The team used the Paris-Erdogan law to model the fatigue crack growth:
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.
where ac is the critical crack length.
where Y is a geometric factor that depends on the crack configuration and the component geometry.
The team decided to apply the principles of fracture mechanics to analyze the failure. They used the stress intensity factor (K) to characterize the stress field around the crack tip. principles of fracture mechanics rj sanford pdf pdf work
The team used the following equation to calculate the stress intensity factor:
The team integrated this equation over the number of pressure cycles to estimate the final crack length: The team used the Paris-Erdogan law to model
The team also discovered that the pipeline had been subjected to a series of pressure cycles, with pressures ranging from 500 to 900 psi. These cycles had caused fatigue cracks to form and grow in the weld region.