PSI - Issue 23

Pavol Dlhý et al. / Procedia Structural Integrity 23 (2019) 185–190 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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This way, a set of deflections is obtained, from which the tangential residual stress values in the layers can be calculated. The calculation is based on the theory of curved beam bending. It is assumed that the total bending moment acting on the ring is a sum of contributions caused by the stress in every layer. The total bending moment is known, because it can be calculated from the measured deflection of every ring. The only unknown values are the values of stress. If the sum is written for every ring, a system of linear equations is obtained. Solving the system of equations including a condition of balance (sum of the tangential stress values must be zero) yields the discrete tangential stress values in the layers. To determine tangential residual stress in the railway axle, it is necessary to cut out a cylindrical segment directly from the axle. Due to axle geometry it was possible to cut out only a 280 mm long segment. Therefore, it was necessary to determine the optimal number of rings and layers. To do that, FEM investigation of the slit ring procedure was carried out. Parametrical models of rings with geometry corresponding to proposed experiment was created. Only one quarter of the ring was modelled taking advantage of two symmetry planes. The linear elastic isotropic material model of steel was used in the simulation, Young's modulus of 210000 MPa and Poisson number of 0.3. The model was simulated with different boundary conditions for the non-slit ring (Fig. 2 a) and for the slit ring (Fig. 2 b). In case of the slit ring, the symmetry condition in the x direction is applied at only one surface, the other is left free (unlike the non-slit ring, where both surfaces are fixed). Leaving one end unconstrained allows tangential residual stress to release and the whole ring gets distorted by total bending moment caused by the residual stress. Distortion and tangential stress distribution inside the non-slit ring and the slit ring can be seen in Fig. 3 a and Fig. 3 b, respectively. The distortion of the ring in Fig. 3 b is intentionally enlarged to be visible in presented size. Also, there is no material removed by cutting, the deformation of the model represents the behavior caused by residual stress. The deflection was calculated for all dimensions of rings that would be used in an experiment. The number of rings and their dimensions depend on the assumed number of layers – several variants were simulated. Then, the tangential residual stress values were

Fig. 2 Boundary conditions for the non-slit ring (a) and for the slit ring (b)

Fig. 3 Tangential stress distribution in the non-slit ring (a) and in the slith ring (b)