A Constitutive Equation for Grain Boundary Sliding: An Experimental Approach
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INTRODUCTION
TIME-DEPENDENT creep deformation depends on the temperature, stress, and grain size, among other factors, and the steady-state creep rate can be expressed as[1] ADGb b p r n ; ½1 e_ ¼ kT d G where A is a dimensionless constant, D is the diffusion coefficient, G is the shear modulus, b is the magnitude of the Burgers vector, K is Boltzmann’s constant, T is the absolute temperature, d is the grain size, r is the applied stress, and p and n are termed the inverse grain size exponent and stress exponent, respectively. The diffusion coefficient can be expressed as D = D0 exp(Q/ RT), where D0 is a pre-exponential term, Q is the activation energy for the appropriate process, and R is the gas constant. The rate controlling creep mechanisms are identified by comparing the theoretical and experimental values of n, p and Q, together with relevant microstructural characterization. Grain boundary sliding (GBS) is an important deformation mechanism under some experimental conditions,[1–3] and it is frequently responsible for cavitation failure during high-temperature testing.[4,5] In some materials such as Mg alloys, with a limited number of slip systems, GBS has been reported during roomtemperature deformation.[6] GBS has also been considered as a possible deformation mechanism in ultrafine grained and nanocrystalline materials.[7,8] Despite its RAJESH KORLA, Graduate Student, and ATUL H. CHOKSHI, Professor, are with the Department of Materials Engineering, Indian Institute of Science, Bangalore 560 012 India. Contact e-mail: [email protected] Manuscript submitted October 29, 2012. Article published online October 30, 2013 698—VOLUME 45A, FEBRUARY 2014
importance under a wide range of conditions, there is surprisingly little experimental data available on constitutive equations for GBS. Cannon[9] suggested that GBS can be considered separately as (a) Lifshitz[10] sliding which accompanies diffusion creep, leading to grain elongation along the tensile axis without any increase in the number of surface grains, and (b) Rachinger[11] sliding involving the retention of an equiaxed grain structure with an increase in the number of surface grains. Following Langdon and Vastava,[12] it is convenient to examine models for GBS broadly as intrinsic and extrinsic. Intrinsic models relate to sliding where there is no need to consider an accommodation process, such that sliding is limited by an intrinsic process. In contrast, extrinsic models consider an accommodation process that controls the rate of sliding. In principle, it is possible to develop an expression for strain rate by GBS, e_ GBS , in a manner similar to Eq. [1], with the subscript GBS to denote the values of the various parameters for GBS. Table I summarizes expressions developed for several models for GBS.[13–21] It has been noted that the experimental data for GBS are not consistent with many of the models proposed.[12] Excluding data from superplasticity studies and bicrystals, there have been only four reports with data for GBS constit
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