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Fracture Mechanics
 
Problem 14
This question illustrates some aspects of material selection in the design of a pressure vessel, which experiences a range of operating temperatures. Hence material toughness, as a function of temperature, forms an important part of the fracture-safe design process. This is demonstrated graphically in the question. It should take around 15 minutes to complete. Power generation pressure vessels are usually thick walled, operate at a range of temperatures from ambient to elevated and are required to be fail-safe (leak-before-break). In one particular case, a spherical pressure vessel is proposed which will operate at an internal pressure (p) of 40 MPa and at temperatures from 0ºC to 300ºC. The proposed wall thickness (t) is 100 mm and the diameter (D) is 2 m. Two candidate steel alloys have been suggested: Steel A steel: For this steel, KC = (150 + 0.05T) MPa m1/2 where T is operating temperature in degrees centigrade, and the yield strength varies in a linear fashion from 549 MPa at 0ºC to 300 MPa at 300ºC. Steel B steel: Here KC = (100 + 0.25T) MPa m1/2, and the yield strength varies linearly from 650 MPa at 0ºC to 500 MPa at 300ºC. Graphically determine, by inspection, the range of temperatures over which each of these alloys would have the highest safety factor with respect to fast fracture. Through-thickness cracks can be assumed to be critical and the stress intensity factor for such cracks in this geometry is given by: 
The membrane stress in the pressure vessel wall may be taken as pD/4t Scientific Calculator | RPN Calculator | Graph Plot | Theory Hint | Solution |
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Failure Analysis - Fracture Mechanics - Failure As A Design Criterion |