Use of a dislocation-based boundary element model to extract crack growth rates from depth distributions of intergranular stress corrosion cracks Anke Stoll, Angus J. Wilkinson ⇑ Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK Received 8 March 2012; received in revised form 2 June 2012; accepted 3 June 2012 Available online 22 July 2012 Abstract A dislocation-based boundary element model was used to simulate intergranular stress corrosion crack propagation in virtual micro- structures. A Monte Carlo approach was used in which the propagation of approximately 100 cracks was calculated for different Voronoi generated microstructures. At every simulation step the model gave the position of the crack tip together with stress intensity factors K I and K II . Using a simple power-law-type crack growth rate da=dt ¼ D p K mp , the depth of each particular crack can be calculated knowing the time the samples were exposed to the stress and corrosive environment. Existing experimental data giving crack depth distributions for Alloy 600, and XM-19 and 304 stainless steel are investigated and the best-fit crack growth law established. Alloy 600 in a light water reactor environment and XM-19 in high-temperature water both lead to m p = 3. While for 304 stainless steel in the more aggressive K 2 S 4 O 6 /H 2 SO 4 (pH 2) an exponent m p = 0.8 was found. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Stress corrosion cracking, Crack growth rate; Alloy 600; XM-19; 304 Stainless steel; Nuclear materials 1. Introduction Empirical relationships between the crack growth rate due to stress corrosion cracking (SCC) and fracture mechanics parameters such as stress intensity factors (SIFs) have been shown in various studies and are utilized to pre- dict the growth of cracks detected in nuclear power plants for fitness-for-service assessment. Pre-cracked fracture mechanics specimens in which a single macroscopic crack is introduced and its growth monitored as the applied SIF with crack propagation are widely used [1]. The linear elastic fracture mechanics parameter SIF has been found to be very useful in characterizing SCC growth behavior. Spe- cifically, the SIF can be used to describe the crack tip stress field and thus the mechanical driving force necessary for the growth of the stress corrosion cracks [2]. The SCC growth rate when plotted in terms of log(da/dt) vs. K often shows three distinct regions, as shown in Fig. 1. In stage I, or the linear region, the crack growth rate increases with an increase in K. In stage II, or the steady- state crack growth region, the crack growth rate is rela- tively independent of SIF, whereas in stage III, or the fast fracture region, the crack growth rate again accelerates with an increase in K. In stage I and III da/dt is strongly dependent on K, while stage II is (almost) independent log(da/dt) of K. In stage I there is a threshold stress inten- sity K ISCC below which cracks do not propagate under sus- tained load. K ISCC can be obtained by time-to-failure tests in which pre-cracked specimens are loaded at various stress intensity levels, thereby failing at different times. Empirically, the crack growth rate da/dt in stage I can be described as a function of the mode I stress intensity factor K I : da=dt ¼ D p K mp ; ð1Þ 1359-6454/$36.00 Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2012.06.002 ⇑ Corresponding author. E-mail address: angus.wilkinson@materials.ox.ac.uk (A.J. Wilkinson). www.elsevier.com/locate/actamat Available online at www.sciencedirect.com Acta Materialia 60 (2012) 5101–5108