The influence of inclusion spacing and microstructure on the
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I.
INTRODUCTION
E X P E R I M E N T A L studies 1'2 and the Rice and Johnson model 3 for ductile fracture suggest that the critical crack tip opening displacement of ultra high strength steels should scale with the inclusion spacing. Unfortunately. predictions based on Rice and Johnson's treatment are often in marked disagreement with experimental results. 4 As observed by McMeeking, 5 a possible reason for the disagreement between these predicted and measured toughness values is the fracture criterion used by Rice and Johnson. Considering a single spherical void, or particle unbound to the matrix, of radius Ro a distance Xo ahead of an initially sharp crack, Rice and Johnson assumed fracture would initiate when the ligament between the blunting crack and the growing void equaled the radius of the void perpendicular to the crack plane. However, through strain localization (as pointed out by McMeeking 5) or by void sheet coalescence, 6~7 the voids initiated at inclusions near the crack tip could coalesce at lower values of the crack tip opening displacement than predicted by Rice and Johnson. At fracture the voids resulting from strain localization and/or void sheet coalescence will be smaller than the voids resulting from primary void coalescence and reflect the lower strains to fracture in the former case. As a consequence, void sizes at fracture could be a useful parameter in modeling ductile fracture. Motivated by the results of McMeeking's numerical calculations of void growth 5'~ for the same geometry employed by Rice and Johnson, one of the authors has suggested 9'1~ that the crack tip opening displacement at fracture initiation, Sic, will scale as
6tc ~ Xo(Rv/RI)]R0
[11
W.M. GARRISON, Jr. is Assocmte Professor, Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh. PA 15213. N. R. MOODY is Member, Technical Staff, Sandia National Laboratories, Lwermore, CA 94550. Manuscript submitted February 13, 1986. METALLURGICAL TRANSACTIONS A
where X0 is the average three-dimensional nearest neighbor distance between inclusions and (Rv/RI)IRo is the void radius (Rv) divided by the radius of the inclusion nucleating the void (Rt) evaluated at the average inclusion radius R0. The void radii are measured directly from the fracture surface and thus are a measure of void size at fracture. The ratio Rv/Rt is believed to be of greater relevance than Rv because the stress-strain history at the crack tip determines Rv /Rt. 12 This study tested this approach at high strength levels and determined the extents to which inclusion spacing and microstructure influenced the toughness of AF1410. AFI410 achieves very high toughnesses at a yield strength of 1500 M N / m 2 when aged at 510 ~ Speich's w o r k j4 with a 0 . 1 3 C / 1 0 N i / 8 C o / 2 C r / 1 M o steel which is similar to AF1410 suggests the fracture toughness of AF1410 on aging at 425 ~ will be much lower than after aging at 510 ~ but that yield strengths for the two aging temperatures will be comparable. Thus, a strong
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