PSI - Issue 25

Victor Rizov / Procedia Structural Integrity 25 (2020) 112–127

127

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Author name / Structural Integrity Procedia 00 (2019) 000–000

the calculations show that the strain energy release rate decreases with increasing of h b / , p b / and q b / ratios (these ratios characterize the geometry of the T-shape). It is found also that when the beam has a circular cross section, the strain energy release rate decreases with increasing of the radius of the cross-section. Concerning the effect of the location of the crack along the beam height, the investigation reveals that the strain energy release rate has minimum when the crack is located near the mid-plane of the beam and increases when the crack approaches the lower or the upper surfaces of the beam. It is found that when the material has different moduli of elasticity in compression and tension, the strain energy release rate decreases with increasing of cUB tUB E E / , cUB cUD E E / , ratios. The lengthwise fracture behaviour is analyzed also assuming that the four beam cross-section geometries have the same area. The analysis indicates that the strain energy release rate is the lowest when the beam has a T-shape cross-section. Thus, the T-shape cross-section is the most efficient among the considered cross-section geometries for improving the lengthwise fracture performance of the beam. The results obtained in the present paper can by used in structural design of inhomogeneous beams with considering of their lengthwise fracture behaviour. Acknowledgements The present study was carried-out with the financial support of the Research and Design Centre (CNIP) of the University of Architecture, Civil Engineering and Geodesy (UACEG), Sofia (Contract BN – 217/2019). References Erdogan, F., 1995. Fracture mechanics of functionally graded materials. Computational Engineering 5, 753-770. Gan-Yun Huang, Yue-Sheng Wang, Dietmar Gross, 2003. Fracture analysis of functionally graded coatings: plane deformation. European journal of mechanics A/solids 22, 535-544. 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. Jin, Z-H, Batra, R. C., 1996. Some basic fracture mechanics concepts in functionally graded materials. J. Mech. Phys. Sol. 44, 1221-34. Kawasaki, A., Watanabe, R., 1997. Concept and P/M fabrication of functionally gradient materials. Ceramics International 23, 73-83. Mahamood, R.M., Akinlabi, E.T., 2017. Functionally Graded Materials. Springer. Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A., Ford, R.G., 1999. Functionally Graded Materials: Design, Processing and Applications. Kluwer Academic Publishers, Dordrecht/London/Boston. Nemat-Allal, M.M., Ata, M.H., Bayoumi, M.R., Khair-Eldeen, W., 2011. Powder metallurgical fabrication and microstructural investigations of Aluminum/Steel functionally graded material. Materials Sciences and Applications 2, 1708-1718. 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, 158-177. 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. Tilbrook, M.T., Moon, R.J., Hoffman, M., 2005. Crack propagation in graded composites. Composite Science and Technology 65, 201-220. Tokovyy, Y., Ma, C.-C., 2008. Analysis of 2D non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders. J. Eng. Math 61, 171 – 184. Tokovyy, Y., Ma, C.-C., 2013. Three-Dimensional Temperature and Thermal Stress Analysis of an Inhomogeneous Layer. Journal of Thermal Stresses 36, 790 – 808. Tokova, L., Yasinskyy, A., Ma, C.-C., 2017. Effect of the layer inhomogeneity on the distribution of stresses and displacements in an elastic multilayer cylinder. Acta Mechanica 228, 2856-2877. Tokovyy, Y., Ma, C.-C., 2016. Axisymmetric Stresses in an Elastic Radially Inhomogeneous Cylinder Under Length-Varying Loadings. ASME Journal of Applied Mechanics 83, 111-007-111-007-7. cLB tLB E E / and cLB cLD E E /