PSI - Issue 45

Yuanpeng Zheng et al. / Procedia Structural Integrity 45 (2023) 96–103 Author name / Structural Integrity Procedia 00 (2019) 000–000

101

6

4.2. Fatigue life prediction Fatigue life estimation is conducted by an integral of a polynomial fitting function which correlates the calculated values of SIF range Δ K num and crack lengths a as Fig. 8 serves as an example. The comparison between experimental and numerical fatigue life results is shown in Fig. 9. The predictions offer good agreement as well, mostly conservative, though there is an overestimation of the fatigue life of Specimen R-D-4 which is discussed in the next section.

400

Numerical Experimental

+33.8%

350

X % Prediction Error (Consevative, Risky)

300

-21.2%

250

100 Fatigue life (×10 3 cycles) -7.41% 150 200

-4.24%

= 1 ( Δ num ) 1 0

50

0

R-S-2

R-D-1

R-D-2

R-D-4

Specimen No.

Fig. 9. The comparison between experimental and numerical fatigue life results

Fig. 8. Numerical fatigue life estimation of Specimen R-D-1

5. Discussions 5.1. Reasons for the error

The error between numerical and experimental SIF range values before the final stage of crack propagation could actually be more limited as the crack grows faster with size increase and thus secant method for FCGR calculation underrates the true FCGR d a /d N as Fig. 10 illustrates, leading to an underestimation of experimental SIF range Δ K exp . The numerical SIF range estimation Δ K num near the final fracture is inaccurate as the numerical model doesn’t include the damage of CFRP itself, which was observed in the experiment. As the vertical crack in the digital image correlation (DIC) result of Specimen R-D-2, Fig. 11, shows, beyond the damage of adhesion, shear stress along the fiber direction of CFRP patches, induced by the bending moment within the CT specimen, worsen the performance of the reinforcement system.

8 100(10 -6 ) 7 347 6 594 5 841 5 088 4 334 3 581 2 828 2 075 1 322 569

a /mm

Specimen R-D-2 After the 16 th base-line cycle round Horizontal strain field ε xx

d a /d N (secant)

( N 2 , a 2 )

a 1 a 2

d a /d N (secant)

d a /d N (true)

( N 1 , a 1 )

-184 -938

-1 691 -2 444 -3 197 -3 950

y

Vertical crack (DIC result)

N 1

N 2

O

N /cycles

x

Fig. 10. Secant method and experimental FCGR underestimation

Fig. 11. A vertical crack in the carbon fiber sheets

The experimental fatigue life of Specimen R-D-4 has already fallen short of Specimen R-D-2, below intrinsic and numerical expectations, suggesting other disadvantages of CFRP over-patching besides the randomness of the fatigue