Olivier Castelnau

Dynamic recrystallization and texture development in ice as revealed by the study of deep ice cores in Antarctica and Greenland

The preferred c axis orientation of ice from polar ice sheets develops essentially as a result of intracrystalline slip; but dynamic recrystallization appears to alter the kinetics of the development of deformation textures and is, at high temperature, at the origin of recrystallization textures. The purpose of this work is to obtain a better understanding of recrystallization processes that occur in polar ice sheets and to clarify the relationship between dynamic recrystallization and textures. The study was based on two deep ice cores from Greenland and Antarctica, the GReenland Ice core Project (GRIP) and Vostok ice cores. The structure along the GRIP core displays normal grain growth in the first 100 m of the ice sheet and rotation recrystallization and migration recrystallization near the bottom. Only grain growth and rotation recrystallization appear to occur in the Vostok ice core. The transition between these recrystallization regimes was studied, estimating, for interglacial ice, the evolution with depth of the dislocation density. This calculation has shown the efficiency of grain boundary migration for the absorption of dislocations. At Vostok, the highest value of the dislocation density is found at a depth of about 1000 m and the continuous decrease in the dislocation density below this depth is related to the increase of the grain boundary migration rate. It is shown that the driving force required to initiate migration recrystallization is not reached in interglacial ice at Vostok. The observed textures were compared with those predicted by the self-consistent approach. Recrystallization textures are interpreted by assuming that the less stressed grains, i.e., the best oriented for basal slip, are favored by the size advantage of subgrains. The recrystallization textures are compared with those of other materials.

Viscoplastic modeling of texture development in polycrystalline ice with a self‐consistent approach: Comparison with bound estimates

Ice crystals deform easily by dislocation glide on basal planes, which provides only two independent easy slip systems. The necessary slip on other systems limits the strain rate of polycrystalline ice. The preferred c axis orientation of ice from polar ice sheets develops as a result of intracrystalline slip. An anisotropic viscoplastic self-consistent (VPSC) approach is used for predicting texture development and mechanical behavior of polycrystalline ice. Results are compared with lower and upper bound estimations. It is assumed that ice crystals deform by basal, prismatic, and pyramidal slip. The resistance of each slip system is determined from experimental data on monocrystals and isotropic polycrystals. The VPSC model can predict the behavior of isotropic polycrystalline ice on both the macroscopic and microscopic scale. This is not the case for the lower and upper bounds. Fabrics simulated in uniaxial extension and compression are qualitatively similar for all models. However, large differences in the rate of fabric development are found. This is explained by the different interaction stiffness between grain and matrix. Fabric concentration obtained with the VPSC model for uniaxial deformation is in close agreement with those observed in polar ices. In simple shear, the single maximum fabric found in situ cannot be reproduced without an extensive (and probably unrealistic) activity of nonbasal systems. The preferential growth of grains well oriented for basal glide associated with rotation recrystallization could be at the origin of the discrepancy between model results and natural simple shear fabrics. Distorted grain shape is found to slightly slow down fabric development.

Modelling viscoplastic behavior of anisotropic polycrystalline ice with a self-consistent approach

Abstract A ViscoPlastic Self-Consistent (VPSC) model has been applied to polycrystalline ice in order to characterize the relation between the texture of the material and the instantaneous anisotropic mechanical behavior. We assume that ice crystals deform by basal, prismatic, and pyramidal slip. The resistance of these slip systems is determined by an inverse approach, based on the comparison between model results and results of several mechanical tests. The VPSC model well reproduces all experimental macroscopic behavior only if we introduce a small—but not negligible—amount of pyramidal slip, which is not observed experimentally. The introduction of this probably unrealistic slip system possibly corrects the errors linked to the assumptions of the model, that we discuss. We finally use the model to describe the behavior of some typical polar ices in relation to the symmetries of the texture.

Compressive creep of ice containing a liquid intergranular phase: Rate‐controlling processes in the dislocation creep regime

Experiments have been conducted to investigate the effect of melt on the creep behavior of polycrystalline ice deformed in the dislocation creep regime. The transition between a mode with a stress exponent n = 3 and a mode with n < 2 is observed for both melt-free and melt-added ice samples. The large influence of the melt phase is not related to the wetting characteristics of the liquid. Owing to the large plastic anisotropy of the ice crystal, the liquid phase would attenuate the internal stress field which develops during the primary creep. The contribution to the deformation of the basal slip (the weaker slip system) would increase with the melt content.

Numerical simulations of texture development and associated rheological anisotropy in regions of complex mantle flow

[1] The development of Lattice Preferred Orientations (LPO) within olivine aggregates under flow in the upper mantle leads to seismic and rheological (or viscoplastic) anisotropies. We compare predictions from different micromechanical models, applying several commonly used theoretical descriptions to an upwelling flow scenario representing a typical oceanic spreading center. Significant differences are obtained between models in terms of LPO and associated rheology, in particular in regions where the flow direction changes rapidly, with superior predictions for the recently proposed Second-Order approach. This highlights the limitations of ad hoc formulations. LPO-induced rheological anisotropy may have a large effect on actual flow patterns with 1–2 orders of magnitude variation in directional viscosities compared to the isotropic case. Citation: Castelnau, O., D. K. Blackman, and T. W. Becker (2009), Numerical simulations of texture development and associated rheological anisotropy in regions of complex mantle flow, Geophys. Res. Lett., 36, L12304,

