Abstract
The analysis of FGM structures requires the implementation of sophisticated mechanical behavior simulation tools, and the interaction between design and manufacturing and the risks associated with cracks play an important role in understanding the mechanical behavior of crack structures. The effect of cracking on the functional gradient plate was studied in this research. In our study and for damage tolerance insurance, the stress intensity factor was determined for the purpose of predicting the behavior of cracked structures similar to the examples studied i.e. type of combination of FGM materials, type of applied load and type of crack, the numerical evaluation of this factor is determined using the displacement extrapolation technique (DET) and the generalized displacement correlation method (GDC) in an APDL (Ansys Parametric Design Language) numerical code to prove the evolution, the continuous variations of the material properties are incorporated by specified parameters at the centroid of each element. The crack growth paths with different FGM gradient parameters under mechanical and thermal loads are investigated and compared with reference solutions. The current DET, GDC, and reference solution results are in good agreement.
Similar content being viewed by others
References
Niino, M., Hirai, T., Watanabe, R.: The functionally gradient material. J. Japan Soc. Compos. Mater. 13(6), 257–264 (1987)
Shanmugavel, P., Bhaskar, G.B., Chandrasekaran, M., Mani, P.S., Srinivasan, S.P.: An overview of fracture analysis in functionally graded materials. Eur. J. Sci. Res. 68(3), 412–439 (2012)
Atai, A.A., Nikranjbar, A., Kasiri, R.: Buckling and post-buckling behavior of semicircular functionally graded material arches: a theoretical study. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 226(3), 607–614 (2012)
Koizumi, M., Niino, M.: Overview of FGM research in Japan. Mrs Bull 20(1), 19–21 (1995)
Wang, S.S.: Fracture mechanics for delamination problems in composite materials. J. Compos. Mater. 17(3), 210–223 (1983)
Yang, J., Hao, Y.X., Zhang, W., Kitipornchai, S.: Nonlinear dynamic response of a functionally graded plate with a through-width surface crack. Nonlinear Dyn. 59(1), 207–219 (2010)
Mahamood, R.M., Aknlabi, E.T., Shukla, M., Pityna, S.: Functionally graded material: an overview. In: Proceedings of the World Congress on Engineering WCE, vol. 3, pp. 1593 – 1597. (2012)
Li- Cheng, G., Naotake, N.: Dynamic investigation of a functionally graded layered structure with a crack crossing the interface. Int. J. Solids Struct. 45, 336–357 (2008)
Li, M., Tian, Y.L., Wen, P.H., Aliabadi, M.H.: Anti-plane interfacial crack with functionally graded coating: static and dynamic. Theor. Appl. Fract. Mech. 86, 250–259 (2016)
Ait Ferhat, Y., Boulenouar, A.: Computation of SIFs for cracks in FGMs and TBC under mechanical and thermal loadings. Int. J. Interact. Des. Manuf. (IJIDeM). 14(4), 1347–1356 (2020a)
Boulenouar, A., Benseddiq, N., Mazari, M., Benamara, N.: FE model for linear elastic mixed mode loading: estimation of SIFs and crack propagation. J. Theor. Appl. Mech 52(2), 373–383 (2014)
Ait Ferhat, Y., Boulenouar, A., Benamara, N., Benabou, L.: Generalized displacement correlation method for mechanical and thermal fracture of FGM. Int. J. Comput. Mater. Sci. Eng 9(1), 2050004 (2014)
Rousseau, C.E., Tippur, H.V.: Evaluation of crack tip fields and stress intensity factors in functionally graded elastic materials: cracks parallel to elastic gradient. Int. J. Fract. 114(1), 87–112 (2002)
El-Hadek, M.A., Tippur, H.V.: Dynamic fracture parameters and constraint effects in functionally graded syntactic epoxy foams. Int. J. Solids Struct 40(8), 1885–1906 (2003)
Guo, L.C., Wu, L.Z., Zeng, T., Cao, D.H.: The transient response of a coating–substrate structure with a crack in the functionally graded interfacial layer. Compos. Struct. 70(1), 109–119 (2005)
Ma, L., Wu, L.Z., Guo, L.C., Zhou, Z.G.: Dynamic behavior of a finite crack in the functionally graded materials. Mech. Mater. 37(11), 1153–1165 (2005)
Tilbrook, M., Rutgers, L., Moon, R.J., Hoffman, M.: Fracture and fatigue crack propagation in graded composites. Mater. Sci. Forum 492, 573–580 (2005)
Martínez-Pañeda, E., Gallego, R.: Gallego numerical analysis of quasi-static fracture in functionally graded materials. Int. J. Mech. Mater. Des. 11(4), 405–424 (2015)
Alshoaibi, A.M., Bashiri, A.H.: Adaptive finite element modeling of linear elastic fatigue crack growth. Materials 15(21), 7632 (2022)
