 | | 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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| << Previous article | Volume 40, Issue 5 / 2005 | Next article >> |
| R. I. Nepershin, "Pressure of a flat round die on a perfectly plastic half-space with allowance for contact friction," Mech. Solids. 40 (5), 115-121 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
5 |
Pages |
115-121 |
| Title |
Pressure of a flat round die on a perfectly plastic half-space with allowance for contact friction |
| Author(s) |
R. I. Nepershin (Moscow) |
| Abstract |
We give a numerical solution of the problem on the pressure of a flat round
die on a perfectly plastic half-space under the full plasticity condition
with allowance for contact friction modeled by the Prandtl and Coulomb
laws. We show that a rigid zone whose size depends on contact friction is
formed at the die center and sliding occurs outside the rigid zone on the
interface between the die and the plastic domain. We find the limiting
values of the friction coefficients for which the rigid zone occupies the
entire interface between the die and the plastic half-space and compute the
pressure on the die versus the friction coefficients.
The problem on the initial plastic flow of a perfectly plastic half-space
under the pressure of a smooth flat or spherical die was solved in [1, 2].
The solution of the problem on the pressure exerted on a perfectly plastic
half-space by a flat round rough die with central rigid zone moving
together with the die under the no-slip condition on the interface is given
in [3]. In this solution, the limiting load is much larger than for a
perfectly smooth die and is realized at considerably large contact friction
stresses. In what follows, we give a numerical solution of the problem on
the pressure of a flat round die on a perfectly plastic half-space with
allowance for contact friction stresses varying from zero to the limiting
value at which the central rigid zone occupies the entire interface surface
of the die. |
| References |
| 1. | A. Yu. Ishlinskii, "An axisymmetric plasticity problem and the
Brinell test," PMM [Applied Mathematics and Mechanics], Vol. 8, No. 3,
pp. 201-224, 1944. |
| 2. | A. Yu. Ishlinskii and D. D. Ivlev, Mathematical Theory of
Plasticity [in Russian], Fizmatlit, Moscow, 2001. |
| 3. | G. Eason and R. T. Shield, "The plastic indentation of a
semi-infinite solid by perfectly rough circular punch," Z. Angew. Math.
Phys., Vol. 11, No. 1, pp. 33-43, 1960. |
| 4. | D. D. Ivlev and A. Yu. Ishlinskii, "Full plasticity in the theory
of a perfectly plastic solid," Doklady AN, Vol. 368, No. 3, pp. 333-334,
1999. |
| 5. | V. V. Sokolovskii, Theory of Plasticity [in Russian], Vyssh. Shk.,
Moscow, 1969. |
| 6. | A. D. Tomlenov, Theory of Plastic Deformation of Metals [in
Russian], Metallurgiya, Moscow, 1972. |
| 7. | B. A. Druyanov and R. I. Nepershin, Theory of Technological Plasticity [in Russian],
Mashinostroenie, Moscow, 1990. |
|
| Received |
03 December 2003 |
| << Previous article | Volume 40, Issue 5 / 2005 | Next article >> |
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