Part XII - Communications - Calculation of the Deformation Caused By Grain Boundary Sliding During the Creep of Polycrystalline Solids

GRAIN boundary sliding plays a part in the high-temperature deformation of polycrystalline solids, and many investigations1-11 have been carried out to determine the deformation contributed by this mechanism. The principal method employed has been to measure one of the components of the grain boundary displacement, see Fig. 1, at a large number of boundaries, and from the mean value so obtained to calculate the elongation contributed by sliding. A formula connecting these mean values and the elongation contributed is evidently required, and many have been derived. They are usually of the form where Egh is the tensile elongation contributed by sliding, is the mean value of the component, x, N is the mean number of grain boundaries intersecting a line of unit length, and K is a dimensionless parameter known as the averaging factor. Table I summarizes the equations used by various investigators. Examination of these shows that their derivations usually involve doubtful assumptions, and are often in serious error. The purpose of this note is to point out that rigorous solutions to the problem of calculating Egb from x have been available in the literature for some years.' Since this is so little known, and also the original derivations do not make some important points clear, it is proposed to rederive the basic equations. These will be extended further, and the conditions in which the extended equations may be applied will be indicated. The mean values of the components of the sliding vector (I, d, and I:, Fig. 1) will depend on the method by which boundaries are sampled in order to make measurements.3,11 Boundaries are usually sampled by marker lines parallel to the stress axis, or lines perpendicular to the stress axis, the measurement being made at the point where the marker line intercepts the boundary. We will denote the mean values determined by these various sampling methods as follows. lT, dT and vT are mean values obtained by making measurements at pointswhere a transverse line intercepts the boundary while lL, dL, and vl, are the mean values from a longitudinal line. The number of boundaries per unit length also may depend on the direction of measurement, and so we define NT and Nl to be the number of boundaries per unit length, after creep, in the transverse and longitudinal directions, respectively.