PSI - Issue 23

Hector A. Tinoco et al. / Procedia Structural Integrity 23 (2019) 529–534 H.A. Tinoco/ Structural Integrity Procedia 00 (2019) 000 – 000

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2.2. Finite element modelling

A finite element analysis was performed for a center-crack tension (CCT) specimen made of the railway axle steel EA4T under plane stress conditions as shown in Figure 1a. Mechanical properties of the material are listed in Table 1. As noted, the specimen is symmetric and therefore only 1/4 of the specimen is considered for the analysis. Under plane stress state, a 2D model was used and the displacement constraints imposed as boundary conditions that are demarked and illustrated in Figure 1b. A multi-linear material model with kinematic hardening based on the cyclic stress-strain curve determined for a railway axle steel (Pokorny et al. 2017; Vojtek et al., 2019). In order to control the triangular mesh size around the crack tip, a geometric strategy was proposed as depicted in Figure 1c. This consisted in dividing the geometry until getting a scale of 10000:1 to achieve a distance of the first node to 99.5 nm of the crack tip as evidence in Figure 1c, section E-E. Therefore, the distance ratio (distance ratio of the first node and the crack length) was 3 2 10 %   , which is smaller than the minimum ratio of 1% recommended by Shivakumar and Newman (1989). The loading was applied as one and a half cycles without propagation, i.e. a constant crack length of 5 mm, as detailed in Figure 1c, section A-A. The finite element simulation was conducted with 225 load steps using the ANSYS 16.1 software.

Table 1. Mechanical properties of the EA4T railway axle steel. Mechanical property Value Young’s modulus ( E ) 204 GPa Poisson’s ratio ( v ) 0.3 Yield stress – cyclic ( σ y ) 420 MPa

Fig. 1. (a) Center-crack tension (CCT) specimen. (b) Symmetry of the CT specimen (quarter model) and its boundary conditions; (c) Finite element meshes in different multiscale geometries; (d) Applied loading to the specimen in steps. 3. Results and discussion In Figure 2, Von Mises stress distribution plots for three loading stages (loading stage I, unloading and loading stage II) are shown. It is pointed out that in the first one loading stage, plastic stress fields start to grow around the crack tip until the maximum load of 23000 N. After reaching this loading level, unloading began by gradual decrease of the force, where the plastic zones were given by the residual compressive stresses. For example, the contours in Fig. 2 obtained for the same loading 5400 N, 10800 N and 16200 N during loading and unloading can be compared and differences in the stress distributions can be seen clearly.