PSI - Issue 33

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 402–415 Author name / Structural Integrity Procedia 00 (2019) 000–000

415

14

beam. The solution holds for beam made of layers which have individual widths and material properties. Also, the number of layers is arbitrary. The solution derived is verified by applying the compliance method. The time dependent solution is used to study the variation of the strain energy release rate with the time due to the viscoelastic behaviour of the material. The analysis indicates that the strain energy release rate increases with the time. Two three-layered functionally graded cantilever beams are considered in order to evaluate the influence of the delamination crack location along the width of the beam on the strain energy release rate. It is found that the strain energy release rate is higher when the delamination crack is located between layers 2 and 3. Concerning the effects of material gradient along the width of layers, the calculations show that the strain energy release rate decreases with increasing of 11 q , 21 q and 31 q (the parameters, 11 q , 21 q and 31 q , control the material gradient along the width of layers). The investigation reveals that the strain energy release rate decreases with increasing of 1 2 1 1 / L L E E and 1 3 1 1 / L L E E ratios. The increases of 2 1 / L L   and 1 3 / L L   ratios lead also to decrease of the strain energy release rate. The results obtained in the present paper give important information about the effects of location of the delamination crack, material gradients and the external loading on the delamination behaviour of the multilayered functionally graded viscoelastic beams. References Andrew, J., Goupee Senthil, Vel, S., 2007. Multi-objective optimization of functionally graded materials with temperature-dependent material properties, Materials & Design 28, 1861-1879. Bao-Lin Wang, Yiu-Wing Mai, Xing-Hong Zhang, 2004. Thermal shock resistance of functionally graded materials. Acta Materialia 52, 4961 4972. 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. 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 Reddy, J.N., Chin, C.D., 1998. Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses 21, 593-626 . 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., 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., 2020. Influence of the viscoelastic material behaviour on the delamination in multilayered beam, Procedia Structural Integrity 25, 88– 100. Rizov, V., 2020. Inhomogeneous beam of linearly varying height under three-point bending: a longitudinal fracture analysis, Structural Integrity and Life 20, 137-142. 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. Shrikantha Rao, S., Gangadharan, K. V., 2014. Functionally graded composite materials: an overview. Procedia Materials Science 5, 1291-1299. Alloy Composites. Frattura ed Integrità Strutturale 13, 370-376. Popov, E., 1998, Introduction to mechanics of solids, Prentice-hall.