Failure probability analysis based on FRI model for SCC growth introducing stress intensity factor distribution as function of crack depth

Failure probability of welds by stress corrosion cracking (SCC) in austenitic stainless steel piping is analyzed by probabilistic fracture mechanics (PFM) approach based on an electro-chemical crack growth model named FRI model[1] through which a basic equation is derived. Introducing the relation among dK/dt, da/dt and dK/da (K: stress intensity factor, a: crack depth and t: time) into the basic equation, modified basic equation is derived which can give da/dt in explicit form in contrast to the fact that the basic equation is transcendental and can be solved only numerically by iterative method. From numerical evaluation of K distribution at a crack tip under bending stress, it is realized that there exists a relation between a and K and it can be expressed approximately by quadratic function, i.e. K=K_m{1-(a-a _m)²/a_m ²}. By examining K as function of a, a_m is proved to be a linear function of membrane stress to bending stress ratio. These findings are incorporated into the modified basic equation which is shown to be able to calculate da/dt without instability and needs no iteration. Stratified Monte-Carlo method is introduced which defines two dimensional sampling space composed of a/c (c is crack length at surface) ranging from 0 to 1 and K from 0 to Kw which has to be defined referring to KSCC. Log-normal distributions are anticipated for a/c and K probability distributions. The median of K is decided referring to median of a in Brückner model. Parameter surveys for cumulative failure probability (CFP) performed with the basic equation and the modified basic equation give very close results. In this study, the residual stress distribution generated by residual stress at welding is anticipated to be tensile on inner surface and compressive on outer surface like bending stress distribution. Therefore the simulation is performed under bending dominative condition. The modified basic equation is proved to need about 1/2 calculation time of needed by the original basic equation in the CFP simulation.