PSI - Issue 77

Victor Rizov et al. / Procedia Structural Integrity 77 (2026) 397–404 Author name / Structural Integrity Procedia 00 (2026) 000–000

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J can be explored in Fig. 5. Growth of l l / 1 ratio results in rise of the integral J as one can see in Fig. 5. The integral J reduces when h b / ratio grows (Fig. 5). 4. Conclusions The longitudinal fracture in a statically indeterminate non-linear elastic beam structure whose ends are built in is explored by the integral J . The beam is subjected to increased temperature. Due to continuous material inhomogeneity along the beam length, the material properties including the coefficient of thermal expansion change in longitudinal direction. It is found that increasing of 2 1 / t t ratio (this ratio characterizes the change of the temperature along the beam thickness) has a negative influence of the longitudinal fracture behaviour since the integral J grows. Growth of the integral J is observed also as a result of increase of lft rght α α / ratio. The inhomogeneity is presented by lft rght L L / and lft rght H H / ratios. The exploration reveals that the growth of these ratios leads to rise of the integral J . The growth of 2 / a l ratio (this ratio characterizes the crack length) also leads to increase of the integral J . Effect of geometrical parameters like l l / 1 and h b / ratios on the integral J under increased temperature is explored too. It is observed that rise of l l / 1 ratio has a negative influence on the longitudinal fracture behaviour since the integral J grows. The longitudinal fracture can be improved by increasing of h b / ratio since this reduces the integral J . Bohidar, S. K., Sharma, R., Mishra, P. R., 2014. Functionally graded materials: A critical review, International Journal of Research 1, 289-301. Broek, D., 1986. Elementary engineering fracture mechanics. Springer Netherlands. Dowling, N., 2007. Mechanical Behavior of Materials. Pearson. El-Galy, I.M., Saleh, B.I., Ahmed, M.H., 2019. Functionally graded materials classifications and development trends from industrial point of view, SN Appl. Sci. 1, 1378. Hirai, T., Chen, L., 1999. Recent and prospective development of functionally graded materials in Japan, Mater Sci. Forum 308-311, 509-514. Kou, X.Y., Parks, G.T., Tan, S.T., 2012. Optimal design of functionally graded materials, using a procedural model and particle swarm optimization, Computer Aided Design 44, 300-310. Mahamood, R.M., Akinlabi, E.T., 2017. Functionally Graded Materials. Springer. Reichardt, A., Shapiro, A.A. , Otis, R., Dillon, R.P. , Borgonia, J.P., Mc-Enemey, B.W., 2020. Advances in additive manufacturing of metalbased functionally graded materials, International Materials Reviews 66, 1-29. Rizov, V.I., 2017. Analysis of longitudinal cracked two-dimensional functionally graded beams exhibiting material non-linearity. Frattura ed Integrità Strutturale 41, 498-510. Rizov, V.I, Altenbach, H., 2020. Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length, Frattura ed Integrità Strutturale 53, 38-50. Saiyathibrahim, A., Subramaniyan, R., Dhanapl, P., 2016. Centrefugally cast functionally graded materials – review. International Conference on Systems, Science, Control, Communications, Engineering and Technology, 68-73. Tsankov, T., 1996. Theory of Plasticity. Science. Yan Li, Zuying Feng, Liang Hao, Lijing Huang, Chenxing Xin, Yushen Wang, Emiliano Bilotti, Khamis Essa, Han Zhang, Zheng Li, Feifei Yan, Ton Peijs, 2020. A review on functionally graded materials and structures via additive manufacturing: from multi-scale design to versatile functional properties. Adv Mater Technol. 5,1900981. References