applied fracture mechanics

Structural Reliability Improvement Using In-Service Inspectionfor Intergranular Stress Corrosion of Large Stainless Steel Piping 345could be performed to determine the entire crack size distribution as a function of time, suchas shown by the dotted line in Fig.4. The cumulative failure probability at or before ts is thengiven by Point B in Fig. 4. Such a procedure requires extensive fracture mechanicscalculations of crack growth in order to accurately define the crack size distribution atvarious times. An alternative procedure is to define atol(t) to be the size of a crack at t = 0(initially) that will just grow to ac in time t (Fig. 4) schematically shows atol(t). Theprobability of failure at or before t is then simply the probability of initially having a crackbigger than atol(t). That ishP' (ax) 0 P (y)P0 ND(y)dy(26)a tol (t)Hence, once atol(t) is known, the cumulative (conditional) failure probability is calculated ina straightforward manner. The failure rate, or hazard function, is equal to (dP/dt)/(1—P). Inthe case where P(tf < t)