The influence of grain size on the physical yield strength of the polycrystal is considered by the method of cellular automata. The physical yield strength of the polycrystal in this model is defined as the stress at which, the plastic deformation covers the entire cross section of the sample from one edge to another. Three mechanisms of plastic deformation are considered. The first one is an initiation of plastic flow from grain to grain by dislocation pile-ups. The second one is plastic flow in different grains independently of each other under the action of external stress and the third one is intergranular slippage. Computer simulations have shown that at large grain sizes (d > 200 nm) deformation propagates from grain to grain by initiating dislocations pile-ups, since in this case pile-ups are quite powerful and have a large effect on neighboring grains. At average values of grain size (20 nm <d <200 nm) plastic deformation occurs in the grains independently of each other, and the external strain give a major influence on plastic deformation. With further reduction of the grain sizes (d <20 nm) the main mechanism of deformation is intergranular slippage. because in grains of this size are quite large image stresses that do not allow large dislocation clusters. In small grains the image forces are quite large to prevent large dislocation pile-ups formation, but the mass and volume of grain are quite small to turn or slip its under the action of external stresses. In accordance with these mechanisms, on the calculated dependence of the physical yield strength vs grain size, there are three areas with different angles of inclination in logarithmic coordinates. Keywords: yield point, grain size, Hall―Petch low.
Influence of grain size on mechanisms of plastic deformation and yield stress
