Scholarly article on topic 'Variability and Lower Bound of Fracture Toughness of Welds in the Ductile to Brittle Transition Regime'

Variability and Lower Bound of Fracture Toughness of Welds in the Ductile to Brittle Transition Regime Academic research paper on "Materials engineering"

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Abstract of research paper on Materials engineering, author of scientific article — H.J. Schindler, D. Kalkhof, H.W. Viehrig

Abstract The reference temperature T0 was measured for both T-S and T-L- specimen orientation in 24 layers across the thickness of the beltline weld of a reactor pressure vessel. It turned out to vary in a bandwidth of more than 40K. Because of a high scatter, no clear pattern of T0 as a function of the thickness position could be recognized. A more detailed analysis revealed that the median of KJc was considerably steeper than predicted by the Master-Curve, which leads to a bias of T0 with respect to the test- temperature relative to T0. By a modified evaluation procedure, the scatter of the reference temperature could be significantly reduced, which enabled the global pattern of T0 to be recognized. By comparing the theoretical lower bound to KJc-data of the used specimens with the individual measured KJc a representative T0 that characterizes the overall toughness behaviour of the weld was determined. It turned out to be about 10K lower than the maximum local T0.

Academic research paper on topic "Variability and Lower Bound of Fracture Toughness of Welds in the Ductile to Brittle Transition Regime"

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Procedia Materials Science 3 (2014) 732 - 737

20th European Conference on Fracture (ECF20)

Variability and Lower Bound of Fracture Toughness of Welds in the

Ductile to Brittle transition regime

H. J. Schindlera*, D. Kalkhof6, H. W. Viehrigc

aMat-Tec AG, Unterer Graben 27, 8401 Winterthur, Switzerland bSwiss Federal Nuclear Safety Inspectorate (ENSI), CH-5200 Brugg, Switzerland c Helmholtz-Zentrum Dresden-Rossendorf Dresden, Germany

Abstract

The reference temperature T0 was measured for both T-S and T-L- specimen orientation in 24 layers across the thickness of the beltline weld of a reactor pressure vessel. It turned out to vary in a bandwidth of more than 40K. Because of a high scatter, no clear pattern of T0 as a function of the thickness position could be recognized. A more detailed analysis revealed that the median of KJc was considerably steeper than predicted by the Master-Curve, which leads to a bias of T0 with respect to the test-temperature relative to T0. By a modified evaluation procedure, the scatter of the reference temperature could be significantly reduced, which enabled the global pattern of T0 to be recognized. By comparing the theoretical lower bound to KJc-data of the used specimens with the individual measured KJc a representative T0 that characterizes the overall toughness behaviour of the weld was determined. It turned out to be about 10 K lower than the maximum local T0.

© 2014Publishedby ElsevierLtd. Thisisanopen access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/3.0/).

Selectionandpeer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of Structural Engineering

Keywords:

1. Introduction

In the ductile to brittle transition (DTB) regime of ferritic steels the scatter of fracture toughness is one of the key issues in fracture mechanics. There are two well known concepts to cope with it: One is the probabilistic approach

* Corresponding author. Tel.: +41 52 202 5444; fax: +41 52 202 5445. E-mail address: schindler@mat-tec.ch

2211-8128 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of Structural Engineering doi: 10.1016/j.mspro.2014.06.120

based on the Master-Curve (MC) suggested by Wallin (1995), the other the lower bound according to the ASME reference curve (ASME (2004)). The former is based on the observation that the median of KJc of standard 1T-specimens follows a unique curve given by

Kc / ^ = 30 + 70 • exp [0.019 • (T - T0)]

where T0 is the reference-temperature according to ASTM E1921 (2012). The ASME reference curve Kc/med = 36.5 + 22.8 • exp[0.036 • (T - T0 - 19.4K)]

was found as an empirical lower envelope of numerous valid KIc-values of RPV-steels (ASME (1999)).

In case of inhomogeneous materials, the situation is more complex. There is an increased scatter in the individual KJc-data of a test series, which increases the measurement uncertainty of T0. As pointed out by Kalkhof and Schindler (2012) another source of uncertainty of T0 may be the shape of the median of KJc(1T)(T). The latter may be significantly steeper than predicted by (1), depending on the loading rate, specimen size and possibly the material. This effect increases the measurement uncertainty. It can be minimized by testing at temperatures close to T0. However, in case of inhomogeneous material, testing close to T0 is hardly achievable because of the variability of KJc and T0. These issues are dealt with in the present paper experimentally and theoretically. Furthermore, the relation between local T0 and the lower bound of KJc(T) in case of weld material is explored.

