PSI - Issue 42

Shahin Takht Firouzeh et al. / Procedia Structural Integrity 42 (2022) 1069–1073 Shahin Takht Firouzeh / Structural Integrity Procedia 00 (2019) 000–000

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4. Cohesive Zone Model

Based on the experimental observation, the crack initiated at the hole tip and the crack propagates along the vertical diameter. In this regard, a three dimensional finite element model was created in Abaqus FEA for the numerical simulation of BDTs. The model includes cohesive zone elements along the crack path. Only a forth of the volume was modeled for the sake of calculation cost, due to the existing symmetry lines along the x- and z-direction. The thickness of the cohesive elements was taken as 0 . 0001 mm. The maximum of the cohesive traction-separation curve namely the cohesive strength t 0 , and the separation at the maximum traction s 0 are the main features of the cohesive law. Bi-linear cohesive law was applied in this work. E cz = t 0 / s 0 is given as the sti ff ness of the cohesive zone. Damage of the cohesive zone D cz begins to evolve if the maximum separation stress t 0 at the given separation length s 0 is reached. In addition the separation energy Γ 0 , which is the area under the bi-linear curves is another parameter that is taken as input to the model.

Fig. 3. Bilinear cohesive law and schematic view of the model

These mentioned parameters are obtained by minimizing the di ff erence between the force amplitude obtained from the experiments and the simulation outputs using a Levenberg–Marquardt optimization algorithm.

5. Results

Due to the high porosity of the filter materials the applied loads at the disc circumference creates contact point problems regarding y-displacement data accuracy. In addition to this, the magnitude of the applied loads at high temperatures make the ceramic parts of the test setup prone to deformations. Therefore, measured force data on the specimens until failure was used to identify the high temperature material parameters. To obtain cohesive parameters of the material the scheme given in Fig. 4 was applied. Therefore, elastic modulus and cohesive zone parameters could be obtained. Resulting fracture toughness is obtained using the equations (1) given below. K I c = Γ 0 E ′ with E ′ = E (1 − ν 2 ) (1) Determined high temperature cohesive parameters for Al 2 O 3 -C, Al 2 O 3 -L-T-5:1 and Al 2 O 3 -L-T-3:1, as well as the fracture toughness values are given in Table 2. As shown in Fig. 4, the obtained simulation results provide a good agreement to the experimental results. The derived fracture toughness values match the values obtained with B3B tests for Al 2 O 3 -C in Zielke et al. (2016).

6. Conclusion

To obtain the high temperature behavior of the developed filter materials, BDT was applied. Considering the ge ometry of the specimens the crack path is favored along the loading diameter. Based on this assumption, a cohesive