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Transactions, SMiRT-23 Manchester, United Kingdom - August 10-14, 2015 Division II Fracture Mechanics and Structural Integrity

RE-EVALUATION OF THE POTENTIAL DROP TECHNIQUE FOR MEASURING CREEP CRACK INITIATION AND GROWTH Keith Tarnowski1, Catrin Davies1, David Dean2 and Kamran Nikbin1 1 2

Department of Mechanical Engineering, Imperial College London, UK High Temperature Specialist, EDF Energy, UK.

ABSTRACT During a creep crack growth (CCG) test, any change in PD after the initial load-up is attributed to crack growth however, creep strains which accumulate at the crack tip will also influence the PD. This is a possible source of error in the measurement of incubation time subsequent crack growth. A method of differentiating between the influence of creep strains and crack growth is therefore required, particularly for ductile materials where the influence of these strains on PD during may be significant. It has been predicted using finite element modelling that the relationship between load-line displacement (LLD) and PD is different during incubation and crack growth. A point of inflection on a plot of PD against LLD should therefore identify the onset of crack growth, similar to the approach often employed during J-R curve testing. This paper presents experimental validation of the proposed new method. Three nominally identical CCG tests were performed on C(T) specimens manufactured from ex-service type 316H stainless steel and interrupted after different amounts of crack extension. The proposed new method of interpreting the PD data can accurately identify the onset of crack growth. The incubation time can be very different to the time for 0.2 mm of crack growth to occur which is the current definition of crack initiation in ASTM E1457-13. This difference in incubation period can also effect the subsequent crack growth rate measurements, particularly for tests where small amounts of crack growth occur. INTRODUCTION The PD technique is one of the most common methods of predicting crack length in laboratory tests. When using this technique on ductile materials one source of error is the large strains which accumulate at the crack tip [Saxena (1980, Bakker (1985)]. These strains can cause a change in PD which is equivalent to a significant amount of crack extension [Tarnowski et al. (2014)]. Lowes and Fearnehough (1971) developed a method for differentiating between an increase in PD due to strain and due to crack growth for monotonically loaded specimens at room temperature. They identified that the change in PD due to plastic deformation, in the absence of crack growth, was proportional to Crack Opening Displacement (COD). Initiation of crack growth was therefore identified from a plot of PD against COD where it deviates from this initial linear trend. Any subsequent change in PD was attributed to crack growth. The approach was validated by performing a series of interrupted tests at various loads. It has since been successfully implemented by numerous authors as discussed by Wilkowski and Maxey (1983), and also incorporated into some standards e.g. ISO 12135 (2002). There is currently no equivalent approach for creep crack growth (CCG) testing. ASTM E1457 (2013) is the most common standard for performing CCG tests. In this standard, once the load is applied to the specimen, any subsequent change in PD is attributed to crack growth. This removes the effects of elastic and plastic strains on the PD that occur during load-up although, it does not

23rd Conference on Structural Mechanics in Reactor Technology Manchester, United Kingdom - August 10-14, 2015 Division II Fracture Mechanics and Structural Integrity

differentiate between crack growth and creep stains. During tests performed to this standard, crack growth is often predicted to initiate immediately after load-up however, for creep ductile materials, the initial change in PD is likely due to creep strains. To account for this limitation, the incubation period is often approximated as the time for 0.2 mm crack extension to occur. Tarnowski et al. (2015) recently proposed an approach similar to the one developed by Lowes and Fearnehough (1971), for CCG tests. It has been shown that during the incubation stage of a CCG test the relationship between PD and LLD is different to that of a growing crack. A point of inflection on a plot of PD against LLD may therefore be used to identify the onset of crack growth and any subsequent change in PD may be used to approximate crack extension. The aim of this paper is to validate the proposed new method by preforming a series of interrupted CCG tests. METHODOLOGY Three interrupted CCG tests, labelled CCG_CT01, CCG_CT02 and CCG_CT03, have been performed with different amounts of crack growth. Significant crack growth was allowed to occur in test CCG_CT01 with the test interrupted prior to failure once the crack growth rate was accelerating rapidly. CCG_CT02 was interrupted once the PD predicted a crack extension of 0.2 mm which is the crack extension associated with initiation in ASTM E1457 (2013). CCG_CT03 was stopped when the PD predicted the onset of crack growth i.e. at a point of inflection on a plot of PD against LLD. The specimens were manufactured from ex-service type 316H stainless steel (Cast 55882) and tests were performed at 550°C. The results from the three tests were analysed using the new method discussed above and the method currently in ASTM E1457 (2013). Specimens The CCG tests were performed using side-grooved compact tension, C(T), specimens. The geometry of the specimens is shown in Figure 1 and the key dimensions and loading conditions are summarised in Table 1. The notch was generated using Electrical Discharge Machining (EDM) with a tip radius of 0.15 mm.

