The phase modulation, of periodic dislocation patterns which were observed during transmission electron microscopic studies of some monocrystalline metal samples, was analyzed in terms of non-linear dynamics. The Ginsburg-Landau equation for the soft-mode instability in the weakly non-linear regime was derived for the Walgraef-Aifantis model for a coupled system with 2 populations of dislocations. It was demonstrated that the phase modulation of dislocation patterns could be described by using the concept of Eckhaus instability. The latter described one of the most fundamental basic mechanisms of wavelength-changing. The timescale of wavelength-changing processes in dislocation systems could become very wide when the system was close to the Eckhaus stability limit. This implied that metastable phase-modulations of the dislocation patterns could survive almost unchanged for long periods. Numerical simulations showed that the Eckhaus instability could be the underlying physical cause of the modulated ladder structures which were seen in persistent slip bands in cyclically deformed metallic alloys.

Eckhaus Instability – a Possible Wavelength Changing Mechanism in the Evolution of Dislocation Patterns. S.N.Rashkeev, M.V.Glazov, F.Barlat: Computational Materials Science, 2001, 21[2], 230-42