PSI - Issue 80

Pavel Šandera et al. / Procedia Structural Integrity 80 (2026) 169–176 Šandera / Structural Integrity Procedia 00 (2025) 000 – 000

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Appendix B. Roughness parameters Roughness parameters S a (the arithmetical mean height) and S dr (the developed interfacial area ratio) for the created fracture surfaces were determined according to ISO 25178 as follows: 1 ( , ) d d a A S Y x z x z A =  , ( , )d d 0 A Y x z x z =  . Here A is the area of projection of the tortuous surface to the xz plane, Y ( x,z ) is the “ height ” of the crack profile in the point with coordinates x, z , measured from so-called reference height. 2 2 1 ( , ) ( , ) 1 1 d d dr A y x z y x z S x z A x z           = + + −                . The roughness parameter R L (the mean relative crack path length) for the created fracture surface was introduced for each coordinate z along the crack front relative to the projection length (i.e. the size of the plastic zone) and averaged along the crack front length l as follows: 2 1 1 ( , ) 1 d d pz L pz l R y x z R x z l R x       = +            . The real calculations of parameters S a , S dr , and R L are performed by numerical integration. From the values obtained for individual configurations of void grid positions relative to the primary crack, the arithmetic mean and standard deviation are always statistically determined. Note that S dr and R L are the most important parameters useful for the quantitative description of both the shielding processes and the crack path length. Indeed, the parameter R L directly expresses the mean relative crack path length, and quantity 1 + S dr expresses the relative area of the new tortuous crack surface towards the flat area. References Azar, A.S., 2024. Exploring the stress concentration factor in additively manufactured materials: A machine learning perspective on surface notches and subsurface defects, Theor. Appl. Fract. Mech. 130, 104298. Han, Q., Wang, C., Chen, H., Zhao, X., Wang, J., 2019. Porous tantalum and titanium in orthopedics, ACS Biomater. Sci. Eng. 5, 5798 – 5824. Murakami, Y., 2012. Material defects as the basis of fatigue design, Int. J. Fatigue 41, 2 – 10. Nakamura, T., Wang, Z., 2001. Simulations of Crack Propagation in Porous Materials, J. Appl. Mech. 68, 242 – 251. Noraphaiphipaksa, N., Putta, T., Manonukul, A., Kanchanomai, C., 2012. Interaction of plastic zone, pores, and stress ratio with fatigue crack growth of sintered stainless steel, Int. J. Fract. 176, 25 – 38. Pokluda, J., Šandera, P., Horníková J., 200 4. Statistical approach to roughness‐induced shielding effects, Fat. Fract. Eng. Mater. Struct. 27, 141 – 157. Pokluda, J., Šandera, P., 2010. Micromechanisms of fracture and fatigue: In a multi-scale context. Springer Ltd., London. Pokluda, J., Švejcar, J., 1999. Structural analysis of fatigue crack growth in ferritic ductile iron. In: Fatigue'99: Seventh International Fatigue Congress, EMAS, pp. 487 – 492. Putra, N.E., Moosabeiki, V., Leeflang, M.A., Zhou, J., Zadpoor, A.A., 2024. Biodegradation-affected fatigue behavior of extrusion-based additively manufactured porous iron – manganese scaffolds. Acta Biomater. 178, 340 – 351. Sarfarazi V., Haeri, H., 2016. Investigation of Micro Defect on the Shear Crack Growth Properties Using FRANC2D. In: 2nd Annual International Conference on Advanced Material Engineering, Atlantis Press, pp. 754 – 765. Skalka, P., Slámečka, K., Montufar, E.B., Čelko, L., 2019. Estimation of the effective elastic constants of bone scaffolds fabricated by direct ink writing, J. Eur. Ceram. Soc. 39, 1586 – 1594. Slámečka, K., Kashimbetova, A., Pokluda, J., Zikmund, T., Kaiser, J., Montufar, E. B., Čelko, L., 2023. Fatigue behaviour of titanium scaffolds with hierarchical porosity produced by material extrusion additive manufacturing, Mater. Des. 225, 111453. Slámečka, K., Skalka, P., Pokluda, J., 2024. Modeling mechanical properties of titanium scaffolds with variable microporosity. Adv. Eng. Mater. 2400535. Underwood, E., Banerjee, K., 1992. Quantitative fractography in: Metals handbook vol. 12, 193 – 210. Zhang, H., Toda, H., Hara, H., Kobayashi, M., Kobayashi, T., Sugiyama, D., Kuroda, N., Uesugi, K., 2007. Three-Dimensional Visualization of the Interaction between Fatigue Crack and Micropores in an Aluminum Alloy Using Synchrotron X-Ray Microtomography, Metallurgical and Materials Transactions A 38, 1774 – 1785.