PSI - Issue 51

Victor Rizov et al. / Procedia Structural Integrity 51 (2023) 206–212 V. Rizov / Structural Integrity Procedia 00 (2022) 000–000

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The variation of the TDSERR with time is examined first. One can get an idea about the variation of TDSERR with time from Fig. 4 where TDSERR is plotted against normalized time at three values of 1 g (the time is normalized as 1 1 / 0 D L L N t tE   ). Fig. 4 indicates that the TDSERR diminishes. One can observe also TDSERR increases with increasing of 1 g (i.e., increase of 1 D E with time leads to increase of the TDSERR). The results shown in Fig. 5 indicate that the TDSERR increases with increasing of 1  and 1  . Since the material gradient in layer 1 depends on 1  and 1  , it can be concluded that stronger material gradient leads to increase of the TDSERR. 4. Conclusions A delamination in a multilayered beam with relaxation is studied analytically in terms of the SERR. A linear viscoelastic model with three components (two springs and a dashpot) is used for describing the relaxation of the beam layers. The modulus of elasticity of one of the springs changes with time according to exponential law. The relation between stress, strain and time is found by analyzing the equilibrium of the components of the viscoelastic model and by considering the dependences between the strains in the components. A solution of TDSERR with considering the relaxation behaviour and the change of the modulus of elasticity with time is derived by analyzing TDSE. The layers have different properties and widths. Also, a solution of TDSERR is obtained by the compliance. The results are identical (this fact is a verification of the solutions). A parametric study is performed. It is found that the TDSERR diminishes with time. The analysis reveals that the TDSERR increases with increasing of 1  , 2  , 1  , 2  , 1  and 2  . It is found also that the TDSERR increases with increasing of the angles of rotation of two crack arms. References 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. Dolgov, N. A., 2005. Determination of Stresses in a Two-Layer Coating. Strength of Materials 37, 422-431. Dolgov, N. A., 2016. Analytical Methods to Determine the Stress State in the Substrate–Coating System Under Mechanical Loads. Strength of Materials, 48, 658-66. Gururaja Udupa, Shrikantha Rao, S., Rao Gangadharan, K., 2014. Functionally Graded Composite Materials: An Overview. Procedia Materals Science 5, 1291-1299. 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., 2021. Delamination crack study of a multilayered inhomogeneous beam exhibiting stress relaxation. Journal of Theoretical and Applied Mechanics 51, 407-420. Rizov, V.I., 2021. Lengthwise fracture of functionally graded beams: a study of stress relaxation effects. Procedia Structural Integrity 33, 428–442.