From transient to steady state deformation and grain size: A thermodynamic approach using elasto-visco-plastic numerical modeling

Abstract

Numerical simulation experiments give insight into the evolving energy partitioning during high-strain torsion experiments of calcite. Our numerical experiments are designed to derive a generic macroscopic grain size sensitive flow law capable of describing the full evolution from the transient regime to steady state. The transient regime is crucial for understanding the importance of microstructural processes that may lead to strain localization phenomena in deforming materials. This is particularly important in geological and geodynamic applications where the phenomenon of strain localization happens outside the time frame that can be observed under controlled laboratory conditions. Our method is based on an extension of the paleowattmeter approach to the transient regime. We add an empirical hardening law using the Ramberg-Osgood approximation and assess the experiments by an evolution test function of stored over dissipated energy (lambda factor). Parameter studies of, strain hardening, dislocation creep parameter, strain rates, temperature, and lambda factor as well as mesh sensitivity are presented to explore the sensitivity of the newly derived transient/steady state flow law. Our analysis can be seen as one of the first steps in a hybrid computational-laboratory-field modeling workflow. The analysis could be improved through independent verifications by thermographic analysis in physical laboratory experiments to independently assess lambda factor evolution under laboratory conditions.

Hierarchical creep cavity formation in an ultramylonite and implications for phase mixing

“…9). This is typically interpreted as indicating a transition from GSI creep to GSS creep accommodated by viscous grain-boundary sliding (Mitra, 1978;Etheridge and Wilkie, 1979;Kerrich et al, 1980;Behrmann and Mainprice, 1987;Závada et al, 2007;Kilian et al, 2011;Herwegh et al, 2014;Menegon et al, 2015;Viegas et al, 2016).…”

“…Generally speaking, with ongoing deformation the proportion of fine-grained material deforming by GSS creep increases synkinematically so that the polyphase domains form an interconnected weak layering. It is the establishment of these well-mixed, anti-clustered polyphase domains that is recognised to ultimately promote a switch in the bulk rheology of the rock (Handy, 1994;Kilian et al, 2011;Herwegh et al, 2014). However, the exact modes by which these domains are established are still poorly understood and the subject of intense research.…”

Small quantity but large effect — How minor phases control strain localization in upper mantle shear zones

“…Various theoretical and empirical relations for the steady-state grain size of monomineralic minerals have been derived De Bresser et al, 2001;Herwegh et al, 2014;Karato et al, 1980;Shimizu, 1998;Van der Wal et al, 1993). Deformation experiments on single crystal olivine (Karato et al, 1980) and dunites (Van der Wal et al, 1993) have shown that the dynamically recrystallized olivine grain size is dependent mainly on stress, and an empirical relation between grain size and differential stress has been derived.…”

A Thermomechanical Framework for Analysis of Microstructural Evolution: Application to Olivine Rocks at High Temperature

“…To characterize the nonlinear behavior of materials, constitutive models are composed of evolution laws and equations of state for the relevant state variables (e.g., temperature and grain size). In the geophysics literature, there has been a recent and necessary movement toward developing such constitutive models in the context of thermodynamics of irreversible processes (TIP; e.g., Bercovici et al, ; Cooper et al, ; Covey‐Crump, ; Hackl & Renner, ; Herwegh et al, ; Karrech et al, ; Ricard & Bercovici, ; Rozel et al, ; Sherburn et al, ; Stone et al, ). The essential idea is to define internal state variables that regulate the storage of energy in the material structure and the dissipation of energy through various deformation mechanisms.…”

“…In this case, λ AE (our added subscript) is the fraction of energy available for deformation that is diverted into changing the grain size instead of being dissipated as dislocation creep (Austin & Evans, , ). The value of λ is a primary unknown and is either considered to be constant (Austin & Evans, , ) or has an assumed functional form (Herwegh et al, ; Ricard & Bercovici, ; Rozel et al, ). One of the motivations for our study is to determine the partitioning of energy between storage and dissipation (i.e., the λ ); the thermodynamic framework utilized here yields this partitioning as a result, not as an assumption.…”