Engineering Transactions, 68, 3, pp. 253–268, 2020

Lengthwise Fracture Study of Transversely Inhomogeneous Rods

Victor Iliev RIZOV
University of Architecture Civil Engineering and Geodesy

A lengthwise crack in a rod that exhibits smooth (continuous) material inhomogeneity in the transverse direction is studied. The rod has a circular cross-section. The lengthwise crack is located arbitrarily along the thickness of the rod. A solution to the strain energy release rate is derived assuming that the moduli of elasticity in tension and compression are distributed continuously in the transverse direction. The strain energy release rate is also analyzed by applying the compliance method for verification. The influences of various factors such as the crack location, material inhomogeneity and the different mechanical behavior of the material in tension and compression on the fracture are investigated and discussed in detail.
Keywords: continuous material inhomogeneity; circular cross-section rod; lengthwise crack
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).


Yasinskyy A., Tokova L., Inverse problem on the identification of temperature and thermal stresses in an FGM hollow cylinder by the surface displacements, Journal of Thermal Stresses, 40(12): 1471–1483, 2017, doi: 10.1080/01495739.2017.1357455.

Tokova L., Yasinskyy A., Ma C.-C., Effect of the layer inhomogeneity on the distribution of stresses and displacements in an elastic multilayer cylinder, Acta Mechanica, 228: 2865–2877, 2016, doi: 10.1007/s00707-015-1519-8.

Koizumi M., The concept of FGM, Ceramic Transactions, Functionally Gradient Materials, 34: 3–10, 1993.

Neubrand A., Rödel J., Gradient materials: An overview of a novel concept, Zeitschrift für Metallkunde, 88(5): 358–371, 1997.

Gasik M.M., Functionally graded materials: bulk processing techniques, International Journal of Materials and Product Technology, 39(1–2): 20–29, 2010, doi: 10.1504/IJMPT.2010.034257.

Nemat-Alla 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(12): 1708–1718, 2011, doi: 10.4236/msa.2011.212228.

Bohidar S.K., Sharma R., Mishra P.R., Functionally graded materials: A critical review, International Journal of Research, 1(7): 289–301, 2014.

Al-Huniti N.S., Alahmad S.T., Transient thermo-mechanical response of a functionally graded beam under the effect of a moving heat source, Advances in Materials Research, 6(1): 27–43, 2017, doi: 10.12989/amr.2017.6.1.027.

Mahamood R.M., Akinlabi E., Functionally graded materials, Springer, 2017, doi: 10.1007/978-3-319-53756-6.

Rizov V.I., Delamination analysis of a layered elastic-plastic beam, International Journal of Structural Integrity, 8(5): 516–529, 2017.

Rizov V.I., Analysis of delamination in two-dimensional functionally graded multilayered beam with non-linear behaviour of material, Engineering Transactions, 66(1): 61–78, 2018.

Rizov V.I., Non-linear fracture in bi-directional graded shafts in torsion, Multidiscipline Modeling in Materials and Structures, 15(1): 156–169, 2019, doi: 10.1108/MMMS-12-2017-0163.

Hutchinson J.W., Suo Z., Mixed mode cracking in layered materials, Advances in Applied Mechanics, 29: 63–191, 1991, doi: 10.1016/S0065-2156(08)70164-9.

Alexandrov A.V., Potapov V.D., Fundamentals of the theory of elasticity and plasticity [in Russian], Izd-vo “Vyshaya Shkola”, Moscow, 1990.

Kissiov I., Strength of materials, Technics, 1995.

DOI: 10.24423/EngTrans.1064.20200804