Modeling Temperature-Driven Ductile-to-Brittle Transition Fracture in Ferritic Steels

  • Babür DeliktaşEmail author
  • Ismail Cem Turtuk
  • George Z. Voyiadjis
Reference work entry


The most catastrophic brittle failure in ferritic steels is observed as their tendency of losing almost all of their toughness when the temperature drops below their ductile-to-brittle transition (DBT) temperature. There have been put large efforts in experimental and theoretical studies to clarify the controlling mechanism of this transition; however, it still remains unclear how to model accurately the coupled ductile∕brittle fracture behavior of ferritic steels in the region of ductile-to-brittle transition.

Therefore, in this study, an important attempt is made to model coupled ductile∕brittle fracture by means of blended micro-void and micro-cracks. To this end, a thermomechanical finite strain-coupled plasticity and continuum damage mechanics models which incorporate the blended effects of micro-heterogeneities in the form of micro-cracks and micro-voids are proposed.

In order to determine the proposed model material constant, a set of finite element model, where the proposed unified framework, which characterizes ductile-to-brittle fracture behavior of ferritic steels, is implemented as a VUMAT, is performed by modeling the benchmark experiment given in the experimental research published by Turba et al., then, using these models as a departure point, the fracture response of the small punch fracture testing is investigated numerically at 22C and − 196C and at which the fracture is characterized as ductile and brittle, respectively.


Ductile-Brittle transition Porous plasticity Damage mechanics Small punch test Ferritic steels 


