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Computational Mechanics

, Volume 44, Issue 3, pp 433–445 | Cite as

Multi-length scale micromorphic process zone model

  • Franck VernereyEmail author
  • Wing Kam LiuEmail author
  • Brian Moran
  • Gregory Olson
Original Paper

Abstract

The prediction of fracture toughness for hierarchical materials remains a challenging research issue because it involves different physical phenomena at multiple length scales. In this work, we propose a multiscale process zone model based on linear elastic fracture mechanics and a multiscale micromorphic theory. By computing the stress intensity factor in a K-dominant region while maintaining the mechanism of failure in the process zone, this model allows the evaluation of the fracture toughness of hierarchical materials as a function of their microstructural properties. After introducing a multi-length scale finite element formulation, an application is presented for high strength alloys, whose microstructure typically contains two populations of particles at different length scales. For this material, the design parameters comprise of the strength of the matrix–particle interface, the particle volume fraction and the strain-hardening of the matrix. Using the proposed framework, trends in the fracture toughness are computed as a function of design parameters, showing potential applications in computational materials design.

Keywords

Multiscale micromorphic theory Fracture mechanics Materials design Ductile failure Multi-length scale finite elements 

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References

  1. 1.
    Aravas N, McMeeking RM (1985) Microvoid growth and failure in the ligament between a hole and a blunt crack tip. Int J Fract 29: 21–38CrossRefGoogle Scholar
  2. 2.
    Baaser H, Gross D (2003) Analysis of void growth in a ductile material. Comput Mater Sci 26: 28–35CrossRefGoogle Scholar
  3. 3.
    Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, New YorkzbMATHGoogle Scholar
  4. 4.
    Chen JY, Wei Y, Huang Y, Hutchinson JW, Hwang KC (1999) The crack tip fields in strain gradient plasticity: the asymptotic and numerical analyses. Eng Fract Mech 64: 625–648CrossRefGoogle Scholar
  5. 5.
    Ghosal AK, Narasimhan R (1996) Mixed-mode fracture initiation in a ductile material with a dual population of second-phase particles. Mater Sci Eng A 211: 117–127CrossRefGoogle Scholar
  6. 6.
    Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth. Part 1. Yield criteria and flow rules for porous ductile media. ASME J Eng Mater Technol 99: 2–15Google Scholar
  7. 7.
    Hao S, Liu WK, Moran B, Vernerey F, Olson GB (2004) Multiple-scale constitutive model and computational framework for the design of ultra-high strength, high toughness steels. Comput Methods Appl Mech Eng 193: 1865zbMATHCrossRefGoogle Scholar
  8. 8.
    Huang Y, Zhang TF, Guo TF, Hwang KC (1997) Mixed mode near-tip fields for cracks in materials with strain gradient effects. J Mech Phys Solids 45: 439–465zbMATHCrossRefGoogle Scholar
  9. 9.
    Hutchinson JW (1968) Plastic stress and strain fields at crack tip. J Mech Phys Solids 16(5): 337–347CrossRefMathSciNetGoogle Scholar
  10. 10.
    Kanninen MF, Popelar CH (1985) Adv Fract Mech. Oxford Engineering Series, OxfordGoogle Scholar
  11. 11.
    Li S, Liu WK (2004) Meshfree particle methods. Springer, Heidelberg, p 502zbMATHGoogle Scholar
  12. 12.
    Liu WK, McVeigh C (2008) Predictive multiscale theory for design of heterogeneous materials. Comput Mech 42(2): 147–170zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Liu WK, Jun S, Zhang YF (1995a) Reproducing kernel particle methods. Int J Numer Methods Fluids 20: 1081–1106zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Liu WK, Jun S, Li S, Adee J, Belytschko T (1995b) Reproducing kernel particle methods for structural dynamics. Int J Numer Methods Eng 38: 1655–1679zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Liu WK, Karpov EG, Zhang S, Park HS (2004) An introduction to computational nanomechanics and materials. Comput Methods Appl Mech Eng 193: 1529–1578zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Liu WK, Karpov EG, Parks HS (2006) Nano mechanics and materials, theory, multiscale, methods and applications. Wiley, New YorkGoogle Scholar