Figure 1. C(T) Specimen Geometry including PD probe locations


Table 1. Specimen Summary a0 W B Bn P σref [mm] [mm] [mm] [mm] [kN] [MPa]

 ref  0.2

K(a0) [MPa√m]

25.0

0.99

47.3

50.0

25.0

20.0

24.5

190

Final Crack Length Measurements At the end of each test, the specimen was cooled to room temperature and cut along the mid-thickness plane. One half of the specimen was polished and viewed under an optical microscope to view the morphology of the crack. The other half of the specimen was fatigue loaded (maximum load of 10kN, R=0.1) until a significant amount of crack growth occurred. The specimen was then pulled apart to reveal the through thickness profile of the crack. The fatigue crack growth ensured that negligible plastic deformation occurred in the region of the creep crack. The crack area was measured using image processing software ImageJ (2014). This was divided by the net specimen thickness, Bn, to calculate the average crack length. Since only half of the specimen was broken open it was assumed that the crack profile was symmetrical about the mid-thickness plane. PD Measurements The PD was recorded using a low frequency alternating current potential drop (ACPD) system similar to one used by Madhi et al. (2011). A current frequency of 2 Hz was applied such that, for this specimen geometry and material, the so called ‘skin effect’ was negligible and the current distribution is the same as it would be for a direct current potential drop (DCPD) system. The main benefit of the low frequency ACPD system is a much improved signal-to-noise ratio compared with DCPD. The locations of the current injection leads and the PD probes are shown in Figure 1. These locations were selected because the calibration function which relates crack extension and change in PD is not sensitive to small errors in probe location or to other sources of strain such as the pin holes [Tarnowski et al. (2014)]. One of the PD probes is located on the front face, whilst the other is located on the back face to account for any uneven crack growth through the thickness of the specimen. The current injection leads were attached at the mid-thickness of the specimen. The specimen, including the inside of the loading holes, was coated with high temperature paint to electrically isolate it from the testing machine. To estimate crack extension a 3rd order polynomial calibration function was derived using COMSOL (2012) finite element software for the specific specimen geometry and probe locations shown in Figure 1. This calibration function is provided in Equation 1, where R is the resistance corresponding with a specific crack length, a, and R0 is a reference resistance corresponding to the initial crack length, a0. It is in terms of resistance because this is what the low frequency ACPD system measures however, the same calibration function can be also be applied to a typical constant current DCPD system by substituting R/R0 with V/V0 . Equation 1 is valid for 10 mm of crack growth. 3

2

 R   R   R  a  0.0726    0.3055    0.8014   a0  R0   R0   R0 

(1)


If the final crack length predicted by the calibration function, apf, doesn’t match the value measured from the fracture surface, af, ASTM E1457 (2013) provides a linear correction, Equation 2, where ap is an intermediate crack length predicted by the PD.   a f  a0   a a p  a0   a0    a pf  a0  

(2)

RESULTS & DISCUSSION

Figure 2 compares the load-displacement response during load-up of the three interrupted CCG tests. Figure 3 shows the variation of LLD with time for the three tests. This figure does not include any displacement due to load-up. Figure 3(a) shows all of the test data whilst Figure 3(b) focuses on the initial 200 hours which is approximately the incubation period of the three tests. During incubation, the increase in LLD is primarily due to creep strain. It can be seen from Figure 3(b) that the creep strain in CCG_CT01 and CCG_CT03 are almost identical, whilst for CCG_CT02 it is slightly less. This difference becomes more pronounced at longer times where crack growth begins to dominate the LLD response. Whilst there is some variation between the three nominally identical tests, it is small relative to typical scatter expected during CCG testing. Figure 2 and Figure 3 provide confidence that the structural response is similar for all three tests. 25000

Load [N]

20000 15000 10000

CCG_CT01 CCG_CT02 CCG_CT03

5000 0 0.00

0.10

0.20 0.30 LLD [mm]

0.40

0.50

Figure 2. Load vs. LLD for the three interrupted CCG tests.

(b)

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00


LLD [mm]

LLD [mm]

(a)

0.05 0.04

0.03 0.02


0.01 0.00 0

400 Time [h]

800

0

100 Time [h]

200

Figure 3. LLD during the creep phase for the three tests showing (a) all data and (b) the initial 200 hrs.


