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Research Papers: Materials and Fabrication

Procedure for Uncertainty Estimation in Determining the Master Curve Reference Temperature1

[+] Author and Article Information
T.-L. Sham

Materials Science and Technology Division,
Oak Ridge National Laboratory,
1 Bethel Valley Road,
P.O. Box 2008, MS 6115,
Oak Ridge, TN 37831
e-mail: shamt@ORNL.gov

Daniel R. Eno

Bechtel Marine Propulsion Corporation,
P.O. Box 1072,
Schenectady, NY 12301

This manuscript has been co-authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725, and by Bechtel Marine Propulsion Corporation under Contract No. DE-NR0000031, with the U.S. Department of Energy.

The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the Journal of Pressure Vessel Technology. Manuscript received February 16, 2011; final manuscript received April 3, 2012; published online September 16, 2013. Assoc. Editor: Xian-Kui Zhu.

J. Pressure Vessel Technol 135(5), 051401 (Sep 16, 2013) (7 pages) Paper No: PVT-11-1029; doi: 10.1115/1.4024434 History: Received February 16, 2011; Revised April 03, 2012

The master curve reference temperature, T0, characterizes the fracture performance of structural steels in the ductile-to-brittle transition region. For a given material, this reference temperature is estimated via fracture toughness testing. A methodology is presented to compute the standard error of an estimated T0 value from a finite sample of toughness data, in a unified manner for both single temperature and multiple temperature test methods. Using the asymptotic properties of maximum likelihood estimators, closed-form expressions for the standard error of the estimate of T0 are presented for both test methods. This methodology includes statistically rigorous treatment of censored data, which represents an advance over the current ASTM E1921 methodology (“E1921-10, Standard Test Method for Determination of Reference Temperature, T0, for Ferritic Steels in the Transition Range,” ASTM International, West Conshohocken, PA, 2010). Through Monte Carlo simulations of realistic single temperature and multiple temperature test plans, the recommended likelihood-based procedure is shown to provide better statistical performance than the methods in the ASTM E1921 standard.

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References

Figures

Grahic Jump Location
Fig. 1

Plots of parameter β as a function of the excess temperature, T − T0, and of the 1T median toughness, for single temperature fracture toughness tests

Grahic Jump Location
Fig. 4

Plot of the observed coverage levels of 95% UBs, 95% LBs, and 90% two-sided confidence intervals, for T0 at different test temperature and sample size. The results are from the Monte Carlo simulations of multiple temperature fracture toughness tests, with margins computed via the likelihood-based method (Eq. (19)).

Grahic Jump Location
Fig. 5

Summary plot of average standard error (one standard deviation) of T0 as a function of sample size obtained from the Monte Carlo simulations of single temperature and multiple temperature fracture toughness tests

Grahic Jump Location
Fig. 6

Plot of the observed coverage levels of 95% UBs, 95% LBs, and 90% two-sided confidence intervals, for T0 at different test temperature and sample size. The results are from the Monte Carlo simulations of single temperature fracture toughness tests, with margins computed via the E1921 standard method (Eq. (19)).

Grahic Jump Location
Fig. 7

Plot of the observed coverage levels of 95% UBs, 95% LBs, and 90% two-sided confidence intervals, for T0 at different test temperature and sample size. The results are from the Monte Carlo simulations of multiple temperature fracture toughness tests, with margins computed via the E1921 standard method (Eq. (19)).

Grahic Jump Location
Fig. 2

Plot of the percentage reduction of the parameter β, (a) given in Eq. (25) and (b) given in Eq. (26), from the β values tabulated in E1921

Grahic Jump Location
Fig. 8

Summary plot of average standard error (one standard deviation) of T0 as a function of sample size obtained from the Monte Carlo simulations of multiple temperature fracture toughness tests, for both the likelihood-based method and the E1921 standard method (Eq. (19))

Grahic Jump Location
Fig. 3

Plot of the observed coverage levels of 95% UBs, 95% LBs, and 90% two-sided confidence intervals, for T0 at different test temperature and sample size. The results are from the Monte Carlo simulations of single temperature fracture toughness tests, with margins computed via the likelihood-based method (Eq. (19)).

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