PSI - Issue 66

Ramdane Boukellif et al. / Procedia Structural Integrity 66 (2024) 55–70 Ramdane Boukellif et al. / Structural Integrity Procedia 00 (2025) 000 – 000

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aim of this work is also to apply the developed method for the investigations of crack growth for practically relevant issues e.g., the rolling contact in planetary gears (Boukellif et al. (2024)). 1.1. Theoretical framework The 1 ′ -criterion from Schöllmann et al. (2002) was used for the prediction of the crack path. This criterion is based on the assumption that crack grows perpendicular to the direction of 1 ′ which represents a special maximum principal normal stress (see Fig. 1). The Stress 1 ′ is defined by the near-field stresses , and as follows: 1 ′ = ( + )⁄2 + 1⁄2 √( − ) 2 +4 2 (1) The description of the crack growth direction in a three-dimensional structure is done by 0 , the local kinking of the crack front and 0 , the local twisting (see Fig. 1). Fig. 1. Definition of 1 ′ , the kinking angle 0 and the twisting angle 0 (Schöllmann et al. (2001)). To determine the propagation angles, the stress intensity factors are calculated for all three crack opening modes , and . In ADAPCRACK3D, these stress intensity factors are calculated using the MVCCI method (Rybicki et al. (1977)). The crack propagates perpendicular to the direction of 1 ′ . From this assumption, the kinking angle 0 is calculated as 1 ′ ⁄ | = 0 = 0 2 1 ′ 2 ⁄ | = 0 <0 (2) The twist angle 0 can then be found by the calculation of the angle of the principal normal stress as follows: 0 = 1⁄2 (2 ( 0 ) ( 0 )− ( 0 ) ⁄ ) (3) For cracks subjected to superimposed loading, it is advantageous to use a comparative stress intensity factor for 3D Mixed-Mode-Loading so that