This calculation indicated that the crack was not critical at the time of inspection. However, the team realized that the crack had grown over time due to fatigue.
The team used the Paris-Erdogan law to model the fatigue crack growth:
a = 2 inches + (2.5 * 10^(-5) inches/cycle * 10,000 cycles) = 4.5 inches principles of fracture mechanics rj sanford pdf pdf work
The team concluded that the pipeline had failed due to a fatigue crack that had grown to a critical size. The crack had formed in the weld region, which had a lower toughness than the base metal.
The stress intensity factor is a measure of the stress field around a crack tip, and is defined as: This calculation indicated that the crack was not
K = (900 psi * √(π * 2 inches)) * 1.5 = 85 MPa√m
K = 85 MPa√m < KIC = 100 MPa√m
da/dN = C * (ΔK)^m