Avalanches and Scaling in Plastic Deformation

Plastic deformation of crystalline materials is a complex nonhomogeneous process characterized by avalanches in the motion of dislocations. We study the evolution of dislocation loops using an analytically solvable phase-field model of dislocations for ductile single crystals during monotonic loading. The distribution of dislocation loop sizes is given by $P(A)\sim A^{-\sigma }$, with $\sigma =1.8\pm 0.1$. The exponent is in agreement with those found in acoustic emission experiments. This model also predicts a range of macroscopic behaviors in agreement with observation, including hardening with monotonic loading, and a maximum in the acoustic emission signal at the onset of yielding.