Dislocation Patterns and the Similitude Principle: 2.5D Mesoscale Simulations

During plastic flow of crystalline solids, dislocations self-organize in the form of patterns, with a wavelength that is inversely proportional to stress. After four decades of investigations, the origin of this property is still under discussion. We show that dislocation patterns verifying the principle of similitude can be obtained from dynamics simulations of double slip. These patterns are formed in the presence of long- and short-range interactions, but they are not significantly modified when only short-range interactions are present. This new insight into dislocation patterning phenomena has important implications regarding current models.

Figure 1

(a) Shear stress vs the square root of the total dislocation density in dimensionless variables. Simulations starting with different initial densities are superimposed, yielding a linear slope $\alpha \approx 0.65$. (b) Total density vs plastic strain curves for various initial densities. The arrow indicates the conditions at which the pattern shown in Fig. 2 is obtained and $m$ is the implemented multiplication rate.

Figure 2

(a) A periodic 2D pattern ($\lambda \approx 2.5\mu \mathrm{m}$, $L=14\mu \mathrm{m}$, $\rho =1.8\times {10}^{13}{\mathrm{m}}^{-2}$). The Fourier transform of this pattern is shown in the inset; the diffraction spots corresponding to the two wall spacings are encircled. (b) Snapshot of a magnified cell wall (vertical after rotation).

Figure 3

Numerical check of the similitude principle: scaled resolved stress vs the inverse of the scaled wall periodicity $b/\lambda$ (two values are plotted when the two types of walls do not have exactly same periodicity). ▵: all interactions included. ▾: short-range interactions only.