Delamination Analysis of Multilayered Functionally Graded ‎Beams which Exhibit Non-linear Creep Behavior

Document Type : Research Paper

Author

Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., Sofia - 1046, Bulgaria‎

Abstract

General solution of the time-dependent strain energy release rate for delamination cracks in multilayered functionally graded load-bearing beam structures which exhibit non-linear creep is derived. The material is functionally graded along the length of layers. The Ramberg-Osgood stress-strain relation is used by assuming that the material in each layer behaves differently in tension and compression. The second term in the Ramberg-Osgood relation includes time dependence to treat the non-linear creep. The solution derived holds for multilayered functionally graded beams with arbitrary number of layers which have different width and material properties. The solution is applied for a delamination in a multilayered beam with a built-in end. An analysis is performed also by considering the balance of the energy in the multilayered beam configuration for the sake of verification. The effect of time is also studied. It is found that the strain energy release rate grows with the time. The results obtained here are useful for understanding the time-dependent delamination in multilayered functionally graded structural components subjected to non-linear creep.

Keywords

Main Subjects

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[1] Butcher, R.J., Rousseau, C.E., Tippur, H.V., A functionally graded particulate composite: Measurements and Failure Analysis, Acta Materialia, 47(2), 1999, 259-268.
[2] Markworth, A.J., Ramesh, K.S., Parks, Jr.W.P., Review: modeling studies applied to functionally graded materials, Journal of Materials Science, 30(3), 1995, 2183-2193.  
[3] Kursun, A., Topcu, M., Yücel, U., Stress analysis of a rotating fgm circular disc with exponentially-varying properties, In: Proceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition IMECE2012, November 9-15, Houston, Texas, USA, 2012.
[4] Kursun, A., Topcu, M., Thermal Stress Analysis of Functionally Graded Disc with Variable Thickness Due to Linearly Increasing Temperature Load, Arabian Journal for Science and Engineering, 38, 2013, 3531–3549.
[5] Kursun, A., Kara, E., Cetin, E., Aksoy, S., Kesimli, A., Mechanical and thermal stresses in functionally graded cylinders, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 8(2), 2014, 303-308.
[6] Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A., Ford, R.G., Functionally Graded Materials: Design, Processing and Applications, Kluwer Academic Publishers, Dordrecht/London/Boston, 1999.
[7] Hirai, T., Chen, L., Recent and prospective development of functionally graded materials in Japan, Materials Science Forum, 308-311, 1999, 509-514.
[8] Han, X., Xu, Y.G., Lam, K.Y., Material characterization of functionally graded material by means of elastic waves and a progressive-learning neural network, Composites Science and Technology, 61(10), 2001, 1401-1411.
[9] Gasik, M.M., Functionally graded materials: bulk processing techniques, International Journal of Materials and Product Technology, 39(1-2), 2010, 20-29.
[10] Arda, M., Axial dynamics of functionally graded Rayleigh-Bishop nanorods, Microsystem Technologies, 27, 2021, 269–282.
[11] Arda, M., Aydogdu, M., Torsional wave propagation of CNTS via different nonlocal gradient theories, In: The 23rd International Congress on Sound and Vibration 8ICSV23, Athens (Greece), 2016.
[12] Aydogdu, M., Arda, M., Filiz, S., Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter, Advances in Nano Research, 6(3), 2018, 257-278.
[13] Nemat-Allal, M.M., Ata, M.H., Bayoumi, M.R., Khair-Eldeen, W., Powder metallurgical fabrication and microstructural investigations of Aluminum/Steel functionally graded material, Materials Sciences and Applications, 2(5), 2011, 1708-1718.
[14] Shrikantha Rao, S., Gangadharan, K.V., Functionally graded composite materials: an overview, Procedia Materials Science, 5(1), 2014, 1291-1299.
[15] Wu, X.L., Jiang, P., Chen, L., Zhang, J.F., Yuan, F.P., Zhu, Y.T., Synergetic strengthening by gradient structure, Materials Research Letters, 2(1), 2014, 185–191.  
[16] Saiyathibrahim, A., Subramaniyan, R. Dhanapl, P., Centrefugally cast functionally graded materials – review, In: International Conference on Systems, Science, Control, Communications, Engineering and Technology, 2016.
[17] Mahamood, R.M., Akinlabi, E.T., Functionally Graded Materials, Springer, 2017. 
[18] Dolgov, N.A., Effect of the elastic modulus of a coating on the serviceability of the substrate-coating system, Strength of Materials, 37(2), 2002, 422-431.
[19] Dolgov, N.A., Determination of Stresses in a Two-Layer Coating, Strength of Materials, 37(2), 2005, 422-431.
[20] Dolgov, N.A., Analytical Methods to Determine the Stress State in the Substrate–Coating System Under Mechanical Loads, Strength of Materials, 48(1), 2016, 658-667.
[21] Hsueh, C.H., Tuan, W.H., Wei, W.C.J., Analyses of steady-state interface fracture of elastic multilayered beams under four-point bending, Scripta Materialia, 60, 2009, 721-724.
[22] Hutchinson, J.W., Suo, Z., Mixed mode cracking in layered materials, Advances in Applied Mechanics, 64, 1992, 804-810.   
[23] Rizov, V.I., Analysis of the Strain Energy Release Rate for a Delamination Crack in a Multilayered Beam with Material Non-Linearity, IOP Conference Series: Materials Science and Engineering, 473, 2019, 012002.
[24] Rizov, V.I., Influence of material non-linearity on delamination in multilayered three-point bending beams, Journal of Theoretical and Applied Mechanics, 50, 2020, 70-82.
[25] Rizov, V.I., Influence of the viscoelastic material behaviour on the delamination in multilayered beam, Procedia Structural Integrity, 25, 2020, 88–100.
[26] Rizov, V.I., Inhomogeneous beams with different behaviour in tension and compression: a longitudinal crack study, Journal of Applied Mechanics and Technical Physics, 60, 2019, 908–915.
[27] Dowling, N., Mechanical Behavior of Materials, Pearson, 2007.