Multiphase Aggregates Research Articles

Elastic behaviour of orientation-correlated grains in multiphase aggregates.

Diffraction elastic constants (DEC) describe the elastic response of a sub-set of orientation correlated grains which share a common lattice vector. DEC reflect the elastic behaviour of the single crystal constituents through their dependence on grain orientation. DEC furthermore depend on the behaviour of the polycrystal aggregate both through the dependence on preferred orientation and through the average elastic interaction of the grains in the sub-set with their surroundings. The latter is also known as grain-matrix interaction which is grain shape dependent. Both dependencies can make the DEC uniquely sensitive to the elastic effects of the grain shape, texture, and phase composition. Several micro-mechanical models are explored with respect for use both in calculating diffraction elastic constants and overall elastic constants. Furthermore, it is shown how discrete data from electron backscatter diffraction on grain shape, grain orientations, and neighbouring grains can be used for DEC calculations. Lastly, the inverse problem of calculating single crystal elastic constants from DEC is discussed in detail. All calculations discussed in this work can be verified using the freely available computer program IsoDEC.

Deformation of two-phase aggregates with in situ X-ray tomography in rotating Paris-Edinburgh cell at GPa pressures and high temperature.

High-pressure (>1 GPa) torsion apparatus can be coupled with in situ X-ray tomography (XRT) to study microstructures in materials associated with large shear strains. Here, deformation experiments were carried out on multi-phase aggregates at ∼3-5 GPa and ∼300-500°C, using a rotational tomography Paris-Edinburgh press (RoToPEc) with in situ absorption contrast XRT on the PSICHE beamline at Synchrotron SOLEIL. The actual shear strain reached in the samples was quantified with respect to the anvil twisting angles, which is γ ≤ 1 at 90° anvil twist and reaches γ ≃ 5 at 225° anvil twist. 2D and 3D quantifications based on XRT that can be used to study in situ the deformation microfabrics of two-phase aggregates at high shear strain are explored. The current limitations for investigation in real time of deformation microstructures using coupled synchrotron XRT with the RoToPEc are outlined.

Slag resistance mechanism of MgO–Mg2SiO4–SiC–C refractories containing porous multiphase aggregates

The slag resistance of MgO–SiC–C (MSC) refractories should be improved because of the mismatch in the thermal expansion coefficient between the aggregates and matrix, as well as the defects caused by the affinity between periclase and slag. In this study, MgO–Mg2SiO4–SiC–C (MMSC) refractories were prepared using porous multiphase MgO–Mg2SiO4 (M-M2S) aggregates to replace dense fused magnesia aggregates. Compared to MSC, the slag penetration index of MMSC decreased by 43.5%. The structure of the porous aggregates increased the surface roughness, and the multiphase composition of the aggregates decreased the mismatch of the thermal expansion coefficient with the matrix, thus reducing debonding between the aggregates and matrix. The aggregates and matrix in the MMSC formed an interlocking structure, which bound them more tightly to improve the slag resistance. The slag viscosity at different depths from the initial slag/refractory interface was calculated using the Ribond model. The M-M2S aggregates increased SixOyz− in the slag, which increased the slag polymerization and slag viscosity. The aggregates and matrix in the MMSC reacted with the slag to form high melting point phases, which reduced the channel of the slag. In addition, the penetration depth and velocity derived from the Washburn Equation were modified for the CaO–SiO2–Al2O3–MgO–FeO slag and magnesia based refractory to accurately evaluate slag penetration.

Fabrication and thermal shock behavior of periclase-forsterite aggregates with micro-nanometer dual-pore-size structures

To improve the service life of periclase-forsterite refractories, it is important to develop aggregates with high thermal shock resistance. In this study, periclase-forsterite aggregates with good resistance to thermal shock and micro-nanopores were prepared using high-silicon magnesite, silica, and silica sol. Microcracks were generated in the multiphase aggregates, which inhibited the continuous propagation of cracks during thermal shock through mismatched thermal expansion coefficients. Based on Hasselman's thermal shock stability factor, the reduction in the average thermal expansion coefficient and improved mechanical characteristics were critical factors in improving the thermal shock resistance of the multiphase aggregates. As a binder, silica sol provided nano-SiO2 and superplasticity, which facilitated the formation of micro-nanopores and strengthened the combination of the various phases in the aggregates.