Texture dependent plastic behavior of Zr 702 at large strain

Abstract Three polycrystalline samples of Zr702α are deformed at room temperature under channel die compression until about 40% strain. Samples are oriented differently in the die with respect to their texture, so that the influence of the initial texture on the stress–strain response, the activated deformation systems, and the subsequent texture evolution can be assessed. Experimental results are interpreted by using a viscoplastic self-consistent (VPSC) polycrystalline model in which a saturating anisotropic intracrystalline hardening law is introduced. It is shown that the orientation dependence of the activated slip systems strongly depends on the texture of the polycrystal. The main effect of intracrystalline hardening is found to be a redistribution of slip from the primary to the secondary systems, but in a moderate way such that it does not affect significantly the development of texture. A simple analysis shows that the increasing activity of the secondary slip systems can be assessed directly from the macroscopic stress–strain curves.

In situ diffraction strain analysis of elastically deformed polycrystalline thin films, and micromechanical interpretation

In situ tensile tests have been carried out under synchrotron radiation on supported gold (Au) thin films exhibiting a pronounced crystallographic texture. The 2θ shift of X-ray diffraction lines has been recorded for different specimen orientations and several loading levels in the elastic domain. The data obtained demonstrate the large strain heterogeneities generated within the specimen because of the intergranular interactions associated with the large elastic anisotropy of Au grains. To interpret these results, the use of a multi-scale micromechanical approach is unavoidable. The theoretical background of such methods is described, and the points where exact results can be obtained and where approximations have to be introduced are highlighted. It is shown that the Vook–Witt model, for which a general formulation is provided, is the exact solution for polycrystals exhibiting a laminate microstructure, which is a significant departure from the standard thin-film microstructures. Among several standard models used in the field, the self-consistent model is the only one that reproduces the experimental data correctly. This is achieved by accounting for the actual crystallographic texture of the specimen, and assuming pancake-shaped two-point statistics for the morphological texture. A discussion of the limitations of this approach, originally developed for bulk materials, is given for the specific case of thin films.

A “quasi-elastic” affine formulation for the homogenised behaviour of nonlinear viscoelastic polycrystals and composites

The derivation of the overall behaviour of nonlinear viscoelastic (or rate-dependent elastoplastic) heterogeneous materials requires a linearisation of the constitutive equations around uniform per phase stress (or strain) histories. The resulting Linear Comparison Material (LCM) has to be linear thermoviscoelastic to fully retain the viscoelastic nature of phase interactions. Instead of the exact treatment of this LCM (i.e., correspondence principle and inverse Laplace transforms) as proposed by the “classical” affine formulation, an approximate treatment is proposed here. First considering Maxwellian behaviour, comparisons for a single phase as well as for two-phase materials (with “parallel” and disordered morphologies) show that the “direct inversion method” of Laplace transforms, initially proposed by Schapery (1962), has to be adapted to fit correctly exact responses to creep loading while a more general method is proposed for other loading paths. When applied to nonlinear viscoelastic heterogeneous materials, this approximate inversion method gives rise to a new formulation which is consistent with the classical affine one for the steady-state regimes. In the transient regime, it leads to a significantly more efficient numerical resolution, the LCM associated to the step by step procedure being no more thermoviscoelastic but thermoelastic. Various comparisons for nonlinear viscoelastic polycrystals responses to creep as well as relaxation loadings show that this “quasi-elastic” formulation yields results very close to classical affine ones, even for high contrasts.

Isothermal flow of an anisotropic ice sheet in the vicinity of an ice divide

Simulations of glacier flow are commonly based on the assumption that ice has an isotropic viscosity. Here we examine the plane flow of ice in the special region of an ice divide using a constitutive relation for an anisotropic, incompressible viscous body that is orthotropic and transversally isotropic. Ice is assumed to be isotropic at the ice sheet surface, with the continuous development of a vertical single maximum c axis fabric with increasing depth. We consider the theoretical case of an isothermal ice sheet over a horizontal bedrock, with no slip at the ice-bedrock interface. The ice sheet surface elevation is imposed, and the flow corresponding to the steady state is calculated, using a two-dimensional finite difference model based on the resolution of a pressure-Poisson equation. In this model, all components of the stress and strain rate tensor are calculated. The main conclusion is that for a fixed surface elevation, the general flow pattern accelerates when the anisotropic behavior of the ice is taken into account due to the greater fluidity with respect to shear stress. The downward motion of the ice is faster, despite a higher resistance to vertical deformation. As a result, the dominance of shear strain rate in the flow of polar ice is stronger in the anisotropic case than in the isotropic case. The shear stresses are slightly relaxed, while the longitudinal stresses are significantly increased in the anisotropic case.

Modeling the mechanical response of polycrystals deforming by climb and glide

This paper presents a crystallographically-based constitutive model of a single crystal deforming by climb and glide. The proposed constitutive law is an extension of the rate-sensitivity approach for single crystal plasticity by dislocation glide. Based on this description at single crystal level, a homogenization-based polycrystal model for aggregates deforming in a climb-controlled thermal creep regime is developed. To illustrate the capabilities of the proposed model, we present calculations of effective behavior of olivine and texture evolution of aluminum at warm temperature and low strain rate. In both cases, the addition of climb as a complementary single-crystal deformation mechanism improves the polycrystal model predictions.