(b)

30 25 20 15 10 5 0 -5


0.00

0.10

0.20 0.30 LLD [mm]

0.40

2.5 2.0 1.5 1.0 0.5 0.0 -0.5

ΔR [mΩ]

ΔR [mΩ]

(a)


0.00

0.02

0.04 0.06 LLD [mm]

0.08

0.10

Figure 4. Change in resistance against LLD for the three tests showing (a) all data and (b) the early stages of each test including the point of inflection. Figure 4 is a plot of change in resistance against LLD for the three tests. This data does not include the effects of load-up. Figure 4(a) shows all of the test data whilst Figure 4(b) focuses on the early stage of the tests. All three tests follow a similar trend with a point of inflection at a LLD of approximately 0.04 mm which is attributed to the end of the incubation period and the onset of crack growth. Some small differences between the electrical response of the three tests are apparent in Figure 4(b). Tests CCG_CT01 and CCG_CT02 are approximately linear either side of the point of inflection. Before the point of inflection, where creep strain is dominating the electrical response of the specimen, the gradient is slightly different for these two tests. After the point of inflection, when crack growth is dominating the electrical response, the gradients are very similar. The difference prior to the point of inflection is possibly due to different grain orientations close to the crack tip. It has been shown that the electrical current density increases significantly towards the crack tip [Tarnowski et al. (2015)] which makes the PD measured across the crack particularly sensitive to strain in this region. A difference in grain orientation will affect the strain at the crack tip and may therefore have a measureable effect on the PD. Unlike the first two tests, CCG_CT03 demonstrates a small initial decrease in resistance however, after this drop an approximately linear region exists with a gradient comparable to CCG_CT01 and CCG_CT02. At the point where CCG_CT03 was interrupted, this gradient was starting to increase significantly suggesting the onset of crack growth. An initial drop in resistance has been identified by other authors and is commented on in ASTM E1457 (2013). Whilst not uncommon, the cause of this drop is not fully understood although Freeman and Neate (1980) have suggested that it may be due to dislocation rearrangement. Assuming that the point of inflection corresponds to the onset of crack growth the resistance at this point should be used for the value of R0 in Equation 1. This approach ensures that any increase in PD due to creep strains which occur during incubation are not erroneously interpreted as crack growth. As discussed above, the data either side of this point of inflection is approximately linear so the intersection of two linear regressions fitted to the data has been used to calculate the value of R0. These linear regression fits for CCG_CT01 and CCG_CT02 are provided in Figure 5(a) and Figure 5(b) respectively. The resistance and LLD values in this figure are absolute and therefore include load-up.


(b)

460 455 450 445 440 435 430 425

R [mΩ]

R [mΩ]

(a)

0.35

0.45

0.55 0.65 LLD [mm]

433 432 431 430 429 428 427

0.75

0.40 0.42 0.44 0.46 0.48 0.50 0.52 LLD [mm]

Figure 5. Linear regression fits used to calculate the value of R0 for (a) CCG_CT01 and (b) CCG_CT02. The values of R0 for the three tests are summarised in Table 2 along with the final resistance measurement, Rf. For CCG_CT01 and CCG_CT02 the values of R0 have been calculated from the linear regression fits shown in Figure 5. For CCG_CT03, which was interrupted at the point of inflection, R0 is the same as Rf. Also included in Table 2, are the predicted final crack extension, Δapf, calculated from Equation 1 and the average final crack extension, Δaf, measured from the fracture surface. Table 2. Inputs to Equations 1 and 2 used to estimate the crack length for the three interrupted CCG tests. Test

R0 [mΩ]

Rf [mΩ]

Δapf Δaf [mm] [mm]

CCG_CT01 427.36 455.85

1.30

2.44

CCG_CT02 428.47 432.74

0.20

0.62

CCG_CT03 431.08 431.08 0.00 0.00* *A small amount of, localised crack extension is evident, but it is not continuous along the crack front. The fracture surfaces of the three specimens are shown in Figure 6 where the dark region ahead of the EDM notch denotes creep crack growth. This region has been measured using image processing software to estimate the average final crack extension, Δaf. Figure 7 contains optical microscope images of the crack at the mid-thickness plane of each specimen. It is worth noting that crack length measurements from Figure 7 are in good agreement with the length of the dark region on the right-hand side of each image in Figure 6 providing confidence that the dark region does correspond to the region of creep crack growth. Test CCG_CT03 was interrupted at the point of inflection on a plot of resistance against LLD. The fracture surface, shown in Figure 6(c), suggests a very small amount of crack growth has occurred although it is localised and not continuous along the crack front. The majority of the cracking is mainly in the region of the mid-thickness plane of the specimen (the right-hand side the figure). The crack shape at the mid-thickness plane is shown in Figure 7(c). At this location the crack is approximately 0.15 mm long however it is discontinuous and not yet linked up with the EDM notch. It appears from Figure 6(c) and Figure 7(c) that test CCG_CT03 was interrupted at a point where significant damage ahead of the crack tip was about to link up with the starter notch. Whilst in reality the onset of creep crack growth is not a clearly defined event, it would appear that the point of inflection on a plot of resistance against LLD does coincide with a point which could reasonably be considered crack initiation.