  1. CEN, Cen workshop agreement: small punch test method for metallic materials. Technical Report CWA 15627 (2006)Google Scholar
  2. R. Abu Al-Rub, G. Voyiadjis, On the coupling of anisotropic damage and plasticity models for ductile materials. Int. J. Solids Struct. 40, 2611–2643 (2003)CrossRefGoogle Scholar
  3. T. Anderson, Fracture Mechanics: Fundamentals and Applications, Taylor & Francis Group, Boca Raton (CRC Press, 2004)zbMATHGoogle Scholar
  4. P. Baloso, R. Madanrao, M. Mohankumar, Determination of the ductile to brittle transition temperature of various metals. Int. J. Innov. Eng. Res. Technol. 4, 1–27 (2017)Google Scholar
  5. F. Basbus, M. Moreno, A. Caneiro, L. Mogni, Effect of pr-doping on structural, electrical, thermodynamic,and mechanical properties of BaCeo3 proton conductor. J. Electrochem. Soc. 161(10), 969–976 (2014)CrossRefGoogle Scholar
  6. R. Batra, M. Lear, Simulation of brittle and ductile fracture in an impact loaded prenotched plate. Int. J. Fract. 126, 179–203 (2004)CrossRefGoogle Scholar
  7. F.M. Beremin, A local criterion for cleavage fracture of a nuclear pressure vessel steel. Met. Trans. A 14A, 2277–2287 (1983)CrossRefGoogle Scholar
  8. J.-M. Bergheau, J.-B. Leblond, G. Perrin, A new numerical implementation of a second-gradient model for plastic porous solids, with an application to the simulation of ductile rupture tests. Comput. Method. Appl. M 268, 105–125 (2014)MathSciNetCrossRefGoogle Scholar
  9. J. Besson, G. Cailletaud, J. Chaboche, S. Forest, Non-linear Mechanics of Materials (Springer, Berlin, 2010)CrossRefGoogle Scholar
  10. J. Chaboche, Sur l’utilisation des variables d’ètat interne pour la description de la viscoplasticitè cyclique avec endommagement, in Symposium Franco-Polonais de Rhèologie et Mècanique, 1977, pp 137–159Google Scholar
  11. J. Chaboche, M. Boudifa, K. Saanouni, A CDM approach of ductile damage with plastic compressibility. Int. J. Fract. 137, 51–75 (2006)CrossRefGoogle Scholar
  12. P. Chakraborty, B. Biner, Modeling the ductile brittle fracture transition in reactor pressure vessel steels using a cohesive zone model based approach. Int. Work. Struct. Mater. Innov. Nucl. Syst. (72):1–10 (2013)Google Scholar
  13. C. Chow, J. Wang, An anisotropic theory of continuum damage mechanics for ductile fracture. Eng. Fract. Mech. 27, 547–558 (1987a)CrossRefGoogle Scholar
  14. C. Chow, J. Wang, An anisotropic theory of elasticity for continuum damage mechanics. Int. J. Fract. 33, 3–18 (1987b)CrossRefGoogle Scholar
  15. C. Chu, A. Needleman, Void nucleation effects in biaxially stretched sheets. J. Eng. Mater. Technol. 102, 249–256 (1980)CrossRefGoogle Scholar
  16. J.P. Cordebois, F. Sidoroff, Damage induced elastic anisotropy. In: JP. Boehler, (eds), Mech. Behav. Anisotropic Solids / Comportment Mech. des Sol. Anisotropic. Springer, Dordrecht 761–774 (1982)CrossRefGoogle Scholar
  17. D. Curry, F. Knott, The relationship between fracture toughness and micro-structure in the cleavage fracture of mild steel. Mater. Sci. 10, 1–6 (1976)Google Scholar
  18. D. Curry, J.F. Knott, Effect of microstructure on cleavage fracture toughness in mild steel. Metal Sci. 13, 341–345 (1979)CrossRefGoogle Scholar
  19. F. Erdogan, G.C. Sih, On the crack extension in plates under plane loading and transverse shear. J. Bas. Eng. 85, 519–529 (1963)CrossRefGoogle Scholar
  20. L.B. Freund, Y.J. Lee, Observations on high strain rate crack growth based on a strip yield model. Int. J. Fract. 42, 261–276 (1990)CrossRefGoogle Scholar
  21. P. Germain, Q. Nguyen, P. Suquet, Continuum thermodynamics. J. Appl. Mech. 50, 1010–1020 (1983)CrossRefGoogle Scholar
  22. A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part I- Yield Criteria and Flow Rules for Porous Ductile Media, J. Eng. Mater. Technol 99, 2–15 (1977)CrossRefGoogle Scholar
  23. P. Hakansson, M. Wallin, M. Ristinmaa, Thermomechanical response of non-local porous material. Int. J. Plasticity 22, 2066–2090 (2006)CrossRefGoogle Scholar
  24. V. Hardenacke, J. Hohe, V. Friedmann, D. Siegele, Enhancement of local approach models for assessment of cleavage fracture considering micromechanical aspects, in Proceedings of the 19th European Conference on Fracture, Kazan (72), pp. 49–72 (2012)Google Scholar
  25. K. Hayakawa, S. Murakami, Thermodynamical modeling of elastic-plastic damage and experimental validation of damage potential. Int. J. Damage Mech. 6, 333–362 (1997)CrossRefGoogle Scholar
