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

534 6

constant c 1 = 0.194

K

CTOD CTOD  



1 0.194

2 eff





10.2 nm 41 b  , where b = 0.248 nm is the magnitude of the Burgers vector in iron. Due to anisotropy and discrete nature of plastic deformation at nanoscale, the result obtained from the continuum mechanics must be corrected. According to Riemelmoser et al. (2001) and based on the discrete dislocation dynamics, the correction is suggested as follows: 0.15 CTOD CTOD DDD    , which gives b 1.53nm 6 CTOD    . This value is in a very good agreement with the crack propagation rate of 1 b per cycle at threshold loading and leads to a relation Δ a /Δ N = (1/6) ΔCTOD. If the correction found in this work was not used, the relation would be Δ a /Δ N = (1/32) ΔCTOD which seems less probable. Pippan et al. (2011) reported the proportionality constants in between Δ a /Δ N and ΔCTOD in air; i.e. For aluminum alloy (1/6.1) and for austenitic steel (1/4.3), which is comparable to our value of 1/6. This paper was focused on the estimation of the plastic zone size and crack-tip opening displacement by means of a nonlinear finite element analysis. A multiscale mesh on a center-crack tension (CCT) specimen was constructed to achieve a resolution of 99.5 nm in the first node that represented the distance from the crack tip. Crack tip opening displacement (CTOD) dependences and cyclic plastic zone sizes were determined. The analytical equations were calibrated by the numerical results using correction factors 1 c and 2 c for the railway axle steel EA4T. The corrected values corresponded to more realistic estimation of the crack propagation rate. 2 2 y E    Conclusions Anderson , T.L., 1995. Fracture mechanics: fundamentals and applications, CRC press. Caputo, F., Lamanna, G., & Soprano, A. (2013). On the evaluation of the plastic zone size at the crack tip. Engineering Fracture Mechanics, 103, 162 - 173. Chen, J., Jiang, L., & Huang, Y., 2017. A quantitative study on the influence of compressive stress on crack - tip opening displacement. Ocean Engineering, 143, 140 - 148. Hoh, H.J., Xiao, Z.M., & Luo, J., 2010. On the plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a circular inclusion. Acta mechanica, 210(3 - 4), 305 - 314. Jingjie, C., Yi, H., Leilei, D., & Yugang, L., 2014. A new method for cyclic crack - tip plastic zone size determination under cyclic tensile load. Engineering Fracture Mechanics, 126, 141 - 154. Liaw, P. K., Lea, T. R., & Logsdon, W. A. (1983). Near - threshold fatigue crack growth behavior in metals. Acta Metallurgica, 31(10), 1581 - 1587. Paul, S. K., 2016 a . Numerical models of plastic zones and associated deformations for a stationary crack in a C (T) specimen loaded at different R ratios. Theoretical and Applied Fracture Mechanics, 84, 183 - 191. Paul, S.K., 2016b. Numerical models of plastic zones and associated deformations for elliptical inclusions in remote elastic loading – unloading with different R - ratios. Engineering Fracture Mechanics, 152, 72 - 80. Pippan, R., Zelger, C., Gach, E., Bichler, C., & Weinhandl, H. (2011). On the mechanism of fatigue crack propagation in ductile metallic materials. Fatigue & Fracture of Engineering Materials & Structures, 34(1), 1 - 16. Pokorný, P., Vojtek, T., Náhlík, L., & Hutař, P., 2017. Crack closure in near - threshold fatigue crack propagation in railway axle steel EA4T. Engineering Fracture Mechanics, 185, 2 - 19. Riemelmoser, F. O., Gumbsch, P., & Pippan, R., 2001. Dislocation modelling of fatigue cracks: an overview. Materials transactions, 42(1), 2 - 13. Shivakumar, K.N., & Newman Jr, J.C., 1989. Numerical fracture simulation of bend specimens using a CTOD criterion. Engineering fracture mechanics, 32(2), 203 - 210. Yi, H., Jingjie, C., & Gang, L., 2010. A new method of plastic zone size determined based on maximum crack opening displacement. Engineering Fracture Mechanics, 77(14), 2912 - 2918. Vojtek, T., Pokorný, P., Kuběna, I., Náhlík, L., Fajkoš, R., &Hutař, P., 2019. Quantitative dependence of oxide - induced crack closure on air humidity for railway axle steel. International Journal of Fatigue, 123, 213 - 224. Acknowledgements Financial support was provided by infrastructural project m-IPMinfra (CZ.02.1.01/0.0/0.0/16_013/0001823). The equipment base of research infrastructure IPMinfra were used during the research activities. References