Some previous fracture probability and statistic equations are shown to be special cases of this equation and the defect density and the cumulative fracture probability play an important role.

Finally, the methods for calculating fatigue life based on fracture mechanics for welded node and cumulative damage theory for bolted sphere node respectively have been presented.

The results show that using the encapsulated delayed release breaker may improve the proppant pack fracture conductivity and increase the cumulative oil and gas production capacity.