Dynamic recrystallization and texture development in deformed olivine polycrystals

When an olivine polycrystal (dunite) is deformed in simple shear, the expectation value of the [100] axis orientation follows the long axis of the finite strain ellipsoid (FSE) for small shear strains γ < 50%, but for larger strains rotates toward the shear plane more rapidly than does the FSE (Zhang & Karato, Nature, 1995; ZK95). This observation implies that texture in dunites is not a unique function of the finite strain when dynamic recrystallization (DRX) is active. We propose a simple kinematic model for DRX that explains the experimental observations. We model DRX by adding an inhomogenous term f J (where J has zero mean over all orientations) to the right-hand side of the standard evolution equation for the orientation distribution function (ODF) f. We then posit J = λ F(Δ), where λ is a dimensionless recrystallization rate, Δ = (e - E)², e is the strain rate tensor within a crystal, and E is the macroscopic strain rate tensor imposed on the polycrystal. We choose the function F(Δ) such that crystals poorly oriented for slip on the dominant slip system (i.e., crystals with larger Δ) gradually disappear by DRX in favor of well-oriented crystals. We solve the resulting ODF evolution equation analytically (for small strains) and numerically (for large strains). We find that for λ  = 3 the predictions of our model agree remarkably well with a simple shear texture at γ = 140% obtained by Lee et al. (Tectonophys., 2002). An important advantage of our new model is that it has only a single free parameter, as opposed to e.g. the three-parameter model implemented in D-Rex (Kaminski et al., Geophys. J. Int., 2004).