Modulated dislocation patterns in plastically deformed metals

Phase modulations of periodic dislocation patterns observed in transmission electron microscopy (TEM) studies of some single crystalline metals, are analyzed using the nonlinear amplitude Ginzburg-Landau (GL) equation for the soft mode instability. We demonstrate that phase modulations of dislocation patterns can be described using the concept of the Eckhaus instability which describes one of the most fundamental "generic" mechanisms of wavelength-changing and which was successfully used before for the analysis of nonlinear systems of different physico-chemical nature. The timescale of wavelength-changing processes in dislocation systems can be very large if the system is dose to the Eckhaus stability limit, i.e., the metastable phase modulations of dislocation pattern can survive nearly unchanged for a long time. The results of numerical simulations for realistic values of the parameters show that the Eckhaus instability could be the underlying physical reason of modulated ladder structures of Persistent Slip Bands (PSBs) in cyclically deformed metallic alloys.