United States Nuclear Regulatory Commission - Protecting People and the Environment

Temperature Dependence of Weibull Stress Parameters: Studies Using the Euro-Material Similar to ASME A508 Class-3 Steel (NUREG/CR-6930)

On this page:

Download complete document

Publication Information

Manuscript Completed: January 2007
Date Published:
March 2007

Prepared by:
B. Wasiluk, J.P. Petti and R.H. Dodds, Jr.

Department of Civil and Environmental Engineering
University of Illinois at Urbana-Champaign
205 N. Mathews Avenue
Urbana, IL 61801

S.N.M. Malik, NRC Project Manager

Prepared for:
Division of Fuel, Engineering and Radiological Research
Office of Nuclear Regulatory Research
U.S. Nuclear Regulatory Commission
Washington, DC 20555-0001

NRC Job Code Y6951

Availability Notice


The so-called Beremin model describes the stochastic effects of the cleavage fracture process in ferritic steels at the metallurgical scale. The Beremin model, coupled with large-scale finite element analyses, can be used to understand the effects of constraint loss on the macroscale toughness measured in laboratory test specimens and in full-scale pressure vessels. This process provides the basis for the quantitative transferability of fracture toughness measured with a variety of test specimens to structures. The Beremin model leads to a quantity termed the Weibull stress which depends on a number of model parameters. This work demonstrates the temperature invariance of the Weibull stress modulus, m, for a 22NiMoCr37 pressure vessel steel through calibrations at two extreme temperatures of the ductile-to-brittle transition. This temperature invariance reflects the characterization of microcrack size distribution in the material described by the Weibull modulus. The calibrations performed here also demonstrate the clear dependence of the Weibull stress scale parameter, σu, on temperature. The increase of σu with temperature reflects the increase in microscale toughness of ferritic steels. The calibration procedure employs a three parameter Weibull stress model, which includes the effects of a minimum (threshold) toughness, Kmin. The calibrations suggest that Kmin increases gradually with temperature. Finally, an engineering procedure is presented to enable practical applications of the Weibull stress model for defect assessments. This procedure combines the demonstrated temperature invariance of m, a recently developed method for predicting the variation of σu with temperature using the ASTM E-1921 Master Curve, and the calibration of the Weibull stress parameters at one temperature. The (calibrated) temperature invariant m and the estimated σu as a function of temperature are used to predict the cumulative probability of fracture for several large datasets without direct calibration.

Page Last Reviewed/Updated Tuesday, August 20, 2013