PSI - Issue 17

D. Camas et al. / Procedia Structural Integrity 17 (2019) 894–899 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 3 shows the evolution of the stress-strain curves at the surface and in the mid-plane with the number of load cycles applied after the last node release. The stresses are normalized by the yield strength and are obtained in the nodes at the crack front. Positive values mean tension and negative ones, compression. Therefore, the crack opens when the stresses go over compression to tension and closes when go over tension to compression. As expected, the stresses at the surface are much smaller than the values in the mid-plane. Garcia-Manrique et al. (2013) showed that the stress distribution along the thickness is uneven, supporting more stress the interior than the surface. Besides, the crack closure effect influences the stress distribution, being more prominent at the surface than in the bulk of the material. It can be clearly seen the ratchetting effect in the mid-plane while at the surface, the curves collapse from the first cycle.

ͲǡͶ Ͳǡͷ Ͳǡ͸ Ͳǡ͹ Ͳǡͺ Ͳǡͻ Ͳ ʹ Ͷ ͸ ͺ (a)

ͲǡͶ Ͳǡͷ Ͳǡ͸ Ͳǡ͹ Ͳǡͺ Ͳǡͻ Ͳ ʹ Ͷ ͸ ͺ —„‡” ‘ˆ …›…Ž‡• ͳǡͷͲ ͳǡ͵ͻ ͳǡʹͺ ͳǡͲʹ Ͳǡ͸ͳ Ͳǡ͵Ͷ ͲǡͲͲ (b)

––…ŽȀ ƒš

––‘’Ȁ ƒš

—„‡” ‘ˆ …›…Ž‡• ͳǡͷͲ ͳǡ͵ͻ ͳǡʹͺ ͳǡͲʹ Ͳǡ͸ͳ Ͳǡ͵Ͷ ͲǡͲͲ

Fig. 4. Influence of the number of loading cycles after releasing the last set of nodes on tip tension (a) opening and (b) closure values.

Fig. 4 shows the crack opening and closure values based on the y -stresses along the thickness for the different number of loading cycles after releasing the last set of nodes. These values are normalized by the K max . It can be seen that both, opening and closure values are bigger at the surface than in the interior. As expected, the closure values are bigger than the opening values as the material is harmed while the load is applied, in particular during the plastic behavior which is responsible for the crack growth (Antunes et al. (2019)). The opening values at the surface are almost not affected by the number of loading cycles applied, while the ones in the interior slightly change, but the relative differences with respect K max are small and in the order of 0.5%. Closure results are much more stable all along the thickness. There is a slight linear relationship between the number of loads applied and the closure values, but the slope is so small that the influence of the loads applied can be neglected. The results based on the stresses are very stable and can be concluded that the number of loading cycles are not affecting much to the results.

4. Conclusions

The analysis developed in the present study set out to determine the influence of the number of loading cycles after releasing the last set of nodes on the crack opening and closure values based on y -stresses. It has been found that this parameter hardly influences the results obtained when considering this material. Therefore, the numerical effort should be focused on other numerical parameters that are affecting more to the accuracy of the results obtained.

Acknowledgements

This work has been supported by the Ministerio de Economía y Competitividad of the Spanish Government through grant reference MAT2016-76951-C2-2-P and by Universidad de Málaga through Plan Propio de Investigación y Transferencia. Besides, authors would like to acknowledge to Ministerio de Educación, Cultura y Deporte in the framework of the Programa Estatal de Promoción del Talento y su empleabilidad en I+D+i, Subprograma Estatal de Movilidad, del Plan Estatal de I+D+i through grant reference CAS18/00251 and the European Regional Development