PSI - Issue 26

Victor Rizov et al. / Procedia Structural Integrity 26 (2020) 86–96 Rizov / Structural Integrity Procedia 00 (2019) 000 – 000

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One can get an idea about the influence of continuous variation of d s and d f along the length of the beam on the fracture behaviour from Fig. 8 where the strain energy release rate in non-dimension form is plotted against dF dC s s / ratio at three dF dC f f / ratios. It can be observed in Fig. 8 that the strain energy release rate increases with increasing of dF dC s s / and dF dC f f / ratios.

4. Conclusions

An analytical investigation of the time-dependent lengthwise fracture in the continuously inhomogeneous elastic plastic double cantilever beam is performed with taking into account the aging of the material. The beam exhibits continuous material inhomogeneity in the height, width and length directions. The fracture is studied in terms of the strain energy release rate by analyzing the beam complementary strain energy. In order to verify the solution derived, the strain energy release rate is obtained also by considering the balance of the energy. The effects of material inhomogeneity along the height, width and length of the beam and the aging on the fracture are evaluated. It is found that the strain energy release rate increases with the time (this behavior is due to the aging of the material). The analysis reveals that the strain energy release rate decreases with increasing of g d K K / , g l K K / , g d m m / and gF gC m m / ratios. The increase of d g s s / , l g s s / , d g f f / and l g f f / ratios leads to increase of the strain energy release rate. The analysis developed in the present paper contributes for the understanding of the lengthwise fracture in continuously inhomogeneous elastic-plastic beam structures which exhibit aging of the material. References Gasik, M.M., 2010. Functionally graded materials: bulk processing techniques. International Journal of Materials and Product Technology 39, 20-29. Hirai, T., Chen, L., 1999. Recent and prospective development of functionally graded materials in Japan. Mater Sci. Forum 308-311, 509-514. Knoppers, J.W., Gunnink, J., den Hout, Van, Van Vliet, W., 2003. The reality of functionally graded material products, TNO Science and Industry, The Netherlands 2, 38 – 43. 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. Le, K.C., 2017, An asymptotically exact theory of functionally graded piezoelectric shells, Int. J. Eng. Sci., 112C, 42-62. Mahamood, R.M., Akinlabi, E.T., 2017. Functionally Graded Materials. Springer. Mao, J.J., Ke, L.L., Wang, Y.S., 2014. Thermoelastic contact instability of a functionally graded layer and a homogeneous half-plane, International Journal of Solids and Structures, 51, 3962-3972. Mihailov, A., 1998. Strength of materials. Science. 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 4 6, 158-177. Rizov, V.I., 2019. Influence of material inhomogeneity and non-linear mechanical behavior of the material on delamination in multilayered beams. Frattura ed Integrità Strutturale 47, 468 -481. 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. Wu, X.L., Jiang, P., Chen, L., Zhang, J.F., Yuan, F.P., Zhu, Y.T., 2014. Synergetic strengthening by gradient structure, Mater. Res. Lett., 2, 185 – 191. Zhang, Y., Sun, M.JZhang, D., 2010. Designing functionally graded materials with superior load-bearing properties, Acta Biomater, 8, 1101 – 1108. Zuiker, J.R., 1995. Functionally graded materials: choice of micromechanics model and limitations in property variation, Composite Engineering, 5, 807-819.