A micromechanics-based damage constitutive model considering microstructure for aluminum alloys

Aluminum alloys undergoing deformation exhibit complex multi-type-void damage evolution driven by microscale heterogeneous deformation; in return, the accumulated damage evolution would affect the microscale heterogeneous deformation. Meanwhile, the above interaction depends significantly on the microstructure characteristics and determines the macroscale flow and ductile fracture behaviors. These make it difficult to model the deformation response and ductile fracture of aluminum alloys with various microstructures. Aiming at this issue, a micromechanics-based damage constitutive model considering the mutual effects between microstructure, micro/macro-scale deformation, and damage and fracture was developed in this study for deformation of aluminum alloys under tension-dominated loading conditions. During the modeling, the damage was characterized in terms of the evolutions of coexisting multi-type voids. The multiple-type voids were modeled separately as functions of the local micro-strain/stress of their respective phases and microstructure characteristics according to the micromechanical mechanisms. Furthermore, a self-consistent method was employed to calculate the heterogeneous micro-strain/stress of phases and the overall macroscale flow behavior of the multiphase aggregate. In particular, the constitutive behavior of each phase in the self-consistent method was modeled by coupling the softening effect of void evolution and microstructure characteristics, thus the interaction between microscale heterogeneous deformation and damage evolution was captured. The model parameters were determined by matching the calculated and experimental evolutions of the multi-type voids measured via in-situ synchrotron radiation X-ray computed tomography and load-displacement curves during deformation. Applied to the 2219 aluminum alloy, this model accurately predicts the flow stress, damage evolution and fracture behavior under various microstructures and those of tailor-welded blanks with a gradient microstructure. Furthermore, the model clarifies the mutual effects between the microstructure, damage evolution and deformation behavior of aluminum alloys. The developed model can also be generalized to other multiphase metals containing a distribution of hard-brittle particles. And it is thus believed to be with a well general prediction for the deformation response and ductile fracture of this kind of multiphase metals with various microstructures or gradient microstructures, and further facilitates the understanding of their complex damage evolution and flow behavior.

Investigation of microwave-induced cracking behavior of shale matrix by a novel phase-field method

Microwave heating is a potential and effective technology for enhancing shale gas recovery. The microwave radiation may induce cracking of the shale matrix, which further improves the permeability of reservoirs. Therefore, it is important to study the cracking characteristics of shale matrices to evaluate the permeability enhancement effect of microwave radiation on shale. This study proposes a novel dual-scale phase-field model to investigate the mechanisms of intergranular and transgranular fractures within a shale matrix subjected to microwave radiation. The model combines microwave heating modeling at the macro-scale and fracture modeling at the micro-scale with shale microstructures created through Voronoi tessellation. Each mineral grain has an elastic isotropic behavior, and multiphase aggregates (quartz, feldspar, pyrite, clay, calcite, and dolomite) are considered. Intergranular fractures are modeled using a lower-dimensional interfacial element formulation. The responses of temperature and cracking are analyzed based on combined simulations at the macro- and micro -scales. The simulations showed that the microwave heating efficiencies of clay and pyrite are significantly higher than those of the other minerals. Microwave-induced cracking within the shale matrix preferentially occurs in quartz particles, resulting from the lower critical energy release rate and mismatched thermal expansion of the various components of the shale matrix. The fracture modes are highly dependent on the shape and distribution characteristics of the mineral particles.

