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IssuesArchive of Issues2001-1pp.93-101

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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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