Nonequilibrium dynamics of a two-defect system under severe load

In the framework of a two-defect model, based on a variation of the Landau technique, the kinetics of structural defect generation in solids under severe external load is investigated. The approach is based on a special form of kinetic equation in terms of internal energy, which is applied here to the description of an important practical problem of fine-grained structure formation in metals under severe plastic deformation. It unifies strengthening curves over the entire range of deformation, including the Hall-Petch and linear strengthening sections.

Figure 1

Regularities of defect formation during SPD: (a) kinetics of defects: 1, density of grain boundaries; 2, density of dislocations and (b) unified strengthening curve: 1, region of the Hall-Petch law; 2, region of the linear law of strengthening. Points A–C highlight the formation of the most typical regions of kinetics and strengthening. Dots on the strengthening curve correspond to equal time steps.

Figure 2

Strengthening curves (a) including the effect of GB slip: 1, $w=0$; 2, $w=1.2\times {10}^{-11}$; 3, $w=5\times {10}^{-11}$ and (b) with the parameter ${\phi }_{0g}$ increased 50 times: 1, ${\phi }_{0g}^{*}=0.4\text{J}{\text{m}}^2$; 2, ${\phi }_{0g}^{*}=20\text{J}{\text{m}}^2$; B and C are the same points as in Fig. 1.