PSI - Issue 40

N. Kondratev et al. / Procedia Structural Integrity 40 (2022) 239–244 N. Kondratev et. al. / Structural Integrity Procedia 00 (2022) 000 – 000

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From the point of view of describing a grain structure for the statistical model, the data of grain boundaries facets have greatest interest. The histogram of the facets areas distribution s and the straight pole figure of facet normals n i are shown in Fig. 3 (a) and (b) respectively. A distribution of grains facets number N is not directly set when generating Laguerre polyhedra by Neper. This characteristic can be used to verify the generated grain structure. In (DeHoff R. T. & Liu G. Q. (1985)) based on the analysis of experimental data of various materials, it is noted that there is a linear relationship between the equivalent grain size d eq and the number of grain facets N . Fig. 3 (c) shows the relationship between N and d eq in generated grain structure, which is linear and correlates with the data (DeHoff R. T. & Liu G. Q. (1985)).

(a)

(b)

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Fig. 3. The histogram of the facets area distribution s (a), the straight pole figure of facet normals ni (b), the dependence of facets number N on equivalent volume deq (c) 4. Conclusion The grain structure generating procedure for the modified statistical multilevel model has been considered and implemented. Based on the analysis of experimental data, statistical laws have been established for the grain size distribution and sphericity of copper polycrystalline. Using the free software Neper, the grain structure of copper has been formed in three-dimensional space. The obtained data have been processed, for each grain the values of parameters (volume v , facet areas s i , normals n i ) have been got and transmitted into the modified statistical model determining a grain structure therein. In addition to a grain structure, the most important parameter in statistical multilevel models is the orientation distribution of the crystallographic axes for the grains. The problem of specifying grains orientations in the considered polycrystal volume remains relevant and requires further solution. Acknowledgments This study was carried out with a financial support from the Ministry of Education and Science of the Russian Federation (the basic part of the PSTU state assignment, project no. FSNM-2020-0027) and the Russian Foundation for Basic Research and Perm Territory (project no. 20-41-596002). References Armstrong, R. W., 1970. The influence of polycrystal grain size on several mechanical properties of materials. Metallurgical and Materials Transactions B, 1(5), 1169-1176. Beyerlein, I. J., Knezevic, M., 2018. Review of microstructure and micromechanism-based constitutive modeling of polycrystals with a low symmetry crystal structure. Journal of Materials Research, 33(22), 3711-3738. Brent, R. P., 2013. Algorithms for minimization without derivatives. Courier Corporation. Cruzado, A., Lucarini, S., LLorca, J., Segurado, J., 2018. Crystal plasticity simulation of the effect of grain size on the fatigue behavior of polycrystalline Inconel 718. International Journal of Fatigue, 113, 236-245.