Issue34

T. Makino et alii, Frattura ed Integrità Strutturale, 34 (2015) 334-340; DOI: 10.3221/IGF-ESIS.34.36 337 indicated by lines on the SEM views of Fig. 3. Cracks parallel to the surface and perpendicular to the defect were observed. The cracks are referred to as horizontal crack in this paper. In a comparison of the CT image and the SEM view, the shapes of defects and the locations of the horizontal cracks were almost the same respectively, but the shapes of vertical cracks in CT images (Fig. 3 (b), (d)) were smaller in the deeper region than those in SEM views. These results provide the validity of CT imaging and future task for optimizing imaging condition. Crack shapes and sizes between different number of cycles and defect lengths were compared from SEM views. Fig. 4 summarizes the comparison result in the same scale. A vertical crack initiated from a defect of 50  m length propagated in x and z (depth) direction from N = 1×10 4 to 1×10 6 . In comparison under the same cycles, horizontal cracks initiated from longer defects propagated longer. 50μｍ 1×10 6 L=50μｍ N= 1×10 4 L=100μｍ L=200μｍ y x z :Front line of vertical crack :Horizontal crack Diameter of defect : 15μm Rolling contact surface Defect Figure 4 : Comparison of crack shape and size between different number of cycles and defect lengths. F INITE ELEMENT ANALYSIS OF STRESS STATES UNDER ROLLING CONTACT E analysis was conducted using models with a circular hole and/or a crack to evaluate the effect of defect length on the stress states around the defect and the stress intensity factors (SIFs) of the RCF cracks. ABAQUS Ver. 6.12 was used for the FE analysis. FE modelling and analytical condition A numerical FE model for the RCF test was developed as shown in Fig. 5. The FE model comprises a rectangular block for the disc specimen and a hemisphere for the ball specimen taking symmetry into account. A circular hole of the same size as the artificial defect, whose diameter was 15  m, in the experiment was modeled in a small rectangular section. The section was tied at the centre of the disc specimen model. Models are classified into three types (i.e., defect without crack, vertical crack without defect, and defect and vertical crack; Fig. 5(b–d)). The defect model (Fig. 5(b)) comprises a hole with depth L = 0 (plane, no defect), 50, 100, 150, and 200  m. The vertical crack model (Fig. 5(c)) comprises a vertical crack with the surface half length c of 15  m and depth of 50  m. The crack size was determined from the CT imaging result. The defect and vertical crack model (Fig. 5(d)) comprises a hole with the various depths mentioned above and a vertical crack with the above size. A fine mesh was applied to the region around the crack tip; the minimum length between nodes was 0.0005 mm at crack tip and 0.00125 mm on the internal surface of the hole. The number of elements was 242,093 and 32,914 in the rectangular model and hemisphere model, respectively. Friction coefficients between the ball and disc specimen model and between crack faces were zero with the consideration of the oil lubrication. The elastic modulus and Poisson’s ratio were 205.8 GPa and 0.3, respectively. In the case of elastic– plastic FE analysis, an experimentally measured stress–strain curve was applied in the disc specimen model. A vertical force was applied to obtain the same Hertzian stress p max (5.22 GPa) as the experiment, then the half-width of the contact F