Modeling pitting corrosion damage of high-level radioactive-waste containers using a stochastic approach

A Phenomenological Approach to Simulating the Evolution of Radioactive-Waste Container Damage Due to Pitting Corrosion

“…In previous models, these permanent pits were assumed to grow an increment in depth during each simulated time step only if a random number, 0 5 R < 1, is less than the growth probability where 0 I y I 1. This approach led to the time evolution of a distribution of pit depths [3]. However, these distributions did not exhibit the positive skew frequently observed experimentally [4-71, in which the majority of pits have small depths and a long "tail" to the distribution exists at large depths.…”

“…Following earlier work [3], Monte Carlo computer codes have been used to simulate the apparently random initiation of permanent pits on a unit surface area of metal in contact with an aggressive environment. In previous models, these permanent pits were assumed to grow an increment in depth during each simulated time step only if a random number, 0 5 R < 1, is less than the growth probability where 0 I y I 1.…”

“…Items (1) and (4) already are included in the phenomenological model through the stochastic treatment of permanent pit initiation [3]. Items (3) and (4) suggest that individual pits grow at a range of rates, which is simulated in the stochastic model through the growth probability per time step, y [3].…”

“…Items (3) and (4) suggest that individual pits grow at a range of rates, which is simulated in the stochastic model through the growth probability per time step, y [3]. To accommodate observation (2), a new stochastic variable was introduced: the probability that during any given time step a pit will permanently cease to grow, q.…”

“…Figure 2 illustrates the capability of the new model to simulate the complex time evolution of the pit depth distribution. For this simulation, the probability of initiating a new pit embryo was decreased exponentially with exposure time [3] such that no new pits were initiated for exposures greater than approximately 50 time steps. The parameters affecting the growth of these pits, 'y, q, A and p , were chosen arbitrarily and are given in the figure.…”