Lynn Evans

Elle: the numerical simulation of metamorphic and deformation microstructures

Abstract We present a generalised framework for the numerical simulation of the evolution of rock microstructures during deformation and metamorphism. This approach is based upon a data structure that describes a polycrystalline material using a two-dimensional network of nodes and connecting boundaries that allows micro-processes to be analysed at a range of scales. The nodes may possess attributes of position, topology and chemistry; and polygonal domains defined by these nodes may possess attributes of mineralogy, rheology and lattice orientation. We represent the complex behaviour of deforming and metamorphosing rocks at the grain scale as the interaction of a set of locally-defined driving forces and micro-processes, calculated for small time steps. A central program controls the evolution of extrinsic variables such as temperature and defines the history of deformation or metamorphic processes. The central program then passes the data structure to distinct process algorithms, which interact with this data structure, both by using it to determine the local values of driving forces, and by altering the attributes to simulate the progress of the process. We outline the function of the different aspects of the modelling task, provide simple examples showing porphyroblast growth during deformation and static grain growth, and describe the data structure that we have developed which enables us to handle multi-process simulations.

Dominance of microstructural processes and their effect on microstructural development: insights from numerical modelling of dynamic recrystallization

Abstract The influence of the dominance of different processes on the microstructural development of a quartzite was investigated using the numerical model ‘ELLE’. Dynamic recrystallization of a polycrystalline aggregate was simulated by the concurrent operation of viscous deformation, lattice rotation, subgrain formation, rotational recrystallization, nucleation of new grains from strongly strained grains and recovery. The different observed microstructural characteristics depend on the relative rates at which grain boundary migration, subgrain formation, recrystallization by rotation and nucleation affect the microstructure. Observed sizes of recrystallized grains are significantly influenced by these different relative rates of processes. These rates are determined by parameters that mainly depend on temperature, fluid absence or presence, shear stress and strain rate. Therefore, the specific conditions at which deformation took place have to be taken into account if recrystallized grain sizes are used for palaeopiezometry. Comparison and combination of our results with experimental data and observations in natural examples provide the possibility of interpreting microstructures quantitatively in terms of temperature and shear strain rate.

Instability of a lithospheric step beneath western North Island, New Zealand

Lithospheres of different thicknesses are often juxtaposed by movement on a continental-transform boundary. Such a boundary with a step change in densities may trigger a gravitational instability as lateral pressure gradients are created where normal mantle lithosphere terminates against less dense asthenospheric mantle. Here we show, for plausible values of the lithospheric viscosity, a mechanism by which the thicker mantle lithosphere will drip off into the lower density asthenosphere. As the mantle deforms it also progressively thickens and then thins the overlying crust, creating a topographic wave that migrates in concert with the removal of mantle lithosphere. Within western North Island, New Zealand, geophysical data define a sharp lithospheric step across the Taranaki-Ruapehu line, and geological observations provide a history of uplift and subsidence that has propagated southward in the past 12 m.y. The rate of observed north to south migration of the wave (∼30 mm/yr), its wavelength (∼250 km), and amplitude (∼±1 km) are compatible with it being caused by progressive removal of mantle lithosphere, if the viscosity of the uppermost lithospheric mantle is ∼5 × 10 20 Pa⋅s, providing one of the clearest examples yet of this fundamental geological process.

Strain localization and porphyroclast rotation

It has been debated for decades whether rigid inclusions, such as porphyroclasts and porphyroblasts, do or do not rotate in a softer matrix during deformation. Experiments and numerical simulations with viscous matrix rheologies show ongoing rotation of circular inclusions, whereas using Mohr-Coulomb plasticity results in nonrotation. Because the rocks in which inclusions are found normally undergo deformation by dislocation creep, we applied a full-field crystal plasticity approach to investigate the rotation behavior of rigid circular inclusions. We show that the inclusion9s rotation strongly depends on the anisotropy of the matrix minerals. Strongly anisotropic minerals will develop shear bands that reduce the rotation of inclusions. Inhibition of rotation can only occur after a significant amount of strain. Our results may help to explain why geologic rigid objects often show evidence for rotation, but not necessarily in accordance with the viscous theory that is usually applied to these systems.

Competition between grain growth and grain-size reduction in polar ice

Static (or ‘normal’) grain growth, i.e. grain boundary migration driven solely by grain boundary energy, is considered to be an important process in polar ice. Many ice-core studies report a continual increase in average grain size with depth in the upper hundreds of metres of ice sheets, while at deeper levels grain size appears to reach a steady state as a consequence of a balance between grain growth and grain-size reduction by dynamic recrystallization. The growth factor k in the normal grain growth law is important for any process where grain growth plays a role, and it is normally assumed to be a temperature-dependent material property. Here we show, using numerical simulations with the program Elle, that the factor k also incorporates the effect of the microstructure on grain growth. For example, a change in grain-size distribution from normal to log-normal in a thin section is found to correspond to an increase in k by a factor of 3.5.

Substructure Dynamics in Crystalline Materials: New Insight from In Situ Experiments, Detailed EBSD Analysis of Experimental and Natural Samples and Numerical Modelling

The understanding of the dynamics of substructures during deformation and annealing is fundamental in our ability to predict microstructural and physical properties such as rheological behaviour of crystalline materials. Here, we present an overview of new insights into substructure dynamics through a combination of in-situ heating experiments, detailed Electron Backscatter Diffraction (EBSD) analysis and numerical modelling.

Numerical Experiments into the Localization of Deformation during Recrystallization Flow

The localization of deformation in recrystallizing materials is investigated via a series of two-dimensional grain-scale numerical simulations. These simulations couple a grain size and strain dependant viscous rheology with grain size reduction and grain growth processes. The simulations are able to predict the mechanical, microstructural and strain evolution of the polycrystals to high strain, and allow us to examine the nature of the time dependent feedback between mechanical and microstructural behavior. It was found that significant strain localization occurred only when the grain size dependence of the viscosity was non-linear, and was greatly enhanced by the activity of the grain size modifying processes. The intensity and location of the zone of strain localization varied spatially and temporally, with the result that the finite strain state showed a much broader, and hence less intense, zone of localized deformation than the instantaneous state.

Case studies and coupling of processes

This chapter with eight authored sections presents a selection of possible application of microdynamic simulation to address geological questions. The various processes that have been introduced in the previous chapter were used, sometimes with minor additions or modifications. Because processes in rocks never operate in isolation, the reader will see that the various authors in this chapter have combined two or more processes to simulate the microstructural development under investigation. As such the authors have fully taken advantage of the possibility of the Elle software to couple processes.