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Modeling the brittle–ductile transition in ferritic steels: dislocation simulations

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Abstract

We present a model for the brittle–ductile transition in ferritic steels based on two dimensional discrete dislocation simulations of crack-tip plasticity. The sum of elastic fields of the crack and the emitted dislocations defines an elasto–plastic crack field. Effects of crack-tip blunting of the macrocrack are included in the simulations. The plastic zone characteristics are found to be in agreement with continuum models, with the added advantage that the hardening behavior comes out naturally in our model. The present model is composed of a macrocrack with microcracks ahead of it in its crack-plane. These microcracks represent potential fracture sites at internal inhomogeneities, such as brittle precipitates. Dislocations that are emitted from the crack-tip account for plasticity. When the tensile stress along the crack plane attains a critical value σ F over a distance fracture is assumed to take place. The brittle–ductile transition curve is obtained by determining the fracture toughness at various temperatures. Factors that contribute to the sharp upturn in fracture toughness with increasing temperature are found to be: the increase in dislocations mobility, and the decrease in tensile stress ahead of the macrocrack tip due to increase in blunting, and the slight increase in fracture stress of microcracks due to increase in plasticity at the microcrack. The model not only predicts the sharp increase in fracture toughness near the brittle–ductile transition temperature but also predicts the limiting temperature above which valid fracture toughness values cannot be estimated; which should correspond to the ductile regime. The obtained results are in reasonable agreement when compared with the existing experimental data.

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References

  • ASTM Standard Test Method E 1921-02: Standard Test Method for Determination of Reference Temperature, T0, for Ferritic Steels in the Transiton Range. Annual Book of ASTM Standards, vol. 03.01, p 1139–1163

  • Beremin, F.M.: Local criterion for cleavage fracture of a nuclear pressure vessel steel. Metall. Trans. A 14, 2277–2287 (1983)

    Article  Google Scholar 

  • Bowen, P., Druce, S.G., Knott, J.F.: Effects of microstructure on cleavage fracture in pressure vessel steel. Acta Metall. 34, 1121 (1986)

    Article  Google Scholar 

  • Bowen, P., Druce, S.G., Knott, J.F.: Micromechanical modelling of fracture toughness. Acta Metall. 35, 1735–1746 (1987)

    Article  Google Scholar 

  • Bowen, P., Knott, J.F.: Size effects on the microscopic cleavage fracture stress, σ*, in martensitic microstructures. Metall. Trans. A 17, 231–241 (1986)

    Google Scholar 

  • Cleveringa, H.H.M., Van der Giessen, E., Needleman, A.: Discrete dislocation analysis of mode I crack growth. J. Mech. Phys. Solids 48, 1133–1157 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  • Creager, M., Paris, P.C.: Elastic field equations for blunt cracks with reference to stress corrosion cracking. Int. J. Frac. Mech. 3, 247–252 (1967)

    Google Scholar 

  • Curry, D.A., Knott, J.F.: Effect of microstructure on cleavage fracture toughness of quenched and tempered steels. Met. Sci. 13, 341–345 (1979)

    Google Scholar 

  • Hirsch, P.B., Roberts, S.G.: Brittle-ductile transition in silicon. Phil. Mag. A 64, 55–80 (1991)

    Article  Google Scholar 

  • Hirsch, P.B., Roberts, S.G.: Modelling crack tip plastic zones and the brittle-ductile transition. Phil. Trans. R. Soc. Lond. A 355, 1991–2001 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  • Hirsch, P.B., Roberts, S.G., Samuels, J.: The brittle-ductile transition in silicon-II. Interpretation. Proc. R. Soc. Lond. A 421, 25–53 (1989)

    Article  Google Scholar 

  • Hutchinson, J.W.: Singular behaviour at the end of a tensile crack in a hardening material. J. Mech. Phys. Solids 16, 13–31 (1968)

    Article  MATH  Google Scholar 

  • Lakshmanan, V., Li, J.C.M.: Edge dislocations emitted along inclined planes from a mode I crack. Mater. Sci. Eng. A 104, 95–104 (1988)

    Article  Google Scholar 

  • McMahon, C.J. Jr, Cohen, M.: Initiation of cleavage in polycrystalline Iron. Acta Metall. 13, 591–604 (1965)

    Article  Google Scholar 

  • McMeeking, R.M.: Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture. J. Mech. Phys. Solids 25, 357–381 (1977)

    Article  Google Scholar 

  • Natishan M.E., Kirk M.T.: Micromechanical evaluation of the Master Curve. In: Paris, P.C., Jerina, K.L. (eds.) Fatigue and Fracture Mechanics, vol. 30, p. 51–60. ASTM STP 1360, ASTM, West Conshohocken, PA (2000)

    Google Scholar 

  • Noronha, S.J., Ghoniem, N.M.: Dislocation simulation of brittle-ductile transition in ferritic steels. Metall. Mater. Trans. A 37, 539–544 (2006)