Deformation of ZrSiO4 -MgO aggregates: Deviatoric stress as a control on deformation mechanisms

Deformation behavior of multiphase aggregates has great significance for materials design and understanding the dynamics of the Earth. Here we studied the deformation of zircon (${\mathrm{ZrSiO}}_{4}$)-MgO aggregates and found that the introduction of MgO reduced overall deviatoric stress in the aggregates and thus controlled deformation mechanisms of the zircon phase. Zircon primarily deforms by a dominant ${101}\ensuremath{\langle}10\ensuremath{-}1\ensuremath{\rangle}$ slip; however, activity of zircon ${100}\ensuremath{\langle}010\ensuremath{\rangle}$ slip increases with the introduction of an increased ratio of MgO into the aggregates, as suggested by the experiments and simulations. We also found both zircon and MgO in the aggregates retained strong deformation texture, which is likely related to the symmetric variants of the dominant slip system of the hard zircon phase. Our results help to clarify the discrepancies in previous studies and understand which phase may dominate the seismic anisotropy in geosciences.

Fast grain-boundary ionic conduction in multiphase aggregates as revealed by electrical conductivity measurements

Fast grain-boundary ionic conduction in multiphase aggregates as revealed by electrical conductivity measurements

Numerical shear experiments of quartz-biotite aggregates: Insights on strain weakening and two-phase flow laws

For progressively deforming multi-phase aggregates, it is unclear to what extent the change in geometry and orientation of the involved phases leads to textural strain weakening and thus may control strain localization. Consequently, the question arises how the ductile flow of multi-phase rocks can be described or determined. To contribute to the understanding of these knowledge gaps, two-dimensional numerical shear experiments of quartz-biotite aggregates were conducted at variable conditions. Textural variations after a shear strain of γ ≈ 10 appear to be dependent on the viscosity contrast between the minerals involved. To estimate whether a numerical experiment is undergoing strain weakening or hardening, the temporal evolution of the mean second invariant of the deviatoric stress tensor was tracked. The results suggest that strain weakening occurs if biotite is distinctly isolated in form of strong or weak inclusions and that it is more effective under conditions with larger viscosity contrasts between matrix and inclusions. However, observed stress drops in experiments purely based on textural strain weakening are low compared to other strain weakening processes. Numerical results from experiments with variable strain rate, temperature and biotite content were combined to determine two-phase flow law parameters for quartz-biotite aggregates, which are in broad agreement with existing analytical mixed-aggregate flow laws.

Preliminary data for melt inclusions in garnet porphyroblasts from Ograzhden metapelites, SW Bulgaria

Micro-inclusions in garnet porphyroblasts from high-grade Ograzhden metapelites, SW Bulgaria, have been studied by SEM and micro-Raman Spectroscopy. Micro-inclusions are presented by single grains with facetted outlines parallel to rational crystallographic orientations of the host garnet or by multiphase aggregates with negative crystal shape. Many of studied micro-inclusions can be formed by the presence of melt. The morphology of some of them suggests formation under high pressure metamorphism.

How semi-coherent b.c.c. hydride interfacial interactions affect the inelastic deformation and fracture behavior of h.c.p. zirconium alloys

We analyzed how b.c.c. semi-coherent interfaces, within an h.c.p. matrix, have a central effect on the fracture of these multi-phase aggregates. We obtained 36 unique Orientation Relations (ORs) related to semi-coherent interfaces between the hydrides and the parent matrix, and calculated interfacial misfit strains between the matrix and hydride crystalline structures. We then coupled these microstructural interactions to a dislocation-density framework with a fracture nucleation and propagation approach to understand and predict different failure scenarios. The analysis indicates that misfit strains have a dominant mechanistic effect that is essential for an understanding of multi-phase crystalline aggregate behavior that spans different length scales.

