Role of grain boundary segregation in diffusional creep
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DIFFUSION CREEP IN PURE METALS
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POLYCRYSTALLINE materials deform at high temperatures under light stresses by the viscous mechanism first proposed by Nabarro t and analyzed in detail by Herring. 2 This involves matter transfer between sources and sinks located at grain boundaries and free surfaces held under compression or tension by applied stresses. For a grain structure subjected to a tensile stress tr, the flow of vacancies is from boundaries in tension to boundaries in compression, as shown in Figure 1. Herring's analysis yielded the well-known equation describing the creep rate, = Blo'~Dv/d2kT
[1]
where 1) is the atomic volume, Dv the lattice diffusion coefficient, d the grain size, k Boltzmann's constant, and T the absolute temperature; the numerical constant B1 varies with specimen geometry. These values have been recently tabulated by Burton3 in his review monograph. The earliest observations of diffusional creep were byproducts of experiments designed to measure surface energies of metals using fine cylindrical (wire) specimens with single grains occupying the cross-section and boundaries perpendicular to the stress axis--the so-called "bamboo" structure. 4 At temperatures near the melting point and at very low stresses, such wires or thin foils tend to shrink under capillary forces, whereas higher loads produce an extension. Here, the "zero creep" stress (corresponding to the surface tension) is found by interpolation. In these measurements, strain rates depend linearly on the stress and in numerous studies, for example those on gold4'5 or Fe-Si, 6 E.D. HONDROS, Superintendent, and P.J. HENDERSON, Scientific Officer, are with Division of Materials Applications, National Physical Laboratory, Teddington, Middlesex, United Kingdom TW11 0LW. This paper is based on a presentation made at the symposium "The Role of Trace Elements and Interfaces in Creep Failure" held at the annual meeting of The Metallurgical Society of AIME, Dallas, Texas, February 14-18, 1982, under the sponsorship of The Mechanical Metallurgy Committee of TMS-AIME. METALLURGICALTRANSACTIONS A
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0 Fig. 1 - - T h e flow of vacancies (shown by arrows) in a grain under a tensile stress o-.
there is excellent support for the Nabarro-Herring creep mechanism in that the diffusion coefficient derived from Eq. [1] compares well with the radiotracer lattice diffusivity. In such comparisons, the relevant strain rates are those experienced in the "stable" deformation regime. During the earlier deformation stages, very different strain rates are recorded--here, for copper7 and nickels diffusion coefficients calculated from the Herring equation were an order of magnitude higher than the radiotracer lattice diffusion coefficients. Jones 9 examined this anomaly and suggested that the creep rates were probably measured during a period of transient creep, when dislocations may act as additional vacancy sources and sinks. This is clearly the most plausible explanation for this effect. There is broad agreement that in pure polycrystals, creep rates
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