 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| A. I. Khromov, "Fracture of rigid-plastic bodies and fracture constants," Mech. Solids. 40 (3), 109-122 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
3 |
Pages |
109-122 |
| Title |
Fracture of rigid-plastic bodies and fracture constants |
| Author(s) |
A. I. Khromov (Komsomolsk-on-Amur) |
| Abstract |
The theory of ideal rigid-plastic bodies is one of the most elaborated branches of solid mechanics.
Within the framework of that theory, the main attention has been given to problems of the limiting
equilibrium, i.e., the initiation of plastic flow. Only few solutions have been obtained for problems
that take into account the geometry of the body and pertain to the plastic flow. In this
connection, we mention the following problems: a wedge indented half-space, a flat punch crushing a
wedge [1-3]; uniaxial tension of a plane sample [4] or a cylindrical sample [5]; tension of a
strip with V-shaped notches [6]. In [7-9], on the basis of these solutions, a class of
solutions was obtained for contact problems for bodies of an arbitrary shape; these solutions take
into account changes in the geometry of the free surface. When solving such problems, strains were
evaluated visually by observing distortions of a rectangular mesh. A more precise description of
the deformation process requires the utilization of tensor characteristics as the measure of strain
(distortion tensor, Almansi strain tensor, etc.). Solutions that take into account the geometry of
the body are especially needed for calculating strains near the surfaces of displacement rate
discontinuities or other singularities of the plastic region.
Another issue of the theory of rigid-plastic bodies is the nonuniqueness of the position and the
shape of the plastic region, and therefore, the nonuniqueness of the displacement rate field that
determines the geometrical changes of the body. For practical utilization of theoretical
solutions, one requires a criterion for choosing a particular plastic flow and one has to
formulate the conditions that determine the change of the plastic region.
Fracture of rigid-plastic bodies was studied in [10, 11].
In this paper, an approach is proposed to further development of the said aspects of the theory of
rigid-plastic bodies subject to fracture in the case of plane axisymmetric strain. |
| References |
| 1. | R. Hill, E. H. Lee, and S. J. Tupper, "The theory of wedge indentation of ductile
materials," Proc. Roy. Soc. Ser. A, Vol. 188, No. 101, pp. 273-289, 1947. |
| 2. | R. Hill, "Some special problems of indentation and compression in plasticity," in Proc.
7th Intern. Congr. Appl. Mech. I, Vol. 1, pp. 365-377, 1948. |
| 3. | R. Hill, The Mathematical Theory of Plasticity, Clarandon Press, Oxford, 1950. |
| 4. | E. Onat and W. Prager, "The necking of a tension specimen in plane plastic flow," J.
Appl. Phys., Vol. 25, No. 4, pp. 491-493, 1954. |
| 5. | R. T. Shield, "On the plastic flow of metals under conditions of axial symmetry," Proc.
Roy. Soc. London, Ser. A, Vol. 233, No. 1193, pp. 267-287, 1955. |
| 6. | O. Richmond, "Plane strain necking of V-shaped and un-notched tensile bars," J. Mech.
and Phys. Solids, Vol. 17, No. 2, pp. 83-90, 1969. |
| 7. | G. I. Bykovtsev and A. I. Khromov, "Plane strain of perfect rigid-plastic bodies with
boundary variation taken into account," Izv. AN SSSR. MTT [Mechanics of Solids], No. 2, pp. 71-78,
1979. |
| 8. | G. I. Bykovtsev and A. I. Khromov, "Plane problem of punch indentation of a perfect
rigid-plastic half-space," Izv. AN SSSR. MTT [Mechanics of Solids], No. 6, pp. 47-52, 1981. |
| 9. | A. I. Khromov, Deformation and Fracture of Rigid-plastic Bodies [in Russian], Dal'nauka,
Vladivostok, 1996. |
| 10. | L. M. Kachanov, Basic Principles of Fracture Mechanics [in Russian], Nauka, Moscow, 1974. |
| 11. | F. A. McClintock, "Plastic aspects of fracture," in Fracture. Volume 3 [Russian translation], Mir,
Moscow, 1976. |
| 12. | S. K. Godunov, Elements of Continuum Mechanics [in Russian], Nauka, Moscow, 1978. |
| 13. | A. I. Khromov, "Localization of plastic strains and fracture of perfect rigid-plastic
bodies," Doklady AN, Vol. 362, No. 2, pp. 202-205, 1998. |
| 14. | T. Thomas, Plastic Flow and Fracture in Solids [Russian translation], Mir, Moscow, 1964. |
| 15. | Ya. B. Fridman, Mechanical Properties of Metals. Part 2. Mechanical Tests. Structural
Strength [in Russian], Mashinostroenie, Moscow, 1974. |
| 16. | A. I. Khromov and K. A. Zhigalkin, "Mathematical modeling of material deformation,"
Dal'nevostochn. Mat. Zh., Part. 3, No. 1, pp. 93-101, 2002. |
| 17. | A. I. Khromov, "Deformation and fracture of a rigid-plastic strip under tension," Izv.
AN. MTT [Mechanics of Solids], No. 1, pp. 136-142, 2000. |
| 18. | B. N. Arzamasov (Editor), Structural Materials. Handbook [in Russian], Mashinostroenie, Moscow,
1990. |
| 19. | O. V. Kozlova and A. I. Khromov, "Fracture constants for perfect rigid-plastic bodies,"
Doklady AN, Vol. 385, No. 3, pp. 342-345, 2002. |
| 20. | A. I. Khromov and O. V. Kozlova, "Deformation and fracture of a rigid-plastic cylinder,"
in Problems of Mechanics of Inelastic Deformation [in Russian], pp. 343-350, Fizmatgiz, Moscow, 2001. |
| 21. | A. Nadai, Plasticity and Fracture of Solids. Volume 2 [Russian translation], Mir, Moscow, 1969. |
|
| Received |
03 April 2003 |
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