 | | 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
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| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| V. V. Glagolev, K. A. Kuznetsov, and A. A. Markin, "A model of splitting of solids," Mech. Solids. 38 (6), 49-54 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
6 |
Pages |
49-54 |
| Title |
A model of splitting of solids |
| Author(s) |
V. V. Glagolev (Tula)
K. A. Kuznetsov (Tula)
A. A. Markin (Tula) |
| Abstract |
A plane-strain model for the description of splitting of a
material is proposed. Splitting of an elastic plane by a concentrated wedging force is considered on the basis of this model. Material characteristics are examined with regard to their influence on splitting. Splitting is considered as a process of formation of new material surfaces as a result of mechanical actions on a deformable body. The theory of splitting proposed here is a continuous theory, according to the terminology of [1], and is based on a constitutive relation that describes the material behavior at the stage of stable deformation and that of unstable deformation, with the stability understood in the sense of Drucker. In contrast to the approach developed in [2], we use piecewise linear approximation of the relation between stress and strain tensors. Near the splitting surface, there is an interaction layer formed by the material which will pass to the stage of unstable deformation. The minimal thickness of this interaction layer is assumed to be a characteristic constant for a given material. It is assumed, in addition, that the stress-strain state of the interaction layer is uniform in the direction of the normal to the splitting surface; and this allows one to avoid infinite stress values. The distribution of the interaction forces between the formed surfaces is not given apriori, as was the case in [3-5], but is obtained as a result of solving an appropriate boundary-value problems. We find the conditions ensuring the initiation of splitting of an infinite space with a semi-infinite cut, the distance between its edges being equal to the thickness of the interaction layer. The splitting is due to concentrated forces acting in opposite directions on the edges of the cut. The problem is solved within the framework of plane-strain elasticity and is reduced to systems of integral equations for the displacements of the boundaries of the interaction layer. Among unknown parameters, these equations contain the critical values of wedging forces. Using numerical methods, we find the critical and the maximal values of the wedging forces and the corresponding stress distributions along the boundaries of the interaction layer. We also describe the influence of the material parameters on the region of the interaction layer in which the material undergoes unstable deformation. A method is proposed for the evaluation of the thickness of the interaction layer in terms of the critical value of the stress intensity factor. |
| References |
| 1. | G. P. Cherepanov,
"Modern problems in fracture mechanics,"
Probl. Prochnosti, No. 8, pp. 3-13, 1987. |
| 2. | V. M. Alexandrov and I. I. Kudish,
"Asymptotic methods in the Griffith problem,"
PMM [Applied Mathematics and Mechanics], Vol. 5, No. 4, pp. 665-671, 1989. |
| 3. | J. F. Nott, Fundamentals of Fracture Mechanics [Russian translation],
Metallurgia, Moscow, 1978. |
| 4. | V. V. Panasyuk,
Mechanics of Brittle Fracture [in Russian], Naukova Dumka, Kiev, 1991. |
| 5. | V. Z. Parton and E. M. Morozov,
Mechanics of Elastoplastic Fracture [in Russian], Nauka, Moscow, 1985. |
| 6. | A. I. Lur'e, Theory of Elasticity [in Russian], Nauka, Moscow, 1970. |
| 7. | S. L. Crouch and A. M. Starfield, Boundary Element
Methods in Solid Mechanics [Russian translation], Mir, Moscow,
1987. |
| 8. | V. V. Panasyuk, A. E. Andreikiv, and S. E. Kovchik,
"Determination of fracture toughness K1C of structural materials in terms
of their mechanical characteristics and structural parameters,"
Fiz.-Khim. Mekh. Materialov, No. 2, pp. 120-122, 1977. |
|
| Received |
08 August 2001 |
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