We study and compare the evolution into the stagnant lid regime with a non-Newtonian water ice and a silicate rheology by solving the equations of thermal convection. Dislocation creep of water ice is characterized by a larger stress dependence (n = 4) than silicates (n = 3) and with this water ice rheology, the stagnant lid regime is attained at a temperature determined viscosity contrast greater than 1010 and at an effective viscosity contrast of ~105. We also determine a Nusselt-Rayleigh number scaling law for the n = 4 rheology.