Power laws in dislocation plasticity

Abstract

Starting from the idea that plastic flow produces dislocation structures in a state of self-organised criticality, it is shown that one expects power-law relationships between variables. If slip bands are modelled as avalanches of shear with an ellipsoidal shape, slightly tilted from the crystallographic slip plane, limited in size by interaction with secondary slip, the observed exponents of the power laws can be rationalised. In some cases, the constant of proportionality can also be estimated, and found to agree with experiment, even though the detailed mechanism of avalanche formation is not addressed. To analyse creep data and slip-band statistics, it is further assumed that the role of cross-slip is to eliminate screw dislocation dipoles, removing them entirely at stresses found in Stage III of work-hardening. If physical constants, such as the atomic vibration frequency, play a role, the dimensionless power-law relationships do not apply. One then finds creep rates linear in stress and absolute temperature, proportional to the logarithm of time, obeying an equation of state, as observed.

Keywords:

• Dislocations
• plasticity
• slip bands
• avalanches

Acknowledgements

I am indebted to Robinson College and to the Cavendish Laboratory for support, also to Dr. Stephen Walley of the SMF group, who keeps me up to date on relevant literature. I am grateful to two anonymous referees whose careful reading of the manuscript has helped clarify several points and eliminated an error.