Simulation of ductile fracture initiation in steels using a stress triaxiality–shear stress coupled model

  • Yazhi Zhu
  • Michael D. Engelhardt
  • Zuanfeng PanEmail author
Research Paper


Micromechanics-based models provide powerful tools to predict initiation of ductile fracture in steels. A new criterion is presented herein to study the process of ductile fracture when the effects of both stress triaxiality and shear stress on void growth and coalescence are considered. Finite-element analyses of two different kinds of steel, viz. ASTM A992 and AISI 1045, were carried out to monitor the history of stress and strain states and study the methodology for determining fracture initiation. Both the new model and void growth model (VGM) were calibrated for both kinds of steel and their accuracy for predicting fracture initiation evaluated. The results indicated that both models offer good accuracy for predicting fracture of A992 steel. However, use of the VGM leads to a significant deviation for 1045 steel, while the new model presents good performance for predicting fracture over a wide range of stress triaxiality while capturing the effect of shear stress on fracture initiation.


Ductile fracture Void growth Stress triaxiality Shear stress ratio ASTM A992 steel AISI 1045 steel 



Y.Z. Zhu and M.D. Engelhardt thank the funding support of the National Science Foundation (Grant 1344592). Z.F. Pan gratefully acknowledges the support of the National Natural Science Foundation of China (Grant 51778462) and the National Key Research and Development Plan (Grants 2017YFC1500700 and 2016YFC0701400).


