  Numerical experiments of convection with grain-damage are used to develop
scaling laws for convective heat flow, mantle velocity, and plate velocity
across the stagnant lid and plate-tectonic regimes. Three main cases are
presented in order of increasing complexity: a simple case wherein viscosity is
only dependent on grainsize, a case where viscosity depends on temperature and
grainsize, and finally a case where viscosity is temperature and grainsize
sensitive, and the grain-growth (or healing) is also temperature sensitive. In
all cases, convection with grain-damage scales differently than Newtonian
convection due to the effects of grain-damage. For the fully realistic case,
numerical results show stagnant lid convection, fully mobilized convection that
resembles the temperature-independent viscosity case, and partially mobile or
transitional convection, depending on damage to healing ratio, Rayleigh number,
and the activation energies for viscosity and healing. Applying our scaling
laws for the fully realistic case to Earth and Venus we demonstrate that
increasing surface temperature dramatically decreases plate speed and heat
flow, essentially shutting down plate tectonics, due to increased healing in
lithospheric shear zones, as proposed previously. Contrary to many previous
studies, the transitional regime between the stagnant lid and fully mobilized
regimes is large, and the transition from stagnant lid to mobile convection is
gradual and continuous. Thus planets could exhibit a full range of surface
mobility, as opposed to the bimodal distribution of fully mobile lid planets
and stagnant lid planets that is typically assumed.
