results obtained by Hull on copper tested at temperatures as low as 4.2 K [17, 61]. More recently, Coupeau, Girard and Rabier have provided excellent observations via scanning probe microscopy of slip step heights at opposing dislocation pile-ups on parallel planes and evaluated the results in terms of mutually blocking dislocation pile-ups [62]. Head had reported the first numerical calculations of such opposing dislocation pile-ups [63]. A major result from the dislocation modeled behavior was that at sufficient applied shear stress and corresponding local stress concentration, the leading dislocations passed each other and formed dipoles. The behavior is in agreement with the associated slip band structure becoming more pronounced in PSBs in part because the self-stress associated with individual dislocation dipoles decreases more rapidly with distance, of the order of ~(Δr)-2 as compared with the normal (1/Δr) individual dislocation behavior, and therefore leading to many more dislocations being fitted into a cyclically-defined slip band length. A sub-surface role of diffusion of atomic vacancies that has generated later research interest should be additive in the process [16]. 7. Summary A number of Sir Alan Cottrell’s notable contributions, with colleagues too, on the dislocation mechanics of fracturing have been briefly described on four sub-topics. The listed contributions have been in the sequence of: (a) conditions for a ductile to brittle transition in steel and related metals; (b) evaluation of the theoretical limiting strength of crystals; (c) dislocation-modeled crack growth in relation to a fracture mechanics description; and, (d) geometrical aspects of the development of persistent slip band structures in fatigue. The purpose was to provide cogent examples, first, of the importance of original insights provided by Cottrell in producing a better understanding of relevant issues and, secondly, to show a positive connection with further developments already made or continuing to be made on the same subjects. In this regard, a note is added from the interview of Sir Alan at ICF4 in Waterloo, Canada, to the effect that more work needed to be done on multiple dislocation group dynamics, a topic that has been pursued in the interim time period and continues to be an important research activity [64]. Acknowledgments It is a great pleasure for the author to thank colleagues, David Taplin and Stephen Antolovich, for encouragement to produce the present article. Involvement in the ductile to brittle transition topic began in 1958 during a post-doctoral appointment with Norman Petch, when at Leeds, and which appointment was suggested by Harold Paxton and assisted by Sir Alan. A grand remembrance was the joined recollection of the post-doctoral year and subsequent activities at morning tea with Sir Alan in 1984 at Jesus College, Cambridge. A much appreciated later sabbatical leave from the Westinghouse Research Laboratory during 1964 at the Commonwealth Scientific and Industrial Research Organization, Division of Tribophysics, spent with Walter Boas and Alan Head on a related fracturing topic [65], should also be mentioned. References [1]. J.A. Charles and G.C. Smith, editors, Advances in Physical Metallurgy, Sir Alan Cottrell’s 70th Birthday Meeting, Institute of Metals, London, 1990. [2]. A.S. Argon, editor, Physics of Strength and Plasticity, M.I.T. Press, Boston, MA, 1969.
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