Issue34

T. Makino et alii, Frattura ed Integrità Strutturale, 34 (2015) 334-340; DOI: 10.3221/IGF-ESIS.34.36 339 Δ K II increased with increasing L , but Δ K I slightly decreased simultaneously. A case of L = 50  m implies that the vertical crack tip reaches the bottom of the defect. On the other hand, a case of L > 50  m implies that the vertical crack tip is before reaching the bottom of the defect. Δ K II at L = 50  m was larger than that at L = 100  m. This result suggests that when the vertical crack tip reaches the bottom of the defect, the increase of Δ K II due to crack propagation exhibits slowdown or decrease; the propagation of the vertical crack is retarded. -1500 -1000 -500 0 500 1000 1500 -3 -2 -1 0 1 2 3 Shear stress τ ｙz [MPa] y/a Plane (W/O defect) L=100μm L=150μm L=200μm z=0.1mm Figure 7 : Variation in shear stress at 0.1 mm depth during rolling contact obtained from elastic–plastic FE analyses. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 50 100 150 200 250 SIF [MPa√m] Defect length in depth direction L [μm] V-S, KI V-B, KII(Plane stress) V-B, KII(Plane strain) Figure 8 : Comparison of Δ K I at the surface edge of vertical crack and Δ K II at the bottom of vertical crack between different defect lengths (V:vertical crack, S:surface, and B:bottom). D ISCUSSION ynthesizing the above experimental and analytical results, the authors believe that the degradation of flaking life due to the longer length of defect with the diameter of 15  m is caused by the following mechanism. Vertical cracks are likely to form at surface edge of defects because a remarkably large tensile residual stress is generated and tension– compression and alternate shear stresses vary widely during rolling contact. Vertical cracks propagate in depth direction along defects, later, when the vertical crack tip reaches the bottom of the defect, the propagation of the vertical crack is retarded. Therefore, longer defects lead to rapid propagation of vertical crack. The authors’ previous study [6] revealed that the existence of vertical cracks accelerates the propagation of horizontal cracks causing flaking. Above process implies that longer defects shorten the flaking life. On the other hand, flaking life in the case including a defect with the diameter of 50  m does not change regardless of the difference of the defect lengths. This is probably because the horizontal cracks form and propagate before vertical cracks grow to the effective size. S