PSI - Issue 43

Robert Szlosarek et al. / Procedia Structural Integrity 43 (2023) 41–46 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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2. Methods 2.1. Experimental Setup

Within the research a bolt joint of a nominal diameter of 22 mm and a sheet made of S355MC (1.0976) is investigated. The yielding limit of the material is about 370 MPa and the fracture limit about 560 MPa, cf. Szlosarek et al. (2022). This combination is in reference to a hub rim connection of a tractor. Fig. 2 depicts the used specimen as well as the test setup. The specimen is made out of hot-rolled sheet material with a thickness of 5 mm. The borehole has a diameter of 24 mm. The borehole is bolted with a bolt of size M22 with a pitch of 1.5 mm. A spacer is used to get a realistic elasticity in the system. The bolt is assembled with strain gauges to enable a measurement of the preload. The counterpart of the bolt is a nut of size M22. This nut has a pressure disk as it is used for tractors. The bolted sheet is fixed at both ends and tensed by a hydraulic actuator using a sine signal with a load ratio of R=0.1. A more detailed description of the test can be found in Szlosarek et al. (2022).

Fig. 2. (a) specimen; (b) test setup.

2.2. Numerical Model The calculation of the load cycles to crack was performed in two stages. First, a finite element analysis was done using the solver Optistruct 2021.2 to compute the local stress distribution. Second, the estimation of the fatigue damage and the expectable load cycles to crack was done in the software Hyperlife 2021 by a strain-based fatigue analysis. Fig. 3 (a) shows a section view of the used finite element model. The sheet material is meshed with hexahedron elements whereas the element size in the interesting zone around the borehole is about 0.5 mm. Both ends of the sheet are constrained by a rigid body while one end is fixed and on the opposite end the force is applied as it happens in the test rig. The bolt is simplified by a beam. This beam has the elastic properties of the real bolt. One end of the bolt is connected to the spacer via a rigid body and the other end to the pressure disk of the nut via a rigid body. Between the spacer and the sheet and the pressure disk and the sheet a surface to surface contact is modelled. The static coefficient of friction was determined in pretests with 0.23. The specimen is modelled with a pure elastic material model ( = 210000 , = 0.3 ) Fig. 3 (b) depicts all simulation steps. In step ① the bolt gets preloaded. This means that the pretension force is applied to the bolt and a pressure stress is induced in the sheet and the spacer. This could be seen as a simulation of the bolting process. This stress and deformation situation is transferred to step ② , hence the preload remains. Here, the minimum tension force of 13 kN is applied. Again, the stress and deformation is transferred to the next step where the maximum tensile force of 130 kN is applied, step ③ . Normally, a simulation of the minimum and maximum force wo uld be enough to perform a fatigue analysis. In this example it isn’t. In particular it is necessary to consider the continuous sliding of the pressure disk due to the alternating tensile force. Hence, more than one repetition has to be simulated to reach a stationary situation. A prior simulation pointed out that it is valid to perform the fatigue analysis using steps ④ and ⑤ .