PSI - Issue 45

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

100

5

are shown in Table 2, defined as an isotropic material in the simulation. The thickness and material properties of carbon fiber sheets are listed in Table 2 as well, playing its role as an orthotropic material. All of the values are based on experimental measurements in Zheng et al. (2022) and Chen et al. (2019). Both sides of the cohesive elements are tied to the carbon fiber sheet or steel surface with their mechanical behavior described using a revised bond-slip model explained above. The mesh size of the components remains 0.8 mm, though there are four layers and one layer of elements, respectively, through the thickness of each carbon fiber sheet and adhesive layer. Specimen R-D-1 in the modeling is shown in Fig. 6 as an example.

Isotropic

Adhesive

Orthotropic, Engineering Constants

Crack defined using XFEM

Cohesive elements , trac�on - separa�on response , mode-independent

Specimen R-D-1

Fig. 6. Specimen R-D-1 in the numerical simulation

1400

R-S-2 R-D-1 R-D-2 R-D-4

1200

1000

1/2 )

Δ K num > Δ K exp Conservative SIF range estimation

800

600

+20%

400 Δ K num (MPa·mm

Near the final fracture

-20%

Δ K num < Δ K exp Insufficient SIF range estimation

200

0

0

200

400

600

800 1000 1200 1400

1/2 )

Δ K exp (MPa·mm

Fig. 7. The comparison between experimental and numerical SIF range values

4. Results and comparison 4.1. Stress intensity factor range

Paris law in which d a /d N = C ( Δ K ) m offers the chance to back-calculate the experimental stress intensity factor ranges Δ K exp of each specimen at different crack sizes as the corresponding experimental FCGR are known. Two Paris law constants C and m are calibrated by the beach marks on the fracture surfaces of unrepaired specimen U-1 in a way that has been explained in Hosseini et al. (2017) and Zheng et al. (2022). The value of C and m are 3.76×10 -13 and 2.89, respectively, matching the FCGR unit of mm/cycle and SIF unit of MPa·mm 1/2 . Fig. 7 presents the comparison between experimental and numerical SIF ranges at the same crack lengths of FCGR and SIF range calculation. Overall, the detailed simulation offers relatively accurate and mostly conservative SIF estimations. The error of overestimated values is all below 20%. There are some underestimated values with an error beyond 20% and the possible reasons are discussed in the next section.