This work reviewed the current understanding of two scaling laws which were ubiquitous in the modelling of monotonic plastic deformation in face-centered cubic metals. A compilation of the available data allowed extending the domain of application of these scaling laws to cyclic deformation. The strengthening relation tells that the flow stress was proportional to the square root of the average dislocation density, whereas the similitude relation assumed that the flow stress was inversely proportional to the characteristic wavelength of dislocation patterns. The strengthening relation arose from short-range reactions of non-coplanar segments and applies all through the first three stages of the monotonic stress vs. strain curves. The value of the proportionality coefficient was calculated and simulated in good agreement with the bulk of experimental measurements published since the beginning of the 1960s. The physical origin of what was called similitude was not understood and the related coefficient was not predictable. Its value was determined from a review of the experimental literature. The generalization of these scaling laws to cyclic deformation was carried out on the base of a large collection of experimental results on single and polycrystals of various materials and on different microstructures. Surprisingly, for persistent slip bands, both the strengthening and similitude coefficients appeared to be more than two times smaller than the corresponding monotonic values, whereas their ratio was the same as in monotonic deformation. The similitude relation was also checked in cell structures and in labyrinth structures. Under low cyclic stresses, the strengthening coefficient was found even lower than in persistent slip bands. A tentative explanation was proposed for the differences observed between cyclic and monotonic deformation. Finally, the influence of cross-slip on the temperature dependence of the saturation stress of persistent slip bands was discussed in some detail. This works takes into account current discussions on the microstructural aspects of cyclic deformation and highlights further work that was required for fully understanding the physical origin of the two scaling laws.

Scaling Laws for Dislocation Microstructures in Monotonic and Cyclic Deformation of FCC Metals. M.Sauzay, L.P.Kubin: Progress in Materials Science, 2011, 56[6], 725-84