PSI - Issue 47

6

Abderrahim Khtibari et al./ Structural Integrity Procedia 00 (2023) 000–000

A. Khtibari et al. / Procedia Structural Integrity 47 (2023) 855–862

860

1.0

0.8

0.6

0.4

Stage I

Stage II

Stage III

Static damage

0.2

0.0

0.0

0.2

0.4

0.6

0.8

1.0

Life fraction

Fig. 5. The evolution of static damage versus life fraction.

As shown in Fig.5 we can note that the damage process of Chlorinated Polyvinyl Chloride specimens is schematized by a concave curve. We can also remark that there are three damage stages: Stage I which is the fraction of life β = [0, 20%] it is damage initiation, this is due to the molecular chains extremely low mobility. Stage II is situated in the interval β = [20, 78%], stage progressive damage. The crucial life fraction arises at the conclusion of this stage β c = 78 %, This value relates to the critical damage needed for industrial usage of predictive maintenance. Stage III is distinguished by ferocious damage with unexpected acceleration of the damage and an uncontrollable element. 3.3. Quantification of damage by unified theory Miner's law is one of the earliest laws, having been formulated by Miner (1945). This law is predicated on the premise that material's cumulative damage. It is unaffected by loading levels and evolves linearly with the life fraction β . The unified theory developed by Bui Quoc et al. (1971) serves as an important tool for evaluating damage while taking into consideration the loading level. To do this, the correlation between damage and loading level has to be established. Normalized damage is defined as follows, with loads replaced by stress Wahid et al. (2020).

β

  3

D=

m          u γ

      

γ γ

β +(1- β )

   

- γ

1

with: γ = ஢ ஢ ୳ ୳ ୰ and γ u ൌ ஢ ஢ ୳ ୟ