__Michael R. Riedel__, Shun Karato, Dave A. Yuen

We calculate the amount of viscous dissipation
during subduction of a lithospheric plate
as constrained by experimental rock mechanics.
The maximum bending moment M_{crit} that can be sustained by a slab
is of the order of 10^{19} Nm per m
according to M_{crit} ~ s_{p} * h^{2}/4,
where s_{p} is the Peierl's stress limit of slab materials and
h is the slab thickness.
Near M_{crit}, the amount of viscous dissipation
grows strongly as a consequence of a lattice
instability of mantle minerals (dislocation glide in olivine).
The value of M_{crit} is about 1-2 orders of magnitude too high to
be reached by a ridge push of typically 10^{12} N per m
at convergent plate boundaries, but unusual tectonic
settings like a thick sedimentary load of the lithosphere
or a shallow angle of slab penetration at the transition zone
can help to overstep this bending moment threshold.
The immediate consequence is a sudden drop of the effective
viscosity to below 10^{21} Pas, so that the observed
weakening effect serves as a self-regulating mechanism to adjust
plate tectonics on Earth against strong viscous resistance forces.

Strong growth of viscous dissipation DeltaQ in dependence of the bending moment M for 3 different sets of constitutive equations for olivine creep (subduction speed 10 cm/yr, slab thickness 85 km):

(a) complete set including Peierls mechanismAlso shown is the minimum slab bending curvature R

(b) reduced set: only diffusion and power-law creep included

(c) linear rheology: only diffusion creep included

Dominant deformation mechanisms in subducting slabs. Initial temperature distribution corresponds to that for a 100 myr oceanic lithosphere of 85 km thickness. The cases for subduction velocities of 4 cm/yr and 10 cm/yr are shown. Because stress, temperature, pressure and grain-size change significantly in space for a given slab, dominant mechanisms of deformation change in a complicated fashion. In high stress, low temperature regions, the Peierls mechanism dominates. In moderate stress, moderate to large grain-size-regions, power- law creep dominates. Diffusion creep plays an important role in cold, fine-grain regions in the center of labs after a phase tranformation. Note that such a pattern also depends on the velocity of subduction, which controls the temperature distribution and the magnitude of stress.

Domain diagram showing the critical range of bending moments for a slab with 85 km thickness where the lithosphere is subject to thermo-mechanical instabilities (peak shear-heating rate inside the slab larger than 10