where da/dN is the crack growth rate, C and m are material constants, and ΔK is the stress intensity factor range.
The team compared this value to the fracture toughness:
In a large industrial plant, a critical component, a high-pressure pipeline, failed catastrophically, resulting in significant damage and downtime. The pipeline was made of a high-strength steel alloy, with a wall thickness of 2 inches and an outside diameter of 12 inches. It was designed to operate at pressures up to 1000 psi.
where σ is the applied stress, a is the crack length, and π is a constant.
The team used the following equation to calculate the stress intensity factor:
K = 85 MPa√m < KIC = 100 MPa√m
K = (900 psi * √(π * 2 inches)) * 1.5 = 85 MPa√m
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.
where Y is a geometric factor that depends on the crack configuration and the component geometry.
The stress intensity factor is a measure of the stress field around a crack tip, and is defined as:
