Tectonic plate generation and two-phase damage: Void growth versus grain size reduction

The generation of plate tectonics from mantle convection requires shear localization in order to yield narrow, weak plate boundaries separating broad strong plates. A plausible shear- localizing mechanism involves damage ( e. g., distributed microcracking), one theoretical model of which involves two- phase mechanics. Two- phase damage theory employs a nonequilibrium relation between interfacial surface energy, pressure, and viscous deformation, thereby providing a description of void generation and microcracking, and hence weakening, failure, and shear localization. Here we examine the application of this theory to the problem of generating plate- like behavior from convective- type divergent/ convergent ( poloidal) motion through a source- sink formulation. We extend the previous damage theory to consider two possible damage effects: ( 1) growth and nucleation of voids associated with dilation of the host matrix and ( 2) increasing fineness ( i.e., reducing coarseness) of the mixture by, for example, grain size reduction. Void- generating damage is found to be poor at plate generation because of the predominance of dilational motion that is adverse to the development of plate- like flow. Fineness- generating damage is found to be very efficient at generating plate- like behavior if we assume that the matrix viscosity is a simple function of grain/ void size, as is typical for diffusion creep. The implied grain size reduction mechanism is different from that of dynamic recrystallization and appears to be more capable of generating the requisite shear localization for forming tectonic plates from mantle flow.