Abstract
In assessing the fracture mechanism of materials, it is often necessary to treat it as a stochastic process. This report discusses the distribution of time to failure when the fracture is regarded as the (r+1) states-(r) steps stochastic process.
By analyzing the distribution of time to failure on the assumption that the failure probability of each state obeys the Weibull distribution, the function of the failure probability for the (r+1) states-(r) steps stochastic process could be obtained.
By using the function derived, a simulation for the failure probability of (3) states-(2) steps stochastic process was performed with a computer, and the results were plotted on the Weibull paper to investigate the features of the distribution of time to failure on the paper. The main features are summarized as follows: (1) the distribution of time to failure can be approximately expressed as either one straight line (simple Weibull distribution) or two straight lines the slopes of which differ each other (composite Weibull distribution), and (2) the number of cracks appearing on a test specimen, as well as other testing conditions, has a significant effect, e.g. the distribution is more likely expressed as one straight line on the Weibull paper with an increase in the number of cracks.
