an enhanced calibration scheme for the edm hole-drilling strain gage method for the measurement of...

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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 ofIS 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:10.2320/matertrans.MER2008098]

(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 theresidual stress value. However, the drilling operation inevi-

tably 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) Further-

more, HS drilling techniques have the advantages of simple

experimental setup, straightforward operation and improved

precision.4,5)

Accordingly, the ASTM E837 standard explic-itly 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.

Previous studies79) 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 com-

pensating the measurement error.1012) However, it was also

noted that the value ofIS 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 lowerinduced 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 conductiv-

ities 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*Graduate Student, National Cheng-Kung University

Materials Transactions, Vol. 49, No. 8 (2008) pp. 1905 to 1910#2008 The Japan Institute of Metals EXPRESS REGULARARTICLE
http://dx.doi.org/10.2320/matertrans.MER2008098http://dx.doi.org/10.2320/matertrans.MER2008098


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study were performed in accordance with the ASTM E837

standard using a TEA-06-062RE strain gage rosette and a

P-3500 strain indicator (both manufactured by the VishayMeasurements 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

D0 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 indica-

tor. 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 minimumand maximum principal residual stress.

(m,min),(m,max) "3 "1=4A "3 "12

"3 "1 2"220:5=4B:

1

A and B are material-dependent coefficients, whose values

are derived directly from the tables presented in ASTM

E837 depends on Youngs modulus and Poissons 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 of1.5 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 stress-

free 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.1012)

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 m1 K1, respectively.

Finally, further checkup aimed at the validity and precisionof 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 IP=on=off settings of 4A/23ms/23ms

and 12A/23ms/23ms were 157:9 MPa/136:4 MPa and

170:2MPa/155:6MPa, respectively. These stress values

were greater than 48% of the yield strength of AISI 1045

carbon steel (ys 285MPa) 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/9ms/9ms and 12A/9ms/9 ms were comparatively much

lower, where those corresponding values were 40:4MPa/

30:2 MPa and 43:0 MPa/35:0MPa, respectively. How-

ever, 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. 1 Schematic illustration of rosette strain gage.

Fig. 2 Hole-drilling induced stress generated under various combinations

of IP=on=off parameters with solid CuW electrode in AISI 1045 stress-

free specimens.

1906 H. T. Lee, C. Liu, F. C. Hsu and J. M. Hsu


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parameter settings of 12A/9ms/9ms and 4A/9 ms/9ms, the

discrepancies between

IS,max and

IS,min were more than20% 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/30ms as shown in Fig. 2, the data for IS,max and IS,minwere found to be 25:8MPa 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 discrep-

ancy 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,maxand 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 (IP), the voltage (Vg) between the electrode and the

workpiece, and the pulse-on duration (on), i.e. E IP

Vg on. Theoretically, it seems reasonable to expect that a

lower discharge energy will also result in a lower hole-

drilling induced stress. However, this is found not to be the

case in practice. Under the five EDM parameter settings as

shown in Fig. 2, Vg voltage was restricted to the range 45

48 V. And thus five sets of EDM conditions can be rankedaccording to energy level as follows: 12A/23ms/23ms >

12A/9ms/9 ms > 4A/23ms/23ms > 12A/6ms/30ms > 4A/

9 ms/9ms, 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/23ms > 4A/23ms/23ms > 12A/9ms/

9 ms > 4A/9 ms/9ms > 12A/6ms/30ms. 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 IP and on. Numerous experi-

ments were performed in this study, we found that the hole-

drilling 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 succes-

sive 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 SEMmicrograph 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 beaccumulated 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

(Csta) was introduced here in order to detect the occurrence

of the secondary discharge. Figure 4 presented a schematic

illustration showing several scope patterns of workingvoltage 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, Ron (see eq. (2a)).

Ron on=d on off 2a

In the current study, an electronic monitoring system was

designed to detect the Ron values 100 times every 350 ms.

The Ron data were then used to compute its mean (Ron) and

standard deviation (sR) 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 sR should be converted into an

equivalent relative variability coefficient, designated as CVR,

(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.

An Enhanced Calibration Scheme for the EDM Hole-Drilling Strain Gage Method for the Measurement of Residual Stress 1907


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where CVR = standard deviation/mean (see eq. (2d)). The

relative stability coefficient of the discharge duty ratio (Csta)

was then defined as 1 CVR (see eq. (2e)).

