PSI - Issue 18

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

735

5

3.3. Damage according to unified theory Many models were developed to represent the nonlinear nature of the damage. Some of these nonlinear models include the unified theory Bui-Quoc (1982) which summarizes the work of Shanley (1957), Valluri (1965) and Sorensen (1969). This is an approach based on reducing the strength and endurance limit of the studied material. It assesses the impact of cumulative damage at different level of loadings. This is a theory that was used in the many research works to investigate the strength of materials, which are steel cables Tijani et al (20117) and Mouhib (2015), high-density polyethylene HDPE pipes Majid et al (2017) and polypropylene random copolymer pipes (PPR) Ouardi et al (2018). The damage by the unified theory is as follows:



(5)



D

m           u  

     







1  

  



1  

  

F F

F

u 0

Where  ; 0 F The endurance limit of the virgin strand equal the residual ultimate force multiplied by the  coefficient, which is the inverse of the strand safety coefficient. For our experimentation, the coefficient of utilization of the metallic strands is equal to 2.5 MIFA, which gives 0.4.   So 0 u F .F   . 4. Results and discussions 4.1. Mechanical behavior characterization of specimens The tensile curves of virgin and other corroded samples at different corrosion levels are shown in Fig. 2. They indicate the reduction in supported force due to the strand specimen damage, they also show the residual ultimate forces �� . In general, the virgin strand has an ultimate force � which gradually decreases as the immersion time increases to reach ����� (total damage of the strand wires). The virgin strand parameters are listed in Table 4. Table 4. Mechanical properties of strand. Elastic Modulus E(GPa) Poisson’s Ratio Yield Stress σ � ����� Ultimate Stress σ � ����� Strain ���� 182 0.3 1726 1943 1.63 The values of the residual failure forces of specimens are indicated in the following table. 0 F   , u γ

Table 4. Values of failure forces of damaged strands. Immersion time (h) 0 4

8

16

24

32

Residual ultimate force of strand (N)

3799

3585

3194

1989

1181 856 .4