A thin elastic plate of an isotropic medium (matrix) containing inclusions of another material and subjected to bending is considered. It is assumed that the medium is weakened by rectilinear cracks arbitrarily placed near the inclusion. The service life of the composite plate depends on the distribution of stresses in the zones of interaction of its elements. The serviceability of the composite can be improved by changing the geometry of binder and inclusion joint. A fracture mechanics problem for determining the optimum form of inclusion which minimizes the stress intensity factors (moments) near crack tips is solved. A fracture criterion and a solution method for the problem on preventing the composite from fracture under the action of a given system of external bending loads are proposed. A closed system of equations permitting one to obtain a solution to the optimum design problem according to the geometrical and mechanical characteristics of the binder and inclusions is obtained. The cross-sectional shape found for the elastic foreign inclusion provides an increased load-carrying capacity of the composite.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Fudzii and M. Dzako, Fracture Mechanics of Composite Materials [Russian translation], Mir, Moscow (1982).
D. N. Reshetov, “State-of-the-art and tendencies in the development of machine parts,” Vest. Mashinostr., No. 10, 11-15 (2000).
L. V. Andreev, In the Realm of Shells [in Russian], Znanie, Moscow (1986).
V. M. Mirsalimov and E. A. Allahyarov, “The breaking crack build-up in perforated planes by uniform ring switching,” Int. J. Fract., 79, No. 1, 17-21 (1996).
G. Kh. Gadzhiev and V. M. Mirsalimov, “Inverse problem of fracture mechanics for the compound cylinder of a contact pair,” in: D. M. Klimov (ed.), Probl. Mekh. Coll. Works to 90th anniversary of A. Yu. Ishlinskii, Fizmatlit, Moscow (2003), pp. 196-207.
V. M. Mirsalimov, “Inverse periodic problem of the theory of bending of plates with elastic inclusions,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 3, 171-179 (2006).
V. M. Mirsalimov, “Optimal design of a compound plate weakened by a periodic system of cracks,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 75-86 (2007).
V. M. Mirsalimov, “Inverse problem of fracture mechanics for a compound cylinder,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 1, 115-173 (2009).
N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1966).
V. V. Panasyuk, M. P. Savruk, and A. P. Datsyshin, Stress Distribution near Cracks in Plates and Shells (in Russian), Naukova Dumka, Kiev (1976).
E. G. Ladopoulos, Singular Integral Equations: Linear and Nonlinear Theory and Its Applications in Science and Engineering, Springer Verlag, Berlin-Heidelberg (2000).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Mekhanika Kompozitnykh Materialov, Vol. 51, No. 6, pp. 1049-1060 , November-December, 2015.
Rights and permissions
About this article
Cite this article
Mirsalimov, V.M., Askarov, V.A. Minimization of Fracture Parameters of a Composite at Bending. Mech Compos Mater 51, 737–744 (2016). https://doi.org/10.1007/s11029-016-9544-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11029-016-9544-9