PSI - Issue 76

N. Zani et al. / Procedia Structural Integrity 76 (2026) 59–66

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CT scanning at 160 kV, 2 µ m voxel size, 667 ms exposure, 1200 projections 3D images were reconstructed via FBP. Sub-surface cracks from surface defects (Figure 3d) had low contrast, so a Hessian matrix-based method ( Xiao and Bu ffi ere (2021)) was used to extract planar features and segment cracks (Figures 3e–f). For rolling contact fatigue crack propagation analysis, it is important to quantify the crack propagation length along the rolling direction versus transverse on the rolling direction. The propagation lengths of the crack in the above two directions are defined as the projected distances between the two opposite crack tips subtracted by the diameter of the hole bottom ( d = 0 . 36 mm) within central tomography slices. For example, as shown in Figure 3, the crack propagation length transverse is detected as ( L − d ).

Fig. 3. Schematic of the process of 3D characterization of cracks within disc-shape specimens (a) Geometry of disc-shape specimens; (b) The cut sample to meet the requirements of high resolution and X-ray penetration in tomography; (c) Laboratory tomography scans (voxel size about 2 µ m ;(d) Reconstructed slice (along the rolling direction); (e) Crack segmentation image by Hessian Matrix based method Xiao and Bu ffi ere (2021) (f) 3d rendering of crack image. The stress intensity factor ranges of cracks nucleated at the edge-bottom for bidisc samples were estimated using finite element (FE) models developed in ABAQUS ® . Figure 4 shows the flat plate model representing the bearing, where a half-symmetric, linear-elastic setup was used ( E = 210 GPa, ν = 0 . 3). The bottom surface was clamped, and the rolling contact was simulated via a moving Hertzian load passing over the defect in 24 time-steps, covering a total distance of 5 mm to replicate one complete load cycle. A general contact interaction with a friction coe ffi cient of 0.6 was applied on the crack surfaces. The crack was modeled as a ring at the bottom hole edge, with a radius ranging from 0.180 to 0.700 mm, and was finely meshed (0.002 mm) near the tip to ensure convergence. Mode II (rolling direction) and Mode III (transverse direction) ∆ K were calculated from the quarter-node displacements using Williams’ equations (Kuna (2013)):

E 2 π r 8(1 − ν 2 )

K II = ( u 1 − u 2 ) ·

(3)

E π 2 r 4(1 + ν )

(4)

K III = ( w 1 − w 2 ) ·

where u 1 , u 2 , w 1 and w 2 are the crack shear displacements (CSD) at the tip and r is the distance of the quarter nodes from the crack tip. Figure 5 shows the dimensionless SIF range ∆ K II /∆ K I , th and ∆ K III /∆ K I , th as a function of the crack radius under various contact pressures.