Ait Ferhat, Y., Blaoui, M.M., Chorfi, H., Abacha, I., Benchikh, L., Kebaili, M., Boulenouar, A.: Mixed-mode stress intensity factor evaluation by interaction integral method under thermal and mechanical loads. J. Serbian Soc. Comput. Mech. 16(1), 109–124 (2022)
Natarajan, S., Baiz, P.M., Bordas, S., Rabczuk, T., Kerfriden, P.: Natural frequencies of cracked functionally graded material plates by the extended finite element method. Compos. Struct. 93(11), 3082–3092 (2011)
Tran, L.V., Ly, H.A., Lee, J., Wahab, M.A., Nguyen-Xuan, H.: Vibration analysis of cracked FGM plates using higher-order shear deformation theory and extended isogeometric approach. Int. J. Mech. Sci. 96, 65–78 (2015)
Joshi, P.V., Jain, N.K., Ramtekkar, G.D.: Analytical modeling for vibration analysis of thin rectangular orthotropic/functionally graded plates with an internal crack. J. Sound Vib. 344, 377–398 (2015)
Fantuzzi, N., Tornabene, F., Viola, E.: Four-parameter functionally graded cracked plates of arbitrary shape: a GDQFEM solution for free vibrations. Mech. Adv. Mater. Struct. 23(1), 89–107 (2015)
Gupta, A., Jain, N.K., Salhotra, R.: Effect of crack orientation on vibration characteristics of partially cracked FGM plate: an analytical approach. Mater. Today Proc. 4(9), 10179–10183 (2017)
Rahimabadi, A., Natarajan, S., Bordas, S.P.: Vibration of functionally graded material plates with cutouts and cracks in thermal environment. Key Eng. Mater. 560, 157–180 (2013)
Dorduncu, M., Olmus, I., Rabczuk, T.: A peridynamic approach for modeling of two dimensional functionally graded plates. Composite Structures 279, 114743 (2022)
Zhang, P., Qi, C., Sun, X., Fang, H., Huang, Y.: Bending behaviors of the in-plane bidirectional functionally graded piezoelectric material plates. Mech. Adv. Mater. Struct. 29(13), 1925–1945 (2022)
Wang, L., Liu, Y., Liao, Z., Zhou, Y., Yang, F.: Gradient reproducing kernel based Hermite collocation method (GHCM) for eigenvalue analysis of functionally graded thin plates with in-plane material. Eng. Anal. Boundary Elem. 148, 73–89 (2023)
Babaee, A., Jelovica, J.: Large amplitude vibration of annular and circular functionally graded composite plates under cooling thermal shocks. Thin-Walled Struct. 182, 110142 (2023)
Majeed, M.H., Kadhim, D.E., Abdullah, O.I., Schlattmann, J.: Numerical analysis of thermal problem in dry friction clutches based on the interactive design approach. Int. J. Interact. Des. Manuf. (IJIDeM). 14(3), 1091–1101 (2020)
Madhav, V.V., Chaitanya, C., Prasanthi, P.P., Gupta, A.V.S.S.K.S., Spandana, V.V., Saxena, K.K., Prakash, C.: Design and analysis of angle-ply arrangement on fracture properties of FRP composite structure under thermo-mechanical loading conditions subjected to central circle cut-out. Int. J. Interact. Design Manuf. (IJIDeM). 1–8. (2022)
Ait Ferhat, Y., Boulenouar, A.: Computation of SIFs for cracked FGMs under mechanical and thermal loadings. Arch. Mech. Technol. Mater. 40 (2020)
Peng, L., Yi, P., Lai, X.: Design and manufacturing of stainless-steel bipolar plates for proton exchange membrane fuel cells. Int. J. Hydrog. Energy. 39(36), 21127–21153 (2014)
Selvaraj, P., Radhakrishnan, P., Adithan, M.: An integrated approach to design for manufacturing and assembly based on reduction of product development time and cost. Int. J. Adv. Manuf. Technol. 42(1), 13–29 (2009)
Huang, C.Y., Chen, Y.L.: Design and impact resistant analysis of functionally graded Al2O3–ZrO2 ceramic composite. Mater. Design. 91, 294–305 (2016)
Barsoum, R.S.: On the use of isoparametric finite element in linear fracture mechanics. Int. J. Numer. Methods Eng. 10, 25–37 (1974)
Pengcheng, F., Johnson, S.M., Settgast, R.R., Carrigan, C.R.: Generalized displacement correlation method for estimating stress intensity factors. Eng. Fract. Mech. 88, 90–107 (2012)
Bhattacharya, S., Sharma, K., Sonkar, V.: Numerical simulation of elastic-plastic fatigue crack growth in functionally graded material using the extended finite element method. Mech. Adv. Mater. Struct. 24(16), 1367–1380 (2017)
Bhattacharya, S., Singh, I.V., Mishra, B.K.: Mixed-mode fatigue crack growth analysis of functionally graded materials by XFEM. Int. J. Fract. 183(1), 81–97 (2013)
Awasthi, A., Pant, M.: A revamped element-free Galerkin algorithm for accelerated simulation of fracture and fatigue problems in two-dimensional domains. Iranian J. Sci. Technol. Trans. Mech. Eng. .1–28. (2022)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Ait Ferhat, Y., Chorfi, H., Abacha, I. et al. Evaluation of stress intensity factors in functionally graded plate under mechanical and thermal loadings. Int J Interact Des Manuf 17, 2745–2753 (2023). https://doi.org/10.1007/s12008-023-01212-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12008-023-01212-z