Shielding of cracks in a plastically polarizable material
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In this paper, we address some fundamental questions regarding the response of a crack to externally generated dislocations. We note that since dislocations that formed at external sources in the material must be in the form of loops or dipoles, the theory must be couched in terms of crack shielding in a plastically polarizable medium. There are strong analogies to dielectric theory. We prove two general theorems: (1) Dipoles formed in the emission geometry relative to a crack tip always antishield the crack and (2) when dipoles are induced during uniform motion of a crack through a uniformly plastically polarizable material, then the net shielding is always positive. We illustrate these general theorems with a number of special cases for fixed and polarizable sources. Finally, we simulate the self consistent time dependent response of a crack to a polarizable source as the crack moves past it. The results show that the crack is initially antishielded, but that positive shielding always dominates during later stages of configuration evolution. The crack may be arrested by the source, or it may break away from it, depending upon the various parameters (source strength and geometry, dislocation mobility, Griffith condition for the crack, etc.). The results indicate that the time dependence of crack shielding in the presence of a nonuniform density of sources will be very important in practical cases of brittle transitions in materials.
I. INTRODUCTION In this paper we will explore in a small way one of the remaining fundamental problems relating to fracture; that is, how the sources of deformation strain in the material external to the atomic vicinity of a crack tip contribute to fracture toughness, and the conditions under which this externally produced deformation can totally shield and arrest a crack against an applied load. Our interest in this problem stems from the fact that there are two independent ways for dislocations to inhibit brittle behavior—if they are emitted from the crack tip at levels below the Griffith load, then they not only shield the crack, but they also change its character from a cleavable sharp crack into a noncleavable blunted notch.1 The cleavage/emission conditions for a crack have been studied extensively for many years, and the crack tip ductility can be quite complex,2-3 but in a very rough qualitative sense, a material like copper is dominated by the intrinsic weakness in shear of the atomic bonding at the tip of any crack. Then, the question remains, what are the prospects (and more precisely, what are the conditions) for the material surrounding a brittle crack to supply such copious quantities of shielding dislocations, that the material is ductile in an extrinsic sense? The
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'Part of this work was performed at the Institute of Corrosion and Protection of Metals, Acaderaia Sinica, Shenyang, People's Republic of China.
object of study will then be any material that can sustain an atomically sharp crack without shear breakdown and dislocation emission, and that will be capable
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