Influence of grain size variability on the strain rate dependence of the stress exponent in mixed-mode power law and dif
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I. INTRODUCTION
POWER LAW creep and diffusional creep represent the two principal mechanisms of high-temperature deformation in metals. The first, being primarily related to the climb and the substructure of dislocations, depends only on the properties of the grain matrix. Instead, diffusional creep depends on mass transport across distances of the grain size, and is therefore sensitive to the grain size, which we call d. The existence of two independent paths for diffusion, one through the grainmatrix[1] and the other along the grain boundaries,[2] means that diffusional creep can depend predominantly on either lattice or volume self-diffusion, DV, or on grain boundary selfdiffusion, DB. Power law creep,[3] on the other hand, being a crystal dislocation phenomenon, depends only on DV. These three mechanisms, thus, contribute independently and addi# tively to the total strain rate , which may now be written as # # # # [1] P V B # where P represents the strain rate from power law creep, # # and V and B the strain rates from volume diffusion and grain boundary diffusion dominated diffusional creep. Using the notation of Frost and Ashby,[4] Eq. [1] can be explicitly written as DV Gb s nˆ s DV s pdB DB # a b 14 A 2 14 kT G kT d kT d3
[2]
The parameter d represents the size of the grains in a twodimensional view of the polycrystal. It is, therefore, directly proportional to the mean intercept length of the grain size in a planar cross section. The other parameters in Eq. [2] are as follows: is the atomic volume; b, the interatomic spacing, is assumed equal to 1/3, and G is the shear modulus. The strain rate and the J. BAI, Research Associate, and R. RAJ, Professor, are with the Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, CO 80309-0427. Contact e-mail: [email protected] Manuscript submitted February 19, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS A
stress refer to a simple uniaxial tensile (or compressive) test. # # Note that B differs from V by a factor of B/d, where B is the effective diffusive width of the boundary: this factor reflects the ratio of the effective diffusion cross section for volume and boundary diffusivities for transporting atoms across these grains. The power law stress exponent is nˆ (its ideal value), which lies between 4 and 5 for most pure metals. Equation [2] has special features that can be tested experimentally. (a) The stress dependence: the power law stress exponent represents dislocation creep, while a linear relationship between stress and strain rate indicates the dominance of diffusion creep. (b) Grain size dependence: diffusional creep depends strongly on the grain size, while power law creep is independent of it. (c) Temperature dependence: the activation energy for boundary diffusion is about six-tenths the value for volume diffusion, which can serve to distinguish volume and boundary diffusion-controlled mechanisms of diffusional creep. The most satisfying evidence for the presence of power law creep and
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