PSI - Issue 46

J. Bialowas et al. / Procedia Structural Integrity 46 (2023) 49–55 J. Bialowas et al. / Structural Integrity Procedia 00 (2021) 000–000

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These multiple rollovers cause a complex stress state and plastic deformations at the surface. Perenda et al. (2015) used for these requirements a combined isotropic-kinematic hardening material law that is calibrated to a small number of cycles. (ii) The most common simplification of the axle geometry for deep rolling simulations is a cylinder sector. Both the aperture angle and the length of the sector must not only be chosen appropriately to the process parameters feed and load but also to the geometries of the axle and the work roller. However, the boundary conditions at the remaining free surfaces in tangential direction of these cutouts represent one of the difficulties of modelling the deep rolling process. Previous works try to replace the remaining axle of the cutout cylinder sector with various boundary conditions, see Perenda et al. (2016) and Majzoobi et al. (2016). (iii) So far, these boundary conditions have resulted in models that are divided into two domains, one near the center and one close to the boundaries, see for example Klocke et al. (2009). Most modeling approaches evaluate the results in this central domain called region of interest. The remaining geometry called auxiliary region serves the sole purpose of minimizing the boundary effects on the region of interest. Recently Meyer et al. (2021) proposed the use of periodic boundary conditions on cyclic wheel rail simulations. This method minimizes the auxiliary region and provides evenly distributed results. Moreover, it significantly reduces the number of degrees of freedom and thus reduces the computation time. The following chapter gives a guideline to implement the cyclic material behaviour and a simplified geometry in an implicit finite element model using such coupled boundary conditions and so-called shadow elements with the commercial software Abaqus. 2. Method In the first step of modeling the deep rolling process, the geometry of the axle is reduced to a representative cylinder sector as depicted in Fig. 2. The second simplification is a change in the kinematics of the process, because the computation is more efficient when elements move as little as possible. The work roller is modeled as an analytical rigid fully defined by D WR and R WR , see Fig. 1. Therefore, the axle remains stationary and the roller performs the relative movement exclusively. The kinematics are modeled with connector elements based on Balland et al. (2013). This setup allows for both a force and a displacement-controlled process. Furthermore, this can impose every motion of the roller from gliding to rolling, with or without considering friction. The choice of a cylinder sector as a simplified geometry inevitably leads to the work roller having to be lifted off and reset at the end of each rollover. This is accomplished by dividing each rollover into five steps: preload, load, rolling, unload and return, as indicated in Fig. 2 (a). The purpose of the preload step is to establish contact between the work roller and the surface of the axle. Since this surface changes after each rollover, the exact position of it is unknown before the analysis. The setting of the contact controls is adjusted in this step to allow a force-controlled movement of the roller towards the surface (Abaqus). In the following steps, this setting is reset to the automatic setting and is only activated again in the preload step of the following rollover. Although the simplifications transform the continuous process of deep rolling into a discontinuous one, the aim is to implement the continuous characteristics of this process in the model. In previous models the rolling starts and ends with sufficient distance to the boundaries in tangential direction generating inhomogeneous distributions of results, especially close to these boundaries. These numerical artifacts, created by boundary effects, extend over large areas of the model and allow results to be extracted only in a small central region. A step towards a more homogeneous distribution of results would be to roll over the entire surface up to and including the boundaries. Coupling these boundaries with each other instead of applying an ordinary bearing can further reduce boundary effects. This creates a periodic cell that behaves as if several work rollers were simultaneously deep rolling the axle. Therefore, the displacement degrees of freedom of the nodes on the tangential faces of the cylinder sector are coupled (cf. coupled boundary conditions in Fig. 2). In order to remain independent of the aperture angle of the cylinder sector, the coupling requires local coordinate systems that are deflected from each other by the aperture angle. Thus, the behavior of the nodes � � � and � � � � in Fig. 2 (b) coincides in the respective coordinate system. The faces of the cylinder sector in axial direction are supported similar to a locating and non-locating bearing arrangement: One face is fixed and the other face is free to deform in axial direction.