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Mathematics and Mechanics of Solids
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Transient Stress Concentration in Diffusional Creep of a Thin Foil with Heterogeneous Grain Boundary Diffusivity

T.K. Bhandakkar

Division of Engineering, Brown University, 182 Hope St, Providence, RI 02912, USA

Y. Wei

Division of Engineering, Brown University, 182 Hope St, Providence, RI 02912, USA

H. Gao

Division of Engineering, Brown University, 182 Hope St, Providence, RI 02912, USA

Coble creep in thin films with heterogeneous grain boundary (GB) diffusivity and non-uniform grain size is investigated in the model problem of a thin foil with a high diffusivity GB joined with a low diffusivity GB of unequal length and subjected to a far field uniaxial tensile stress. It is found that a transient stress peak emerges near the GB junction on the characteristic time scale of the high diffusivity boundary and then disappears when the system reaches steady-state on the characteristic time scale of the low diffusivity boundary. We show that for a given GB size ratio, this stress depends logarithmically on the GB diffusivity ratio. Based on the GB diffusivity and size ratios, we present a diagram demarcating the regime in which peak stress is determined by the steady state solution and that determined by the transient stress solution.

Key Words: Diffusivity • grain boundary • grain size • integral equation

Mathematics and Mechanics of Solids, Vol. 14, No. 1-2, 179-191 (2009)
DOI: 10.1177/1081286508092610
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