  The rheology of rocks transitions from a localized brittle behaviour to
distributed plastic behaviour with increasing pressure and temperature. This
brittle-plastic is empirically observed to occur when the material strength
becomes lower than the confining stress, which is termed Goetze's criterion.
Such a criterion works well for most silicates but is not universal for all
materials. We aim to determine the microphysical controls and stress-strain
behaviour of rocks in the brittle-plastic transition. We use a micro-mechanical
approach due to Horii and Nemat-Nasser, and consider representative volume
elements containing sliding wing-cracks and plastic zones. We find solutions
for frictional slip, plastic deformation and crack opening at constant
confining pressure, and obtain stress-strain evolution. We show that the
brittle-plastic transition depends on the confining stress, fracture toughness
and plastic yield stress but also critically on the friction coefficient on
preexisting defects. Materials with low friction are expected to be more
brittle, and experience transition to fully plastic flow at higher pressure
than anticipated from Goetze's criterion. The overall success of Goetze's
criterion for the brittle-plastic transition in rocks is likely arising from
the low toughness, high strength, and medium friction coefficient character of
most rock forming minerals.
