PSI - Issue 35

Vera Friederici et al. / Procedia Structural Integrity 35 (2022) 106–114 V. Friederici et. al / Structural Integrity Procedia 00 (2019) 000–000

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of crack propagation in for example rotation bending specimens, the information of crack propagation rate for this R value is of great importance. A good prediction of crack propagation curves for various R values was introduced by Kujawski et al. (2001) and Dinda (2004). They introduce a crack driving force independent of crack closure mechanisms: ∆ = ∗ (1 − ), < 0, ℎ ∗ = ( ) ∗ ∆ ( 1− ) = 1 ∆ − (2) The value α is determined from the slope of the log-log plot of K max vs. ∆ K + (positive part of the applied stress intensity factor) for a given da/dN = constant. Using this approach crack propagation curves for different R ratios can be predicted. Another important input parameter for simulation is the threshold of crack propagation ∆ K th . A linear-extrapolation method was introduced by Döker (1997). He suggests to use a linear plot of the da/dN -data and extrapolation of the regression line to da/dN = 0. By this ∆ K th values can be determined easily. To assess the complete service life the overarching question is what proportion of the service life of a bearing is accounted for by the crack initiation and crack propagation phases. The experimentally obtained SN-curves are composed of an initiation and a propagation component (Barsom, 1987). However, since the fatigue tests to determine the SN-curves are performed on smooth, un-notched specimens, it is practically impossible to distinguish between the crack initiation and crack propagation phases. By linking SN-curves with knowledge of crack propagation rates, a crack initiation curve can be calculated by FE simulation. The estimation of the time required for crack nucleation is based on the idea of correlating the results of crack propagation simulation with rotation-bending fatigue tests. Assuming uniform propagation between the initiation site and the residual fracture surface based on Paris' law the number of oscillation cycles during the crack propagation stage can be predicted. This approach is carried out for different heat treatment conditions of 42CrMo4 bearing steel using Abaqus XFEM simulation. Assuming that the sum of the cycle number for crack initiation N i and the cycle number for crack propagation N p results in the number of cycles for total service life N t , N i can be calculated (Friederici, 2021). In order to be able to use the crack initiation SN-curve for the calculation of service life of a large bearing a conversion needs to be done regarding the highly loaded volume. The volume of a rotation-bending specimen is much smaller than that of a bearing. In order to minimize the error of this volume dependence, a FE calculation has to be done to determine the highly stressed surface area (Radaj, 2007) of the bearing ring A ring . Afterwards the fatigue life (crack initiation SN-curve) can be calculated by: 50 , = 50 , � � 1 (3) 2. Experimental 2.1. Materials characteristics and quasi-static parameters A slewing bearing made from 42CrMo4 steel (4 point contact, diameter of 2.3 m) was used as raw material. Various types of test specimen were cut out of the homogeneous area of the outer ring of the bearing (in the following called core). Tensile test and compact tension samples were only taken in “S-T”-orientation, rotation-bending and push-pull specimen also in the “L-S” orientation, as defined in ASTM E-399. After sampling the test specimen were divided into three batches. To mimic the hardened raceway and the transition region between core and raceway of the bearing different heat treatments, developed in dilatometric pre-trials, were carried out. Core material samples were used in the “as received” state. Tensile tests were carried out on 8-10 samples for each material condition on cylindrical tensile test specimen of 70 mm length and 5 mm diameter. Tests were run on servo-hydraulic tensile test frame (Schenck RM 250, Carl