  1. 1.
    Rice, J.R., Tracey, D.M.: On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Solids 17, 201–217 (1969)CrossRefGoogle Scholar
  2. 2.
    McClintock, F.A.: A criterion for ductile fracture by the growth of holes. J. Appl. Mech. 35, 363–371 (1968)CrossRefGoogle Scholar
  3. 3.
    Gurson, A.L.: 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
  4. 4.
    Weck, A., Wilkinson, D.S., Maire, E., et al.: Visualization by X-ray tomography of void growth and coalescence leading to fracture in model materials. Acta Mater. 56, 2919–2928 (2008)CrossRefGoogle Scholar
  5. 5.
    Barsoum, I., Faleskog, J.: Rupture mechanisms in combined tension and shear-experiments. Int. J. Solids Struct. 44, 1768–1786 (2007)CrossRefGoogle Scholar
  6. 6.
    Bai, Y., Wierzbicki, T.: A new model of metal plasticity and fracture with pressure and Lode dependence. Int. J. Plast. 24, 1071–1096 (2008)CrossRefGoogle Scholar
  7. 7.
    Li, H., Fu, M.W., Lu, J., et al.: Ductile fracture: experiments and computations. Int. J. Plast. 27, 147–180 (2011)CrossRefGoogle Scholar
  8. 8.
    Kiran, R., Khandelwal, K.: Experimental studies and models for ductile fracture in ASTM A992 steels at high triaxiality. J. Struct. Eng. 140, 04013044 (2013)CrossRefGoogle Scholar
  9. 9.
    Dos Santos, F.F., Ruggieri, C.: Micromechanics modelling of ductile fracture in tensile specimens using computational cells. Fatigue Fract. Eng. Mater. Struct. 26, 173–181 (2003)CrossRefGoogle Scholar
  10. 10.
    Pardoen, T., Hutchinson, J.W.: An extended model for void growth and coalescence. J. Mech. Phys. Solids 48, 2467–2512 (2000)CrossRefGoogle Scholar
  11. 11.
    Ristinmaa, M.: Void growth in cyclic loaded porous plastic solid. Mech. Mater. 26, 227–245 (1997)CrossRefGoogle Scholar
  12. 12.
    Kiran, R., Khandelwal, K.: A coupled microvoid elongation and dilation based ductile fracture model for structural steels. Eng. Fract. Mech. 145, 15–42 (2015)CrossRefGoogle Scholar
  13. 13.
    Barsoum, I., Faleskog, J.: Rupture mechanisms in combined tension and shear-micromechanics. Int. J. Solids Struct. 44, 5481–5498 (2007)CrossRefGoogle Scholar
  14. 14.
    Anderson, T.L.: Fracture Mechanics: Fundamentals and Applications. CRC Press, Boca Raton (2017)CrossRefGoogle Scholar
  15. 15.
    Freudenthal, A.M.: The Inelastic Behavior of Solids. Wiley, New York (1950)Google Scholar
  16. 16.
    Cockcroft, M.G., Latham, D.J.: Ductility and workability of metals. J. Inst. Met. 96, 33–39 (1968)Google Scholar
  17. 17.
    Wierzbicki, T., Xue, L.: On the effect of the third invariant of the stress deviator on ductile fracture. Impact and Crashworthiness Laboratory, Technical Report. (136) (2005)Google Scholar
  18. 18.
    Zhang, Z.L., Thaulow, C., Ødegård, J.: A complete Gurson model approach for ductile fracture. Eng. Fract. Mech. 67, 155–168 (2000)CrossRefGoogle Scholar
  19. 19.
    Lemaitre, J.: A continuous damage mechanics model for ductile fracture. J. Eng. Mater. Technol. 107, 83–89 (1985)CrossRefGoogle Scholar
  20. 20.
    Chaboche, J.L.: Continuum damage mechanics: part II—Damage growth, crack initiation, and crack growth. J. Appl. Mech. 55, 65–72 (1988)CrossRefGoogle Scholar
  21. 21.
    Brünig, M., Chyra, O., Albrecht, D., et al.: A ductile damage criterion at various stress triaxialities. Int. J. Plast. 24, 1731–1755 (2008)CrossRefGoogle Scholar
  22. 22.
    Zhuang, X., Ma, Y., Zhao, Z.: Fracture prediction under nonproportional loadings by considering combined hardening and fatigue-rule-based damage accumulation. Int. J. Mech. Sci. 150, 51–65 (2019)CrossRefGoogle Scholar
  23. 23.
    Chi, W.M., Kanvinde, A.M., Deierlein, G.G.: Prediction of ductile fracture in steel connections using SMCS criterion. J. Struct. Eng. 132, 171–181 (2006)CrossRefGoogle Scholar
  24. 24.
    Kanvinde, A.M., Deierlein, G.G.: The void growth model and the stress modified critical strain model to predict ductile fracture in structural steels. J. Struct. Eng. 132, 1907–1918 (2006)CrossRefGoogle Scholar
  25. 25.
    Kanvinde, A.M., Deierlein, G.G.: Finite-element simulation of ductile fracture in reduced section pull-plates using micromechanics-based fracture models. J. Struct. Eng. 133, 656–664 (2007)CrossRefGoogle Scholar
  26. 26.
    Mackenzie, A.C., Hancock, J.W., Brown, D.K.: On the influence of state of stress on ductile failure initiation in high strength steels. Eng. Fract. Mech. 9, 167IN13169–168IN14188 (1977)CrossRefGoogle Scholar
  27. 27.
