Melt-band instabilities with two-phase damage

Rudge, John F.; Bercovici, David

doi:10.1093/gji/ggv040

Cited by 16 publications

(14 citation statements)

References 28 publications

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“…Linear stability analysis shows that melt bands are expected to initially grow at a rate proportional to a weakening factor

α = normald \log η false/ normald ϕ

(Spiegelman, ; Stevenson, ), which is plotted as a function of porosity for the rheologies considered here in Figure . Modeling work on this instability (e.g., Bercovici & Rudge, ; Katz et al, ; Rudge & Bercovici, ; Takei & Katz, ) has typically used an empirical rheological law of the form

η \propto \exp false(αϕ false)

, with constant α ∼− 26, based on a fit to experimental data by Mei et al (). As pointed out by Takei and Holtzman () for Coble creep, the microscale calculations predict a weakening factor α which varies with porosity.…”

Section: Discussionmentioning

confidence: 99%

The Viscosities of Partially Molten Materials Undergoing Diffusion Creep

Rudge

2018

JGR Solid Earth

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Partially molten materials resist shearing and compaction. This resistance is described by a fourth‐rank effective viscosity tensor. When the tensor is isotropic, two scalars determine the resistance: an effective shear and an effective bulk viscosity. Here calculations are presented of the effective viscosity tensor during diffusion creep for a 2‐D tiling of hexagonal unit cells and a 3‐D tessellation of tetrakaidecahedrons (truncated octahedrons). The geometry of the melt is determined by assuming textural equilibrium. The viscosity tensor for the 2‐D tiling is isotropic but that for the 3‐D tessellation is anisotropic. Two parameters control the effect of melt on the viscosity tensor: the porosity and the dihedral angle. Calculations for both Nabarro‐Herring (volume diffusion) and Coble (surface diffusion) creep are presented. For Nabarro‐Herring creep the bulk viscosity becomes singular as the porosity vanishes. This singularity is logarithmic, a weaker singularity than typically assumed in geodynamic models. The presence of a small amount of melt (0.1% porosity) causes the effective shear viscosity to approximately halve. For Coble creep, previous modeling work has argued that a very small amount of melt may lead to a substantial, factor of 5, drop in the shear viscosity. Here a much smaller, factor of 1.4, drop is obtained for tetrakaidecahedrons. Owing to a Cauchy relation symmetry, the Coble creep bulk viscosity is a constant multiple of the shear viscosity when melt is present.

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“…Linear stability analysis shows that melt bands are expected to initially grow at a rate proportional to a weakening factor

α = normald \log η false/ normald ϕ

η \propto \exp false(αϕ false)

Section: Discussionmentioning

confidence: 99%

The Viscosities of Partially Molten Materials Undergoing Diffusion Creep

Rudge

2018

JGR Solid Earth

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“…This behavior, along with the fact that melt bands form for a larger

(α, R)

parameter space away from the inclusion than near it, are indications that in our models the pressure shadows around the inclusion are dominant over any bands that form in simulations with random heterogeneities. Several recent studies investigate alternative constitutive relations [ Takei and Katz , ; Katz and Takei , ; Rudge and Bercovici , ] that could potentially affect the balance of pressure shadows and melt‐rich band formation near the inclusion.…”

Section: Discussionmentioning

confidence: 99%

Torsion of a cylinder of partially molten rock with a spherical inclusion: Theory and simulation

Alisic

Rhebergen

Rudge

et al. 2016

Geochem Geophys Geosyst

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The processes that are involved in migration and extraction of melt from the mantle are not yet fully understood. Gaining a better understanding of material properties of partially molten rock could help shed light on the behavior of melt on larger scales in the mantle. In this study, we simulate threedimensional torsional deformation of a partially molten rock that contains a rigid, spherical inclusion. We compare the computed porosity patterns to those found in recent laboratory experiments. The laboratory experiments show emergence of melt-rich bands throughout the rock sample, and pressure shadows around the inclusion. The numerical model displays similar melt-rich bands only for a small bulk-to-shearviscosity ratio (five or less). The results are consistent with earlier two-dimensional numerical simulations; however, we show that it is easier to form melt-rich bands in three dimensions compared to two. The addition of strain-rate dependence of the viscosity causes a distinct change in the shape of pressure shadows around the inclusion. This change in shape presents an opportunity for experimentalists to identify the strain-rate dependence and therefore the dominant deformation mechanism in torsion experiments with inclusions.

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“…This raises the question of whether the strain rate field, through its influence on viscosity and grain size, can explain melt focusing in the full model. Various studies have shown that if there is an instantaneous balance of the rates of grain growth and reduction on the right‐hand side of equation , then the mean grain size is given by a power law of the strain rate (Barr & McKinnon, ; Rozel et al, ; Rudge & Bercovici, ). This can be substituted into equation for shear viscosity, and hence, the grain‐size dependence can be combined with the strain rate dependence into a single power law with an exponent

n_{e} = [n (p + 1) + m] / (p - m + 1)

.…”

Section: Model Sensitivitymentioning

confidence: 99%

“…Beyond the question of the active deformation mechanism(s), these differences in n e arise from uncertainities in the grain growth exponent p and grain rheology exponent m . Hence, it is appropriate to consider the dynamics across a range of values of the effective stress dependence (e.g., Rudge & Bercovici, ).…”

Section: Model Sensitivitymentioning

confidence: 99%

Magmatic Focusing to Mid‐Ocean Ridges: The Role of Grain‐Size Variability and Non‐Newtonian Viscosity

Turner

Katz

Behn

et al. 2017

Geochem Geophys Geosyst

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Melting beneath mid‐ocean ridges occurs over a region that is much broader than the zone of magmatic emplacement that forms the oceanic crust. Magma is focused into this zone by lateral transport. This focusing has typically been explained by dynamic pressure gradients associated with corner flow, or by a sublithospheric channel sloping upward toward the ridge axis. Here we discuss a novel mechanism for magmatic focusing: lateral transport driven by gradients in compaction pressure within the asthenosphere. These gradients arise from the covariation of melting rate and compaction viscosity. The compaction viscosity, in previous models, was given as a function of melt fraction and temperature. In contrast, we show that the viscosity variations relevant to melt focusing arise from grain‐size variability and non‐Newtonian creep. The asthenospheric distribution of melt fraction predicted by our models provides an improved explanation of the electrical resistivity structure beneath one location on the East Pacific Rise. More generally, we find that although grain‐size and non‐Newtonian viscosity are properties of the solid phase, their effect on melt transport beneath mid‐ocean ridges is more profound than their effect on the mantle corner flow.

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Melt-band instabilities with two-phase damage

Cited by 16 publications

References 28 publications

The Viscosities of Partially Molten Materials Undergoing Diffusion Creep

The Viscosities of Partially Molten Materials Undergoing Diffusion Creep

Torsion of a cylinder of partially molten rock with a spherical inclusion: Theory and simulation

Magmatic Focusing to Mid‐Ocean Ridges: The Role of Grain‐Size Variability and Non‐Newtonian Viscosity

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