Issue 64

F. Gugouch et alii, Frattura ed Integrità Strutturale, 64 (2023) 218-228; DOI: 10.3221/IGF-ESIS.64.14

Damage-reliability relationship To relate reliability to the damage parameter D through the fraction of life, any variable physical parameter must be expressed as a function of the fraction of life. Starting first with the Eqn. (11) which can be given bu the expression below:

P

ur u a u



1

P P P



D

(14)



1

which give:

         1 1 a u P D P

P

ur

(15)

P

u

We replace the Eqn. (1) in (15) we get:

          3 1 2 1 1 a a u P a a e D P 

(16)

From Eqn. (16) we can extract the expression of the fraction of life in function of damage

1

  

 

 1 log 1

a



3



    D a



(17)

1

a

2

This gives the expression of reliability in function of damage:



1

    

    

  

 

 1 log 1

a

3



    D a



1

a

2

 R e

(18)

The Fig. 10 shows the graphical illustration of reliability versus damage.

Figure 10: Graphic illustration of reliability versus damage.

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