Elastic plastic self-consistent (EPSC) modeling of plastic deformation in fayalite olivine

Abstract

Elastic plastic self-consistent (EPSC) simulations are used to model synchrotron X-ray diffraction observations from deformation experiments on fayalite olivine using the deformation DIA apparatus. Consistent with results from other in situ diffraction studies of monomineralic polycrystals, the results show substantial variations in stress levels among grain populations. Rather than averaging the lattice reflection stresses or choosing a single reflection to determine the macroscopic stress supported by the specimen, an EPSC simulation is used to forward model diffraction data and determine a macroscopic stress that is consistent with lattice strains of all measured diffraction lines. The EPSC simulation presented here includes kink band formation among the plastic deformation mechanisms in the simulation. The inclusion of kink band formation is critical to the success of the models. This study demonstrates the importance of kink band formation as an accommodation mechanism during plastic deformation of olivine as well as the utility of using EPSC models to interpret diffraction from in situ deformation experiments.

Elastic plastic self-consistent (EPSC) modeling of San Carlos olivine deformed in a D-DIA apparatus

“…The deviation from pure elastic behavior is temperature dependent with the slope deviating more at higher temperatures. Second, for each experiment, the relative difference between the lattice strains changes markedly at the yield point where the lattice strain vs. sample strain curves bend over as the sample yields (Burnley 2015;. This spreading of the lattice strains can be seen in both the compressional and transverse directions.…”

“…The single-crystal elastic constants used in each model were calculated for the appropriate experimental temperature and pressure from constants given in (Isaak 1992;Anderson and Isaak 1995;Abramson et al 1997;Liu and Li 2006) and are listed in the supplementary material. Typically for olivine, we model the eight commonly observed slip systems in olivine as well as three unidirectional slip systems to simulate the formation of kink bands (Burnley 2015;. For this study, we also used an additional isotropic deformation mechanism that will be discussed below.The EPSC model uses a Voce hardening law to describe the evolution of the critical resolved shear stress (τ) for each slip system with shear strain (Γ) as follows:…”

“…However, finding EPSC fits for diffraction from olivine deforming at high temperature has been more challenging (Hilairet et al 2012). We have shown (Burnley 2015;) that including a kink band deformation mechanism to close the yield surface produces more satisfactory EPSC models, however modeling the slope of olivine stress-strain curves at low strain remains a challenge especially at high temperature (cf. Hilairet et al 2012).…”

“…The average of the measured stresses is typically used, however the resulting average depends upon which diffraction lines the experimenter happens to measure. Significant success has been achieved with elastic plastic selfconsistent (EPSC) modeling that has been used extensively to interpret neutron and X-ray diffraction from deforming metals (Turner and Tome 1994;Turner et al 1995;Agnew et al 2006;Merkel et al 2009) as well as X-ray diffraction from in situ deformation experiments on MgO (Li et al 2004), quartz (Burnley and Zhang 2008), alumina (Raterron et al 2013;, and olivine (Hilairet et al 2012;Burnley 2015;. EPSC models simulate the response of crystals based on their orientation with respect to the loading boundary conditions, and they include groups of grains (grain populations) observed by diffraction as well as the mechanical contribution of "silent" grains that are not participating in produc-ing diffraction.…”

Measurement of Activation Volume for Creep of Dry Olivine at Upper‐Mantle Conditions

“…Seen at ψ = 90°, grains in the diffraction condition can lie at a range of orientations from weak to strong. Burnley () modeled the specific case of low‐ T , high‐ σ creep in fayalite and found the inaccuracy of the straightforward application of the Singh relationship can be dramatic for some, but not the majority, of ( hkl ) reflections. Again, modeling of the deformation systems in San Carlos olivine is well beyond the resources of the community at present, so the best we can do is assert that our measurements are qualitatively correct and are accurate for some but not necessarily all ( hkl ) conditions.…”