Computer simulation of titanium yield stress in a wide range of grain sizes

Abstract

In this paper, the simulation of the relay mechanism of the origin of plastic deformation from grain to grain is performed. It is shown that for large grains, the work of a dislocation source in the neighbor grain slightly depends on the applied stress due to the large number of dislocations of chaos. For smaller grain sizes, the stress at which the sources are triggered is proportional to the square root of the grain size — the Hall—Petch's law is fulfilled. It is shown that the free term in the Hall—Petch equation is equal to the lattice friction stress at grain sizes greater than 10 μm and is proportional to the smaller ones. The coefficient of proportionality Ky is proportional to the stress of the start of the dislocation source at average grain size (from 10 to 1 μm).