PSI - Issue 13

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

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length , the complete fracture of remaining cross section occurs which mean that two neighboring cell are connected with a seam and the complete procedure for next critical location is repeated.

Fig. 4. Schematic procedure of crack initiation period (a.1) AUX_1 maximum stress concentration; (a.2) AUX_1 initial crack; (b.1) AUX _2 maximum stress concentration (b.2) AUX _2 initial crack.

Crack propagation period The crack initiation period of each critical cross section is finished with the formation of initial crack of length after the appropriate number of loading cycles . The crack propagation period is then calculated using equation (2). The material parameters and are considered from Melson (2014), while the critical stress intensity factor ∆ is taken from Dowling (2000):   14 3.64 / 9.83 10 ; 3.64; 917.1 Ic mm cycle C m K MPa mm MPa mm       Thereafter, the range of stress intensity factor ∆ is determined numerically using Abaqus software, where the equivalent stress intensity range ∆ as a combined value of mixed mode conditions ∆ I and ∆ II is considered:     2 2 2 1 eq I II K K K v        (4) The crack propagation angle in each calculating step is determined using Maximum Tensile Stress (MTS) criterion. The analysis of crack propagation stops when the equivalent stress intensity factor range ∆K Ic exceeds the critical value ∆K Ic or when the crack reaches the vicinity of neighboring cell. At that moment it is assumed that two neighboring cells are connected with a seam and the computational procedure is continued with the crack initiation period in the other critical cell. Figure 5 shows the numerical steps of crack propagation thru the first base cell in re- entrant and rotated re-entrant structure, respectively.

Fig. 5. Schematic procedure of crack propagation period thru the first base cell of porous structure ( a) re-entrant (AUX_1); (b) rotated re-entrant (AUX _2)