PSI - Issue 68

I. Yucel et al. / Procedia Structural Integrity 68 (2025) 1287–1293 Yucel et al. / Procedia Structural Integrity 00 (2024) 000–000

1290

4

where formulations of the failure strain, ε f , for the JC and MMC models can be found in Erdogan et al. (2023). The material is assumed to be initially undamaged ( D = 0), and failure initiates and element deletion starts at D = 1. Material parameter are presented in Table 1. The material is implemented to behave as elastoplastic with isotropic non-linear hardening.

Table 1. Material and model parameters.

p c [MPa]

3 ]

l 0 [mm]

E [GPa]

ρ [g / cm

G

c [N / mm]

W

ν

200

0.294

8.22

200

1300

1

3. Results and Discussion

This section introduces and discusses the experimental and simulation results for two specimens. The experimental data are obtained from Erdogan et al. (2023), and the finite element simulations are compared to assess the ability of the presented model to predict the force versus displacement curves and crack paths. Mesh refinement is performed, and the results for di ff erent damage models are compared with respect to their mesh dependency. In addition, the influence of certain parameters such as fracture toughness, plastic capacity and length scale are presented for the phase field model. Five di ff erent structured mesh configurations are simulated for the plane strain tension model. 1 / 8 portion of the specimen is modeled to reduce computational costs. The element sizes in the gauge region are varied between 0.5 mm and 0.08 mm. The in-plane shear stress model is created as a half model, and sweep and structured mesh types are used in the partition region where the crack is expected to initiate and propagate. The element sizes in this region range from 0.3 mm to 0.03 mm for sweep mesh type whereas the element size is 0.05 mm for the structured one. In Fig. 2, the mesh configurations are presented for PST and ISS specimens. Boundary conditions for both specimens are that they are translationally and rotationally constrained in the bottom, and an upward displacement is prescribed on the upper surface with restricted lateral movement.

(a) PST, structured mesh, min. el ement size = 0.2mm

(b) ISS, sweep mesh, min. ele ment size = 0.1mm

(c) ISS, structured mesh, min. el ement size = 0.05mm

Fig. 2. Mesh configurations for PST and ISS FE models

The force-displacement curves for the PST specimen are presented in Fig. 3. All three models successfully re produce the experimental load-displacement curves, with the phase field model predicting a slightly smaller force due to early material degradation. The models also accurately predict the failure point. Additionally, there is no sig nificant di ff erence between the curves for di ff erent element sizes, indicating that the PST specimen is not highly mesh-sensitive. Fig. 4 displays the crack path results for two di ff erent mesh sizes, which align with the experimentally observed crack paths. The crack path predicted by the JC model is similar to that of the MMC model. The results for the ISS specimen are discussed next. As opposed to the PST specimen, the damage models influence both the force-displacement (see Fig. 5) and the crack path response of the simulations. For the JC model, the mesh convergence is not fully realized because the results do not converge as the element size is reduced. This is also the case for the crack paths as the model is not able to reproduce the experimentally observed cracking behaviour. In Fig. 6, it can be deduced that mesh size has an e ff ect on both the nucleation region of the crack and its path into the