PSI - Issue 17

Michal Vyhlídal et al. / Procedia Structural Integrity 17 (2019) 690–697 Vyhlídal et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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Because of high stress gradients surrounding crack tips and edges, highly refined meshes near the crack tip (Fig. 3a) and the bottom peak of cavity (Fig. 3b) with small elements in all directions are required. The crack was modelled as ideally sharp. Distance d was considered as the length between crack tip and bottom corner of the cavity, which are both potential stress concentrators. According to theories of finite fracture mechanics, see Taylor et al. (2005), Cornetti et al. (2006), Taylor (2017), we suppose, that the region under the distance d corresponds to current crack extension increment of final length. In our case we suppose that the bridge between initial crack (edge notch) and the cavity breaks at once.

Fig. 3. (a) Radial mesh around crack tip; (b) radial mesh around bottom peak of the cavity.

Table 1. Overview of the material’s parameters used in the numerical model. Layer E [GPa] ν [ – ]

K I,c [MPa∙m 1/2 ]

Matrix

44.04

0.20 0.30

0.50

Steel plates – The force loading was applied to the top plate. When applying this force, it must be considered the thickness of the model which is equal to = 1.0 m. To achieve the same stress field in model as in real experiments, the equality of stress acting on the top plate must be satisfied, see Equation (8). The relationship between the force 2 applied in the model and the force 1 applied on the real specimen is as follows ( B 1 is the real thickness and B 2 is the model thickness of the specimen): 1 1 = 2 2 (8) 2 = 1 ⋅ 2 1 = 1 ⋅ 1 4 0 0 00 = 25 ⋅  1 (9) 5. Results It is obvious from the results of finite element analysis (FEA) that the polygonal cavity serves as another stress concentrator and influences the stress state ahead of the crack tip, see Fig. 4. It is necessary to consider this fact when choosing the distance d . Otherwise, we will get a significantly higher applied force which is very dangerous in the case of structural design. From this reason d has been chosen as the whole length between crack tip and the bottom corner of the cavity. By means of the average tangential stress criterion (7), the critical values of the applied force F app were calculated. The first crack extension was evaluated considering varying initial crack (edge notch) length a 0 in the range 12 – 13.5 mm. The results are introduced in the Table 2. As you can see, the value of F app for crack 210