Effects of Cold Work on the Fractal Dimension of Grain Boundaries in Pure Iron

Abstract

The effects of cold work on the fractal dimension of grain boundaries (FDGB) were investigated using cold-worked (cold-upsetted) specimens of pure iron. The change in the grain-boundary configuration with cold work was analysed principally by the coarse-graining method (CGM) using line segments in this study. The FDGB was estimated from the relationship between the length of grain perimeter and the scale length in fractal analysis in the scale range from about 5 x 10 -7 to 3 x 10 -6 m, which was correlated to the size range of slip line spacing (4.5 x 10- 7 to 3.4 x 10 -6 m) in the cold-worked specimens of pure iron. The FDGB increased from about 1.05 to 1.15 with increasing amount of cold work (ACW) in the range from 0% to about 50% of cold reduction, but it remained almost unchanged when the ACW exceeded about 50%. The increase of the FDGB was associated with an increase of the density of slip lines within the grains due to the cold work, since the slip lines caused steps and ledges on the grain boundaries, which resulted in an increase of the FDGB. The box-counting method gave a slightly larger value for the FDGB than the CGM.