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Fracture Mechanics
  Problem 2
This problem presents a simplified crack growth analysis of a cannon barrel, and demonstrates numerical integration of the range of stress intensity factor. It should take perhaps 20 minutes to complete. This simplified analysis, and its prediction of a life of 2 789 cycles, can be compared with a more detailed and accurate analysis (see the reference below) which gives a life of 1 872 cycles. Probabilistic methods indicate that this more accurate value is conservative by some 25% (2 445 cycles), but such methods require much greater effort in the analysis.
Note that cannon barrels are generally designed to wear out by erosion, rather than fail by fracture (which tends to have unpleasant consequences for the gunners). To assist in achieving this, a compressive residual hoop stress is often induced through plastically expanding the interior of the bore in a process known as autofrettaging. This would further complicate the analysis. L Banks-Sills and R Eliasi (1999), Fatigue life analysis of a cannon barrel, Engineering Failure Analysis, Vol. 6 pp.371-385.
The barrel of this cannon has an inner radius of 86 mm and an outer radius of 162.5 mm, and it operates at a firing pressure of 380 MPa. It is made from a 4340 grade steel with a yield strength of 1.13 GPa, a tensile strength of 1.23 GPa and a plane strain fracture toughness value of 125.8 MPa m½. Calculate the fatigue life of the barrel, given that initial defect size in the bore is 0.2 mm. Use numerical integration with increments in crack length between 0.4 mm and 0.6 mm. You may assume that the Paris law holds over the complete range of the growth rate integration, that the exponent m = 2.29 and that the constant C = 0.76x10-10 to give da/dN in m/cycle. Scientific Calculator | RPN Calculator | Graph Plot | Theory Hint | Solution |
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Failure Analysis - Fracture Mechanics - Failure As A Design Criterion |