Ron X100i1

Ron,i=100 2b

sR

X100

i1

Ron,i Ron2

!=100 1

" #0:5

2c

CVR sR=Ron 2d

Csta 1 CVR 2e

When the scope pattern of each discharge duty conforms

exactly to the EDM parameter settings, the Csta 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 ofCsta. Figure 5 illustrated

the Csta 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 Csta value increased. When

the drilling operation was performed using parameter

setting of 12A/6ms/30ms, the value of Csta 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/9ms/9ms, 12A/9 ms/9ms,

4A/23ms/23ms and 12A/23ms/23ms, the corresponding

Csta 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 drillingprocesses, which not only decreased the Csta value, but also

increased the induced stress.

Figure 6 presented a SEM micrograph showing the cross-

section 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 distinc-

tive 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/9ms/9ms had a higher value of

discharge energy than the condition of 4A/23 ms/23ms,

however, the thickness of the corresponding recast layer was

Fig. 5 Relative stability coefficient of discharge duty ratio for various

combinations of IP=on=off parameters. (material: AISI 1045).

Fig. 6 SEM micrograph of recast layer and heat affected zone. (material: AISI 1045; EDM condition: 4A/23ms/23 ms).

Fig. 4 Scope patterns of discharge duty cycle: (A) profile of normal duty

cycle; (B), (C) and (D) profiles of abnormal duty cycle.



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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 Csta (e.g. 0.99 by 12A/6 ms/30ms 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/6ms/30ms ensured that the Cstacoefficient is kept within 0.991 throughout the drilling

operation, we suggest that this condition is optimal for EDM

hole-drilling strain gage method.

In previous studies1012) performed by the current group

demonstrated that the hole-drilling induced stress (IS) wasinsensitive 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) (m,min),(m,max) IS: 3

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 thiscorrection 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/6ms/30ms 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 325:9k0:65, where

R2 0:998. Substituting this expression into eq. (3) yielded

the enhanced EDM hole-drilling strain gage calibration

equation shown in eq. (4).

(cal,min),(cal,max) (m,min),(m,max) 325:9k0:65

"3 "1=4A "3 "12

"3 "1 2"220:5=4B

325:9k0:65 4

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 measure-

ment 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-stressloading, the minimum stress was specified as P,min $ 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 350MPa). The

residual stress (i.e. the pre-stress) within each sample was

then evaluated by conducting an EDM hole-drilling measure-

ment process using the optimal parameter settings of 12A/

6ms/30ms. Figure 9 illustrated the un-calibrated and cali-

brated 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 m1

K1

.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 con-

firmed the precision of the calibration scheme.

In this study, the ideal Csta value of 0.991 was obtained

only using parameter setting of 12A/6ms/30ms. In other

words, it can be inferred that when drilling employed this

EDM condition, pulse-off duration of 30ms was sufficient to

allow the insulating properties of the dielectric fluid to be

restored. By contrast, in the other four parameter settings, the

Fig. 7 Recast layer thickness for various combinations of IP=on=offparameters. Note that Csta values for 12A/9ms/9ms and 4A/23 ms/23 ms

are 0.91 and 0.62, respectively. (material: AISI 1045).

Fig. 8 Regression correlation between hole-drilling induced stress and

thermal conductivity. (EDM conditions: 12A/6 ms/30 ms).

An Enhanced Calibration Scheme for the EDM Hole-Drilling Strain Gage Method for the Measurement of Residual Stress 1909


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pulse-off duration was too short to restore the insulatingproperties, and thus the secondary discharge phenomenon

occurred and yielded a lower Csta value.

In order to further investigate the influence of pulse-off

duration on Csta coefficient, a series of experiments was

performed where IP=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 ofCsta was generally close to 0.99 in every

case. However, it was found that on occasions, the value of

Csta suddenly dropped to a very low value and then oscillated

in an unstable state. The duration of each unstable state was

around 35 seconds. It was conjectured that this phenomenon

was a result of a poor removal of debris from the machiningarea 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 0.991, the secondary dis-

charge phenomenon is effectively suppressed with theresult 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 pulse-

off duration of 30 ms.

(3) When performing the hole-drilling operation using the

suggested parameter setting of 12A/6ms/30ms, 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 relation-ship: IS 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) "3 "1=4A "3 "12

"3 "1 2"220:5=4B 325:9k0:65:

(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,

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Fig. 9 Calibrated (cal,max, cal,min) and un-calibrated (m,min, m,max)

results for principal measurement stress.


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