PSI - Issue 37

Yulia Pirogova et al. / Procedia Structural Integrity 37 (2022) 1049–1056 Yulia Pirogova / Structural Integrity Procedia 00 (2021) 000 – 000

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Correlation functions and physical descriptors (for example, the volume fraction and the average size of particles or grains) can be used as formal morphological characteristics. Among stationary random functions, there is a class of ergodic functions, all the properties of which can be determined by a single sample implementation. The ergodicity hypothesis implies that monitoring of a stochastic system (for example, an evolving microstructure) for a long time will provide the same statistical indicators as many independent implementations of this system over time (Buryachenko, 2007; Fullwood et al., 2010). It allows to study one arbitrarily selected, sufficiently large member of the set to calculate the average value of the function over the volume (Zeman and Šejnoha, 2007) . Complete statistical description is often very difficult, if not impossible, and is not really necessary. Such description of the microstructure allows to go beyond where empirical data is available and find implementations of the structure that lead to certain specified properties. This paper presents the results of a study of the influence of the shape of voids in porous additively manufactured samples on their elastic properties and mechanical behavior based on morphology analysis using multipoint statistical characteristics. 2. RVE geometry models Geometrical models of structures with inclusions of different shapes were built. Tetrahedron, octahedron, cube, icosahedron and sphere were chosen as the inclusion forms. These figures were chosen according to the principle of increasing the number of angles, with transition from sharp-angled figures to a sphere. The inclusions were arranged randomly in the representative volume element. The side of the elementary cubic cell a=10. The maximum radius of the sphere circumscribing an inclusion is 1.5. By varying the value of the volume fraction p , different models of structures were obtained. Examples of some structures are shown in Figure 1.

Fig. 1 A representative volume with the forms of inclusions tetrahedron and cube, а =10, p =0.05 and p =0.25.

The cases for the spherical shape of inclusions were also considered (Fig. 2 and 3). The value of the volume fraction was taken p =0.5, the side of the elementary cubic cell a=10. The maximum radius of the spheres was changed, the minimum radius was fixed: 0.25 min r = (Fig. 2). Influence of dimensions of RVE was investigated (Fig.