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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1. Introduction Advanced 3D metallic porous structures produced by additive manufacturing (AM), known as scaffolds, find applications in biomedicine as the bone implants (e.g. Han et al., 2019). The scaffolds contain interstrand pores controlled by the digital design (fractions of millimeters in size), the so called macroporosity, and intrastrand pores in the scaffold filaments (fibers) controlled by the state of sintering (tens to hundreds of micrometers in size), the so called microporosity. Among various AM techniques, sinter-based methods such as direct ink writing (DIW) provide control over both types of porosity. The microporosity of filaments has many positive effects on implant osseointegration and biomechanical compatibility. On the other hand, the micropores in the material are a concern in fatigue design due to being crack initiators and thus reducing the fatigue life, as reported, e.g. by Murakami (2012). It seems, however, that there could be a rather high level of microporosity still ensuring a sufficiently high resistance to fatigue damage. Indeed, a high normalized fatigue strength was reported for DIW iron – manganese lattices with ~22 % microporosity by Putra et al. (2024). Moreover, our previous research performed by Slámečka et al. (2023) has shown that the titanium scaffolds produced by DIW with the higher 15 % microporosity of filaments (porous scaffolds) exhibited superior fatigue strength, markedly better than the fatigue strength of scaffolds with the smaller 6 % microporosity (compound scaffolds). This improvement was in Slámečka et al. (2023) primarily attributed to crack pore interaction mechanisms, operating during the crack-growth stage, such as crack deflection, branching and crack path extension , described by Pokluda et al. (2004) and Pokluda and Šandera (2010) . The reduction of stress intensity factor (SIF) due to deflection and branching (crack tip shielding) is partially compensated by antishielding effects as an interaction of crack front with the pore surface reported by Zhang et al. (2007) and the porosity-induced reduction of the Young´s modulus , as mentioned by Pokluda and Švejcar (1999) . A two-level finite element model then revealed that the fatigue crack initiation stage in both porous and compact scaffolds is negligibly short (see Slámečka et al. , 2024), thus confirming a decisive importance of the crack growth stage for the fatigue life of scaffolds. This means that a sufficiently reliable quantitative prediction of the dependences of both the fracture surface roughness parameters and the crack-path length on the porosity would be very useful. The aim of this article is to present a first simple version of the model of fatigue crack path in metallic materials with variable porosity. It should provide a primary test of the relevance of basic principles used and reflect the difference between the crack paths in porous and compact filaments in a reasonable way. The final version of the model is then expected to correctly predict a general dependence of scaffold fatigue resistance on the microporosity. Given the high cost and time investments associated with the production of scaffolds and their fatigue testing, the model is assumed to help to define a range of microporosity worthwhile to be tested in subsequent fatigue experiments. It should also improve our basic understanding of the mechanistic response of scaffold filaments and help to optimize their microporosity. 2. Basic principles and design of the model Given the previously published models and in situ observations of crack propagation in porous metals (see Pokluda and Švejcar , 1999, Nakamura and Wang, 2001, Pokluda et al., 2004, Zhang et al., 2007, Noraphaiphipaksa et al., 2012, Sarfarazi and Haeri, 2016, Azar, 2024, Slámečka et al. , 2024), the following basic findings are to be considered: (i) the concentration of pores observed on the fracture surface is higher than that both in the bulk and on the metallographic sections, which means that the crack front inclines towards the nearby pores and passes through them; (ii) a decreasing width of crack-pore ligaments increases SIFs at the crack front, which is therefore attracted by the pores (antishielding); (iii) a rapid crack-pore coalescence begins when the static and/or cyclic plastic zone at the crack front touches the pore surface; (iv) the crack tends to propagate along the shortest path between neighboring pores; (v) in cast metallic materials containing some (limited) level of porosity, the anti-shielding effects compensate for (or even slightly prevail over) the shielding effects; (vi) in the highly porous materials, the crack-pore interactions can significantly extend the fatigue crack path; (vii) the cohesive elements in the numerical crack-growth models may artificially increase the model compliance and introduce numerical errors. Given the above findings, the first version of our model is designed to reflect practically all these principles, but at the same time be as simple and physically transparent as possible. This particularly means that no FE methods and cohesive elements approaches will be used, as this kind of modelling may be too influenced by the way in which the