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Polycrystalline materials exhibit physical properties that are driven by both the interatomic crystallographic structure as well as the nature and density of structural defects. Crystallographic evolutions driven by phase transitions and associated twinning process can be observed in situ in three-dimensional (3D) using monochromatic synchrotron radiation at very high temperatures (over 1000 °C). This paper focuses on continuous measurements of the 3D-reciprocal space maps by high-resolution x-ray diffraction as a function of temperature along a phase transition process occurring between 1200 °C and room temperature. These high precision measurements allow observing the reciprocal space node splitting and the evolution of the diffuse scattering signal around that node as a function of temperature. The capability of this experimental method is illustrated by direct in situ high temperature measurements of the 3D splitting of a reciprocal space node due to phase transition recorded on dense pure zirconia polycrystals. [ABSTRACT FROM AUTHOR]

Progressive deformation of upper mantle rocks via dislocation creep causes their constituent crystals to take on a non-random orientation distribution (crystal preferred orientation or CPO). The resulting anisotropy of the rock's elastic properties can be observed by seismic techniques, and provides a means to constrain mantle convective flow patterns. Existing methods for calculating the evolution of CPO in deforming olivine-dominated rocks rely on unwieldy discrete representations of the crystal orientation distribution in terms of a large number (103–104) of individual grains. Here we propose a more efficient method in which CPO is represented using three continuous analytical functions (structured basis functions or SBFs), each of which represents a virtual CPO produced by the action of just one of the three dominant slip systems of olivine. The SBFs are then combined using an appropriate weighting scheme to represent a realistic CPO that results from the simultaneous activity of all three slip systems. We assume that olivine CPO is a unique function of the finite strain experienced by the aggregate, which implies that the weights of the SBFs depend only on the two ratios of the lengths of the axes of the finite strain ellipsoid (FSE) and the two ratios of the strengths (critical resolved shear stresses) of the slip systems. Our preferred set of weighting coefficients is obtained by least-squares fitting of the SBF expansion to the predictions of a kinematic model (solved by the method of characteristics) in which the amplitudes of the crystallographic spins do not increase with strain. Calculation of CPO using this model is ≈107 times faster than full homogenization approaches such as the second-order self-consistent model, and the result fits the characteristics-based solution with a variance reduction |$\ge 88.6\hbox{ per cent}$| for equivalent strains up to 0.9. Finally, we propose a simple modification of the FSE that prevents the CPO from becoming singular at large strains. [ABSTRACT FROM AUTHOR]

Progressive deformation of upper mantle rocks via dislocation creep causes their constituent crystals to take on a non-random orientation distribution (crystallographic preferred orientation or CPO) whose observable signatures include shear-wave splitting and azimuthal dependence of surface wave speeds. Comparison of these signatures with mantle flow models thus allows mantle dynamics to be unraveled on global and regional scales. However, existing self-consistent models of CPO evolution are computationally expensive when used with 3-D and/or time-dependent convection models. Here we propose a new method, called ANPAR, which is based on an analytical parametrization of the crystallographic spin predicted by the second-order (SO) self-consistent theory. Our parametrization runs ≈2-6 × 104 times faster than the SO model and fits its predictions for CPO and crystallographic spin with a variance reduction >99 per cent. We illustrate the ANPAR model predictions for the deformation of olivine with three dominant slip systems, (010)[100], (001)[100] and (010)[001], for three uniform deformations (uniaxial compression, pure shear and simple shear) and for a corner-flow model of a spreading mid-ocean ridge. [ABSTRACT FROM AUTHOR]

Abstract: The strongly anisotropic rheology of olivine polycrystals, associated to their microstructure, constitutes a key feature affecting the dynamics of the Earth''s upper mantle. High pressure deformation experiments carried out on olivine single crystals under synchrotron radiation, together with estimations of lattice friction based on first-principle calculations, show a transition from easy [100] to easy [001] slips as pressure and temperature (thus depth) increases. We input these data at the slip system level into the second-order extension of the self-consistent scheme to assess microstructure evolution along a typical flow pattern beneath an oceanic spreading center. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

Abstract: An approximate self-consistent modelling is proposed to estimate the effective viscoelastic response of polycrystals presenting an ageing constitutive behaviour. This approach makes use of the equivalence between the Dirichlet series approximation of the viscoelastic functions and an internal variables formulation. An illustrative application is performed for model 2d polycrystals for which the exact expression of the continuous effective relaxation spectrum is given. [Copyright &y& Elsevier]

Abstract: An efficient full-field formulation based on fast Fourier transforms (FFTs) for the prediction of the viscoplastic deformation of polycrystals is applied to the study of the subgrain texture and microstructure evolution in polycrystalline Cu deformed under tension. Direct input from orientation imaging microscopy (OIM) images is used in the construction of the initial unit cell. Average orientations and misorientations predicted after 11% tensile strain are directly compared with OIM measurements, showing good agreement. The differences between misorientations of surface grains compared with bulk grains are estimated, and the orientation dependence of intragranular misorientations is studied. Measurements and simulations agree in that grains with initial orientation near 〈110〉 tend to develop higher misorientations. This behavior can be explained in terms of attraction towards the two stable orientations and grain interaction. Only models that account explicitly for interaction between individual grains, like the FFT-based formulation, are able to capture these effects. [Copyright &y& Elsevier]

From the liquid state to room temperature, two successive solid-state phase transitions occur in pure zirconia. It is well-known that the last one (tetragonal to monoclinic) is martensitic and induces large volume variations and shear strains. Elastic and inelastic behaviors of zirconia-based materials are strongly influenced by this transition and the associated strain fields that it induces. Knowledge of strain and stress at the crystal scale is thus a crucial point. Using fully dense pure zirconia polycrystals obtained by a fuse casting process, we have determined at a sub-micrometric scale, by X-ray Laue microdiffraction, the strains map at room temperature in as-cast specimens and after a post elaboration high temperature thermal treatment. We observed that the fluctuation of deviatoric elastic strain is huge, the standard deviation of normal component being in the range of 1–2%. The heat treatment tends to even further increase this range of fluctuation, despite the development of a multiscale crack network formed during the cooling. Correspondingly, the associated stress level is also huge. It lies in the 5 GPa range with stress gradient amounting 1 GPa μm−1. [ABSTRACT FROM AUTHOR]