 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| V. Yu. Kibardin and V. N. Kukudzhanov, "Modeling of continuum fracture in an elastoviscoplastic material," Mech. Solids. 36 (1), 93-101 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
1 |
Pages |
93-101 |
| Title |
Modeling of continuum fracture in an elastoviscoplastic material |
| Author(s) |
V. Yu. Kibardin (Moscow)
V. N. Kukudzhanov (Moscow) |
| Abstract |
Models of viscoplastic media are widely used in studying
the processes of plastic metal working. A. A. Il'yushin carried out the
first works in this field [1]. In recent years, modeling of fracture in
viscoplastic materials both under working operations and in structures has
become of great interest [2, 3].
The present study is based on the generalized
elastoviscoplastic material model suggested in [4], which takes into
account microdefects. The development of the microdefects leads to the
fracture of a material.
It is assumed that the process of viscoplastic deformation consists
of two successive stages. At the first stage, the viscoplastic flow
occurs, which is accompanied by the growth of the residual stresses and
translational hardening of a material. At the second stage,
micropores nucleate and begin to grow at the intergrain boundaries
of crystals. This leads to the relaxation of the internal stresses,
appearance of porosity, and decrease in the effective yield limit
of the material. At this stage, which immediately precedes the
macrofracture, strips of localized plastic strains appear. The
propagation of these strips reduces the load-carrying capacity of a
structure.
The complete system of constitutive equations of this model is
expressed in terms of macroparameters of a continuum and relates
the tensors of active and residual stresses to the
viscoplastic strain rate tensor and the damage tensor. It is shown that this
system of equations leads to well-posed boundary
value problems not only for the stage of hardening of a material,
but also for softening [4, 5]. To numerically simulate the fracture
processes, we suggest a new numerical method for solving
viscoplastic equations of multidimensional problems taking into
account softening. This method is based on splitting or decomposing
complex rheological equations into simple components. The method
has been successfully employed for similar but simpler equations of
elastoplasticity and viscoplasticity [6, 7]. This
method turned out to be effective also for a substantially
more complex complete system of equations considered in the present
paper. We use this method for solving quasistatic plane and
axisymmetric problems with finite-element discretization of the
basic equations in a weak formulation.
The fracture problems are considered for a cylindrical specimen
subjected to extension. The specimen is weakened by a small cut
perturbing the uniform stress-strain state and is acted on by a
constant load applied at the end surfaces which are moved with
constant velocity. The character of localization of the plastic
strains is analyzed. The development of pore formation and fracture
zones is investigated. |
| References |
| 1. | A. A. Il'yushin, "Deformation of a viscoplastic body,"
Uchen. Zapiski MGU, No. 39, pp. 28-41, 1940. |
| 2. | G. A. Maugin, The Thermomechanics of Plasticity and
Fracture, University Press, Cambridge, 1992. |
| 3. | J. Lemaitre and J. L. Chaboche, Mechanics of Solid
Materials, University Press, Cambridge, 1990. |
| 4. | V. N. Kukudzhanov, "Micromechanical model of fracture
of an inelastic material and its application
to the investigation of strain localization,"
Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 72-87, 1999. |
| 5. | V. N. Kukudzhanov and K. Santaoja, "Thermodynamics of
viscoplastic media with internal parameters," Izv. AN. MTT [Mechanics of
Solid], No. 2, pp. 115-126, 1997. |
| 6. | V. N. Kukudzhanov, Difference Methods for Solving
Problems of Solid Mechanics [in Russian], MFTI, Moscow, 1992. |
| 7. | V. Yu. Kibardin and V. N. Kukudzhanov, "Numerical simulation of
plastic strain localization and fracture of viscoelastic
materials," Izv. AN. MTT. [Mechanics of Solids], No. 1,
pp. 109-119, 2000. |
| 8. | A. L. Gurson, "Continuum theory of ductile rupture by void
nucleation and growth. I. Yield criteria and flow rules for porous ductile
media," Trans. ASME. Ser. H.J. Eng. Materials Technol., Vol. 99, No. 1,
pp. 2-15, 1977. |
| 9. | R. Hill, "The essential structure of constitutive laws for
metal composites and polycrystals," J. Mech. and Phys. of Solids,
Vol. 15, No. 2, pp. 2-15, 1967. |
| 10. | V. N. Kukudzhanov, "One-dimensional problems of
propagation of stress waves in rods," in Reports on Applied
Mathematics [in Russian], No. 6, p. 55, VTs AN SSSR, Moscow, 1997. |
| 11. | T. Suzuki, H. Eshinaga, and S. Takeuchi,
Dislocation Dynamics and Plasticity [Russian translation], Mir, Moscow,
1989. |
|
| Received |
10 January 2000 |
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