Coble-creep response and variability of grain-boundary properties
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A microstructural model of steady-state creep that couples grain-boundary transport, micromechanics, and grain sliding is employed to investigate the grain-boundary diffusional creep response of an idealized microstructure with variable boundary diffusivities. Both numerical and analytical methods were used to determine the stress state and, in some cases, the strain rate associated with an applied uniaxial, tensile stress. Various types of boundaries are considered, and the implications of our results for more general microstructures are discussed.
I. INTRODUCTION
The long-time strain response of creeping systems subjected to a uniaxial stress is an important design consideration for both metals and ceramics. The creep behavior of these systems is often complex and governed by various mechanisms, including those involving diffusional transport and grain-boundary dislocation motion. In particular, diffusional creep occurs via a mass flux in either the bulk and/or at grain boundaries driven by a gradient in the chemical potential field attending the stressed state1–8 while dislocation-based creep occurs via the climb and glide of grain-boundary dislocations.9–12 The dominant mechanism for a given system can sometimes be inferred from the power-law dependence of the strain rate on stress and average grain size by a comparison of extracted exponents with those predicted by simple calculations. The functional form of the grain-boundary diffusional creep law has been determined analytically from highly idealized microstructural models that couple mass transport and grain micromechanics and are based on either the behavior of a representative grain3,13 or the response of spatially uniform systems consisting of a repeat unit.14,15 The restrictive assumptions inherent in these simple models make them tractable while inevitably limiting their applicability to real systems. More sophisticated microstructural models are amenable to numerical analysis and have been employed recently to assess the impact of variable grain size and shape on aggregate creep response.16,17 It should be noted, however, that in many cases the strain rate dependence on grain size is unchanged in more complex microstructures, apart from a prefactor, as can be seen from dimensional analysis. An important factor affecting creep behavior that has not been considered in earlier microstructural models is the variability in grain-boundary properties, especially 348
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J. Mater. Res., Vol. 17, No. 2, Feb 2002 Downloaded: 16 Mar 2015
the diffusivity. In general, the boundary diffusivity correlates with detailed boundary geometry, and some empirical relations have been formulated to quantify this interrelationship between structure and kinetics.18,19 Furthermore, there is evidence that grain-boundary segregation can inhibit diffusion in some systems by constricting nominally fast diffusion pathways.20 Indeed, this “blocking” effect has been invoked to explain the observed decrease in secondary creep rate in selectively doped cer
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