PSI - Issue 45

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

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Before the formal SIF calculation of the CFRP-repaired CT specimens, a comparison between SIFs obtained from traditional FEM and XFEM approaches on a bare CT specimen is conducted. In the FEM model, the crack tip is encircled by C3D6 wedge elements while the crack front is positioned in a C3D8R element in the XFEM model. Besides the crack region, the type of all elements is C3D8R, according to Hill et al. (2020), offering higher accuracy for XFEM modeling. The size of each element is around 0.8 mm, meaning 10 layers of elements through the specimen thickness direction. The boundary conditions are in accordance with BC4 in Xin et al. (2021). The mesh details of the XFEM and FEM models are shown in Fig. 1. SIF range values derived from XFEM and FEM corresponding to ten different crack sizes are plotted in Fig. 2. The XFEM and FEM results show satisfying consistency and accuracy compared to the analytical solution in the handbook of Tada et al. (2000). To speed up the analysis, the upcoming numerical investigation is conducted using the XFEM approach.

1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 SIF (MPa·mm 1/2 )

Tada Handbook FEM(Remesh) XFEM

XFEM

FEM(Remesh)

10 15 20 25 30 35 40 45 50 55 60 500

Fig. 1. The mesh details of the XFEM and FEM models

Crack length a (mm)

Fig. 2. The comparison of SIFs calculated via XFEM, FEM and the analytical solution

3.2. Traction-separation description of the steel-CFRP bonding The adhesive transfers shear stress from the CT specimen to the high-modulus carbon fiber sheets. The assumptions of the steel-CFRP bonding under fatigue loading in numerical simulation have been developing as researchers gain more knowledge about the mechanical behavior of the composite structure. As research related to the debonded region surrounding the crack pushes forward, the strength and damage evolution of the bonding interfaces calls for more detailed modeling. Some numerical models in which FRP is tied to the steel directly or by an infinitely-elastic adhesive layer indicate that the composite structure is assumed to maintain complete elasticity under fatigue loading, while the damage initiation and evolution of the bonding introduces nonlinearity into the numerical simulation which is closer to reality. The previous elastic assumption enables the SIF range Δ K calculation under a single load of (1- R )· P max , implying a risk of overestimation of the strengthening efficiency. In the contrast, the nonlinearity of the bonding behavior demands a SIF subtraction for a more accurate Δ K prediction, as Fig. 3 demonstrates. To delineate the performance of the steel-CFRP bonding, cohesive elements are deployed in the numerical modeling. A traction-separation description, which can also be referred to as the bond-slip model, characterizes the nonlinear behavior of the steel-CFRP connection. The application of cohesive elements essentially simplifies the failure modes of the CFRP-adhesive and steel-adhesive interfaces, integrating the final debonding and adhesive failure. The overall damage initiation and evolution of the cohesive behavior are controlled by the parameter of mode-II fracture energy G f . To include the effects of fatigue loading on the mechanical behavior of the adhesive, which could be different from its corresponding static behavior as Fig. 4 presents, necessary adjustments are implemented on the values of mechanical parameters labeled in the figures. Wu et al. (2013) point out that the maximum shear stress τ max and the stiffness K have limited degradation between the high-modulus CFRP and adhesive after fatigue loading. As Table 2 presents, the maximum shear stress is then calculated according to Xia and Teng (2005) based on the tensile strength from the datasheet (HUNTSMAN, 2004) without further discount. The stiffness remains consistent with its