  26. D. Hayhurst, F. Leckie, The effect of creep constitutive and damage relationships upon rupture time of solid and circular torsion bar. J. Mech. Phys. Solids 21, 431–446 (1973)CrossRefGoogle Scholar
  27. J. Hockett, O. Sherby, Large strain deformation of polycrystalline metals at low homologous temperatures. J. Mech. Phys. Solids 23(2), 87–98 (1975)CrossRefGoogle Scholar
  28. G. Hutter, Multi-scale simulation of crack propagation in the Ductile-Brittle transition region. PhD. Thesis, Faculty of Mechanical, Process and Energy Engineering, Technische Universitat Bergakademie Freiberg (2013a)Google Scholar
  29. G. Hütter (2013b) Multi-scale simulation of crack propagation in the ductile-brittle transition region. PhD. Thesis, Faculty of Mechanical, Process and Energy Engineering, Technische Universität Bergakademie FreibergGoogle Scholar
  30. G. Hutter, T. Linse, S. Roth, U. Muhlich, M. Kuna, A modeling approach for the complete Ductile-to-Brittle transition region: cohesive zone in combination with a nonlocal gurson-model. Int. J. Fract. 185, 129–153 (2014)CrossRefGoogle Scholar
  31. R. Kabir, A. Cornec, W. Brocks, Simulation of quasi-brittle fracture of lamellar tial using the cohesive model and a stochastic approach. Comput. Mater. Sci. 39, 75–84 (2007)CrossRefGoogle Scholar
  32. L. Kachanov, Time of the rupture process under creep conditions. IsvAkadNaukSSR 8, 26–31 (1958)Google Scholar
  33. D. Krajcinovic, G. Fonseka, The continuous damage theory of brittle materials, parts 1 and 2. J. Appl. Mech. 48, 809–824 (1981)CrossRefGoogle Scholar
  34. F. Leckie, D. Hayhurst, Constitutive equations for creep rupture. Acta Metall. 25, 1059–1070 (1977)CrossRefGoogle Scholar
  35. J. Lemaitre, A continuous damage mechanics model for ductile fracture. J. Eng. Mater. Technol. 107, 83–89 (1985)CrossRefGoogle Scholar
  36. J. Lemaitre, R. Desmorat, Engineering Damage Mechanics (Springer, Berlin/New York, 2005)Google Scholar
  37. J. Lemaitre, R. Desmorat, M. Sauzay, Anisotropic damage law of evolution. Eur. J. Mech. Solids 19, 187–208 (2000)CrossRefGoogle Scholar
  38. T. Linse, G. Hütter, M. Kuna, Simulation of crack propagation using a gradient-enriched ductile damage model based on dilatational strain. Eng. Fract. Mech. 95, 13–28 (2012)CrossRefGoogle Scholar
  39. L. Malcher, F. Andrade Pires, J. Cesar de Sa, An assessment of isotropic constitutive models for ductile fracture under high and low stress triaxiality. Int. J. Plasticity 30–31, 81–115 (2012)CrossRefGoogle Scholar
  40. C. McAuliffe, H. Waisman, A unified model for metal failure capturing shear banding and fracture. Int. J. Plasticity 65, 131–151 (2015)CrossRefGoogle Scholar
  41. F. Mudry, A local approach to cleavage fracture. Nucl. Eng. Des. 105, 65–76 (1987)CrossRefGoogle Scholar
  42. S. Murakami, N. Ohno, A continuum theory of creep and creep damage, in 3rd Creep in Structures Symposium, Leicester, pp. 422–443 (1980)Google Scholar
  43. K. Nahshon, J. Hutchinson, Modification of the gurson model to shear failure. Eur. J. Mech. A/Solids 27, 1–17 (2008)CrossRefGoogle Scholar
  44. K. Nahshon, Z. Xue, A modified gurson model and its applications to punch-out experiments. Eng. Fract. Mech. 76, 997–1009 (2009)CrossRefGoogle Scholar
  45. A. Needleman, V. Tvergaard, Dynamic crack growth in a nonlocal progressively cavitating solid. Eur. J. Mech. A/Solids 17(3), 421–438 (1998)MathSciNetCrossRefGoogle Scholar
  46. A. Needleman, V. Tvergaard, Numerical modeling of the ductile-brittle transition. Int. J. Fract. 101, 73–97 (2000)CrossRefGoogle Scholar
  47. T. Pardoen, J.W. Hutchinson, An extended model for void growth and coalescence, J. Mech. Phys. Solids 48(12), 2467–2512 (2000)CrossRefGoogle Scholar
  48. Y. Rabotnov, Creep Problems in Structural Members (North-Holland, Amsterdam, 1969)zbMATHGoogle Scholar
  49. S. Ramaswamy, N. Aravas, Finite element implementation of gradient plasticity models. Part I: gradient-dependent yield functions. Comput. Methods Appl. Mech. Eng. 163, 33–53 (1998)zbMATHGoogle Scholar
  50. S. Renevey, S. Carassou, B. Marini, C. Eripret, A. Pineau, Ductile – brittle transition of ferritic steels modelled by the local approach to fracture. JOURNAL DE PHYSIQUE IV Colloque C6, supplBment au Journal de Physique III 6, 343–352 (1996)Google Scholar
  51. R. Ritchie, J. Knott, J. Rice, On the relationship between critical tensile stress and fracture toughness in mild steel. J. Mech. Phys. Solids 21, 395–410 (1973)CrossRefGoogle Scholar
