PSI - Issue 18

8

Abdeljalil Jikal et al. / Procedia Structural Integrity 18 (2019) 731–741 Abdeljalil JIKAL et al. / Structural Integrity Procedia 00 (2019) 000–000

738

Fig. 5: Theoretical and experimental damage as a function of the life fraction for damaged strands.

4.4. Adaptive damage based on failure force formula   F  We developed a new formula for failure force calculation, which takes into account the intervals of the life fraction and the characteristic forces shown in Tab. 4. This equation is independent of the limit force’s equations such as Faupel. It is conditioned by the critical life fraction as demonstrated by the Eq. (7) and (8):

        ( )  ( )  r r F F F  F F F    

;[0, ] 

c

max

(7)

c 



;[ ,1] 

c

max



By taking into account the parameter  , we get:

     

) ;[0, ] F 

F

( ) (

 

r

c

(8)

( )              1 F  

F  

;[ ,1]

r

c

The model presented above is an adaptive tool for estimating the failure force through a tensile test of a strand of wire rope as illustrated in Fig. 6. 4.5. Damage by unified theory The damage represented by the empirical relation Eq. (5) is a non-linear damage model representing the evolution of damage for different levels of corrosion based on the reduction of residual ultimate force and endurance limit. Fig. 7 shows the damage by unified theory of the strands compared to the linear damage of the Miner’s rule as a function of the life fraction. In fact, the damage is representative up to a reduction in cross-section of 50% of samples. Beyond these values, the evolution of the damage becomes unstable and the materials almost lose their characteristics until they become totally damaged. The concavity of the damage curves is accentuated for the load levels low. Nevertheless, they gradually tend towards the linearity of the Miner's rule for high loadings. This shows that the minor's rule