A dislocation shielding prediction of the toughness transition during cleavage of semibrittle crystals
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I.
INTRODUCTION
MOST modern theories of brittle fracture b e g i n with Griffith,m and in many ways, it would be satisfying if they ended with Griffith. This is exactly what is proposed here for semibrittle materials. It is further suggested that this applies to both iron and molybdenum and, therefore, other body-centered cubic (bcc) materials as well. T o accomplish this, a very brief historical overview of some m a j o r milestones in fracture theory, up to approximately 1980, will be indicated. A qualitative description of the dislocation emission m o d e l of Rice and Thomson[2~ will then be given along with several Atldnson and Clement t31 type discretized dislocation models, t4,51 Finally, the presently proposed model, which allows for simultaneous plastici~, and cleavage, is compared to recent single-crystal cleavage data obtained over a r a n g e of test temperatures. The emphasis is that the model here is for semibrittle fracture where, although nearly 100 pct cleavage is achieved, there still may be a "ductile-brittle" transition. A . Historical Overview and Proposed M o d e l An historical perspective in Table I considers our view of the important milestones associated w i t h the understanding of brittle fracture transitions. These are placed in the two general disciplines of applied mechanics and dislocation mechanics. For the moment, more subtle aspects of thermodynamics and kinetics will be ignored, although the Griffith criteriontu is clearly thermodynamic in nature. In may be claimed, however, that W.W. GERBERICH, Professor, H. HUANG, Graduate Student, W. ZIELINSKI, Research Associate, and P.G. M A R S H , Graduate Student, are with the Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 5 5 4 5 5 . This article is based o n a presentation made in the symposium " Q u a s i Brittle Fracture" presented during the TMS fall m e e t i n g , Cincinnati, OH, October 2 1 - 2 4 , 1991, under the auspices of the TMS Mechanical Metallurgy C o m m i t t e e and the A S M / M S D F l o w and Fracture Committee. METALLURGICAL TRANSACTIONS A
Griffith's theory of the early 1920s influenced all subsequent models purporting to deal w i t h brittle fracture. In the 1930s, NeubertSJ dealt with nonlinear deviations at notches in a continuum sense, while Taylortgl invoked dislocations as the causes of such nonlinearities in crystalline materials. At that point in time, no connection was possible to solve the boundary value problem, as Neuber's construct was artificial. In the 1940s and 1950s, more precise mathematical descriptions of cracks and their slip line fields, ~1°-131 as well as the consequences of dislocation activity at crackst~21 or in nucleating cracks,~14 ~71 were evolving. The Cottrell-Petch m o d e l 06'171 was a m o n g the first t o make connections between dislocation mechanics and the original Griffith concept. With fracture mechanics concepts just starting t o take hold in the early 1960s, the first major connections between continuum theory and dislo
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