The stress intensity factor is a measure of the stress field around a crack tip, and is defined as:
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.
where ac is the critical crack length.
a = 2 inches + (2.5 * 10^(-5) inches/cycle * 10,000 cycles) = 4.5 inches
da/dN = C * (ΔK)^m
K = 85 MPa√m < KIC = 100 MPa√m
where da/dN is the crack growth rate, C and m are material constants, and ΔK is the stress intensity factor range.
The investigation revealed that the pipeline had been fabricated using a welding process, and that the weld had not been properly heat-treated. As a result, the weld region had a higher yield strength and a lower toughness than the base metal.