Institute of Metals Division - Deformation Resulting from Grain Boundary Sliding

This paber is concerned with the determination of equations relating elongation to the amount of shear taking place both along grain boundaries and in slip planes of poly crystalline aggregates during creep. Certain discrepancies with previously used equations are pointed out. Grain boundaries were observed to become serrated during creep, but it is shown that this does not necessarily prevent further grain boundary sliding. Direct obser-vations of subgrain boundary ingration lead to the conclusion that this migration facilitates sliding along serrated grain boundaries. It is bointed out that the state of stress at triple boints is still unknown. MOST of the mechanisms of deformation contributing to elongation are shear processes, such as slip, kinking, grain boundary sliding, and twinning. For quantitative investigations of individual deformation mechanism it is necessary to know the equation which permits the calculation of speci-tnen elongation from measured amounts of shear. This calculated elongation must then be compared with the observed total elongation. The authors' special interest concerned grain boundary sliding during creep. Although this subject has already been investigated quantitatively by McLean,' Rachinger,' and Fazan, Sherby, and Dorn, calculations indicated that none of the equations used thus far to relate shear with elongation were sufficiently well founded. A basic study of this relationship was thus made and the results of this study (which do not entirely agree with those previously used) are presented. Most of the ideas set forth apply not only to grain boundary sliding but to other mechanisms of shear as well. THE SPEAR-ELONGATION RELATIONSHIP Basic Models—The relationship between shear and elongation is trivial in the simplest case of shear, which is shown in Fig. l(a). The vector A; designates the displacement across the shear interface, and Au, and Aut are its components parallel and normal to the tensile direction, respectively. It is evident that the specimen elongation due to shear is equal to the longitudinal component of the shear vector, and it should be noted that the normal component does not contribute to the elongation of the specimen (there are, of course, two normal components in a three-dimensional model). The model shown in Fig. l(b) may be applied to mechanical twinning and to subgrain boundary tnigration. In this case the width (h) of an already existing shear band increases by the migration of an interface, but the shear angle y (angle of mis-orientation in the case of a subgrain boundary) remains constant. The geometrical relationships indicated in Fig. l(b) permit this case to be reduced to the one shown in Fig. l(a). For the resulting elongation A6 we find: where AV/V = fraction of the volume of the specimen swept by migrating interfaces , and 1 = length of specimen. Thus, assuming for example that the angle of mis-orientation is 1 deg, and that P = 45 deg, we find that the specimen elongates 0.87 pct of its length if the entire volume of the specimen is swept once by such a subgrain boundary. An example of deformation by migration of subgrain boundaries is shown in Fig. 2. The specimen shown was repolished after 9.8 pct creep strain and the test then continued for another \ pct. Since the shear vector has, in general, a component normal to the surface, subgrain boundary migration results in the formation of an inclined band delineating the region swept by the subgrain boundary. These inclined bands become clearly visible when observed with oblique illumina-