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Fracture Mechanics
 
Problem 15
The questions so far in this tutorial have dealt with simple applications of Linear Elastic Fracture Mechanics (LEFM). The more usual design case involves elastic-plastic fracture or so-called Yielding Fracture Mechanics (YFM), as tough ductile alloys are often operated at elevated temperatures. Fracture assessment, therefore, generally involves a two parameter approach where the potential for fast fracture and yield dominated fracture (net-section yield) are assessed independently (see theory card). It usually also involves more generally applicable fracture parameters like the crack tip opening displacement (CTOD, COD) of the J-integral which can cope with localised plasticity. This problem illustrates the type of application where LEFM is not really suitable, although its predictions may still be conservative, and hence quite useful. It should take around 15 minutes to work through. A particular chemical processing plant consists of a number of similar reactors which operate at temperatures ranging from -70ºC to 350ºC. It is desired to use a single alloy to manufacture all the reactor vessels. The fracture toughness and yield strength of this alloy vary with temperature as shown below: KC = (63 + T/10) MPa m1/2 over the range of temperature -100ºC to +400ºC
The vessels have a wall thickness of 15 mm and are to be designed on the basis of 'leak-before-break'. The stress intensity factor can be calculated using: 
a) Based on material performance, rather than operating conditions, determine the temperature at which yield becomes more likely than fracture, i.e. the design criterion changes from fracture to yield control. b) Is the use of LEFM valid up this temperature? If not, determine the range of operating temperatures over which use of YFM would be preferable. You may assume plane stress conditions in the vessel wall and can take the plastic zone size as being: 
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Failure Analysis - Fracture Mechanics - Failure As A Design Criterion |