Weakening effect of grain-size reduction in granitoid shear zones
Authors: Ruh Jonas B. , Tokle Leif , Whitney Behr 
Published: March 2022

&lt;p&gt;Localization of strain during deformation of crustal rocks to form narrow shear zones requires some form of strain weakening. Bulk weakening of a deforming shear zone may for example result from geometric reorganization and interconnection of weak phases, from concentration of fluids or fluid-rich mineral phases, or from local temperature increase due to shear heating. A further potential weakening effect is work-related grain size reduction driven by dislocation creep, and the consequent activation of grain-size-sensitive diffusion creep in recrystallized zones.&lt;/p&gt;&lt;p&gt;To test the importance of grain size reduction for mechanical weakening of granitoid crustal shear zones, a numerical model of initially undeformed granitoid texture was set up and sheared to a total shear strain of 10. The numerical finite difference code solves for the conservation of momentum (Stokes) and mass with a visco-elasto-plastic rheology. The model setup outlines a naturally constrained multi-phase granitoid texture including quartz, plagioclase, and biotite. The domain measures 5x5 cm with top and bottom velocities describing simple shear, while the left and right prescribe periodic boundaries. For both quartz and plagioclase (anorthite), flow laws for dislocation and diffusion creep are implemented and act in parallel. Grain size evolution is implemented in the form of the paleowattmeter with mineral-specific grain growth laws. The 2D numerical setup of a complex multi-phase initial texture allows us to investigate grain size evolution in a progressively evolving system with a spatially and temporally varying stress field and with simultaneous geometric weakening associated with interconnection of weak phases, neither of which can be analyzed using analytical calculations.&lt;/p&gt;&lt;p&gt;Results show a reduction of grain sizes of quartz and plagioclase during shearing with quartz deforming dominantly under dislocation creep. Plagioclase behaves brittlely at low temperatures, with dominant diffusion creep at intermediate temperatures, switching to dislocation creep at high temperatures. Purely textural weakening of &gt;60% occur at 550 &amp;#176;C. At lower temperatures, anorthite strength reduces given the brittle yield envelope and at higher temperatures, dislocation creep strength of quartz and anorthite converge, resulting in bulk shear and less textural weakening. Additional weakening related to grain size reduction relies on the activation of diffusion creep as the dominant deformation mechanism for anorthite. At 350 &amp;#176;C, anorthite strength is limited by brittle yield and no grain-size-induced weakening is detectable. For higher temperatures, additional grain-size-induced weakening ranges between 12&amp;#8211;30 %, and thus represents an important factor for the initiation of granitoid crustal shear zones. The presented numerical study underlines the importance of grain size-related weakening of crustal shear zones, particularly at intermediate temperatures above the brittle-ductile transition (400&amp;#8211;450&amp;#176;C) and below the activation of dislocation creep in plagioclase (&gt;650&amp;#176;C).&lt;/p&gt;