PSI - Issue 47

Victor Rizov / Procedia Structural Integrity 47 (2023) 3–12 Author name / Structural Integrity Procedia 00 (2019) 000–000

12 10

considering the complementary strain energy. It is found that the strain energy release rate at increase of internal, interstitial or external crack has higher, intermediate and lower value, respectively. The analysis reveals that the strain energy release rate decreases with increasing of the values of material properties, q and H . The increase of the value of material property, p , leads to increase of the strain energy release rate. The increases of 1 4 / R R ratio and the radius of the cross-section of the beam lead to decrease of the strain energy release rate. It is found also that non-linear viscoelastic behaviour generates growth of the strain energy release rate. It should also be mentioned that the analysis described in the present paper can be easily developed further to treat inhomogeneous non-linear viscoelastic beam structures with more than three longitudinal circular cylindrical cracks under axial force and bending moment. In other words, the solutions obtained here can be applied for analyzing of multiple longitudinal fracture in non-linear viscoelastic beam structures. References Ayd  n, M., Toker, G.P., Acar, E., Karaca, H.E., 2020, Processing and compressive response of Al/SiC functionally graded composites. Eur Phys J Plus 135, 587-602. Chikh, A., 2019. Investigations in static response and free vibration of a functionally graded beam resting on elastic foundations. Frattura ed Integrità Strutturale 14, 115-126. Ganapathi, M., 2007, Dynamic stability characteristics of functionally graded materials shallow spherical shells, Composite Structures 79, 338 343. Hao, Y.X, Chen, L.H., Zhang, W., Lei, J. G., 2002. Nonlinear oscillations and chaos of functionally graded materials plate. Journal of Sound and vibration 312, 862-892. Hirai, T., Chen, L., 1999. Recent and prospective development of functionally graded materials in Japan. Mater Sci. Forum 308-311, 509-514. Kishkilov, M., Apostolov, R., 1994. Introduction to theory of plasticity. UACEG. 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. Marae Djouda, J., Gallittelli , D., Zouaoui, M., Makke, A., Gardan , J., Recho, N., Crépin, J., 2019. Local scale fracture characterization of an advanced structured material manufactured by fused deposition modeling in 3D printing, Frattura ed Integrità Strutturale, 14, 534-540. Mehrali, M., Shirazi, F.S., Mehrali, M., Metselaar, H.S.C., Kadri, N.A.B., Osman, N.A.A., 2013. Dental implants fromfunctionally graded materials. J Biomed Mater Res Part 101A, 3046–305. Nagaral, M., Nayak, P. H., Srinivas, H. K., Auradi, V., 2019. Characterization and Tensile Fractography of Nano ZrO2 Reinforced Copper-Zinc Alloy Composites. Frattura ed Integrità Strutturale 13, 370-376. 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., 2018. Analysis of cylindrical delamination cracks in multilayered functionally graded non-linear elastic circular shafts under combined loads, Frattura ed Integrità Strutturale 46, 158-17. Rizov, V.I., 2019. Influence of material inhomogeneity and non-linear mechanical behaviour of the material on delamination in multilayered beams. Frattura ed Integrità Strutturale 47, 468-481. 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. Rizov, V.I, 2020. Longitudinal fracture analysis of continuously inhomogeneous beam in torsion with stress relaxation, Procedia Structural Integrity 28, 1212–1225. Rizov , V.I., 2020. Analysis of Two Lengthwise Cracks in a Viscoelastic Inhomogeneous Beam Structure, Engineering Transactions 68, 397– 415. Rizov , V.I., 2021. Delamination analysis of multilayered beams exhibiting creep under torsion, Coupled Systems Mechanics 10, 317-331. Saidi, H., Sahla, M., 2019. Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al2O3) embedded in an elastic medium. Frattura ed Integrità Strutturale 13, 286-299. 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. 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. Zhang, C., Chen, F., Huang, Z., Jia, M., Chen, G., Ye, Y., Lin, Y., Liu, W., Chen, B., Shen, Q., Zhang, L., Lavernia, E.J., 2019. Additive manufacturing of functionally graded materials: A review, Materials Science & Engineering A, 3, 1256-1269.