2. Experimental program and results

A detailed documentation of the testing procedure and experimental results can be found in Viehrig et al (2013, 2014), so we restrict ourselves here to a brief overview. As a representative test material, the beltline welding seam of the RPV of the non-commissioned reactor Biblis C was used. Fig. 1 shows a macrograph and the corresponding dimensions. From two segments of this weld, numerous pre-cracked Charpy size specimens (0.4T SEB) and a few 1T-CT-specimens are machined (Fig. 2). The aim was to determine T0 as a function of s (distance from inner surface), which means that series of 10 - 20 specimens of equal thickness position (s) were machined and tested in separate data-sets. Both the T-L and the T-S crack orientations were considered. The microstructural inhomogeneity along the crack-front differs between these two crack orientations (Fig. 2).

Fig. 1: Macrograph (a) and dimensions of the weld (b)

The distribution of T0 determined by the 0.4T-SEB specimens according to ASTM E1921 is shown in Fig. 3. The loading rate was 1.2 MPa^m05/s, thus within the range of quasi-static testing according to ASTM E1921. Apparently, there is a rather random variation of T0 for both specimen orientations T-L and T-S. The span between maximum and minimum T0 is about the same for both orientations T-L and T-S, although the inhomogeneity along the crack front is different (see Fig. 2). The apparent variation or scatter results not only from the material inhomogeneity but also from the measurement uncertainty, as shown in the following.

"flllllimu

1T C(T)-specimens

Micro-structure along crack-front of T-L-specimens

1 (87.7 mm) |

•v1- ' ^ijJiSiS

Micro-structure along crack-front of T-S-specimens

Fig. 2: Specimen removal from weld segment of the Biblis C RPV, and examples of microstructure along the crack front

-50 -60 -70 -80 -90 -100 -110 -120

BIBLIS c'welding seam: 0 4T-sk(B)'spedmens! T-L '

□ Tc ( a no surveillance specimen äocation) -mean T = -S7 °C; nT = 11 K

SO 100 150 200

distance from the RPV inner wall / mm

Fig. 3: Distribution of T0 across the thickness along the s-axis for T-L (left) and T-S orientation (right) (from Viehrig et al. (2014)).

3. Evaluation of reference temperature T100

As mentioned in the introduction the actual median KJc/med(T) sometimes deviates from (1), which causes a bias in T0 with respect to the testing temperatures, thus increasing the measurement uncertainty. In order to explore its effect on the apparent scatter of T0, the KJc-data were evaluated for comparison by the OEF-method as suggested by Schindler and Kalkhof (2013, 2014). It is based on the more general assumption that the median is described by

Kc / md (1T) = 30 + 70 • exp [p • (T - T^)] (3)

Obviously, T100 is identical with T0, if p = 0.019, but deviates from T0 if p deviates from 0.019 and if the test temperature Ttest deviates from T0. In these cases, T100 is expected to be more precise than T0. It is evident from eq. (3) that the exponent p can be determined from a set of experimental KJc(1T) as the slope of the linear regression in the diagram ln(KJc(1T)-30) vs. T. Applied to the KJc measured by the 0.4T-SEB specimens, p turned out to exhibit a relatively large scatter, which is not surprising regarding the inhomogeneity of the material and the narrow temperature range covered in each data-set. However, the vast majority of p was clearly beyond the nominal value of 0.019. For physical reasons, p has to be the same for all test series, so the simple average of the individual values are supposed to be the best estimate. The following mean values are obtained for the two considered orientations:

T-L-orientation: pav = 0.032 T-S-orientation: pav = 0.039

(4a) (4b)

With p fixed to p = pav eqs. (4a) and (4b) leads to the following simple equation to determine T100 from a data-set

of N KJc(1T)_values:

T100 = l1 • Z— • t4-2485 + Pav ■ T,,) - ln{KMitx0 - 30)]

N 1:1 P,

The resulting T100 are shown in Fig. 4 in comparison with T0 from Fig. 3. Note that at some thickness positions additional tests are performed at a single temperature. The two data-sets were evaluated separately, so two values of T0 and T100, respectively, appear at the same s, whereas in Fig. 4 all data are evaluated in combination as one dataset. Apparently, the scatter of T100 is significantly reduced, compared with the one of T0, and enables the general trend of the reference temperature as a function of s to be recognized much clearer than from Fig. 3.

Fig. 4: Distribution of Tioo in comparison with T0 from T-L-specimens (a) and T-S-specimen (b) across the thickness along the s-axis

25 20 o aA 15 10 10 TS-specimens TL-specimens

40 -30 -2& o ^ -5 - A & C -15-20 -25 1 10 20 3 ° o o

Ttest-T0 [K]

Fig. 5: Dependence of the difference T0 - T100 from the relative test temperature.

For the T-S-orientation, the standard deviation of the T100 values from the general trend shown as the dashed lines is 4.2 K, which is less than the basic (unavoidable) measurement uncertainty as given in ASTM E1921. This means, that the microstructure does not significantly affect the scatter of T100. For T-L orientation, the standard deviation is 6.1K, thus significantly higher, which can be explained by the more pronounced inhomogeneity of the microstructure along the crack-front (see Fig. 2). For T0 the corresponding standard deviations are 8.2 K for T-L and 8.8 K for T-S, thus clearly higher.