Micromechanical modeling of cohesive thermoelastic steady‐state and transient cracking in polycrystalline materials

SummaryIn this paper, a micromechanical formulation is proposed for modeling thermoelastic intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model is based on a multiregion boundary element approach combined with the dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic isotropic behavior, and multiphase aggregates have been considered. Damage evolution along (intergranular or transgranular) interfaces is modeled using thermomechanical cohesive laws, and upon failure, nonlinear frictional contact analysis is introduced to model separation, stick or slip. Steady‐state and transient thermoelastic formulations have been modeled, and numerical simulations are presented, not only to demonstrate the validity but also to study the physical implications of the proposed formulation, in comparison with other numerical methods as well as experimental observations and literature results.

The recognition of former melt flux through high‐strain zones

AbstractHigh‐strain zones are potential pathways of melt migration through the crust. However, the identification of melt‐present high‐strain deformation is commonly limited to cases where the interpreted volume of melt “frozen” within the high‐strain zone is high (>10%). In this contribution, we examine high‐strain zones in the Pembroke Granulite, an otherwise low‐strain outcrop of volcanic arc lower crust exposed in Fiordland, New Zealand. These high‐strain zones display compositional layering, flaser‐shaped mineral grains, and closely spaced foliation planes indicative of high‐strain deformation. Asymmetric leucosome surrounding peritectic garnet grains suggest deformation was synchronous with minor amounts of in situ partial melting. High‐strain zones lack typical mylonite microstructures and instead display typical equilibrium microstructures, such as straight grain boundaries, 120° triple junctions, and subhedral grain shapes. We identify five key microstructures indicative of the former presence of melt within the high‐strain zones: (a) small dihedral angles of interstitial phases; (b) elongate interstitial grains; (c) small aggregates of quartz grains with xenomorphic plagioclase grains connected in three dimensions; (d) fine‐grained, K‐feldspar bearing, multiphase aggregates with or without augite rims; and (e) mm‐ to cm‐scale felsic dykelets. Preservation of key microstructures indicates that deformation ceased as conditions crossed the solidus, breaking the positive feedback loop between deformation and the presence of melt. We propose that microstructures indicative of the former presence of melt, such as the five identified above, may be used as a tool for recognising rocks formed during melt‐present high‐strain deformation where low (<5%) volumes of leucosome are “frozen” within the high‐strain zone.

MMA‐EoS: A Computational Framework for Mineralogical Thermodynamics

AbstractWe present a newly developed software framework, MMA‐EoS, that evaluates phase equilibria and thermodynamic properties of multicomponent systems by Gibbs energy minimization, with application to mantle petrology. The code is versatile in terms of the equation‐of‐state and mixing properties and allows for the computation of properties of single phases, solution phases, and multiphase aggregates. Currently, the open program distribution contains equation‐of‐state formulations widely used, that is, Caloric‐Murnaghan, Caloric–Modified‐Tait, and Birch‐Murnaghan–Mie‐Grüneisen‐Debye models, with published databases included. Through its modular design and easily scripted database, MMA‐EoS can readily be extended with new formulations of equations‐of‐state and changes or extensions to thermodynamic data sets. We demonstrate the application of the program by reproducing and comparing physical properties of mantle phases and assemblages with previously published work and experimental data, successively increasing complexity, up to computing phase equilibria of six‐component compositions. Chemically complex systems allow us to trace the budget of minor chemical components in order to explore whether they lead to the formation of new phases or extend stability fields of existing ones. Self‐consistently computed thermophysical properties for a homogeneous mantle and a mechanical mixture of slab lithologies show no discernible differences that require a heterogeneous mantle structure as has been suggested previously. Such examples illustrate how thermodynamics of mantle mineralogy can advance the study of Earth's interior.

