Conclusions
-
1.
A numerical method was developed of solving various problems of local defects in monotropic materials by replacing the continuum with a discrete lattice. The proposed method is more advantageous than other numerical methods in the case in which it is necessary to solve several problems with various local defects in the same material.
-
2.
The derived dependences of the recovery of the stresses in the ruptured fibers and also the dependences of the stresses on the dimensions, form, and position of the crack may be used in unidirectional composite materials for determining their strength and describing the fracture kinetics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
A. K. Malmeister, V. P. Tamuzh, and G. A. Teters, Strength of Polymer and Composite Materials [in Russian], 3rd ed., Riga (1980).
A. Kelly and G. W. Groves, Crystallography and Crystal Defects [Russian translation], Moscow (1974).
J. A. Johnson, “Empirical potentials and their use in the calculation of energies of point defects in metals,” J. Phys. F: Metal Phys.,3, 295–321 (1973).
R. A. Johnson, “Relationship between two-body interatomic potentials in a lattice model and elastic constants,” Phys. Rev. B,6, No. 6, 2094–2100 (1972).
G. D. Dean and P. Turner, “The elastic properties of carbon fibers and their composites,” Composites,4, No. 3, 174–180 (1973).
P. É. Pikshe, “Modeling of local defects in anisotropic materials using discrete meshes,” Mekh. Kompozitn. Mater., No. 1, 62–67 (1982).
P. É. Pikshe, “Using the linking method for determining the components of Green's tensor of an elastic bcc lattice,” Izv. Akad. Nauk Latv. SSR, Ser. Fiz., No. 2, 65–72 (1981).
A. A. Konkin and N. F. Konnova, “Mechanical and physicochemical properties of carbon fibers,” Zh. Vses. Khim. Ova,23, No. 3, 259–263 (1978).
A. F. Zhigach and A. M. Tsirlin, “Physicochemical properties and strength characteristics of boron filaments and prospects of using these filaments for reinforcing composites,” Zh. Vses. Khim. Ova,23, No. 3, 264–271 (1978).
M. S. Aslanova, “Reinforcement of composite materials with glass fibers,” Zh. Vses. Khim. Ova,23, No. 3, 249–252 (1978).
B. Rozen, “Mechanics of strengthening of composites,” in: Fiber-Reinforced Composite Materials [in Russian], Moscow (1967).
A. S. Ovchinskii, I. M. Kop'ev, E. N. Sakharova, and V. V. Moskvitin, “Redistribution of stresses in rupture of brittle fibers in metallic composites,” Mekh. Polim., No. 1, 19–29 (1977).
P. É. Pikshe, V. P. Tamuzh, and M. Ya. Mikel'son, “On disintegration of fibers in composite materials during loading,” Mekh. Kompozitn, Mater., No. 4, 725–728 (1981).
O. Osamu and I. Miura, “Fiber/fiber interaction in face to face fiber models of short fiber composite alloys,” J. Jpn. Inst. Met.,39, No. 8, 785–791 (1975).
J. M. Hedgepeth and P. van Dyke, “Local stress concentrations in imperfect filamentary composite materials,” J. Compos. Mater.,1, 294–309 (1967).
I. V. Grushetskii, M. Ya. Mikel'son, and V. P. Tamuzh, “Variation of the stiffness of a unidirectional fiber-reinforced composite as a result of fiber disintegration,” Mekh. Kompozitn. Mater., No. 2, 211–216 (1982).
Author information
Authors and Affiliations
Additional information
Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1001–1009, November–December, 1983.
Rights and permissions
About this article
Cite this article
Pikshe, P.É., Tamuzh, V.P. Modeling local defects in monotropic materials by means of hexagonal lattices. Mech Compos Mater 19, 727–734 (1983). https://doi.org/10.1007/BF00603680
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00603680