Evolution of grain-boundary serration in fatigue

Abstract

Mandelbrot and co-workers first found that there is a correlation between the fractal dimension of ffacture surfaces and the absorbed energy in impactloaded and fractured steels [1]. Since then, the concept of fractal geometry has been applied to research work in materials engineering. For example, the ffactal dimension of slip lines was obtained by Kleiser and Bocek on deformed Cu and Co crystals [2], although the physical meaning of the value is not clear [3]. Plastic deformation of polycrystalline metals results in the formation of steps and ledges on grain boundaries and leads to change in the grain-boundary configuration (the change in the fractal dimension of the grain boundary) or shape of the grains [4, 5]. In the study reported here, the change in the fractal dimension of the grain boundary was examined in fatigue specimens (100 mm length, 10 mm width and about 1 mm thickness) of a ferritic l lCr-0.4Ti steel and an austenitic SUS316 steel [6]. The fatigue specimens were electrolytically polished and etched before fatigue tests. The average grain diameter was 50/~m for the 11Cr-0.4Ti steel and 31/~m for the SUS316 steel. The fatigue specimens were cyclically bent to cause the maximum strain amplitude at the broadest specimen surfaces (10 mm x 100 mm) along the length direction, using a strain-controlled fatigue testing equipment of repeated bending type used in the previous study [6]. The maximum strain amplitude at the specimen surface is referred to as the strain amplitude, Ae, in this study. The strain amplitude and the number of cycles to failure (N 0 in the fatigue tests were 0.0106 and about 2450 cycles for the specimen of the l lCr-0.4Ti steel, and 0.0122 and about 8300 cycles for that of the SUS316 steel. Optical or scanning electron micrographs of the specimen surface were taken after a given fatigue cycling. The fractal dimension of the grain boundary in the fatigue specimens was obtained by the coarse-graining method using line segments [7, 8]. The lengths of ten grain boundaries (cracked grain boundaries were excluded) were examined at given fatigue cycles on each specimen in the fractal analysis. Fig. 1 shows the relationship between the length of grain boundaries, L, and the scale of the fractal analysis, s, in the fatigue specimens of l lCr-0.4Ti steel. The relationship cannot be fitted to a single line. The scale range from about 3 x 10 -7 to about 4 x 10 .6 m corresponds to the scale range in which a fractal nature of slip steps was observed on the fracture surface profile of the 31 wt % Mn steel