Ductile Fracture

Fatigue Crack Growth Creep Crack Growth

EDM Notch

(a)

(b)

(c)

Figure 6. Fracture surface of (a) CCG_CT01, (b) CCG_CT02 and (c) CCG_CT03. For each image the left-hand side is the side groove and the right-hand side is the mid-thickness plane of the specimen.

(a)

0.5 mm (b)

(c)

0.5 mm

0.1 mm

Figure 7. Crack profile at the mid-thickness plane of (a) CCG_CT01, (b) CCG_CT02 and (c) CCG_CT03.


It is apparent from Table 2 that the crack growth predicted by the calibration curve, Δapf, for tests CCG_CT01 and CCG_CT02 is significantly less than the crack growth measured from the fracture surface, Δaf. This is consistent with creep crack growth tests performed by Saxena (1980). A possible cause of this discrepancy is the morphology of cracks formed by creep which tend to be discontinuous, as can be seen in Figure 7. The ligaments between the cracked regions will allow the PD to short across the crack faces, reducing the PD measurement and the predicted crack extension. The light areas within the creep crack growth regions in Figure 6 suggest surfaces which have not been exposed to the high temperature environment and may therefore correspond to ligaments which were intact until after the test was stopped. Figure 8 shows the crack growth with time for CCG_CT01 and CCG_CT02. It compares the proposed new method for estimating crack extension, where R0 is taken as the value in Table 2, and the current method in ASTM E1457 (2013), where R0 is taken as the minimum value throughout the test. To account for the difference between the crack growth predicted by the calibration curve, Δapf, and the crack growth measured from the fracture surface, Δaf, all crack growth values have been corrected using Equation 2.

(b)

2.5

New Method ASTM Method

2.0

Crack Growth (mm)

Crack Growth (mm)

(a)

1.5 1.0 0.5

0.0 0

200

400 Time (h)

600

800

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0


0

200

400 Time (h)

600

800

Figure 8. Comparison of the crack growth predictions based on the current method in ASTM E1457 (2013) and the proposed new method for (a) CCG_CT01 and (b) CCG_CT02. Figure 8(a) shows a small difference between the crack growth estimates using the two methods for test CCG_CT01. For test CCG_CT02 however, shown in Figure 8(b), the difference is more apparent. This is because there is much less crack growth, so the increase in PD during incubation, due to creep, becomes more significant. The new method predicts no crack growth during the initial 225 hours whilst the ASTM method, which is not able to differentiate between crack growth and creep strains predicts crack the onset of growth immediately after load-up. The same behaviour is true for test CCG_CT01 however, it is not apparent from Figure 8(a) because to the large increase in PD associated with the significant amounts of crack growth masks the relatively modest increase in PD due to creep strains during incubation. The incubation time, tR0, for each test (when R = R0) is summarised for both methods in Table 3. The time for 0.2 mm of crack growth to occur, t0.2, is also provided. The incubation time is approximately 200 hours for all three tests when analysed using the new method. The ASTM method however predicts that crack growth occurs immediately after load-up for test CCG_CT01 and CCG_CT02 and after 9 hours for CCG_CT03, which is the duration of the initial drop in PD. The time for 0.2 mm of crack growth to occur, which is the definition of incubation in ASTM E1457 (2013), is approximately double the incubation period predicted by the new method.


Table 3. Estimated incubation period, tR0, and time for 0.2 mm crack extension to occur, t0.2, for the proposed new method and the current method in ASTM E1457 (2013). New Method ASTM Method Test

tR0 [h]

t0.2 [h]

tR0 [h]

t0.2 [h]

CCG_CT01

237

478

0

450

CCG_CT02

225

463

0

396

CCG_CT03

194

N/A

9

N/A

The crack growth rate for CCG_CT01 and CCG_CT02 has been correlated with the creep parameter C* in Figure 9(a) and Figure 9(b) respectively. The crack growth rate was calculated from the crack length data shown in Figure 8. Both methods of analysing the PD data are included.