  17. 17.
    McVeigh C, Liu WK (2008a) Multiresolution modeling of ductile reinforced brittle composites. J Mech Phys Solids. doi: 10.1016/j.jmps.2008.10.015
  18. 18.
    McVeigh C, Liu WK (2008b) Linking microstructure and properties through a predictive multiresolution continuum. Comput Methods Appl Mech Eng 197: 3268–3290zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    McVeigh C, Vernerey F, Liu WK, Brinson LC (2006) Multiresolution analysis for material design. Comput Methods Appl Mech Eng 95:37–40, 5053–5076Google Scholar
  20. 20.
    McVeigh C, Vernerey F, Liu WK, Moran B (2007) An interactive microvoid shear localization mechanism in high strength steels. J Mech Phys Solids 55:2, 225–244Google Scholar
  21. 21.
    Needleman A, Tvergaard V (1984) An analysis of ductile rupture in notched bars. J Mech Phys Solids 32: 461–490CrossRefGoogle Scholar
  22. 22.
    Needleman A, Tvergaard V (1987) An analysis of ductile rupture modes at a crack tip. J Mech Phys Solids 35(2): 151–183zbMATHCrossRefGoogle Scholar
  23. 23.
    Needleman A, Tvergaard V (1998) Dynamic crack growth in a nonlocal progressively cavitating solid. Eur J Mech A/Solids 17: 421–438zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Pardoen T, Hutchinson JW (2003) Micromechanics-based model for trends in toughness of ductile metals. Acta Mater 51(1): 133–148CrossRefGoogle Scholar
  25. 25.
    Rice JR (1967) A path independent integral and the approximate analysis of strain concentration by notches and cracks. Report: E39, 49pGoogle Scholar
  26. 26.
    Rice JR, Johnson MA et al (1970) The role of large crack tip geometry changes in plane strain fracture. In: Kanninen MF(eds) Inelastic behavior of Solids. McGraw-Hill, New York, pp 641–672Google Scholar
  27. 27.
    Tvergaard V (1988) 3d-analysis of localization failure in a ductile material containing two size-scales of spherical particles. Eng Fract Mech 31: 421–436CrossRefGoogle Scholar
  28. 28.
    Tvergaard V, Hutchinson JW (1992) The relation between crack growth resistance and fracture process parameters in elastic–plastic solids. J Mech Phys Solids 40: 1377zbMATHCrossRefGoogle Scholar
  29. 29.
    Tvergaard V, Hutchinson JW (1996) On the toughness of ductile adhesive joints. J Mech Phys Solids 44: 789–800CrossRefGoogle Scholar
  30. 30.
    Vernerey FJ, McVeigh C, Liu WK, Moran B, Tewari D, Parks D, Olson G (2006) The 3D computational modeling of shear dominated ductile failure of steel. J Minerals Metals Mater Soc, pp 45–51Google Scholar
  31. 31.
    Vernerey F, Liu WK, Moran B (2007) Multiscale micromorphic theory for hierarchical materials. J Mech Phys Solids 55(12): 2603–2651zbMATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Vernerey F, Liu WK, Moran B, Olson GB (2008) A micromorphic model for the multiple scale failure of heterogeneous materials. J Mech Phys Solids 56(4): 1320–1347CrossRefMathSciNetGoogle Scholar
  33. 33.
    Xia ZC, Hutchinson W (1996) Crack tip fields in strain gradient plasticity. J Mech Phys Solids 44: 1621–1648CrossRefGoogle Scholar
  34. 34.
    Xia ZC, Shih CF (1995a) Ductile crack growth—numerical study using computational cells with microstrucurally-based length scales. J Mech Phys Solids 43: 233–259zbMATHCrossRefGoogle Scholar
  35. 35.
    Xia ZC, Shih CF (1995b) Ductile crack growth. II. Void nucleation and geometry effects on macroscopic fracture behavior. J Mech Phys Solids 43: 1953–1981zbMATHCrossRefGoogle Scholar
  36. 36.
    Xia ZC, Shih CF, Hutchinson W (1994) A computational approach to ductile crack growth under large scale yielding conditions. J Mech Phys Solids 43: 389–413CrossRefGoogle Scholar
  37. 37.
    Yan C, Mai YW (1998) Effect of constraint on void growth near a blunt crack tip. Int J Fract 92: 287–304CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Civil, Environmental and Architectural EngineeringUniversity of Colorado at BoulderBoulderUSA
  2. 2.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA
  3. 3.Department of Civil EngineeringNorthwestern UniversityEvanstonUSA
  4. 4.Department of Material Science and EngineeringNorthwestern UniversityEvanstonUSA

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