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# Nonlinear Analyses for Embedded Cracks Under Pressurized Thermal Shock:  Comparisons with FAVOR and Weibull Stress Approaches (NUREG/CR-6956)

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## Publication Information

**Manuscript Completed:** August 2007**Date Published:** February 2008

**Prepared by:**B. Wasiluk1, X. Qian 2 and R.H. Dodds, Jr.1

1Department of Civil and Environmental EngineeringUniversity of Illinois at Urbana-Champaign205 N. Mathews AvenueUrbana, IL 61801

2Oak Ridge National LaboratoryP.O. Box 2008Oak Ridge, TN 37831

S.N. Malik, NRC Project Manager

**Prepared for:**Office of Nuclear Regulatory ResearchU.S. Nuclear Regulatory CommissionWashington DC 20555-0001

NRC Job Code Y6951

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## Abstract

Thick-walled reactor pressure vessels (RPVs) can potentially experience rapid temperature and pressure changes under pressurized thermal shock (PTS) conditions. This work describes progress towards utilization of a Weibull stress approach for cleavage fracture assessment of RPVs subjected to PTS events. The Weibull stress approach couples the macroscopic crack driving force, *J* or *KJ* , with the local, crack-front conditions for cleavage characterized by the Weibull stress and requires realistic stress analyses. Extensive previous work focused on the conventional, linear-elastic stress-intensity factor (SIF), *KI* values for flaws in RPVs. This study begins by comparing predictions of the macroscopic crack driving force ( *KJ* ) made by the FAVOR (Fracture Analysis for Vessels – Oak Ridge) code with detailed, linear-elastic and elastic-plastic finite element analyses for circumferentially and axially embedded flaws located in a representative RPV and subjected to two well characterized transients, denoted here as transients A and B. These solutions provide needed benchmarks for future efforts to approximate the nonlinear material response near the crack front through a simpler, linear-elastic *KI -T* stress field imposed on a 2-D, smallscale yielding configuration. The postulated loadings considered here include a critical thermal transient with a small change of internal pressure (Transient A) and a mild thermal transient concurrent with significant re-pressurization (Transient B). The RPV models employ ferritic steel for the base material and austenitic steel for the cladding; the combination leads to pronounced mismatches in both the mechanical and thermal properties. The SIF computed from the linear-elastic analyses show lower values than the *KJ* -solutions obtained from the elastic-plastic analyses. Based on previous research for the Weibull stress approach applied to through-crack fracture specimens, the current study concludes with proposals for refined and simplified engineering procedures, as well as a *KI -T* stress methodology, for defect assessments of curved, embedded flaws in RPVs under PTS conditions.

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This report does not contain information collection requirements and, therefore, is not subject to the requirements of the Paperwork Reduction Act of 1995 (44 U.S. C. 3501 et seq.).

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