Failure Probability Analysis by Probabilistic Fracture Mechanics Based on FRI SCC Model

Abstract

Failure Probability of a weld by stress corrosion cracking (SCC) in austenitic stainless steel piping was analyzed by probabilistic fracture mechanics (PFM) approach based on electro-chemical crack growth model (FRI model). In this model, crack growth rate da/dt where a is crack depth is anticipated as the rate of chemical corrosion process defined by electro-chemical Coulomb’s law. The process is also related to the strain rate at the crack tip, taking small scale yielding condition into consideration. Derived transcendental equation is solved numerically by iterative method. Compared to the mechanical crack growth equation like Paris’ law for SCC, FRI model can introduce many electro-chemical parameters such as electric current associated with corrosion of newly born SCC crack surface, the frequency of protective film break and mechanical parameters such as stress intensity factor change with time dK/dt. Stratified Monte-Carlo method was introduced which define the cell of sampling space by the ranges of a/c (c is crack length at surface) and the width of K of sampling space, Kw which has to be defined referring to KSCC below which no SCC is caused. Log-normal distributions were anticipated for a/c distribution and K distribution. Parameter survey performed shows that failure probability which is defined as the ratio of crack number whose depth reached 80% of wall thickness to the total crack number depends on many parameters introduced, especially on yielding stress, electric current decay parameter m, strain hardening index n in Ramberg-Osgood equation and dK/dt. From the requirements of FRI model, two types of threshold value of initial crack depth, cracks having smaller depth than this value can not grow, are proposed. Calculated failure probability does not reach 1 when cracks having smaller initial depth than the threshold value are included in the distribution of analyzing cracks.