Considering the relatively high p=pav values given by eqs. (4) there is no doubt that the procedure of ASTM E1921 leads to errors depending on the relative mean test temperature, Ttest-T0. Particularly in the case of inhomogeneous materials, T0 is not known a priori, so Ttest-T0 is stochastic and its effect on T0 contributes to the measurement uncertainty. Fig. 5 shows the difference between T0 and T100 in function of Ttest-T0. The trend is clear

and corresponds to the temperature-induced bias that is expected on theoretical grounds. Particularly the extreme outliers are clearly associated with a relatively large Ttest-T0.

4. Lower bound of KJc

In a deterministic fracture mechanics analysis T0 serves to quantify the lower bound of KIc by means of (2). In the following the corresponding relation is explored for welds. Lacking experimental valid KIc, the corresponding comparison has to be done based on the measured KJc-data. For this purpose, the lower bound (2) and (3) has to be corrected for the limited thickness B of the used specimens. Schindler and Kalkhof (2013, 2013a) derived the following simple equation to correct (2) for thicknesses B smaller than the one required for plane strain conditions,

^ (B,T) = .J.2?? • K,%) for B < Bsal = ^^ (6)

B025 -JR/Tj sa K

with Rp denoting the yield stress. For B>Bsat, KJc = KIc. Though much simpler, eq. (6) is in good agreement with the approach of Merkle et al. (2002). For homogeneous materials, (6) with KJc from (2) was demonstrated to represent a rather tight (i.e. realistic) lower bound to experimental KJc (Schindler and Kalkhof, (2013), (2013a)). In reverse, as elaborated by Schindler (2014), it is even possible to estimate T0 by fitting KJc to the theoretical scatter-band formed by (6) and (2).

Fig. 6: Experimental Kjc measured by using 1T-CT-specimens in comparison with eq. (6) with B=0.0254 m and T0 = -91°C for T-L-specimens (left) and T0 = -87°C for T-S-specimens (right). The value for T-L at -20°C was measured to be Kjc = 505 MPam05, thus beyond the validity

limit, so it was censored according to ASTM E1921.

Fig. 7: Experimental Kjc measured by using 0.4T-SEB-specimens in comparison with eq. (6) with B=0.01 and T0 = -91°C for T-L-specimens

(left) and T0 = -87°C for T-S-specimens (right)

The 1T-CT specimens are expected to reflect the overall toughness behaviour of the weld better than the small 0.4T SEB specimens. In Fig. 6 the experimental KJc obtained from 1T-CT-specimens taken randomly from the weld are shown. The envelopes shown in Fig. 6 are obtained from (6) and (2) by inserting B=0.0254m and T0= -91°C for the T-L-orientation, and T0= -87°C for the T-S-orientation, respectively. The same T0 with B = 0.01m delivers the theoretical lower bounds of KJc for 0.4T-SEB-specimens. In fact, as shown in Fig. 7, it envelops practically all relevant KJc measured on the 0.4T-SEB-specimens, which is another verification of eq. (6). This means that the corresponding T0 = -91°C and -87°C for T-L and T-S, respectively, can be regarded as physically representative T0-values. Note that they are relatively close to the average values of T0 as given in Fig. 3

5. Conclusions

The reference temperature T0 of the considered beltline weld of an RPV varies in a bandwidth of more than 40 K across the thickness. The variation is due not only to the inhomogeneity of the material, but - to a substantial part -also to the uncertainty of the standard measurement procedure of T0. The uncertainty is increased by more than 20K, compared to homogeneous materials. The main reason for the increased scatter was found to be the slope of the median KJc(T) of the 0.4T-SEB specimens (pre-cracked Charpy specimens), which is significantly steeper than predicted by the MC. This means that the procedure according to ASTM E1921 is biased by the relative test temperature Ttest-T0. The error introduced by the choice of the test temperatures can be as large as ±20 K, even if the testing close to T0 is strived for. It has to be accounted for by an extra safety margin.

Previous investigations on homogeneous material indicated that the exponent p depends on the loading rate and specimen size, so the effect of the test temperatures on T0 may be different at different loading rates. Therefore it is recommended to check the slope of the MC. If the coefficient p of the exponent deviates significantly from 0.019, then the suggested OEF-method delivers improved, less scattering reference temperatures T100.

The lower envelope of the individual Kjc-values was found to correspond to a characteristic reference temperature that is close to the average T0, thus considerably lower than the maximum T0. This means that finding the maximum local T0 is not necessary to characterize the overall toughness behaviour of the weld. The average T0 as determined by a data-set from arbitrary positions in the weld plus some adequate safety margin is sufficient.

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