Theoretical Dependencies of the Distributions in Crack Growth Rate in Type 304SS on Various Factors

A purely empirical Artificial Neural Network (ANN) and the high-level deterministic/mechanistic Coupled Environment Fracture Model (CEFM) have been used to study the effects of normal distributions in five independent variables [Electrochemical Potential (ECP), Conductivity (ҝ), degree of sensitization (EPR), stress intensity factor (KI ), and temperature (T)] on the distribution in the dependent variable (Crack Growth Rate, CGR) for Intergranular Stress Corrosion Cracking (IGSCC) in sensitized Type 304SS in simulated Boiling Water Reactor primary coolant circuits. Both approaches have been useful for gaining a better understanding of the distribution of crack growth rate of stress corrosion cracking in 304SS. We show theoretically that if an independent variable (T, ECP, KI , EPR, ҝ) follows a normal distribution (that is, it is randomly distributed), the crack growth rate is commonly lognormally distributed. Finally, the sizes of the Standard Deviations (SDs) in the above variables relative to the means also have a profound impact on the distributions in the dependent variable. If the SDs are small, the distribution in the dependent variable becomes indistinguishable from a normal distribution. However, if the SDs are large, the distribution in the dependent variable is unequivocally lognormal.