Atsushi Kayama

ESTIMATION OF THE FRACTAL DIMENSION OF FRACTURE SURFACE PATTERNS BY BOX-COUNTING METHOD

In the box-counting method, positioning of images do not significantly affect the estimation of the fractal dimension of river pattern on the brittle fracture surface, and that of dimple pattern on the ductile fracture surface of materials. A reasonable estimation of the fractal dimension can be made using the box-counting method by a single measurement on the fracture surface pattern. The fractal dimension of dimple pattern in pure Zn polycrystals (about 1.50) is larger than that of river pattern in soda-lime glass (about 1.30). Personal difference in image processing does not have a large influence on the estimation of the fractal dimension of grain-boundary fracture surface profile, compared with the effects of local variation in fracture pattern concerning image size.

Size distribution of surface cracks and crack pattern in austenitic SUS316 steel plates fatigued by cyclic bending

The size distribution of surface cracks and the crack pattern were examined on the specimens of the SUS316 steel plates fatigued by cyclic bending. The size distribution of the cracks could be approximated to a logarithmic normal distribution, irrespective of the maximum total strain range or the number of fatigue cycles. The number of the cracks (Nu) of the length (x′) equal to or larger than a given size (X) could be approximated to a power law, Nu∝ X−a, with a scaling exponent a at the larger crack sizes in the fatigued specimens of the SUS316 steel. The value of a decreased with increasing the number of fatigue cycles because of the increase in the number and size of fatigue cracks, and was larger in the specimens tested at the smaller total strain range. Effects of experimental variables on the scaling exponent (a) were also shown in this study. The fractal dimension of spatial crack distribution (the fractal dimension of crack pattern) (D) increased in the range from about 0.9 to about 1.2 with increasing the number of fatigue cycles, and was larger in the specimens fatigued at the larger total strain range. There was a negative correlation between the value of a and the value of D on fatigue cracks, although there was no unique relationship between these two values.

Effects of the creep deformation on the fractal dimension of the grain boundaries in an austenite steel

The change in the fractal dimension of the grain boundaries during creep was investigated using an austenitic SUS304 steel at 973 K. The fractal dimension of the grain-boundary surface profile (the fractal dimension of the grain boundaries, D, 1 < D < 2) in the plane parallel to the tensile direction (in the parallel direction) and in the transverse direction, was examined on specimens deformed up to rupture (about 0.30 creep strain). Grain boundaries became serrated and the fractal dimension of the grain boundaries increased with increasing creep strain, because the density of slip lines which formed ledges and steps on grain boundaries increased as the creep strain increased. The increase in the fractal dimension due to creep deformation was slightly larger under the higher stress (118 MPa) than under the lower stress (98 MPa), while the increase of the fractal dimension with strain was a little larger in the specimens tensile-strained at room temperature (293 K) than in the crept specimens. These results were explained by the grain-boundary sliding and the diffusional recovery near grain boundaries, which lowered the increase of the fractal dimension with the creep strain. The fractal dimension of the grain boundaries in the parallel direction was slightly larger than that in the transverse direction in both creep at 973 K and tensile deformation at room temperature, especially at the large strains. This could be correlated with the shape change of the grains by creep or plastic deformation. Grain-boundary cracks were principally initiated at grain-boundary triple junctions in creep, but ledges, steps and carbide precipitates on serrated grain boundaries were not preferential nucleation sites for the cracks.

Application of slit island method to the evaluation of the fractal dimension of the grain-boundary fracture in high-temperature creep

The slit island method (SIM) has been applied to the evaluation of the fractal dimension of fracture surfaces in steels [1, 2] and ceramics [3, 4]. However, Mandelbrot et al. [1] found that the fractal dimension of fracture surfaces estimated by the SIM increases with decreasing the absorbed energy (namely, with decreasing the fracture toughness) in steels, while Mecholsky et al. [3] reported that the fractal dimension increases with increasing the fracture toughness in ceramics. The fractal dimension estimated by the SIM seems to depend on the box size in the fractal analysis [5–7], and this may lead to different results of the relationship between the fractal dimension and the materials properties [1, 3]. The fractal dimension may be correlated to the characteristic microstructures at the suitable box size [5], whereas one of the prerequisites in the SIM is that the box size used in the fractal analysis should be small enough compared with the sizes of islands used [8]. Let Xn be the number of boxes on the coastline and Sn be the number of boxes inside the coastline in an island. The values of Xn and Sn are proportional to the length of the coastline, P , and the area of the island, A, respectively. If there is the following relationship in a set of Sn and Xn ,

GROWTH AND LINKAGE OF CRACKS AND FORMATION OF CREEP FRACTURE PATTERN SIMULATED BY A MULTICRACK GROWTH MODEL

A computer simulation using a multicrack growth model was carried out on the growth and linkage of cracks and the formation of creep fracture pattern resulting from the initial defects. The percolated crack patterns and the number of steps to percolation were examined by Monte Carlo simulation on a square lattice. Effects of stress and grain size on creep fracture process are then discussed. The stress and grain size dependence of the number of steps to percolation in the simulation was similar to that of grain-boundary sliding in the austenitic 21Cr-4Ni-9Mn heat-resisting steel, which controlled the growth of grain-boundary cracks. The fractal dimension of the percolation crack was also correlated with that of the creep fracture pattern in the 21Cr-4Ni-9Mn steel.

Change in the fractal dimension of the grain boundaries in pure Zn polycrystals during creep

The effects of creep deformation on the shape of grain boundaries were investigated on pure Zn polycrystals at 373 K. The fractal dimension of the grain boundaries D(1≤D≤2) was estimated by the box-counting method. There was then discussion on the relationship between the value of D, the microstructures, and the creep or plastic strain in the deformed specimens of metallic materials.The fractal dimension of the grain boundaries (D) increased with increasing the creep strain in pure Zn polycrystals, but the increase in the value of D levelled off when the creep strain exceeded about 0.30. The value of D decreased as the creep stress decreased. The increase in the value of D with the creep strain was correlated with the increase in the density of slip lines in the grains that formed the ledges and steps on grain boundaries. The value of D on the plane in parallel with the tensile axis was slightly larger than that on the plane transverse to the tensile axis. The mean shear strain on grain boundaries estimated from the value of D was correlated with the creep or plastic strain in the deformed specimens.