    Article  Google Scholar 

  • Noronha, S.J., Roberts, S.G., Wilkinson, A.J.: Multiple slip plane model for crack-tip plasticity. In: Robertson, I.M. et al. (eds.) MRS Proceedings 578, Multiscale Phenomena in Materials––Experiments & Modeling, pp. 309–314. MRS, Warrendale, PA (2000)

    Google Scholar 

  • Odette, G.R., He, M.Y.: A cleavage toughness Master Curve model. J. Nucl. Mater. 283–287, 120–127 (2000)

    Article  Google Scholar 

  • Orowan, E.: Physics of fracture. Trans. Inst. Engrs. Shipbuilders in Scotland 89, 165–215 (1945)

    Google Scholar 

  • Ortner, S.R., Hippsley, C.A.: Two component description of ductile to brittle transition in ferritic steel. Mater. Sci. Tech. 12, 1035–1042 (1996)

    Google Scholar 

  • Price, A.T., Hall, H.A., Greenough, A.P.: The surface energy and self diffusion coefficient of solid iron above 1350°C. Acta Metall. 12, 49–58 (1964)

    Article  Google Scholar 

  • Rice, J.R.: Dislocation nucleation from a crack tip: an analysis based on the Peierls concept. J. Mech. Phys. Solids 40, 239–271 (1992)

    Article  Google Scholar 

  • Rice, J.R., Rosengren, G.: Plain strain deformation near a cack tip in a power-law hardening material. J. Mech. Phys. Solids 16, 1–12 (1968)

    Article  MATH  Google Scholar 

  • Rice, J.R., Thomson, R.M.: Ductile versus brittle behaviour of crystals. Phil. Mag. 29, 73–97 (1974)

    Article  Google Scholar 

  • Ritchie, R.O., Knott, J.F., Rice, J.R.: On the critical relationship between critical tensile stress and fracture toughness in mild steel. J. Mech. Phys. Solids 21, 395–410 (1973)

    Article  Google Scholar 

  • Roberts S.G.: Modelling the brittle to ductile transition in single crystals. In: Kirchner, H.O., Kubin, L.P., Pontikis, V. (eds.) Computer Simulation in Materials Science-nano/meso/macroscopic Space and Time Scales, NATO ASI Series 308, pp. 409–434 (1996)

  • Roberts, S.G., Noronha, S.J., Wilkinson, A.J., Hirsch, P.B.: Modelling the initiation of cleavage fracture of ferritic steels. Acta Mater. 50, 1229–1244 (2002)

    Article  Google Scholar 

  • Saka, H., Nada, K., Imura, T.: Tensile test of foil specimens of iron single crystals at room and low temperatures under observation in high voltage electron microscope. Cryst. Latt. Def. 4, 45–56 (1973)

    Google Scholar 

  • Shi, M.X., Huang, Y., Gao, H.: The J-integral and geometrically necessary dislocations in nonuniform plastic deformation. Int. J. Plasticity 20, 1739–1762 (2004)

    Article  MATH  Google Scholar 

  • Stoller, R.E., Zinkle, S.J.: On the relationship between uniaxial yield strength and resolved shear stress in polycrystalline materials. J. Nucl. Mater. 283–287, 349–352 (2000)

    Article  Google Scholar 

  • Veistinen, M.K., Lindroos, V.K.: Evaluation of the effective surface energy of ferrite in a 26 Cr-1 Mo ferritic stainless steel. Scripta Metall. 18, 185–188 (1984)

    Article  Google Scholar 

  • Wallin, K.: Irradiation damage effects on the fracture toughness transition curve shape for reactor pressure vessel steels. Int. J. Pres. Ves. & Pi** 55, 61–79 (1993)

    Article  Google Scholar 

  • Wallin, K., Saario, T., Törrönen, K.: Statistical model for carbide induced brittle fracture in steel. Metal. Sci. 18, 13–16 (1984)

    Article  Google Scholar 

  • Wang, S., Lee, S.: Analysis of the elastic interaction between an edge dislocation and an internal crack. Mater. Sci. Eng. A 130, 1–10 (1990)

    Article  MathSciNet  Google Scholar 

  • Zerilli, F.J., Armstrong, R.W.: Dislocation-mechanics-based constitutive relations for material dynamics calculations. J. Appl. Phys. 61, 1816–1825 (1986)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the US Department of Energy, Office of Fusion Energy, through Grant DE-FG02-03ER54708 with UCLA.

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  1. S. J. Noronha

    Present address: NSSS Mechanical Engineering Department, AREVA NP Inc, 3315 Old Forest Road, Lynchburg, VA, 24506, USA

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  1. Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA, 90095-1597, USA

    S. J. Noronha & N. M. Ghoniem

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Correspondence to S. J. Noronha.

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Noronha, S.J., Ghoniem, N.M. Modeling the brittle–ductile transition in ferritic steels: dislocation simulations. Int J Mech Mater Des 4, 1–12 (2008). https://doi.org/10.1007/s10999-007-9041-3

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