Jadeite- and dolomite-bearing coesite eclogite from western Tianshan, NW China

Jadeite associated with omphacite has been reported from high-pressure, low-temperature (H P -L T ) rocks worldwide. However, the upper pressure stability of this association is not clear in nature. This study describes an immiscible texture of clinopyroxenes at ultrahigh-pressure (UH P )-L T conditions from western Tianshan, NW China. The host eclogite mainly consists of quartz, garnet, carbonate, albite, omphacite, white mica and Na-Ca amphibole. The modal contents of constituent minerals vary from place to place, and quartz-rich and carbonate-rich domains are developed. Jadeite (Jd 70–91 Aeg 2–16 ) only occurs as inclusion in garnet, mostly accompanied by patchy omphacite. Micro-Raman analyses show that jadeite and omphacite have different diagnostic peaks, consistent with the quantitative microprobe results. Jadeite is locally replaced by secondary sodic phases like paragonite and albite. A composite inclusion occurs in garnet and consists of lath-like paragonite, quartz, omphacite and titanite, with or without glaucophane. Matrix porphyroblastic albite usually encloses paragonite, titanite and barroisite, with or without omphacite, constituting a multi-phase aggregate. These two types of sodic phase-rich aggregates within and outside garnet are interpreted to be pseudomorphic replacements after jadeite at different conditions during retrogression. In addition to coesite in garnet, inclusions of coesite and its pseudomorphs without radial fractures were found in ankeritic dolomite. This first reported paragenesis of dolomite + coesite at low temperatures suggests that dolomite can be stabilized at depths of up to 90 km in a cold subduction zone. This contribution not only reports a new occurrence of Tianshan UH P rocks, but also suggests that UH P -L T metamorphism has impacted a variety of lithologies in addition to paraschist and basaltic eclogite, thus supporting the internal coherence of the UH P terrain of the Chinese western Tianshan.

Multiscale modeling of upper mantle plasticity: From single-crystal rheology to multiphase aggregate deformation

We report a first application of an improved second-order (SO) viscoplastic self-consistent model for multiphase aggregates, applied to an olivine+diopside aggregate as analogue for a dry upper mantle peridotite deformed at 10−15s−1 shear strain rate along a 20-Ma ocean geotherm. Beside known dislocation slip systems, this SO-model version accounts for an isotropic relaxation mechanism representing ‘diffusion-related’ creep mechanisms in olivine. Slip-system critical resolved shear stress (CRSS) are evaluated in both phases – as functions of P, T, oxygen fugacity (fO2) and strain rate – from previously reported experimental data obtained on single crystals and first-principle calculations coupled with the Peierls–Nabarro model for crystal plasticity; and the isotropic-mechanism dependence on T and P matches that of Si self-diffusion in olivine, while its relative activity is constrained by reported data. The model reproduces well the olivine and diopside lattice preferred orientations (LPO) produced experimentally and observed in naturally deformed rocks, as well as observed sensitivities of multiphase aggregate strength to the volume fraction of the hard phase (here diopside). It shows a significant weakening of olivine LPO with increasing depth, which results from the combined effects of the P-induced [100]/[001] dislocation-slip transition and the increasing activity with T of ‘diffusion-related’ creep. This work thus provides a first quantification of the respective effects of [100]/[001] slip transition and diffusion creep on the olivine LPO weakening inducing the seismic anisotropy attenuation observed in the upper mantle.

Self-consistent Scale-bridging Approach to Compute the Elasticity of Multi-phase Polycrystalline Materials

ABSTRACTA necessary prerequisite for a successful theory-guided up-scale design of materials with application-driven elastic properties is the availability of reliable homogenization techniques. We report on a new software tool that enables us to probe and analyze scale-bridging structure-property relations in the elasticity of materials. The newly developed application, referred to as SC-EMA (Self-consistent Calculations of Elasticity of Multi-phase Aggregates) computes integral elastic response of randomly textured polycrystals. The application employs a Python modular library that uses single-crystalline elastic constants Cij as input parameters and calculates macroscopic elastic moduli (bulk, shear, and Young's) and Poisson ratio of both single-phase and multi-phase aggregates. Crystallites forming the aggregate can be of cubic, tetragonal, hexagonal, orthorhombic, or trigonal symmetry. For cubic polycrystals the method matches the Hershey homogenization scheme. In case of multi-phase polycrystalline composites, the shear moduli are computed as a function of volumetric fractions of phases present in aggregates. Elastic moduli calculated using the analytical self-consistent method are computed together with their bounds as determined by Reuss, Voigt and Hashin-Shtrikman homogenization schemes. The library can be used as (i) a toolkit for a forward prediction of macroscopic elastic properties based on known single-crystalline elastic characteristics, (ii) a sensitivity analysis of macro-scale output parameters as function of input parameters, and, in principle, also for (iii) an inverse materials-design search for unknown phases and/or their volumetric ratios.

