PSI - Issue 74

Marta Kianicová et al. / Procedia Structural Integrity 74 (2025) 38–43 Mara Kianicová / St ru ctur al Integrity Procedia 00 (2025) 000 – 000

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Roughness parameters Roughness parameters S a (the arithmetical mean height), S v (the maximum pit depth) and S dr (the developed interfacial area ratio) for the created fracture surfaces were determined according to ISO 25178 as follows:

1

A = ∫∫

,

( , ) d d Y x z x z

S

a

A

( ) min ( , ) v S Y x z = ,

   



2

2

1

( , )

( , )

y x z

y x z

∂

∂

  

      +

  

1 d d 

∫∫

1

S

x z

=

+

−

.

dr

 

A

x

z

∂

∂

A

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

( , ) d d 0 A Y x z x z = ∫∫ .

Note that S dr is the most important parameter useful for the quantitative description of both the shielding processes and the crack path length. Indeed, the quantity 1 + S dr expresses the ratio of the surface area of the tortuous crack and its projected area. The relative extension of the crack path R L can be expressed as R L = 3π (1 + S dr )/4 – see, e.g., Underwood and Banerjee (1992). References Han, Q., Wang, C., Chen, H., Zhao, X., W ang, J., 2019. Porous tantalum and titanium in orthopedics: a review, ACS Biomater. Sci. Eng. 5, 5798 5824. Pokluda, J., Šandera, P., Horníková J., 2004. Statistical approach to roughness‐induced shielding effects, Fat. Fract. Eng. M ater. Struct. 27, 141 157. Pokluda, J., Šandera, P., 2010. Micromechanisms of fracture and fatigue: In a multi -scale context. Springer Ltd., London. 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. Ryan G., Pandit A., Apatsidis D.P., 2006. Fabrication methods of porous metals for use in orthopaedic applications, Biomater. 27, 2651–2670. 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. Slám ečka, K., Skalka, P., Pokluda, J., 2024. Modeling mechanical properties of titanium scaffolds with variable microporosity. Ad v. Eng. Mater. 2400535. Underwood, E., Banerjee, K., 1992. Quantitative fractography in: Metals handbook vol. 12, 193 –210.