Stress concentrations, diffusionally accommodated grain boundary sliding and the viscoelasticity of polycrystals

Abstract

Using analytical and numerical methods, we analyse the Raj-Ashby bicrystal model of diffusionally accommodated grain-boundary sliding for finite interface slopes. Two perfectly elastic layers of finite thickness are separated by a given fixed spatially periodic interface. Dissipation occurs by time-periodic shearing of the viscous interfacial region, and by time-periodic grain-boundary diffusion. Although two time scales govern these processes, of particular interest is the characteristic time t D for grain-boundary diffusion to occur over distances of order of the grain size. For seismic frequencies ut D 1, we find that the spectrum of mechanical loss Q -1 is controlled by the local stress field near corners. For a simple piecewise linear interface having identical corners, this localization leads to a simple asymptotic form for the loss spectrum: for ut D 1, Q −1 ∼ const.u −a . The positive exponent a is determined by the structure of the stress field near the corners, but depends both on the angle subtended by the corner and on the orientation of the interface; the value of a for a sawtooth interface having 120• angles differs from that for a truncated sawtooth interface whose corners subtend the same 120• angle. When corners on an interface are not all identical, the behaviour is even more complex. Our analysis suggests that the loss spectrum of a finely grained solid results from volume averaging of the dissipation occurring in the neighbourhood of a randomly oriented three-dimensional network of grain boundaries and edges.

Mechanisms and geologic significance of the mid-lithosphere discontinuity in the continents

“…Finally, we note that if EAGBS were as ubiquitous as theory implies [14][15][16] , then the interpretation of seismological observations of any hot, solid regions of Earth based on single crystal elasticity would require a significant revision. showing the conditions at which EAGBS occurs (red lines) and geotherms (black lines) for two models, one with homogenous water content (i), and one with a layer of high water content (ii); corresponding seismic velocity versus depth relations are shown in (iii) and (iv), respectively.…”

“…This leads to a reduced elastic modulus and hence a reduced seismic velocity for a polycrystalline aggregate. Elastic accommodation changes gradually to diffusional accommodation at higher temperatures (and lower frequencies) leading to diffusion creep 16 . Both theoretical and experimental studies show that the velocity reduction by EAGBS is large (several per cent) [14][15][16] (for more details, see Supplementary Information section II).…”

“…Elastic accommodation changes gradually to diffusional accommodation at higher temperatures (and lower frequencies) leading to diffusion creep 16 . Both theoretical and experimental studies show that the velocity reduction by EAGBS is large (several per cent) [14][15][16] (for more details, see Supplementary Information section II). Although highly limited, experimental observations that are consistent with EAGBS are available for upper mantle materials [33][34][35] .…”

“…We find that none of these models is consistent with the global presence of the MLD and the nearly depth-independent ages of mantle rocks from many old continents. We propose that this puzzle might instead be resolved by invoking a well-established, but thus far underappreciated subsolidus deformation mechanism -elastically accommodated grain-boundary sliding (EAGBS) -that operates in any polycrystalline material at a modestly elevated temperature [14][15][16][17] . The EAGBS model of the MLD is consistent with the concept of stable continental lithosphere, although the depth of the MLD is predicted to vary depending on the past evolution of the continental lithosphere.…”

Lithospheric low-velocity zones associated with a magmatic segment of the Tanzanian Rift, East Africa

“…Olugboji et al (2013) show that the reduction of velocity produced by EAGBS is recordable by P-receiver functions, depending on the sharpness of the velocity contrast created. This process has already been proposed to explain mid-lithospheric discontinuities (MLD Faul & Jackson 2005;Selway et al 2014) but gradually leads to diffusion creep processes with increasing temperature (Lee et al 2011). EAGBS is then usually restricted to uppermost mantle depth, even if the presence of a secondary phase of low viscosity (e.g.…”