    Marini, B., Mudry, F., Pineau, A.: Ductile rupture of A508 steel under nonradial loading. Eng. Fract. Mech. 22, 375–386 (1985)CrossRefGoogle Scholar
  28. 28.
    Panontin, T.L., Sheppard, S.D.: The relationship between constraint and ductile fracture initiation as defined by micromechanical analyses. In: Reuter, W.G., Underwood, J.H., Newman, Jr., J.C. (eds.) Fracture Mechanics. ASTM STP 1256, vol. 26, pp. 54–85 (1995)Google Scholar
  29. 29.
    Bai, Y.: Effect of loading history in necking and fracture. [Ph.D Thesis], Massachusetts Institute of Technology, Cambridge, MA, USA (2008)Google Scholar
  30. 30.
    Nahshon, K., Hutchinson, J.W.: Modification of the Gurson model for shear failure. Eur. J. Mech. A Solids 27, 1–17 (2008)CrossRefGoogle Scholar
  31. 31.
    Kim, J., Gao, X., Srivatsan, T.S.: Modeling of void growth in ductile solids: effects of stress triaxiality and initial porosity. Eng. Fract. Mech. 71, 379–400 (2004)CrossRefGoogle Scholar
  32. 32.
    Gao, X., Kim, J.: Modeling of ductile fracture: significance of void coalescence. Int. J. Solids Struct. 43, 6277–6293 (2006)CrossRefGoogle Scholar
  33. 33.
    Xue, L.: Ductile fracture modeling-theory, experimental investigation and numerical verification. [Ph.D Thesis], Massachusetts Institute of Technology, Cambridge, MA, USA (2007)Google Scholar
  34. 34.
    Bai, Y., Wierzbicki, T.: Application of extended Mohr–Coulomb criterion to ductile fracture. Int. J. Fract. 161, 1–20 (2010)CrossRefGoogle Scholar
  35. 35.
    Xue, L.: Constitutive modeling of void shearing effect in ductile fracture of porous materials. Eng. Fract. Mech. 75, 3343–3366 (2008)CrossRefGoogle Scholar
  36. 36.
    Lou, Y., Huh, H., Lim, S., et al.: New ductile fracture criterion for prediction of fracture forming limit diagrams of sheet metals. Int. J. Solids Struct. 49, 3605–3615 (2012)CrossRefGoogle Scholar
  37. 37.
    Lou, Y., Yoon, J.W., Huh, H.: Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality. Int. J. Plast. 54, 56–80 (2014)CrossRefGoogle Scholar
  38. 38.
    Lou, Y., Chen, L., Clausmeyer, T., et al.: Modeling of ductile fracture from shear to balanced biaxial tension for sheet metals. Int. J. Solids Struct. 112, 169–184 (2017)CrossRefGoogle Scholar
  39. 39.
    Hu, Q., Li, X., Han, X., et al.: A new shear and tension based ductile fracture criterion: modeling and validation. Eur. J. Mech. A Solids 66, 370–386 (2017)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Mu, L., Zang, Y., Wang, Y., et al.: Phenomenological uncoupled ductile fracture model considering different void deformation modes for sheet metal forming. Int. J. Mech. Sci. 141, 408–423 (2018)CrossRefGoogle Scholar
  41. 41.
    Zhu, Y., Engelhardt, M.D.: Prediction of ductile fracture for metal alloys using a shear modified void growth model. Eng. Fract. Mech. 190, 491–513 (2018)CrossRefGoogle Scholar
  42. 42.
    Tvergaard, V.: On localization in ductile materials containing spherical voids. Int. J. Fract. 18, 237–252 (1982)Google Scholar
  43. 43.
    Noell, P.J., Carroll, J.D., Boyce, B.L.: The mechanisms of ductile rupture. Acta Mater. 161, 83–98 (2018)CrossRefGoogle Scholar
  44. 44.
    Pineau, A., Benzerga, A.A., Pardoen, T.: Failure of metals I: brittle and ductile fracture. Acta Mater. 107, 424–483 (2016)CrossRefGoogle Scholar
  45. 45.
    Zhu, Y., Engelhardt, M.D., Kiran, R.: Combined effects of triaxiality, Lode parameter and shear stress on void growth and coalescence. Eng. Fract. Mech. 199, 410–437 (2018)CrossRefGoogle Scholar
  46. 46.
    Bai, Y., Wierzbicki, T.: A comparative study of three groups of ductile fracture loci in the 3D space. Eng. Fract. Mech. 135, 147–167 (2015)CrossRefGoogle Scholar
  47. 47.
    Arasaratnam, P., Sivakumaran, K.S., Tait, M.J.: True stress-true strain models for structural steel elements. ISRN Civ. Eng. 2011, 656401 (2011)Google Scholar
  48. 48.
    Zhu, Y., Engelhardt, M.D.: A nonlocal triaxiality and shear dependent continuum damage model for finite strain elastoplasticity. Eur. J. Mech. A Solids 71, 16–33 (2018)MathSciNetCrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yazhi Zhu
    • 1
  • Michael D. Engelhardt
    • 2
  • Zuanfeng Pan
    • 1
    Email author
  1. 1.Department of Structural EngineeringTongji UniversityShanghaiChina
  2. 2.Ferguson Structural Engineering Laboratory, Department of Civil, Architectural and Environmental EngineeringUniversity of Texas at AustinAustinUSA

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