PSI - Issue 7

366 Igor Varfolomeev et al. / Procedia Structural Integrity 7 (2017) 359–367 Igor Varfolomeev et Al./ Structural Integrity Procedia 00 (2017) 000–000 achieved by means of multipoint constraints. Overall three symmetry planes are assumed in the analysis, whereas for the sake of clarity a half of the model and the principal symmetry plane = 0 are shown in Fig. 7 (cf. Fig. 8). A field of seed points was first stochastically generated within the defect affected area taking into account the number of non-metallic inclusions (Fig. 3b) and their distance distribution (Fig. 4b). Subsequently, each seed point was assigned a defect size according to the distribution function in Fig. 4a. Finally, one or several elements around seed points were removed from the model in such a way that their area projected onto = 0 plane corresponded to the defect size assigned to particular point. The depth of a defect in the direction was assumed to be equal to the minor defect size in the = 0 plane. Note that due to the three symmetry planes considered, the defect field in Fig. 7 is symmetric about both = 0 and = 0 planes. The modeling approach, as described above, regards the defects as voids, thus taking no account of the contact interaction between the metallic matrix and stiff non-metallic inclusions. The latter effect is intentionally neglected in this study, since its consideration considerably increases uncertainties in the boundary conditions. 8

Fig. 7. Finite-element model of a representative material volume with a defect field. The stress and strain calculations were then performed assuming cyclic tension loading applied in the direction, normal to the principal defect plane. The maximum stress was set to 800 MPa, the stress ratio to = 0.1 , the maximum number of cycles to 5,000. Fig. 8 shows damage patterns predicted around the defect field at different stages of the simulation, between 1,000 and 5,000 cycles. The parameter SDV34 plotted in the diagrams is equivalent to the damage parameter , so that the red area associated with = 1 represents fully damaged material. The results suggest that, after applying 5,000 cycles with the stress magnitude of 800 MPa, a crack is likely to be formed within the whole defect affected area. The respective crack shape is close to an elliptic one with the minor and major axes of about 2 = 1.6 mm and 2 = 2.8 mm, respectively. These results are in a good agreement with the experimental observations reported in Section 2.3. 4. Summary and conclusions Crack initiation and propagation under fatigue loading were investigated in high-performance rotor steel containing natural forging defects distributed in a material volume. The results can be summarized as follows: • In all specimens with defects, the crack formation around the defect field occurred after applying a considerable amount of load cycles with a high stress magnitude. All specimens sustained about 20,000 to 42,000 load cycles at 600 MPa or 800 MPa. • Even though crack initiation in the specimen FZ2 was concluded to start within the first loading block at 600 MPa, the subsequent crack propagation stage was significant.