 | | 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 |
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| A. I. Iskakbaev, "Integral representation of damage kinetics in materials," Mech. Solids. 37 (2), 103-108 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
2 |
Pages |
103-108 |
| Title |
Integral representation of damage kinetics in materials |
| Author(s) |
A. I. Iskakbaev (Almaty) |
| Abstract |
We study the dependence of damage
accumulation rate for isotropic materials on the initial damage,
the loading regime, the trajectory of damage accumulation,
temperature, and the sign of stresses. Kinetic equations of damage
accumulation in terms of stresses or strains
are represented as Volterra integral equations of the second kind.
These
equations allow us to identify the form of the damage kernel using the laws
governing the long-term strength of materials.
We propose a method for determining optimal creep and long-term strength
parameters of materials.
It is shown
that the heredity-type conditions of damage summation obtained in the
present paper are more adequate for the prediction of material durability
than the Bailey-Robinson approach.
In modern fracture mechanics, an important role is played by the
phenomenological approach which is applied not only to the statement of
applied problems, but also to the solution of theoretical problems, in
particular, problems connected with the evaluation of the service life of
structures with a given loading history and the damage accumulation
process in a real body [1]. In order to solve such problems, one uses not
only the equations describing the kinetics of the stress-strain state, but
also the kinetic equations of damage accumulation and fracture
criteria [2-13].
The existing statements of the damage accumulation problem in terms of the
damage measure ω have either the form of hereditary integral
operators [6] or the form of kinetic equations for the
change rate of the damage measure [2-5], and in each equation of damage
accumulation the number of independent constants varies from two to three
(or more). In the general case, the problem becomes weakly well-posed
and it is possible that there is a set of coefficient combinations
satisfying equations with three or more coefficients under the condition ω=1 [4].
It is difficult to describe the actual character of damage accumulation by the
phenomenological method, since the parameter ω used in the kinetic equations
cannot be measured experimentally. Thus, the correct choice of the state parameter
remains an important problem of fracture mechanics. In [3, 7, 8],
the following quantities are taken as damage parameters:
relative variation of strength, relative variation of strain,
relative variation of specific energy dissipation. The aim of this paper
is to apply the ideas of the works mentioned above to the study of
dispersed fracture of a material whose tensile strength differs from its
compression strength. |
| References |
| 1. | V. V. Novoshilov, "Prospects of the Phenomenological Approach to
the Problem of Fracture," Mechanics of Solids and Structures
[in Russian], pp. 349-359, Nauka, Moscow, 1975. |
| 2. | Yu. N. Rabotnov, Introduction to Fracture Mechanics [in Russian], Nauka,
Moscow, 1987. |
| 3. | Yu. I. Boitsov, V. L. Danilov, A. M. Lokoshchenko, and S. A.
Shesterikov, Studies of Creep in Metals Subjected to Tension [in Russian], MGTU,
Moscow, 1997. |
| 4. | V. P. Golub, A. V. Romanov, "On the kinetics of damage in
isotropic materials subject to creep," Prikl. Mekh., Vol. 25, No. 12,
pp. 107-115, 1989. |
| 5. | L. M. Kachanov, Principles of Fracture Mechanics [in Russian], Nauka,
Moscow, 1974. |
| 6. | A. A. Il'yushin, "On a theory of long-term strength," Inzh.
Zh. MTT, No. 3, pp. 21-35, 1967. |
| 7. | A. I. Iskakbaev, "On a model of long-term strength of materials,"
Vestnik Kazakh. Un-ta, Ser. Mat. Mekh. Informat., No. 9, pp. 66-77, 1998. |
| 8. | Yu. N. Rabotnov and S. I. Mileiko, Short-Term Creep [in Russian],
Nauka, Moscow, 1970. |
| 9. | A. L. Arshakuni and S. A. Shesterikov,
"Prediction of long-term strength of heat-temperature metallic materials,"
Izv. AN. MTT [Mechanics of Solids], No. 3, pp. 126-141, 1994. |
| 10. | S. N. Zhurkov and B. N. Narzullaev, "Time dependence of strength
of solids," Zh. Tekhn. Fiziki, Vol. 23, No. 10,
pp. 1678-1689, 1953. |
| 11. | S. A. Shesterikov and M. A. Yumasheva,
"Specific form of the state equation in the theory of creep,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 1, pp. 86-91, 1984. |
| 12. | Yu. V. Suvorova, "A strength criterion based on
damage accumulation and its application to composites,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 4, pp. 107-111, 1979. |
| 13. | P. A. Pavlov and L. I. Ogorodov, "Long-term strength and
evaluation of damage of composite materials with phenol plastic base and
disperse filling under axial compression," Probl. Mashinostr. i Nadezhn.
Mashin, No. 6, pp. 37-44, 1991. |
| 14. | V. V. Moskvitin, Strength of Viscoelastic Materials [in Russian], Nauka,
Moscow, 1972. |
| 15. | Zh. S. Erzhanov (Editor), Creep in Sedimentary Rocks. Theory and
Experiment [in Russian], Nauka, Alma-Ata, 1970. |
| 16. | A. M. Lokoshchenko and S. A. Shesterikov,
"A method for the description of creep and long-term strength under pure
tension," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, No. 3, pp. 155-159,
1980. |
|
| Received |
20 October 1999 |
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