Dislocation simulation of brittle-ductile transition in ferritic steels
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I. INTRODUCTION
IT is now a well-accepted fact that the fracture of ferritic steels in the temperature range in which the fracture propagates by cleavage is originated in microcracks (mostly in precipitates), ahead of the macrocracks; the macrocracks could be either precracks in a test specimen or surface cracks in structures. The extremely high fracture toughness (20 MPa 1m, compared with 1 MPa 1m calculated from the surface energy alone, assuming the pure cleavage of the Fe matrix) observed at low temperatures in ferritic steels is due to the fact that cleavage is initiated and propagated from microcracks ahead of the macrocracks.[1] It has been found by experiments that these microcracks are originated in precipitates,[2,3] and that the propagation of these microcracks into the matrix is assumed to be the controlling step in the fracture of ferritic steels. Another observation, though less ambiguously established, is that the cleavage stress at fracture on these microcracks is invariant with temperature.[4–8] Ritchie, Knott, and Rice[9] used both the solutions developed by Hutchinson-Rice and Rosengren and a finite element analysis (FEA) to simulate the plastic zone; a critical tensile stress achieved over a characteristic distance ahead of the crack is used as the failure criterion. This distance is essentially a fitting parameter, and Ritchie, Knott, and Rice used a value equal to or twice the average grain diameter. The model successfully predicts the lower-shelf fracture toughness, but fails to predict the upturn near the transition temperature. Statistical models were introduced to predict the brittle-ductile transition (BDT) in steels, starting with Curry and Knott;[3] most notable among them were by Beremin[10]
S.J. NORONHA, Lecturer and Research Associate, and N.M. GHONIEM, UC Distinguished Professor, are with the Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 900951597. Contact e-mail: [email protected] This article is based on a presentation made in the symposium “Computational Aspects of Mechanical Properties of Materials,” which occurred at the 2005 TMS Annual Meeting, February 13–17, 2005, in San Francisco, CA, under the auspices of the MPMD–Computational Materials Science & Engineering (Jt. ASM-MSCTS) Committee. METALLURGICAL AND MATERIALS TRANSACTIONS A
and Wallin et al.[11] In both these models, FEA solutions of crack-tip plasticity were used to obtain the stress fields ahead of the crack. In the Beremin model, the maximum principal stress is calculated for each volume element in the plastic zone and a probability of failure is assigned. The total probability of failure is then obtained by summing over the entire plastic zone. Wallin et al. extended the modeling to the transition region by considering the variation in the effective surface energy (s p) with temperature, where s is the true surface energy and p is the plastic work done during propagation. This eventually led to the master curve (MC) hypothesis, which predicts that the BDT of
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