  52. F. Rivalin, A. Pineau, M. Di Fant, J. Besson, Ductile tearing of Pipeline steel wide plates-I: Dynamics and quasi static experiments. Engng Fract. Mech 68(3), 329–345 (2001a)CrossRefGoogle Scholar
  53. F. Rivalin, J. Besson, M. Di Fant, A. Pineau, Ductile tearing of Pipeline steel wide plates-II: Modeling of in-plane crack propagation. Engng Fract. Mech 68(3), 347–364 (2001b)CrossRefGoogle Scholar
  54. G. Rousselier, Ductile fracture models and their potential in local approach of fracture. Nuc. Eng. Des. 105, 97–111 (1987)CrossRefGoogle Scholar
  55. M. Samal, M. Seidenfuss, E. Roos, B.K. Dutta, H.S. Kushwaha, A mesh independent GTN damage model and its application in simulation of ductile fracture behaviour. ASME 2008 Pressure vessels and piping conference volume 3: Design and Analysi, Chicago, Illinois, USA, July 27–31 pp. 187–193 (2008)Google Scholar
  56. I. Scheider, W. Brocks, Simulation of cup-cone fracture using the cohesive model. Eng. Fract. Mech. 70, 1943–1961 (2003)CrossRefGoogle Scholar
  57. A. Shterenlikht, 3D CAFE modeling of transitional ductile-brittle fracture in steels. PhD. Thesis, Department of Mechanical Engineering, University of Sheffield (2003)Google Scholar
  58. J. Skrzypek, A. Ganczarski, F. Rustichelli, H. Egner, Advanced Materials and Structures for Extreme Operating Conditions (Springer, Berlin, 2008)Google Scholar
  59. C. Soyarslan, I. Turtuk, B. Deliktas, S. Bargmann, A thermomechanically consistent constitutive theory for modeling micro-void and/or micro-crack driven failure in metals at finite strains. Int. J. Appl. Mech. 8, 1–20 (2016)CrossRefGoogle Scholar
  60. S. Sutar, G. Kale, S. Merad, Analysis of ductile-to-brittle transition temperature of mild steel. Int. J. Innov. Eng. Res. Technol. 1, 1–10 (2014)Google Scholar
  61. B. Tanguy, J. Besson, R. Piques, A. Pineau, Ductile to brittle transition of an a508 steel characterized by charpy impact test, Part I. Experimental results. Eng. Fract. Mech. 72, 49–72 (2007)CrossRefGoogle Scholar
  62. G. Taylor, H. Quinney, The latent energy remaining in a metal after cold working. Proc. R. Soc. Lond. A143, 307–326 (1934)CrossRefGoogle Scholar
  63. K. Turba, B. Gulcimen, Y. Li, D. Blagoeva, P. Hähner, R. Hurst, Introduction of a new notched specimen geometry to determine fracture properties by small punch testing. Eng. Fract. Mech. 78(16), 2826–2833 (2011)CrossRefGoogle Scholar
  64. I. Turtuk, B. Deliktas, Coupled porous plasticity – continuum damage mechanics approaches in modelling temperature driven ductile-to-brittle transition fracture in ferritic steels. Int. J. Plasticity 77, 246–261 (2016)CrossRefGoogle Scholar
  65. V. Tvergaard, Influence of voids on shear band instabilities under plane strain conditions. Int. J. Fract. 17, 389–407 (1981)CrossRefGoogle Scholar
  66. V. Tvergaard, On localization in ductile materials containing spherical voids. Int. J. Fract. 18, 237–252 (1982a)Google Scholar
  67. V. Tvergaard, Influence of void nucleation on ductile shear fracture at a free surface. J. Mech. Phys. Solids 30, 399–425 (1982b)CrossRefGoogle Scholar
  68. V. Tvergaard, A. Needleman, Analysis of the cup-cone fracture in a round tensile bar. Acta Metall. 32, 157–169 (1984)CrossRefGoogle Scholar
  69. W. Weibull, A statistical distribution function of wide applicability. Jour. App. Mech 18, 293–297 (1953)zbMATHGoogle Scholar
  70. J. Wen, Y. Huang, K. Hwang, C. Liu, M. Li, The modified gurson model accounting for the void size effect. Int. J. Plasticity 21, 381–395 (2005)CrossRefGoogle Scholar
  71. L. Xia, C. Fong Shih, A fracture model applied to the ductile/brittle regime. Journal de Physique IV 6, 363–372 (1996)CrossRefGoogle Scholar
  72. Z.L. Zhang, C. Thaulow, J. Ødegard, A complete gurson model approach for ductile fracture, Eng. Fract. Mech 67(2), 155–168 (2000)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Babür Deliktaş
    • 1
    Email author
  • Ismail Cem Turtuk
    • 2
    • 3
  • George Z. Voyiadjis
    • 4
  1. 1.Faculty of Engineering-Architecture, Department of Civil EngineeringUludag UniversityBursaTurkey
  2. 2.Mechanical Design DepartmentMeteksan DefenceAnkaraTurkey
  3. 3.Department of Civil EngineeringUludag UniveristyBursaTurkey
  4. 4.Department of Civil and Environmental EngineeringLouisiana State UniversityBaton RougeUSA

Personalised recommendations