TY - JOUR
T1 - Dislocation mobility and the concept of flow stress
JF - Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
JO - Proc R Soc Lond A Math Phys Sci
SP - 375
LP - 385
M3 - 10.1098/rspa.1975.0107
VL - 344
IS - 1638
AU -
Y1 - 1975/07/29
UR - http://rspa.royalsocietypublishing.org/content/344/1638/375.abstract
N2 - A formal definition of the flow stress of a metal is established rigorously from first principles for a certain model by studying the stability of equilibrium of the leader in a group of n (n large) coplanar screw dislocations with Burgers vector b, moving on a plane a distance h from a non-coplanar locked dislocation with Burgers vector mb (m < n) under the action of an applied shear stress p yz = o.A ‘ characteristic equation’ of the model is set up and the onset of instability of the leader is identified with the bifurcation of its equilibrium state, which is predicted by the Routh-Hurwitz theorem, well-known in the theory of stability. As an aid in simplifying this process recourse is had to another well-known the orem -that due to Liénard & Chipart. The applied shear stress required to achieve this unstable state is specified within certain bounds. Since these bounds are very close to each other, especially for small m, the critical flow stress can be estimated accurately. It is shown that the flow stress is closer to the lower bound obtained previously and that the superdislocation approach overestimates the critical stress. The paper also discusses certain implications of the present work.
ER -