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Effects of strain rate and deformation heating in tensile testing

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Abstract

The effects of strain, strain rate and deformation heating in tensile testing of sheet steel are numerically analyzed. An experimentally determined strain-hardening formula is used as a basis of the calculation. The effects of heat conduction and free or forced con-vection during the test are taken into account by using the approximate solution method originally given by Bishop for metal extrusion. The calculated values agree well with the experimental data. It is shown that deformation heating considerably affects the uni-form strain. Consequently the stretchability of sheet metals can be improved by using very low forming speeds or more economically by using an effective cooling system.

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Abbreviations

a :

λpc, thermal diffusivity of the material,

b :

3.834 exp (R2ε)/(pczo l0.25), coefficient of heat transfer equation when McAdams formula is used,

c1 :

v/(l oR1)

c2 :

Kc m 1

c :

specific heat

F :

ak/h 2, Fourier number

Gr :

Grashof number

h :

Δl, increment of length,

i :

0, 1, . . . ,m,

j :

0, 1, . . . ,n,

K :

strength coefficient in the equation, σ =Kε n εm(1βθ),

k :

Δ(Δt), subdivision of the increment of timeΔt,

L o :

original nominal gage length,

L c :

gage length corresponding to uniform crosssection,L c > Lo

I :

gage length, initiallyI = l o ≳ Lc > Lo

m :

strain rate sensitivity exponent; number of increments,h

n :

strain hardening exponent; number of subdivisions,k,

o :

subscript corresponding to original dimension, where necessary

Pr :

Prandtl number

Q :

amount of heat,Q = dQ/dt, heat transfer per unit of time, total rate of heat flow through a surface (J/s),

Ra :

Gr ⋅ Pr, Rayleigh number,

R 1 :

l/Z d(α = 0) = (3/2)r2 ⋅(r 1 +l)/(r 1 + r2 + r2 1/2,

R 2 :

(3/2)r 2/[r1 +r 1r2 + r2)(l +r 1]1/2)

r 1 r2 :

anisotropy coefficients in rolling and transverse directions, respectively

T :

temperature

t. :

time

U :

rate of change of internal energy,

v :

v(x), velocity,v = v(l), cross-head speed,

W :

v ∝ wdV, total rate of change of plastic work,

w :

rate of change of plastic work per unit volume,

x, y, z :

and 1, 2, 3, coordinate axes in rolling, transverse and thickness directions, respectively,

Z d :

critical subtangent, diffuse necking

α :

σ 2/σ1, stress ratio,

α :

convection coefficient (heat-transfer coefficient) in Newton’s formula (J/(s m2K)),

β :

coefficient in formula σ =K ε n- εm(1 - βθ)

ε :

effective strain

ε* d :

uniform strain or effective strain to diffuse necking

η:

coefficient determining the amount of plastic work converted into heat per unit of time

θ t - T o :

temperature difference between current and room temperature,

λ:

thermal conductivity (J/(sm2K))

p:

density

σ:

effective stress

σ 1, σ2 :

principal stresses in rolling and transverse directions respectively

References

  1. A. K. Ghosh:Met. Trans. A, 1977, vol. 8A, pp. 1221–32.

    Article  CAS  Google Scholar 

  2. A. Troost and A. El-Schennawi:Arch. Eisenhüttenw., 1975, vol. 46, pp. 729- 33.

    Google Scholar 

  3. G. D. Lahoti and T. Altan:J. Eng. Mater. Technol, Trans. ASME, Ser. H. 1975, vol. 97, pp. 113–20.

    Google Scholar 

  4. H. J. Kleemola and A. J. Ranta-Eskola: Helsinki University of Technology, Helsinki, Finland, unpublished research, 1978.

  5. A. S. Korhonen: Helsinki University of Technology, Helsinki, Finland, unpublished research, 1978.

  6. J. E. Dorn, A. Goldberg, and T. E. Tietz:Metals Technol., 1948, vol. 15, T.P. 2445.

    Google Scholar 

  7. Mechanical Behavior of Materials, A. S. Argon and F. A. McClintock, eds., 1st ed., pp. 190–94, Addison-Wesley, Reading, Mass., 1967.

  8. A. S. Korhonen:J. Eng. Mater. Technol., Trans. ASME, ser. H, 1978, in press.

  9. W. S. Farren and G. I. Taylor:Proc. Roy. Soc. A, 1925, vol. 107, pp. 422–51.

    Article  Google Scholar 

  10. J. R. Simonson:An Introduction to Engineering Heat Transfer, 1st ed., McGraw-Hill, London, 1967.

    Google Scholar 

  11. J. F. W. Bishop:Quart. J. Mech. Appl. Math., 1956, vol. 9, Part 2, pp. 236–46.

    Article  Google Scholar 

  12. T. Altan and S. Kobayashi:J. Eng. Ind., Trans. ASME, Ser. B, 1968, vol. 90, pp. 107–18.

    Google Scholar 

  13. W. H. McAdams:Heat Transmission, 3rd ed., McGraw-Hill, New York, 1954.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mining and Metallurgy, Laboratory of Metal Working and Heat Treatment, Helsinki University of Technology, 02150, Espoo 15, Finland

    A. S. Korhonen (Teaching Assistant) & H. J. Kleemola (Teaching Assistant)

Authors
  1. A. S. Korhonen
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  2. H. J. Kleemola
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Korhonen, A.S., Kleemola, H.J. Effects of strain rate and deformation heating in tensile testing. Metall Trans A 9, 979–986 (1978). https://doi.org/10.1007/BF02649843

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