 | | 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 English (Mech. Solids): | | 3212 |
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| R. I. Nepershin, "Indentation of an Perfectly Plastic Half-space by a Finite Wedge," Mech. Solids. 38 (4), 129-135 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
4 |
Pages |
129-135 |
| Title |
Indentation of an Perfectly Plastic Half-space by a Finite Wedge |
| Author(s) |
R. I. Nepershin (Moscow) |
| Abstract |
We consider unsteady plane plastic flow of a perfectly plastic half-space indented by a wedge of finite width, with contact friction taken into account. The first stage of the indentation is described by a self-similar solution which preserves geometrical similarity of the plastic region. The second stage of indentation is modelled by a field of slip lines and a velocity hodograph with a slip line that corresponds to pure shear and continues up to the boundary of the half-space. We determine the shape of the boundary of the half-space near the wedge and find how the force acting on the wedge depends on the indentation depth, from the point of its contact with the half-space to the steady flow of an unbounded plastic medium about the wedge.
Self-similar solutions are known for unsteady problems of plane plastic flow of a perfectly plastic half-space indented by an infinite smooth wedge (the cases of rectilinear and curvilinear boundaries were considered in [1] and [2], respectively). An unsteady problem for a thin smooth blade indenting an ideal plastic half-space was solved in [3] by the small parameter method.
In [2, 4], the initial stage of the indentation of a smooth wedge of finite width into an perfectly plastic half-space was studied under the assumption that the rigid-plastic boundary moves along the initial boundary of the half-space with the formation of a curvilinear rigid region near the wedge. There are some finite-element calculations of the initial indentation of rigid punches into an elastic-plastic half-space [5-7]. However, the large distortion of the deformed boundary near the edge of the punch, because of singular nature of plastic flow in that region, is a great obstacle to the application of elastic-plastic modeling.
In [8], the unsteady indentation of a plane smooth punch into a perfectly plastic half-space is modeled by a field of slip lines and the hodograph of velocities with an isolated line of pure shear which reaches the boundary of the half-space. Such a model can be used for studying the entire process of unsteady indentation up to the steady-state stage of motion of the punch in an unbounded medium. This approach is taken in the present paper in order to model indentation of a finite wedge from its initial point contact with the half-space up to its steady motion in the unbounded perfectly plastic medium, with contact friction taken into account. |
| References |
| 1. | R. Hill,
The Mathematical Theory of Plasticity, Clarendon Press, Oxford, 1985. |
| 2. | G. I. Bykovtsev and D. D. Ivlev,
Theory of Plasticity [in Russian], Dal'nauka, Vladivostok, 1998. |
| 3. | D. D. Ivlev, Theory of Ideal Plasticity [in Russian],
Nauka, Moscow, 1966. |
| 4. | G. I. Bykovtsev and A. I. Khromov,
"Plane deformation of perfectly elastic-plastic bodies with variable boundaries," Izv. AN SSSR. MTT [Mechanics of Solids], No. 2, pp. 71-78,
1979. |
| 5. | C. H. Lee and S. Kobayashi,
"Elastoplastic analysis of plane strain and axisymmetric flat punch indentation by the finite element method," Intern. J. Mech. Sci., Vol.
12, No. 4, pp. 349-370, 1970. |
| 6. | C. Hardy, C. N. Baronet, and G. V. Tordion,
"The elasto-plastic indentation of a half-space by rigid sphere,"
Intern. J. Num. Mech. Engng., Vol. 3, No. 3, pp. 451-462, 1971. |
| 7. | G. Z. Voyiadjis and N. E. Buckner,
"Indentation of a half-space with a rigid indentor,"
Intern. J. Num. Mech. Engng, Vol. 19, No. 10, pp. 1555-1578. |
| 8. | R. I. Nepershin,
"Indentation of a rigid-plastic half-space by plane punch,"
PMM [Applied Mathematics and Mechanics], Vol. 66, No. 1, pp. 140-146, 2002. |
|
| Received |
25 September 2001 |
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