Size distribution of creep cracks in materials showing a mixed mode fracture simulated by one-dimensional crack growth model

Abstract

The size distribution of creep cracks has been simulated by a logarithmic normal distribution [1, 2] or a normal distribution [3]. Evans [4] summarized the experimental data and concluded that the crack size distribution can be approximated quite well by a logarithmic normal distribution. In the previous study [5], the growth and linkage of grain-boundary cracks was simulated by a two-dimensional multicrack growth model similar to the random walk model proposed by Nishiuma et al. [6, 7]. In the simulation, the crack size distribution could be approximated by a logarithmic normal distribution, and the number of the cracks (N) of the size (x ′) equal to or larger than a given size (X) (the ranking of the crack size) could be approximated by a power law relationship (N (x ′ ≥ X ) ∝ X−a, a: scaling exponent) at the larger crack sizes [5]. The results of the simulation could explain the crack size distribution characteristics on the crept specimens of the austenitic 21Cr-4Ni-9Mn steel, in which creep fracture of specimens is governed by grain-boundary fracture [8, 9]. However, a mixed mode of grain-boundary fracture and transgranular fracture is often observed on the ruptured specimens of materials such as the austenitic SUS304 steel [10]. The difference in the fracture mechanisms may be correlated with the difference in the growth and linkage of cracks and may affect the size distribution of creep cracks in materials. In this study, the simulation of growth and linkage of cracks was made using one-dimensional crack growth model that is similar to the (two-dimensional) multicrack growth model in the previous study [5]. The principal rules in the simulation using the present model are as follows: