Nucleation phenomena in an annealed damage model: Statistics of times to failure

In this paper we investigate the statistical behavior of an annealed continuous damage model. For different model variations we study distributions of times to failure and compare these results with the classical case of metastable nucleation in statistical physics. We show that our model has a tuning parameter, related to the degree of damage reversibility, that determines the model's behavior. Depending on the value of this parameter, our model exhibits statistical behavior either similar to classical reversible nucleation phenomena in statistical physics or to an absolutely different type of behavior intrinsic to systems with damage. This comparison allows us to investigate possible similarities and differences between damage phenomena and reversible nucleation.

Figure 1

Cumulative distribution function of shifted times to failure $t_f$ for postcritical irreversible nucleation: (a) CDF plot and (b) exponential plot.

Figure 2

Cumulative distribution function of times to failure $t_f$ for precritical irreversible nucleation: (a) CDF plot and (b) Weibull plot.

Figure 3

Cumulative distribution function of times to failure $t_f$ for precritical irreversible nucleation of independent locations: (a) CDF plot and (b) Weibull plot.

Figure 4

Cumulative distribution function of times to failure $t_f$ for precritical reversible nucleation: (a) CDF plot and (b) exponential plot.

Figure 5

Cumulative distribution function of times to failure $t_f$ for precritical reversible nucleation of independent locations: (a) CDF plot and (b) Weibull plot. In (a) we rescaled failure times by factors of 80, 320, 510, and 1600 times for the “min of 100”, “min of 500”, “min of 1000”, and “min of 5000” statistics, respectively.

Figure 6

Cumulative distribution function of times to failure $t_f$ for precritical nucleation with damage reversibility: $D=25\%$: (a) CDF plot and (b) Weibull plot; $D=50\%$: (c) CDF plot and (d) Weibull plot; $D=75\%$: (e) CDF plot and (f) Weibull plot.

Figure 7

Cumulative distribution function of times to failure $t_f$ for precritical nucleation of independent locations with damage reversibility $D=50\%$: (a) CDF plot and (b) Weibull plot.