Multi-phase Construction Sequences and Aggregate Site Complexes of the Prehistoric Windward Society Islands (French Polynesia)

ABSTRACT In the Society Islands, concentrations of temple sites, as are found in aggregate site complexes, are considered material equivalents of kin-congregations where lineages proliferated and segmented through time. Such site complexes are ubiquitous in the Windward Society Islands; however, few have been studied in detail, leaving the precise timing of their construction and use unknown. Excavations at ‘Opunohu Valley aggregate complexes in the 1960s suggested that major marae complexes served as elite centers and were a late phenomenon. Here I present a new suite of radiocarbon determinations from ‘Opunohu Valley structures in five aggregate site complexes. The expanded chronology identifies two different phases of site construction, the first dating to ca. AD 1400–1500 and associated with a major inland expansion, the second post-dating AD 1600 and related to a period of intensified chiefly competition whereby new temples and elaborate house sites were constructed or enlarged and elaborated. The initial construction of temple structures within aggregate sites is both earlier than once thought and multi-staged, linked to community and regional socio-political change expressed at the local level. I briefly outline the implications for aggregate site construction and use and correlate these to ethnohistoric references regarding shifting patterns of political control through time.

Scale-Dependent Homogenization of Inelastic Random Polycrystals

Rigorous scale-dependent bounds on the constitutive response of random polycrystalline aggregates are obtained by setting up two stochastic boundary value problems (Dirichlet and Neumann type) consistent with the Hill condition. This methodology enables one to estimate the size of the representative volume element (RVE), the cornerstone of the separation of scales in continuum mechanics. The method is illustrated on the single-phase and multiphase aggregates, and, generally, it turns out that the RVE is attained with about eight crystals in a 3D system. From a thermodynamic perspective, one can also estimate the scale dependencies of the dissipation potential in the velocity space and its complementary potential in the force space. The viscoplastic material, being a purely dissipative material, is ideally suited for this purpose.

High pressure deformation in two-phase aggregates

We investigate the rheological behavior of multi-phase aggregates at high pressure and high temperature. Using synchrotron X-ray radiation as the probing tool, we are able to quantify the stress state of individual phases within the aggregates. This method provides fundamental information in interpreting the behavior of two phase/multi-phase mixtures, which contribute to our understanding of the deformation process at deep earth conditions. We choose MgAl 2O 4 spinel and MgO periclase as our model materials. Mixtures of various volume proportions were deformed in a multi-anvil high pressure deformation apparatus at pressure of 5 GPa and elevated temperatures. Stress is determined from X-ray diffraction, providing a measure of stress in each individual phase of the mixture in situ during the deformation. Macroscopic strain is determined from X-ray imaging. We compare the steady state strength of various mixtures at 1000 °C and 800 °C and at the strain rate in the range of 1.8 to 8.8 × 10 − 5 s − 1 . Our data indicate that the weak phase (MgO) is responsible for most of the accumulated strains while the strong phase (spinel) is supporting most of the stress when the volume proportion is 75% spinel and 25% MgO. The intermediate compositions (40/60) are much weaker than either of the end members, while the grain sizes for the intermediate compositions (submicrons) are much smaller than the end members (5–10 μm). We conclude that a change in flow mechanism resulting from these smaller grains is responsible for the low strength of the intermediate composition mixtures. This study demonstrates an approach of using synchrotron X-rays to study the deformation behaviors of multi-phase aggregates at high pressure and high temperature.