Physico–statistical approach taking defects into account and using binomial distribution - Probabilistic Safety Assessment for Optimum Nuclear Power Plant Life Management (PLiM) - page 94

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Physico-statistical approach taking
defects into account and using binomial
distribution

4.1 Key elements of the behaviour of structures with
crack-type defects

4.1.1 Critical and allowable defect sizes

The critical size of the defect is the size at which instantaneous failure of
the structure takes place.
The permissible size of a discontinuity during operation should not
exceed the value that is equal to the critical size reduced by the appropriate
safety factors.
For example, a pipeline is usually characterised by the viscous state of
the metal. The defect can be schematised as shown in Fig. 4.1.
For cylindrical shells with discontinuities oriented in the circumferential
direction the critical defect sizes a c and c c can be determined by the
formula 5 :

￿ ￿ ￿ ￿ ￿

  s  

 

2 R 2sin 0.5 π− nynx −π

m

− ny nx sin( )

 

   

a ϕ a ϕ

R

   

 

[4.1]

s= ,

b

π

where y = a / s is relative depth of the crack of the critical size; a is the
crack depth in mm; s is the wall thickness of the cylinder in mm; x=C/R c is
the half length of the crack of the critical size; C is the half crack length in
mm; R c is the radius of the cylinder in mm; R is the fracture criterion in the
viscous region; R p 0.2 is the yield strength of the material of the cylinder in
MPa; σ b is bending stress; n a is the safety factor in the depth of the crack;