HR: 17:45h
AN: MR34A-08    [Abstracts]
TI: Modelling the Contrasting Viscoelastic Behaviours of Melt--Free and Melt--Bearing Olivine
AU: * Morris, S
EM: morris@me.berkeley.edu
AF: Mechanical Engineering, University of California, Berkeley, CA 94720 United States
AU: Jackson, I
EM: Ian.Jackson@anu.edu.au
AF: Research School of Earth Sciences, Australian National University, Canberra, ACT 2600 Australia
AB: Torsional oscillation experiments on polycrystalline olivine show that the viscoelastic behaviour is strongly affected by the presence of melt. For melt--free samples, the dissipation Q^-1 per cycle decreases monotonically with increasing oscillation frequency ω, but melt--bearing samples exhibit a dissipation peak. To explain that difference, we analyse a simplified continuum model. In it, the sample occupies the gap -d Met. Trans., 2, 1113, 1971). Analysis of our model shows that the strain γ(t) measured at the boundaries y=± d is given in terms of the applied stress σ(t) by the differential equation 2M(d²γ/dt² +2 dγ/dt)= d²σ/dt² +{2(1+M) +HM} dσ/dt + 2HMσ,    Equation (1)
where time t and strain γ are respectively measured in units η' d/bμ' and σ_s/μ. The control parameters M and H are defined by M=μ/μ' >> and >> H= η' d/bη, so that H is the ratio of the sliding timescale η' d/μ b to the Maxwell timescale η/μ of the grain. The behaviour predicted by (1) proves to be identical to that of a Burgers solid. By solving (1) for periodic forcing, we find there are two cases: (a) if H<1/4, there is a dissipation peak for all values of M; (b) if H>1/4, there is a peak only if M> 2(4H-1)/(H+2). In case (a) the timescales are sufficiently separated that a peak always exists, but in case (b), the timescales are so close together that a peak only exists if sliding is facilitated by making the boundary rigidity μ' sufficiently small compared with the grain rigidity. These conclusions are consistent with those of Faul, Fitz Gerald & Jackson ( JGR, 109, B06202; 58, 60, 2004). Since their microcreep tests demonstrated a continuous evolution from elastic through anelastic to viscous behaviour, they inferred that in their experiments the Maxwell and sliding timescales could not be widely separated. They also argued physically that rounding of grain corners promotes the formation of a dissipation peak by enhancing grain boundary sliding. Their conclusions are consistent with case (b) above, since the work of Raj & Ashby implies that M is increased by decreasing the ratio of grain diameter to grain corner radius. Our model thus consolidates the physical reasoning previously used to interpret the olivine experiments, and also summarizes the processes we need to include in more detailed micromechanical modelling.
DE: 1015 Composition of the core
DE: 1025 Composition of the mantle
DE: 3900 MINERAL PHYSICS
DE: 5100 PHYSICAL PROPERTIES OF ROCKS
DE: 8124 Earth's interior: composition and state (1212, 7207, 7208, 8105)
SC: Mineral and Rock Physics [MR]
MN: Fall Meeting 2005