PSI - Issue 39

Giovanni Pio Pucillo et al. / Procedia Structural Integrity 39 (2022) 700–710 Author name / Structural Integrity Procedia 00 (2019) 000–000

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4. Conclusions and future works An experimental campaign has been conducted on expanded and not-expanded specimens extracted from railway rails, with two load levels and two degree of cold expansion, 2% and 4%. All the specimens have been submitted to stress relieving and to an accurate surface finish treatment, with the aim to be sure that the only parameter affecting the fatigue crack growth rate was the residual stress field due to cold expansion. It is found that with cold expansion degree equal to 2% the fatigue life increases of about 50% to 100%, whereas with 4% of CE an increase of about 200% is found. Data acquired by crack gauges have been analyzed and synthetized, and two crack configurations have been used for the analytical expression of the stress intensity factor. Starting from the data acquired with the not-expanded specimens, the parameters of the propagation law proposed by Forman have been deduced for the specific loading conditions used for the experiments. Successively, for the expanded specimens - at 2% and 4% - fatigue crack growth has been simulated using FE predictive models based on the superposition between the stress intensity factors calculated with the weight function and concerning the residual stress field induced by cold expansion, and the one generated by the external loads. The predictive model overestimates the cycles to rupture by a factor of 2, or 8 in the worst case, which is consistent with the literature. The higher predicted crack growth rates suggest the inadequacy of models based on the Linear Elastic Fracture Mechanics, and future studies will provide for the development of a FE model that is able to take into account diffuse plasticity for the computation of the stress intensity factor in presence of residual stresses and external loads. Appendix A. Finite element formulation The finite element model was built in Abaqus environment (Simulia 2011), modelling only one-eighth of the geometry because of symmetry considerations (Fig. 8). The nonlinear behaviour of the material was simulated using the nominal stress-strain curve σ nom ( ε nom ) measured experimentally with five tensile tests carried out on specimens extracted from the R260 rails. The Young’s modulus is equal to 210 GPa, whereas the yield strength and the Poisson’s are 507 MPa and 0.33, respectively. Because Abaqus requires the input in terms of true stress, σ true , and logarithmic plastic strain, ε p ln , the following well-known relationships were used (see the graphical results in Fig. 9): = (1 + ) ; = (1 + ) ; = − (3)

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Fig. 8. Geometry and boundary conditions of the FE model.