PSI - Issue 13

B. Nečemer et al. / Procedia Structural Integrity 13 (2018) 2261 – 2266 Author name / Structural Integrity Procedia 00 (2018) 000–000

2265

2.2. Computational results Figure 6 shows the global direction of crack propagation for re-entrant and rotated re-entrant auxetic porous structures. The maximum stress concentration appears in one of the corner of the first base cell near the notch tip. Initial failure occurs after certain number of stress cycles (for re-entrant auxetic porous structures � ��� cycles for formation of initial crack of length � ��� �� and � ��� cycles for initial crack propagation until critical crack length � ��� ��� for rotated re-entrant auxetic porous structures � ��� cycles for formation of initial crak of length � ��� �� and � ��� cycles for initial crack propagation until critical length � ��� �� ).

Fig. 6. Crack paths in auxetic porous structures: re-entrant (AUX_1); (b) rotated re-entrant (AUX _2)

Thereafter, the complete computational procedure is repeated in the another cell with a maximum stress concentration. The given computational results are summarized in Table 2. It can be also seen from Fig. 6, that three subsequent cells are analyzed in respect to the formation of critical crack length. The determined total number of stress cycles according to Eq. (1) can be assumed as a total fatigue life of treated auxetic porous structures. Table 2. Computational results for the crack initiation and crack propagation period Critical crack length ���� Cycles for crack initiation Cycles for crack propagation Total fatigue life of cell AUX_1 AUX_2 AUX_1 AUX_2 AUX_1 AUX_2 AUX_1 AUX_2

First cell

0.9

1.3

302

219

325 124

561

627 172

780 117

Second cell Third cell

0.75

0.35

48 11

38

79

9 ∑ �

0.3

0.1

3

71

82

12

881

909

3. Conclusions The computational investigation of the fatigue strength of selected auxetic porous structures made of aluminum alloy 7075-T651 is presented in this paper. The crack initiation period, , is numerical calculated by the Fe-safe program, based on the elastic-plastic finite element model. The crack propagation period, , is determined using Paris equation, where the relationship between the stress intensity factor range and the crack length is determined numerically using Abaqus-software. The crack initiation and crack propagation periods are studied in three subsequent critical base cells until the formation of critical crack length. The total fatigue life, , of the auxetic porous structure under given boundary conditions is determined as a sum of and for each particular cells. The computational analysis has shown that the number of loading cycles required for the crack initiation and crack propagation decreases from cell to cell for the selected auxetic porous structure. The number of loading cycles required for the crack initiation varied between 200 and 300 for both auxetic structures, while the number of loading cycles for the crack propagation until final breakage of the firs cell varied between 300 and 600, which corresponds to the regime of low cycle fatigue. It is interesting that at the end of the crack propagation through the third cell the number of total cycles, , are almost the same for both auxetic structures ( � ��� for re-entrant auxetic porous structure and � ��� for rotated re-entrant auxetic porous structures).