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Dislocation Motions and the Yield Strengths of Solids
At the yield stress of a crystal its behavior suddenly changes from elastic to plastic; in other words, the plastic strain rate suddenly becomes finite and sometimes quite large. In terms of dislocation movements the plastic strain-rate, ˙γ, depends on the Burgers vector, b, of the dislocations in the crystal, the average velocity of the dislocation motions, , and the number of dislocations moving per unit area (ρ). These quantities are related by a simple equation (1): which has been verified by Johnston and Gilman (2) through direct measurements of dislocation densities and velocities in lithium fluoride crystals. Since b is a constant, and ρ cannot change unless dislocations move, the yield stress is related to ¯ν. Thus, in order to understand the nature of the yield stress, the first question that requires an answer is: What determines the stress needed to move dislocations at a large average velocity? Is it the stress needed: (a) to operate sources of dislocations such as Frank-Read sources? (b) To pull dislocations away from Cottrell atmospheres? (c) To drive dislocations through a forest of other dislocations? (d) To overcome an intrinsic “plastic resistance” of the crystal structure? Also, do various types of crystals (metallic, ionic, or covalent) depend on different ones of these factors, or is plastic flow in all crystals dependent on the same factor? The thesis that will be developed here is that factor (d) is the most important one for all single phase crystals.
Gilman, J. J.
Brown University, Providence, R. I.
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