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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necessary preparatory techniques are applied. Such procedures can obscure and modify the natural physical mechanisms associated with crack - pore interactions and thus produce misleading results. Instead, a simple geometric scheme of the crack front with the plastic zone within a defined space distribution of pores will be employed to describe their mutual interactions and connections. In this simplest model variant, the pores with an equal radius of r = 7.82 µm in both the compound and the porous filaments are regularly distributed in space following the repeating structure of the bcc cubic cell. The pore radius nearly reflects the mean pore sizes in the real filaments. Since two pores belong to this cell with the edge a o , the porosity p is defined as p = 8 π 3 /3 o 3 ∙ 100 [%]. Thus, for the compound filaments the porosity of 6 % corresponds to the cube edge a o,c = 40.6 µm, whereas the cube edge a o,p = 29.9 µm for the porous filaments. The basic crack is represented by a half-plane, placed in the Cartesian coordinate system so that its front is identical to the coordinate axis z . The direction of the x -axis represents the direction of crack propagation, values x ≤ 0 lie in the already cracked part of the material ( x = 0 corresponds to the crack front), and values x > 0 lie in the still intact part of the cell. The plastic zone is limited by a constant distance from the crack front (towards positive x values) and thus has the shape of a half-cylinder with the crack front as the cylindrical axis. Its radius (size of the plastic zone) is denoted R pz . The primary lattice (the cubic cell) is oriented so that the cube lies at the origin of coordinates and its edges are identical to the coordinate axes. However, this primary lattice is not used in any model. It is translated and rotated before being used for calculations, thus creating a number of various positions of the lattice with respect to the basic crack (see Appendix A) to simulate the growth through the polycrystalline material. For each position, the new tortuous fracture surface is created by connecting the pores ahead the crack front having a non-empty intersection with the plastic zone area (see Appendix A for more details). In this way, tortuous fracture surfaces composed of rectangular segments simulating the planar slip systems causing the shear fracture of inter-void ligaments inside the plastic zone are created for all positions. Then the statistical averaging is performed to determine the roughness parameters S a , S dr and R L of the model fracture surface (see Appendix B) which can then be compared to those measured on real fracture surfaces. The static (cyclic) plastic zone size is a function of the applied stress intensity factor (SIF), so it varies with the applied stress, the crack length in the filament, and the yield strength (depending on the porosity). Therefore, a sufficiently wide range of possible plastic zone sizes should be considered in the model to cover the conditions of fatigue tests. This model is assumed to be verified by comparing selected computed roughness parameters with those measured on fracture surfaces of scaffold filaments with the porosity of 6 % and 15 % subjected to the cyclic three point bend test. According to our preliminary analysis, a sufficient range of plastic zone sizes at the crack tip related to these tests should be R pz ϵ (10; 150) µm, where the lower values correspond to high -cycle fatigue and the higher values to low-cycle fatigue. 3. Computational results and their discussion The most important parameters useful for the quantitative description of shielding processes and crack path length are S dr and R L (see Pokluda et al., 2004, Pokluda and Šandera , 2010 and Appendix B). Therefore, the computational results of these parameters will be discussed first and in more detail. The dependences of the roughness parameter S dr on the plastic zone size R pz for both porosities are plotted in Fig. 1. The S dr -values are distinctly higher for the higher porosity, which means higher shielding effects indicating a higher fatigue life of porous filaments when compared to the compact ones. As also expected, the S dr -values increase with the increasing R pz -values, i. e., with an increasing fatigue loading and a decreasing number of cycles to failure. Slámečka et al. (2024) computed that the yield strength of the porous filaments is 1.23 times lower than that of the compact filaments, and thus the plastic zone sizes in porous fibers are expected to be 1.5 times higher than those in compact fibers. This is correspondingly expressed by the mutual shift of R pz ranges for compact and porous filaments in Fig. 1. To illustrate the structure of the computational model in more detail, the statistical frequency distributions of S dr -values related to variants of the constructed fracture surface are plotted for both porosities in Fig. 2 as an example for R pz = 60 μm.