A model of the threshold stress intensity factor, K IH , for delayed hydride cracking of Zr±2.5Nb alloy Y.S. Kim * , Y.G. Matvienko 1 , Y.M. Cheong, S.S. Kim, S.C. Kwon Zirconium Team, Korea Atomic Energy Research Institute, P.O. Box 105, Yusong, Taejon 305-600, South Korea Received 6 June 1999; accepted 24 September 1999 Abstract An analytical model to predict a threshold stress intensity factor, K IH , for delayed hydride cracking of Zr±2.5Nb alloy was developed based on a criterion to fracture hydrides: r A max r c r h r c r h f . The hydride platelet is assumed to cover a process zone ahead of the crack tip. By using the cohesive zone model and von Mises yield criterion at the boundary of the cohesive zone, the cohesive stress and the cohesive zone length (or the process zone length) were determined. The maximum stress and a critical distance in the process zone, corresponding to its occurrence, were obtained by assuming an elastic and linearly plastic materials with a constant tangent modulus, E t . The feasibility of the developed K IH model was discussed by comparing the predicted K IH with the measured one by accounting for a temperature dependence of K IH . Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 62.20.M 1. Introduction Delayed hydride cracking (DHC) of zirconium alloys is caused by diusion of hydrogen (or deuterium) atoms to the vicinity of a crack tip, nucleation and growth of hydride platelets and fracture of the platelets. An initi- ation of DHC is controlled by the following two pro- cesses: the precipitation and growth of a hydride near the crack tip and a suciently high tensile stress enough to fracture it [1]. There are three kinds of initiation sites in zirconium alloys: a sharp crack or notch, a shallow and very smooth notch and a nominally smooth surface. However, a dierence in de®ning stress ®elds at the three initiation sites will lead to dierent threshold parameters for crack initiation [2±9]. This study paid an attention to fracture initiation at a sharp crack. The concept of fracture initiation at a sharp crack in zirconium alloys can be based on a local criterion of brittle fracture. The basic idea of the local criterion is that fracture occurs when the local stress reaches a critical value at a distance of r r c ahead of the crack tip inside the process zone [10]. However, the question is how to de®ne the maximum stress and the critical distance, r c in the process zone and the length of the process zone. Shi [6] and Wappling [9] assume that the tensile stress remains constant as the maximum value in the process zone. Further, the critical distance, r c , corresponding to the occurrence of the maximum stress, is assumed to be equal to two times the crack tip opening displacement, or 2d for an elastic- perfectly plastic materials [6]. Besides, the hydride thickness is assumed to be constant independently of temperature even though the hydride thickness precipi- tated ahead of the crack tip increases with an increasing temperature [11]. As a result, there are some restrictions in predicting the threshold stress intensity factor, K IH , leading to a disagreement between the measured and predicted K IH values [6,9]. Journal of Nuclear Materials 278 (2000) 251±257 www.elsevier.nl/locate/jnucmat * Corresponding author. Tel.: +82-42 868 2359; fax: +82-42 868 8346. E-mail address: yskiml@nanum.kaeri.re.kr (Y.S. Kim). 1 Visiting scientist from the Department of Deformation and Fracture Mechanics, Mechanical Engineering Research Institute of the Russian Academy of Sciences, 4 M. Kharito- nievsky Per., 101830 Moscow, Russia. 0022-3115/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 1 1 5 ( 9 9 ) 0 0 2 4 9 - 4