Stochastic modeling of the independent roles of particle size and grain size in transgranular cleavage fracture
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I.
INTRODUCTION
CLEAVAGE fracture in most metals occurs by the nucleation of a microcrack, assisted by the local plastic deformation of the surrounding material, and its continued propagation when the local, concentrated, tensile stress exceeds some critical fracture stress. In mild steels, such microcracks were originally considered to nucleate at grain boundaries, which act as barriers to slip-bands. 1'2'3 Consequently, since the grain size determines the dislocation pile-up length, as well as the distance to the first crack extension barrier (i.e., the next grain boundary), early models of cleavage fracture identified the grain size as the sole, dominant microstructural feature.l'2'3' Later studies4-7 associated the microcracks with the fracture of grain boundary carbide particles. Thus, particle size emerged as an additional key microstructural feature. The relative importance of particle size and grain size is also, in part, dependent on the critical step in the cleavage process. When the critical event involves the continued propagation of the particle microcrack into the matrix, the particle size is clearly the salient dimension (aside from the indirect effect of grain size on yield strength), consistent with the majority of microstructural observations on failure at very low temperatures on the lower toughness shelf. At somewhat higher temperatures, approaching the ductile/ brittle transition region, observations of grain size microcracks suggest that the critical step involves consideration of dynamic propagation and arrest at the next grain boundary, a mechanism favoring grain size as the salient dimension. Most heat treatments change both microstructural dimensions. Consequently, there have been few attempts8 to investigate the separate roles of particle size and grain size. The objective of the present work is to examine this issue. For this purpose, a recently developed statistical model for TSANN LIN, formerly Graduate Student in the Department of Materials Science and Mineral Engineering, University of California, Berkeley, is with IBM Corporation, Yorktown Heights, NY. A.G. EVANS is Professor, Materials Program, University of California, Santa Barbara, CA 93106. R.O. RITCHIE is Professor, Materials and Molecular Research Division, Lawrence Berkeley Laboratory, and Department of Materials Science and Mineral Engineering, University of California, Berkeley, CA 94720. This paper is based on a presentation made at the symposium "Stochastic Aspects of Fracture" held at the 1986 annual AIME meeting in New Orleans, LA, on March 2-6, 1986, under the auspices of the ASM/MSD Flow and Fracture Committee. METALLURGICALTRANSACTIONS A
cleavage fracture at low temperatures 9'1° will be used in conjunction with experiments on simple ferrite/grain boundary carbide microstructures, for which the particle and grain sizes have been varied independently. II.
MECHANISMS OF CLEAVAGE FRACTURE
The process of cleavage fracture in steels seemingly involves three critical steps: crack nucleation at carbide particles, crac
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