Skip to main content
Log in

Uniform Elongation and the Stress-Strain Flow Curve of Steels Calculated from Hardness Using Empirical Correlations

  • Published:
Journal of Materials Engineering and Performance Aims and scope Submit manuscript

Abstract

An empirical relationship between the hardness and uniform elongation of non-austenitic hypoeutectoid steels has been developed. This new hardness-elongation relationship was combined with previously developed correlations of hardness and strength (yield and ultimate tensile strength) to predict the stress-strain flow curve from a single hardness test. The current study considers both power law hardening behavior and exponential hardening behavior. Reasonable agreement was observed between the experimental and predicted flow curves of a high strength, low alloy steel. Additionally, an empirical correlation of the flow strength at instability with hardness is provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. D. Tabor, The Hardness and Strength of Metals, J. Inst. Met., 1951, 79, p 1–18

    Google Scholar 

  2. J.R. Cahoon, W.H. Broughton, and A.R. Kutzak, The Determination of Yield Strength from Hardness Measurements, Metall. Trans., 1971, 2, p 1979–1983

    Google Scholar 

  3. J.R. Cahoon, An Improved Equation Relating Hardness to Ultimate Strength, Metall. Trans., 1972, 3, p 3040

    Article  Google Scholar 

  4. X.-L. Gao, X.N. Jing, and G. Subhash, Two New Expanding Cavity Models for Indentation Deformations of Elastic Strain-hardening Materials, Int. J. Solids Struct., 2006, 43, p 2193–2208

    Article  Google Scholar 

  5. N.A. Branch, G. Subhash, N.K. Arakere, and M.A. Klecka, A New Reverse Analysis to Determine the Constitutive Response of Plastically Graded Case Hardened Bearing Steels, Int. J. Solids Struct., 2011, 48, p 584–591

    Article  Google Scholar 

  6. ASM International, ASM Handbook—Mechanical Testing and Evaluation, Vol 8, ASM International, Metals Park, OH, 2000, p 274–276

    Google Scholar 

  7. C.H. Cáceres, J.R. Griffiths, A.R. Pakdel, and C.J. Davidson, Microhardness Mapping and the Hardness-Yield Strength Relationship in High-pressure Diecast Magnesium Alloy AZ91, Mater. Sci. Eng. A, 2005, 402, p 258–268

    Article  Google Scholar 

  8. E.J. Pavlina and C.J. Van Tyne, Correlation of Yield Strength and Tensile Strength with Hardness for Steels, J. Mater. Eng. Perform., 2008, 17(6), p 888–893

    Article  Google Scholar 

  9. L. Addessio, “The Effect of Strain Rate and Tempering on the Mechanical Properties of Low Carbon Martensite,” MS Thesis T-6267, Colorado School of Mines, Golden, Colorado, 2007

  10. N.E. Aloi, “Hot Deformation, Microstructure, and Property Analysis of Ferritic/Pearlitic and Bainitic Microalloyed Forging Steels,” MS Thesis T-4617, Colorado School of Mines, Golden, Colorado, 1994

  11. P.I. Anderson, “Induction Hardening Response of Ferrite and Pearlite Banded Steel,” MS Thesis T-6083, Colorado School of Mines, Golden, Colorado, 2005

  12. S.F. Biagiotti, “Effect of Nickel on Sulfide Stress Cracking Resistance in Steels,” MS Thesis T-4486, Colorado School of Mines, Golden, Colorado, 1994

  13. J. Cross, “Effects of Microstructure on the Fire-Resistant Properties of HSLA Structural Steels,” MS Thesis T-6102, Colorado School of Mines, Golden, Colorado, 2006

  14. J.L. Cunningham, “Effects of Induction Hardening and Prior Cold Work on a Microalloyed Medium-Carbon Steel,” MS Thesis T-4916, Colorado School of Mines, Golden, Colorado, 1996

  15. N.M. Gaitain, “Effect of Tempering Conditions on the Fatigue and Toughness of 5150H Steel,” MS Thesis T-3840, Colorado School of Mines, Golden, Colorado, 1989

  16. B.A. James, “Interactive Effects of Phosphorus and Tin on Carbide Evolution and Fatigue and Fracture Properties in 5160 Steel,” PhD Thesis T-4616, Colorado School of Mines, Golden, Colorado, 1994

  17. J.A. Johnson, “Fatigue of Microalloyed Bar Steels,” MS Thesis T-5285, Colorado School of Mines, Golden, Colorado, 1999

  18. J.S. Keske, “Reheat-Cracking Sensitivity in ASTM A514 Steels as Influenced by Sulfur and Boron,” MS Thesis T-5279, Colorado School of Mines, Golden, Colorado, 1999

  19. B.G. Kirby, “Microstructural and Performance Optimization of Microalloyed Bar and Forging Steels,” MS Thesis T-4287, Colorado School of Mines, Golden, Colorado, 1992

  20. M.J. Leap, “The Effects of Forging on the Microstructural Development, Strength, and Dynamic Fracture Behavior of Microalloyed Ferrite-Pearlite Steels,” MS Thesis T-3276, Colorado School of Mines, Golden, Colorado, 1987

