Issue 35

S. Glodež et alii, Frattura ed Integrità Strutturale, 35 (2016) 152-160; DOI: 10.3221/IGF-ESIS.35.18 157 Crack propagation period for pores distribution in transversal direction The crack initiation period of each critical cross section is finished with the formation of initial crack of length a i after the appropriate number of stress cycles N i . The crack propagation period is then analyzed using Paris Eq. (3), where the following material parameters have been considered [20]: 12 3.86 m/cycle 4.608 10 (MPa m ) C    ; m = 3.86; th 20.8 MPa m K   ; Ic 30.4 MPa m K   Than, the stress intensity factor is determined numerically using Abaqus FEM software, where the equivalent stress intensity range  K eq as a combined value of mixed mode conditions  K I and  K II has been considered. To analyse the fatigue crack growth under mixed mode conditions the value  K in Eq. (3) has to be replaced with the value  K eq . The crack propagation angle is in each calculating step determined using maximum tensile stress (MTS) criterion. The analysis of crack propagation has been stopped when the equivalent stress intensity factor range  K eq exceeded the critical value  K I c or when the crack reached the vicinity of neighboring pore. At that moment it was assumed that two neighboring pores are connected with a seam and the computational procedure was continued with the crack initiation period in other critical cross section. Fig. 7 shows the numerical procedure of crack propagation in a cross section No. 1. Figure 7 : Schematic procedure of crack propagation period in a cross section No. 1. Crack initiation and propagation period for pores distribution in longitudinal direction When studying the case of pores distribution in longitudinal direction, more homogenous stress and deformation field has been found around the longitudinal pores. This finding is also in agreement with the experimental work published in [10] where authors have pointed out that the stress concentration around the pores is in the case of longitudinal pores lower if compare to the transversal pore distribution. Therefore, the crack initiation and crack propagation period for longitudinal pore distribution has not been studying in the framework of this paper. It was assumed that the fatigue life for crack initiation and further for crack propagation until critical crack length would be much longer if compared to the treated calculation for transversal pores distribution. C OMPUTATIONAL RESULTS AND DISCUSSION ig. 8 shows the numbering of critical cross sections where both, crack initiation and crack propagation period have been studied. The maximum stress concentration appeared first in cross section No. 1 where initial failure occurred after certain number of stress cycles ( N i = 472 cycles for formation of initial crack of length a i = 0.05 mm and N p = 212 cycles for this initial crack to propagate until critical length a c = 0.15 mm). Thereafter, the complete computational procedure is repeated in a cross section No. 2, where the maximum stress concentration occurred in the next calculating step. Here, the seam between neighboring pores in a cross section No. 1 is considered during the numerical analyses. As shown in Fig. 8, seven subsequent cross sections have been analyzed in respect to the crack initiation and crack propagation period in treated lotus-type porous structure with pore distribution in transversal loading F a i = 0.05 mm  K eq = 15.9 MPa  m 0.5 a = 0.10 mm  K eq = 20.7 MPa  m 0.5 a = 0.15 mm  K eq = 27.5 MPa  m 0.5