An application of the extreme theory to the analysis for the facture phenomena of vulcanized rubbers under constand engineering stress is presented. The distribution function, which can describe the statistical fluctuations of observed fracturing time, is given theoretically.
This function can be derived by transformation of the random variable from a distribution function of tensile data under constant strain rate. The analytical form is given by;
Π (
tb) =exp [- {log {(
tb) / (
tb)
1} /log {(
tb)
2/ (
tb)
1}} α
σ],
-∞<log (
tb) <∞, log (
tb)
2≥log (
tb)
1log (
tb) ≥log (
tb)
1, α
σ>0,
where log (
tb)
1 and log (
tb)
2, the smallest value of logarithmic fracturing time and the characteristic logarithmic fracturing time, respectively, are location parameters and α
σ is dimensionless scale parameter.
The numerical analysis by using the published data in the reference leads to the following results; The applicability of this function to experimental data is verified to be reasonable, In a given vulcanized rubber, the characteristic logarithmic fracturing times decrease linearly with initial loads.
On the other hand, the scale parameter is not affected them. Then, the fluctuations of the observed fracturing times under a given initial load can be described by making the former relationship clear numerically.
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