PSI - Issue 4

Hans-Jakob Schindler / Procedia Structural Integrity 4 (2017) 48–55 Author name / tructural Integrity Procedia 00 (2017) 000 – 00

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(a)

(b)

Fig. 5: (a) K I as a function of crack-length on the x-axis (normalized by a unit nominal stress). (b) K I due to the residual stresses shown in Fig. 3(b) and the stresses due to the press-fit as shown in Fig. 4(b).

(a)

(b)

Fig. 6: Crack length as a function of the travelled distance for (a) three magnitudes of residual stresses, and (b) for three different strengths of the press-fit as characterized by d.

5. Discussion and conclusions

From Fig. 6 (a) it is evident that the effect of the residual stresses on the calculated safe life is dramatical. This indicates that a realistic prediction of safe life in presence of a real or hypothetical initial crack-like defect is hardly possible without taking the residual stresses into account. From the presented data and similar measurements reported by Gänser at al. (2016) it seems that the residual stresses in axles made of normalized steel are compressive near the surface. Their magnitude at the surface is in the order of -50 MPa, decreasing slowly with increasing depth. In a depth of about 20 mm the stresses change in sign and stay in the tensile region for the remaining part of the cross-section. However, for the fatigue life the outer regions of the axles are crucial. Therefore, neglecting the residual stresses leads to very conservative theoretical predictions of the fatigue life. Furthermore, as shown by the example in Fig. 3(a), local differences around the circumference may exist, so some positions on the circumference can be more prone to fatigue crack initiation and growth than others. Note that the presented results hold for a sharp pre-crack; in case of a smooth surface, the effect of residual stresses is less pronounced. A suitable method to determine the residual stress profile is the cut compliance method. Its advantage is that the SIF due to the residual stress is automatically determined as an intermediate result. The disadvantage is that it is a destructive measurement method and that it works accurately only in 2D, so global pre-cutting is required in case of a round bar.