PSI - Issue 46

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A. Wetzel et al. / Procedia Structural Integrity 46 (2023) 10–16 Anna Wetzel et al. / Structural Integrity Procedia 00 (2019) 000–000

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d 1

d 2

a)

b)

d strand = 1.48 mm

d rope = 4.16 mm

Fig. 3. a) structure of a 6x7 WSC rope (core strand greyed), b) true stress-strain curves of the two different wires of the core strand.

3. Finite element model 3.1. Stranding

Fig. 4. shows the finite element model of the stranding process of the core strand modeled in Abaqus. The two different diameters and yielding limits for the central and the outer wires are considered. The disk is modeled as a discrete rigid. The geometry is inspired by real stranding disks but the exact geometry and other process parameters for this particular stranding process are not known. Since the wires are lubricated during the stranding process, a friction coefficient μ of 0.1 is assumed. The guidance, where the lubricant in the technical process is applied, is not represented in the FE-model. The stranding process is divided into two single-step analyses starting with all wires parallel. In the first analysis, the ends of the outer wires are moved until they almost contact the central wire in order to obtain the initial position for the stranding process. This first analysis is a static, implicit one. The second analysis simulates the stranding of the outer wires around the inner wire. Deviating from the technical stranding process, this includes simultaneous rotation and longitudinal movement of the stranding disk along with the rotation of the still parallel wire ends. A tension force of 10 N is applied to the unstranded end of each wire to simulate the tension force of the coil break. Due to a large number of contact interactions between stranding disk and wires, as well as between the wires themselves, it was mandatory to model this step as a dynamic explicit analysis. In order to find a balance between inertia forces and calculation time, the velocity curve is smoothed and the rotational speed n is reduced to 2.25 s -1 . As shown in Fig. 4. the stresses at the beginning and the end of the strand are higher due to the boundary conditions. To eliminate these nonuniform stress regions, each wire consists of three separate parts. The single parts are connected via mesh tie constraints using partition cells to ensure a coherent mesh transition between the three parts, despite different mesh sizes. The mesh of the transition area is depicted in Fig. 4., detail A. The middle wire parts are meshed in the circumferential direction with 22 elements and across the diameter with eight hexahedral elements of the type C3D8R. This results in an approximate element size of 0.07 mm. The front and end parts of the wires are meshed coarser using the same element type. When meshing the disk, the focus was on reproducing the geometry as accurately as possible, while keeping the number of elements as low as possible. Therefore, the choice is rigid tetrahedral elements of the type R3D3. To prevent the wires from twisting on both sides of the stranding disk, the still parallel wire ends must rotate along with the disk. As Judge et al. (2012) remark, the difference between stranding and mere twisting is the torsional free support of the outer wires during the stranding process. To achieve this, cylindrical connectors are implemented to the rotating ends of the outer wires. So far, the surface-based contact formulation general contact is used due to the good compatibility between implicit and explicit analyses.