The flow stress of fractal dislocation arrangements

In metals deforming under multislip conditions, fractal dislocation arrangements may develop. The composite model of the flow stress of a dislocation cell structure is generalized for dislocation arrangements which exhibit a broad spectrum of local hardness. Both forest strengthening (cell walls) and the Orowan stress (cell interiors) are taken into account. Relations between the flow stress and the characteristic parameters of the dislocation arrangement such as fractal dimension, maximum and minimum cell size are established. The model is used to calculate stress dependences of fractal dimension and cell wall volume fraction of dislocation patterns in high-symmetry oriented f.c.c. single crystals. The results are in good agreement with experimental observations on Cu and Cu-rich Cu–Mn.