A continuum theory for phase mixing and grain-damage relevant to tectonic plate boundary evolution

Abstract

The unique occurrence of plate tectonics on Earth is rooted in the intricate physics of weakening and shear-localization in the cold ductile lithosphere. The pervasiveness of mylonites at lithospheric shear zones is a key piece of evidence that localization is correlated with reduction in mineral grain-size. The positive feedback leading to such localization, however, is often thought to be paradoxical because grain-size reduction by deformation-induced damage, and grain-size sensitive weakening do not necessarily co-exist in monomineralic materials. However, most lithospheric mylonites are polymineralic and the interaction between mineral phases, such as olivine and pyroxene, especially through Zener pinning, impedes normal grain growth while possibly enhancing grain-reduction via damage, even down to grain-sizes in which grain-size sensitive weakening is active. The efficacy of pinning, however, relies on the mineral phases being mixed and dispersed at the grain scale. Indeed, recent models and experiments imply that enhanced mixing between phases leads to greater grain-size reduction and weakening, whereas unmixed regions remain large-grained and strong. This duality of mixed states leads to a hysteresis effect, wherein slowly deforming states with large grains coexist with mylonitic-like states with rapid deformation, akin to the tectonic state of the Earth, with stiff plates coexisting with rapidly deforming plate boundaries. However, the different deformation states necessarily correspond to heterogeneity in mineral phase volume fractions, where the strong states correspond to monomineralic units of large-grained tectonites, while weaker mylonitic states occur in well-mixed polymineralic units. To model grain mixing between different phases at the continuum scale, we develop a new theory treating grain-scale processes as diffusion between phases, but driven by imposed stresses acting on the interface between phases. Simple one-dimensional (1-D) applications of the theory, and concomitant scaling laws show that diffusive grain mixing enhances grain-reduction by amplifying the influence of Zener pinning. The coupling between inter-phase diffusion and grain-damage promotes a positive mixing-localization feedback, which leads to narrow, weak, well-mixed polymineralic zones at the boundary between monomineralic units, as expected for bands of mylonites and ultramylonites. Flanking these narrow mixed zones are poorly mixed regions that have weaker pinning and grain-reduction, leading to large grains typical of tectonites and protomylonites. Thus, the continuum model for grain mixing and damage also predicts that weak, mylonitized plate boundaries can coexist with strong plate interiors for the same lithospheric temperature and driving stresses.