(b)

1E-1 1E-2 1E-3


1E-4 1E-5

1E-4 C* (MPa.m/h)

1E-3

da/dt (mm/h)

da/dt (mm/h)

(a)

1E-2

1E-3 New Method ASTM Method

1E-4 1E-6

1E-5 1E-4 C* (MPa.m/h)

1E-3

Figure 9. Correlation of crack growth rate with C* based on the current method in ASTM E1457-13 and the proposed new method for (a) CCG_CT01 and (b) CCG_CT02. In the linear portion of Figure 9(a), where steady-state conditions exist, the points for the two data sets lie approximately on top of each other, demonstrating that there is negligible difference between the two methods. In the so-called “tail” region however the differences are significant. The new method predicts a much smaller tail because it ignores the initial change in PD due to creep strain whilst the ASTM method erroneously interprets this is crack growth. The same shorter tail can also be seen in Figure 9(b) for CCG_CT02. In this test the crack growth rate predicted by the new method is consistently higher throughout the test with a vertical offset between the two data sets. This is because the amount of crack growth is small, so the increase in PD due to creep strains during incubation is more significant compared to the increase in PD due to crack growth. The difference in crack growth rate between the two methods can be seen more clearly in Figure 8(b). CONCLUSIONS A point of inflection on a plot of PD against LLD can be used to accurately identify the point of initiation for CCG tests performed on ductile materials. The incubation period predicted using this method can be very different to the time for 0.2 mm of crack growth to occur as predicted using the current method in ASTM E1457 (2013). The proposed new method for identifying creep crack initiation also has


implications for subsequent crack growth rate measurements. This is particularly significant for tests with small amounts of crack growth. In addition it has been demonstrated that a standard calibration curve can significantly underestimate the crack length when compared to measurements from the fracture surface. Tests must therefore always be stopped prior to failure so the final crack extension can be accurately measured and the crack length correction provided in ASTM E1457 (2013) can be applied. REFERENCES

Saxena, A. (1980). "Electrical potential technique for monitoring subcritical crack growth at elevated temperatures," Engineering Fracture Mechanics. Bakker, A. (1985). "A DC Potential Drop Procedure for Crack Initiation and ft-Curve Measurements During Ductile Fracture Tests," Elastic-Plastic Fracture Test Methods: The User's Experience, ASTM STP 856. Tarnowski, K. M., Davies, C. M., Dean, D. W. and Nikbin, K. M. (2014). "The Influence of Plasticity on Crack Length Measurements Using the Potential Drop Technique," Evaluation of Existing and New Sensor Technologies for Fatigue, Fracture and Mechanical Testing, ASTM STP 1584. Lowes, J. M. and Fearnehough, G. D. (1971). "The detection of slow crack growth in crack opening displacement specimens using an electrical potential method," Engineering Fracture Mechanics. Wilkowski, G. and Maxey, W. (1983). "Review and Applications of the Electronic Potential Method for Measuring Crack Growth in Specimens, Flawed Pipes and Pressure Vessels," Fracture Mechanics: Fourteenth Symposium - Volume II: Testing and Applications, ASTM STP 791. ISO 12135:2002 (2002). "Metalic Materials - Unified Method of Test for the Determination of Quasistatic Fracture Toughness," International Organization for Standardization, Geneva. ASTM E1457-13 (2013). "Standard Test Method for Measurement of Creep Crack Growth Times in Metals," Annual Book of ASTM Standards, Vol. 03.01, ASTM International, West Conshohocken, PA. Tarnowski, K. M., Davies, C. M., Dean, D. W. and Nikbin, K. M. (2015). "The Influence of Creep Strain on Crack Length Measurements using the Potential Drop Method," ASME Pressure Vessels & Piping Conference Proceedings. ImageJ v1.48 (2014). National Institute of Mental Health, Bethesda, Maryland, USA. Madhi, E., Sposito, G., Davies, C. M., Cawley, P. and Nagy, P. B. (2011). "In-Situ Creep Monitoring Using The Potential Drop Method," AIP Conference Proceedings. COMSOL Multiphysics v4.3a (2012). COMSOL Ltd., Broers Building, 21 JJ Thomson Avenue, Cambridge, CB3 0FA, UK. Freeman, B. and Neate, G. (1980). "The Measurement of Crack Length During Fracture at Elevated Temperatures Using the D. C. Potential Drop Technique," The Measurement of Crack Length and Shape During Fracture and Fatigue.