbook of Measurement of Residual Stresses, (Lilburn, GA, Fairmont Press, Inc., 1996) p. 229.