Analysis of the stress-strain curves of a modified 9Cr-1Mo steel by the voce equation
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The authors are thankful to Professor Nack J. Kim, POSTECH, and Dr. Sang-Ho Ahn, RIST, for their helpful discussion of this work. REFERENCES 1. K.G. Budinski: Surface Engineering for Wear Resistance, PrenticeHall, Englewood Cliffs, NJ, 1988, ch. 1I. 2. Metals Handbook, vol. 6, Welding, Brazing and Soldering, 9th ed., ASM, Metals Park, OH, 1983, pp. 771-803. 3. K.G. Budinski: Surface Engineering for Wear Reststance, PrenticeHall, Englewood Cliffs, NJ, 1988, pp. 267-69. 4. E.K. Ohriner, T. Wada, E.P. Whelan, and H. Ocken: Metall Trans. A, 1991, vol. 22A, pp. 983-91. 5. S.K. Ray, M. Mandal, P.K. Bandopadhyay, and A.K. Sengupta: J. Mater. Sci. Lett., 1988, vol. 7, pp. 775-77. 6. I. Inglis, E.V. Murphy, and H. Ocken: Surface Coat. Technol., 1992, vol. 53, pp. 101-06. 7. L.E. Svensson, H.K.D.H. Bhadeshia, B. Gretofl, and B. Ulander: J. Mater ScL, 1986, vol. 21, pp. 1015-19. 8. S. Atamert and H.K.D.H. Bhadeshia: Mater. Sci. Eng., 1990, vol. 130, pp. 101-11. 9. N.R. Griffing, W.D. Forgeng, and G.W. Healy: Trans. AIME, 1962, vol. 224, pp. 148-59. 10. R.S. Jackson: J. Iron Steel Inst., 1970, vol. 208, pp. 163-67. 11. W.R. Thorpe and B. Chicco: Metall. Trans. A, 1985, vol. 16A, pp. 1541-49. 12. J.O. Andersson: Metall Trans. A, 1988, vol. 19A, pp. 627-36. 13. M. Hillert and C. Qiu: Metall. Trans A, 1991, vol. 22A, pp. 2187-98.
Analysis of the Stress-Strain Curves of a Modified 9Cr-lMo Steel by the Voce Equation R. KISHORE and T.K. SINHA The representation of stress-strain curves by empirical relations can give first-hand information on the deformation behavior of a material. Although the constants in these equations are simple numerals for smooth fitting of the curves, a theoretical basis using dislocation interaction has been put forth by Bergstrom.m The commonly used empirical equations to represent the stress strain relations are as follows: o" = Ice"
(Hollomon)
[1]
(Ludwik)
[2]
o" = kz (e + e0)"2 (Swift)
[3]
o- = K - (K - D) exp ( - C e) (Voce)
[4]
o" = o"o + k~e "~
where o" and e are the true stress and strain and the other parameters are constants. The most commonly used Hollomon and Ludwik equations fit the o--e data satisfactorily for iron and steel. The n value in Eq. [1] is the strain-hardening exponent and gives the uniform strain in the material, and the o-o in Eq. [2] represents the athermal component of stress. [21 The slope of Oo/Oe - o- in the logarithmic coordinates gives the value of (1 - m), where m = 1/n2 follows from Eq. [3]. If the log o-log e plot shows more than one slope, then as many separate Hollomon equations have to be fitted.t3] The Voce equation is less frequently discussed in the literature despite the fact that it represents the stress-strain relations better than other equations.E41 This is probably because this equation is complex and no less empirical than others. The significance of the empirical constants is also not known. In this article, the Voce equation is reviewed and the influence of the constants on the nature of the stress-strain curves is examined. The stress-strain cu
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