  21. M.J. Merwin, “The Effects of Titanium Nitride Particles and Free Nitrogen on the Heat-Affected Zone Toughness of API-2Y Type Plate Steels,” PhD Thesis T-4961, Colorado School of Mines, Golden, Colorado, 1997

  22. A.J. Nagy Bailey, “Effects of Silicon and Retained Austenite on Direct-Cooled Microalloyed Forging Steels with Bainitic Microstructures,” MS Thesis T-4709, Colorado School of Mines, Golden, Colorado, 1995

  23. E.J. Pavlina, “Assessment of the Mechanical Properties of Dual Phase Steels in Tubular Products,” MS Thesis T-6271, Colorado School of Mines, Golden, Colorado, 2007

  24. S.A. Richardson, “The Effects of Thermal Processing on the Microstructure and Mechanical Properties of HSLA-100 Plate Steel,” MS Thesis T-3949, Colorado School of Mines, Golden, Colorado, 1990

  25. E.J. Schultz, “The Effect of the Hot-Roll Reduction Ratio on Fully Reversed Axial Fatigue Properties of a Continuously-Cast and Hardened 4140 Steel,” MS Thesis T-4267, Colorado School of Mines, Golden, Colorado, 1992

  26. D.A. Shepherd, “The Effect of Strain Rate on the Hot Deformation Behavior of Microalloyed Bar Steels at Warm Forging Temperature,” MS Thesis T-4196, Colorado School of Mines, Golden, Colorado, 1999

  27. L.P. Turner, “The Relationship of Friction, Formability and Normal Anisotropy in SAE 1012 Modified Steel,” MS Thesis T-4554, Colorado School of Mines, Golden, Colorado, 1994

  28. M. Walp, “Fire-Resistant Steels for Construction Applications,” MS Thesis T-5782, Colorado School of Mines, Golden, Colorado, 2002

  29. G.C. Yerby, “The Effects of Direct Quenching After Forging on the Mechanical Properties of Medium-Carbon Steel,” MS Thesis T-4901, Colorado School of Mines, Golden, Colorado, 1996

  30. American Society for Testing and Materials, Hardness Conversion Tables for Metals Relationship Among Brinell Hardness, Vickers Hardness, Rockwell Hardness, Superficial Hardness, Knoop Hardness, and Scleroscope Hardness, E 140-05 2005, Annual Book of ASTM Standards, vol. 3.01. American Society for Testing and Materials, West Conshohocken, PA, p 308–328

  31. American Society for Testing and Materials, Standard Test Methods for Tension Testing of Metallic Materials, E8/8M-11, Annual Book of ASTM Standards, vol. 3.01. American Society for Testing and Materials, West Conshohocken, PA

  32. A.M. Brown, A Step-By-Step Guide to Non-linear Regression Analysis of Experimental Data Using a Microsoft Excel Spreadsheet, Comput. Methods Progr. Biomed., 2001, 65(3), p 191–200

    Article  Google Scholar 

  33. G.E. Dieter, Mechanical Metallurgy, 3rd ed., McGraw-Hill, Boston, MA, 1986, p 289–292

    Google Scholar 

  34. B.S. Levy and C.J. Van Tyne, Effect of Strain-Hardening Rate at Uniform Elongation on Sheared Edge Stretching, J. Mater. Eng. Eng. Perform., 2012, 21(10), p 2147–2154

    Article  Google Scholar 

  35. D.K. Matlock, G. Krauss, and F. Zia-Ebrahimi, Strain Hardening of Dual-Phase Steels: An Evaluation of the Importance of Processing History, Deformation, Processing, and Structure, G. Krauss, Ed., ASM, Materials Park, OH, 1984, p 47–87

    Google Scholar 

  36. W.B. Morrison, The Effect of Grain Size on the Stress-Strain Relationship in Low-Carbon Steel, Trans. ASM, 1966, 59, p 824–846

    Google Scholar 

  37. A.R. Marder, Deformation Characteristics of Dual-Phase Steels, Metall. Trans. A, 1982, 13, p 85–92

    Article  Google Scholar 

  38. W.F. Hosford and R.M. Caddell, Metal Forming: Mechanics and Metallurgy, 4th ed., Cambridge University Press, New York, NY, 2011, p 310

    Book  Google Scholar 

  39. R.G. Davies, On the Ductility of Dual Phase Steels, Formable HSLA and Dual-phase Steels, A.T. Davenport, Ed., Oct 26, 1977 (Chicago), The Metallurgical Society of AIME, Washington, DC, p 25–39

  40. Z. Jiang, Z. Guan, and J. Lian, Effects of Microstructural Variables on the Deformation Behaviour of Dual-Phase Steel, Mater. Sci. Eng. A, 1995, 190, p 55–64

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Erik J. Pavlina.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pavlina, E.J., Van Tyne, C.J. Uniform Elongation and the Stress-Strain Flow Curve of Steels Calculated from Hardness Using Empirical Correlations. J. of Materi Eng and Perform 23, 2247–2254 (2014). https://doi.org/10.1007/s11665-014-1037-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11665-014-1037-1

Keywords

Navigation