Generation of plate tectonics by two-phase grain-damage and pinning

The mechanism of shear localization in the lithosphere is an essential ingredient for understanding how and whether plate tectonics is generated from mantle convection on terrestrial planets. Grainsize reduction and subsequent softening is a leading candidate for deep lithospheric localization. However, the physics of how grains simultaneously reduce and affect the bulk rheology remains enigmatic. Thermodynamic constraints provide for grain reduction through damage (i.e., work done by deformational work creates more grain-boundary surface area). However, damage and grain reduction generally occur in conjunction with dislocation creep, which nominally precludes the requisite self-softening by grainsize-dependent rheology during diffusion creep. Moreover, healing by grain growth or coarsening in single phase continua tends to be fast, which counters the localizing effects of damage and causes shear zones to be short lived. However, in more realistic two-phase (polyminerallic) rock mixtures such as peridotite, the size of secondary phase porphyroblasts or inclusions (e.g., of orthopyroxene) plays an important role through Zener pinning, which can both drastically reduce the rate of grain growth, and promote grain-damage and grainsize reduction. In this paper we present a continuum theory of grainsize evolution in a two-phase medium in the presence of coarsening and damage. Each phase has its own grain evolution, distribution and grain boundary energy. However the phases are also separated by an interface with a unique surface energy and morphology. The density of interfacial area controls the concentration of pinning surfaces and barriers to grain growth in either phase, and more practically quantifies the interfacial curvature which, for example, can be related to the inclusion size of the secondary phase. Damage increases the interfacial area density and curvature, e.g., by reducing the inclusion size through fracture or disaggregation, or increasing its curvature by deformation and stetching. Damage also acts to reduce grainsize in the phases themselves, although direct damage to grains ceases once they enter the diffusion creep regime. However, the increase in interfacial area density and curvature, combined with Zener pinning can by itself readily drive grain reduction and force grains into the diffusion creep regime. Therefore, the combination of effects allows damage, grain-reduction and grain-size sensitive diffusion creep to coexist in a positive feedback that generates plate-like shear-localization. Moreover, when deformation on fine-grained weak zones ceases, grain-growth is again pinned to coarsening of the interface (e.g., by inclusion-growth), which is necessarily extremely slow, thereby permitting long-lived dormant lithospheric weaknesses and inactive plate boundaries, which can be reactivated later. This continuum model provides for the feedback between the evolution of grains and interface density, as would occur in the lithospere, and is possibly the key to plate generation.