Advertisement

Strength of Materials

, Volume 32, Issue 3, pp 277–285 | Cite as

Influence of constant current on the formation of a neck in a porous bar subjected to tension

  • A. A. Bychkov
  • D. N. Karpinskii
Scientific and Technical Section
  • 23 Downloads

Abstract

We study the conditions of neck formation in a thermoviscoplastic bar in tension for a broad range of strain rates and different modes of application of direct electric current. The proposed model takes into account complex determining relations for the material of the bar, the process of heat transfer, and the presence of discontinuities (pores). We determine the conditions of stability of uniform tension of the bar and evolution of perturbations of its uniform deformation for various values of the parameters. It is shown that (i) the critical level of strains for a bar in tension strongly depends on the wave number, especially within the range of its small values, (ii) the action of an electric current on the deformed bar weakens the conditions of neck initiation in the case where the current strength is constant (this effect is more pronounced in the mode of constant current strength than in the mode of constant voltage), (iii) as the porosity of the bar increases, the conditions of neck initiation are weakened for both modes of application of the electric current, (iv) the influence of the amplitude of perturbations and the Thomson effect on the stability of the deformed bar is weak, and (v) for small strain rates, the dependence of the level of strains on the wave number is insignificant.

Keywords

Constant Difference Neck Formation Uniform Solution Uniform Tension Direct Electric Current 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notation

A0

initial cross section of the bar

cd

volume fraction of deformation pores

ε0d

level of strains corresponding to the onset of pore initiation

cd0

initial volume fraction of strain-induced pores

Kd

constant determining the rate of pore initiation

ν

velocity

ε

level of strains

θ

temperature

C

heat capacity

k

specific heat

β

fraction of plastic work transformed into heat

σ

stress

Ft

Bridgman factor

Rc

radius of the neck

R

local radius of the cross section of the bar

\(\dot \varepsilon \)

strain rate

\(\tilde \mu \),n, m, and\(\tilde \nu \)

constants in the determining relations

t

time

x

distance

l0

length of the bar

δε, δσ, δν, δθ, and δFt

amplitudes of perturbations of the corresponding quantities

η

parameter characterizing the growth of perturbations

ξ

wave number

ε0, σ0, ν0, θ0 andFt0

solution uniform in length

a1,a2,a3,a1,a2, anda3

coefficients in the characteristic equation

ρ0

density of the material of the specimen

εp

perturbation of strain

θp

perturbation of temperature

δp

initial amplitude of perturbations

a andb

coordinates of the left and right boundaries of the perturbed region

N

number of a Fourier coefficient

\(\bar \varepsilon _0 \)

initial level of strains

\(\bar \dot \varepsilon _0 \)

initial strain rate

V

velocity of the right end of the bar

δε

relative amplitude of perturbation of strains

δθ

relative amplitude of perturbation of temperature

Δε

distribution of strains along the bar depending on time

λ

Thomson coefficient

γ

specific resistance

γ0

initial specific resistance

α

temperature resistance coefficient

\(\bar j_0 \)

initial current density

s

parameter specifying the mode of application of the electric current

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. A. Nikulin, “Two mechanisms of the loss of stability of flow in tension and the plasticity of alloys,”Fiz. Met. Metalloved.,81, No. 3, 142–158 (1996).Google Scholar
  2. 2.
    V. V. Rybin,High Plastic Strains and the Fracture of Metals [in Russian], Metallurgiya, Moscow (1986).Google Scholar
  3. 3.
    P. G. Cheremskoi, V. V. Slezov, and V. I. Betekhin,Pores in Solids [in Russian], Énergoatomizdat Moscow (1990).Google Scholar
  4. 4.
    V. M. Finkel’,Physical Fundamentals of the Inhibition of Fracture Processes [in Russian], Metallurgiya, Moscow (1977).Google Scholar
  5. 5.
    V. I. Spitsyn and O. A. Troitskii,Electroplastic Deformation of Metals [in Russian], Nauka, Moscow (1985).Google Scholar
  6. 6.
    I. L. Maksimov and Yu. V. Svirina, “Dissipative instabilities of fracture in conducting materials with transport current. 1. Criteria of instability and qualitative analysis,”Zh. Tekh. Fiz.,66, No. 9, 64–74 (1996).Google Scholar
  7. 7.
    I. L. Maksimov and Yu. V. Svirina, “Dissipative instabilities of fracture in conducting materials with transport current. 2. Evolutionary equations and diagrams of instability,”Zh. Tekh. Fiz.,66, No. 9, 75–85 (1996).Google Scholar
  8. 8.
    F. I. Ruzanov, A. M. Roshchupkin, and V. I. Stashenko, “Influence of the strain rate and pulse current on the ultimate elongation of a metal in the mode of superplasticity,”Probl. Mashinostr. Nadezh. Mash., No. 1, 82–89 (1990).Google Scholar
  9. 9.
    C. Fressengeas and A. Molinari, “Inertia and thermal effects on the localization of plastic flow,”Acta Met.,33, No. 3, 387–396 (1985).CrossRefGoogle Scholar
  10. 10.
    A. A. Bychkov and D. N. Karpinskii, “Analysis of the conditions of neck formation for a porous bar subjected to tension,”Probl. Prochn., No. 3, 46–55 (1998).Google Scholar
  11. 11.
    L. D. Landau and E. M. Lifshits,Electrodynamics of Continua [in Russian], GITTL, Moscow (1957).Google Scholar
  12. 12.
    C. Fressengeas and A. Molinari, “Instability and localization of plastic flow in shear at high strain rates,”J. Mech. Phys. Solids,35, No. 2, 185–211 (1987).CrossRefGoogle Scholar
  13. 13.
    E. I. Jury,Inners and Stability of Dynamic Systems, Wiley, New York (1974).Google Scholar
  14. 14.
    Y. Bai and B. Dodd,Adiabatic Shear Localization. Occurrence. Theories and Applications, Pergamon Press, Oxford (1992).Google Scholar
  15. 15.
    I. S. Grigor’ev and E. Z. Meilikhov (eds.),Physical Quantities. A Handbook [in Russian], Énergoatomizdat, Moscow (1991).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • A. A. Bychkov
  • D. N. Karpinskii

There are no affiliations available

Personalised recommendations