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Research Papers: Materials and Fabrication

# A Comparison of the tanh and Exponential Fitting Methods for Charpy V-Notch Energy Data

[+] Author and Article Information
Marjorie Ann EricksonKirk

Phoenix Engineering Associates, Inc., Sykesville, MD 21784erickson.peai@verizon.net

Mark T. EricksonKirk

Nuclear Regulatory Commission, Rockville, MD 20852mark.kirk@nrc.gov

Stan Rosinski

Electric Power Research Institute, Charlotte, NCstrosins@epri.com

Jack Spanner

Electric Power Research Institute, Charlotte, NCjspanner@epri.com

J. Pressure Vessel Technol 131(3), 031404 (Apr 17, 2009) (13 pages) doi:10.1115/1.3109987 History: Received August 29, 2007; Revised June 30, 2008; Published April 17, 2009

## Abstract

In the 1960s and 1970s, when the surveillance programs for currently operating commercial nuclear reactors were established, state of knowledge limitations resulted in the use of Charpy-V notch (CVN) specimens rather than fracture toughness specimens. Reasonable success has since been achieved in correlating CVN and fracture toughness parameters. Such correlations provide an important part of the technical basis for both current regulations and ASME codes. These correlations imply that trends manifest in CVN data must also appear in fracture toughness data, even though empirical evidence demonstrate that this is not always true. For example, the temperature dependence of CVN energy (CVE) in transition is thought to be a unique feature of each specific sample of ferritic steel that is tested, a view in sharp contrast with the now widely accepted view of a “master curve” for transition fracture toughness $(KJc)$. Also, effects of product form on CVE temperature dependence and property correlations are widely reported, despite the fact that product form effects are absent from $KJc$ properties. These observations suggest that the mapping of CVE behavior onto fracture toughness implicit to correlation-based regulations and ASME codes may produce erroneous trends in estimated values of fracture toughness. In this paper we investigate the hypothesis that the apparent differences between CVE and fracture toughness arise due to differences in how the temperature dependence of CVE and $KJc$ data have historically been modeled. Our analysis shows that when CVE data are analyzed in a manner consistent with $KJc$ data (i.e., transition and upper shelf data are partitioned from each other and analyzed separately rather than being fit with a continuous tanh function), the apparent differences between CVE and toughness characterizations are minimized significantly, and may disappear entirely. These findings demonstrate the differences between CVE and fracture toughness data to be an artifact of the tanh analysis method rather than an intrinsic property of CVE.

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## Figures

Figure 1

Empirical correlation between ΔTo and ΔT41 J for a variety of nuclear grade RPV steels (2)

Figure 2

Empirical correlations between both ΔT41 J (top figure) and ΔTo (bottom figure) and the increase caused by irradiation damage in the quasistatic room temperature yield strength for a variety of nuclear grade RPV steels (2). The different slopes of the correlation lines are significantly different (statistically) in the top figure. In the bottom figure all of the correlation slopes are statistically indistinguishable.

Figure 3

All CVE data plotted versus measured temperature

Figure 4

Definition of coefficients in the hyperbolic tangent equation, Eq. 1

Figure 5

The variation in transition slope and upper shelf energy with the degree of hardening (as measured by T28 J) for all CVE data

Figure 6

All CVE data plotted versus the difference between the measured temperature and the 28 J transition temperature (T28 J) estimated using a tanh temperature dependence

Figure 7

Schematic illustrating how filtering CVE data by placing an upper limit on percent shear partitions upper shelf from transition data

Figure 8

Top: All transition CVE data plotted versus the difference between the test temperature and the 28 J transition temperature (T28 J) estimated using an exponential temperature dependence fit to all CVE data tested at temperatures where the highest measured shear fracture area did not exceed 60%. Bottom: CVE-residuals relative to the Eq. 3 fit curve shown on the top figure. There is no statistically significant trend to either the slope or the intercept fit to all of the data.

Figure 9

CVE-residuals relative to the Eq. 3 fit curve shown on Fig. 8. There is no statistically significant trend to either the slope or the intercept fit to all of the data Schematic illustrating how filtering CVE data by placing an upper limit on percent shear partitions upper shelf from transition data.

Figure 10

Top: All transition CVE data (differentiated by product form) plotted versus the difference between the test temperature and the 28 J transition temperature (T28 J) determined using Eq. 3. Bottom: CVE-residuals relative to the Eq. 3 fit curve shown on the top figure. There is no statistically significant trend to either the slope or the intercept fit with product form.

Figure 11

Variation in ΔTo with ΔTCVE, where ΔTCVE is the index temperature for the CVE transition data determined using Eq. 3

Figure 12

Top: High, medium, and low upper shelf materials with tanh fits. Bottom: Same materials with exponential, Eq. 3, fit.

Figure 13

Equation 3 as fit to the 73(U), 72(I), and PTQ-1 data sets shown in Fig. 1 (bottom graph) plotted on a temperature axis normalized to TCVE. Curves for 73(U), 72(I), and PTQ-1 are shown between the minimum measured temperature and the 60% shear cutoff. The values for 73(U) and PTQ-1 have been offset vertically from Eq. 3 for clarity.

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