PSI - Issue 7

Stanislav Žák et al. / Procedia Structural Integrity 7 (2017) 254 – 261

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Stanislav Žák et al. / Structural Integrity Procedia 00 (201 7 ) 000 – 000

Fig. 2. Detail of tortuous crack front in FE model

The sub-model included pseudo-randomly generated shape of the crack front (Fig. 2), similarly as reported in previously published works devoted to in-plane serrated crack front and different specimen dimensions (Horníková et al. (2015 ); Žák et al. (2017)). As an input, maximal dimensions of asperities in direction parallel to the crack front and perpendicular to crack faces were defined along with the length of tortuous portion of the crack front. Maximal dimensions of asperities in the direction perpendicular to crack flanks were, in each point of the crack front, multiplied by a random number between -1 and +1. In the third stage of modeling, the resulting displacements from the first step were inserted as boundary conditions into the boundaries of the sub-model and the local SIFs were evaluated along the tortuous crack front via internal Ansys software calculation procedures developed for SIFs calculations (Ansys Inc. (2017)). An elastic behavior of material was assumed in the whole procedure which was repeated with different randomly generated crack geometries to encompass a statistical distribution of crack shape occurring in real specimens. 2.2. The analytical model for local stress intensity factor components It seems to be difficult to describe a shielding effect of statistically distributed asperities at the precrack front by one universal analytical formula. Nevertheless, a simplified one-facet model can be related to the real-like tortuous geometry as depicted in Fig. 3. This approach was already successfully used to evaluate the influence of different crack-front tortuosity on the fracture toughness measured for very high- strength steels subjected to various heat treatments (Pokluda et al. (2004)), where an analytical solution based on stress tensor transformations and simplified tortuous crack geometry was presented for the remote mode I loading case. Hereafter, this simplified approach will also be adopted for the remote mode II loading case. The model reduces the real crack geometry to one facet that periodically repeats along the crack front with the same characteristic dimensions: d m is the facet (asperity) width, Δ a is the length of the tortuous part and a + Δ a is the total length of the crack. The symmetric kink and twist of the simplified crack front is described by angles α and β respectively (Fig. 3). The twist angle β is calculated from the linear roughness R L of the real-like precrack front (obtained from FE simulations here) or of the real precrack front (obtained, e.g., from the stereophotogrammetrical fractography in the scanning electron microscope):

L       1 R

1

−

.

(1)

cos

β

=