HR: 1340h
AN: MR13C-1402    [Abstracts]
TI: A Finite Element Study of Elastically-Accommodated Grain Boundary Sliding
AU: * Lee, L
EM: likchuan@berkeley.edu
AF: Mechanical Engineering, University of California at Berkeley, 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 0200, Australia
AU: Morris, S
EM: morris@me.berkeley.edu
AF: Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720, United States
AU: Zohdi, T
EM: zohdi@me.berkeley.edu
AF: Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720, United States
AB: Grain--boundary sliding is an important, but still poorly understood aspect of high--temperature viscoelastic behaviour. As a first step in the development of a numerical model of diffusionally--assisted grain boundary sliding in a polycrystalline material, we report on the numerical solution of the Raj--Ashby model. In that model, two identical elastic grains of rigidity μ and mean thickness d are separated by a spatially-periodic boundary having prescribed location. Two constitutive equations relate the normal n and tangential s components of the discontinuity in velocity [∂ u /∂ t] to appropriate components of the stress tensor. The first of these, ℓ σ_ns = η [∂ u_s/ ∂ t], confers Newtonian viscosity η upon the boundary region of thickness ℓ, and the associated sliding timescale is t_η = η d / μ ℓ. Secondly, because we do not include diffusion in the model (at this point), the normal component of velocity is continuous across the interface, i.e, [∂ u_n/∂ t ]=0. The deformation of the sample is driven by a sinusoidally time-varying shear displacement imposed at the distal boundaries of the two grains. The grain boundary is represented by N terms of the Fourier series for a sawtooth (piecewise linear) boundary whose linear segments make angles ± θ with the direction of that imposed displacement. Our numerical results show that the model behaves like a standard anelastic solid, characterized by a Debye dissipation peak. For small θ, our results agree quantitatively with the predictions of the perturbation analysis reported by two of us at this meeting last year. As θ is increased, the sliding amplitude decreases and, as a result, the relaxed shear modulus G_R increases whereas the mechanical loss (i.e. L = \mbox{tan arg } G) decreases. As θ increases from 5° to 45°, L decreases by a factor of about 1000, and for θ > 45°, L increases weakly. In fact, due to the non-monotonic behaviour of L with θ, we predict a value of L ≈ 0.1 for θ=60° and θ=30°; close to the value 0.09 found by Ghahremani (1980) in his finite element study of elastically--accommodated grain boundary sliding in an array of hexagonal crystals. As suggested by Faul et al. (2002), we also find that because sharp corners inhibit sliding by inducing stress concentrations, increasing N inhibits sliding, and so causes the maximum value of L to decrease; increasing N from 1 to 100 reduces L by about 4--fold. We are now adding diffusion to our numerical solution of the Raj-Ashby model.
DE: 3902 Creep and deformation
DE: 5112 Microstructure
DE: 5120 Plasticity, diffusion, and creep
DE: 5144 Wave attenuation
DE: 7260 Theory
SC: Mineral and Rock Physics [MR]
MN: 2007 Fall Meeting