Skip to main content
SpringerLink
Log in

Constitutive behaviors of composites with interface debonding: the extended Mori–Tanaka method for uniaxial tension

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

Debonding of particle/matrix interfaces can significantly affect the macroscopic behavior of composite materials. We have used a nonlinear cohesive law for particle/matrix interfaces to study the effect of interface debonding on the macroscopic behavior of particle-reinforced composite materials subject to uniaxial tension. The Mori–Tanaka method, which is suitable for composites with high particle volume fraction, is extended to account for interface debonding. At a fixed particle volume fraction, small particles lead to the hardening behavior of the composite while large particles yield softening. The interface sliding may contribute significantly to the macroscopic behavior of the composite.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Benveniste Y, Aboudi J (1984) A continuum model for fiber reinforced materials with debonding. Int J Solids Struct 20:935–951

    Article  Google Scholar 

  • Berghout HL, Son SF, Skidmore CB, Idar DJ, Asay BW (2002) Combustion of damaged PBX 9501 explosive. Thermochim Acta 384:261–277

    Article  CAS  Google Scholar 

  • Cady CM, Blumenthal WR, Gray DJ III (2006) Mechanical properties of plastic-bonded explosive bindermaterials as a function of strain-rate and temperature. Polym Eng Sci 46:812–819

    Article  CAS  Google Scholar 

  • Camacho GT, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33:2899–2938

    Article  Google Scholar 

  • Espinosa HD, Zavattieri PD, Dwivedi SK (1998) A finite deformation continuum/discrete model for the description of fragmentation and damage in brittle materials. J Mech Phys Solids 46:1909–1942

    Article  CAS  Google Scholar 

  • Geubelle PH, Baylor JS (1998) Impact-induced delamination of composites: a 2D simulation. Compos B29:589–602

    Article  Google Scholar 

  • Huang Y, Gao H (2001) Intersonic crack propagation. Part I: the fundamental solution. J Appl Mech 68:169–175

    Google Scholar 

  • Kubair DV, Geubelle PH, Huang Y (2002) Intersonic crack propagation in homogeneous media under shear-dominated loading: theoretical analysis. J Mech Phys Solids 50:1547–1564

    Article  Google Scholar 

  • Kubair DV, Geubelle PH, Huang Y (2003) Analysis of a rate-dependent cohesive model for dynamic crack propogation. Eng Fract Mech 50:685–704

    Google Scholar 

  • Luré AI (1964) Three-dimensional problems of the theory of elasticity. Interscience Publishers, New York

    Google Scholar 

  • Mas EM, Clements BE, Blumenthal WR, Cady CM, GrayGTIII, Liu C (2001) A viscoelastic model for PBX binders. In: Furnish MD, Thadhani NN, Horie Y (eds) Proceedings of 2001 conference of the APS topical group on shock compression of condensed matter, American Institute of Physics, Wood-bury, New York

  • Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21:571–574

    Article  Google Scholar 

  • Mura T (1987) Micromechanics of defects in solids. Martinus Nijhoff Publishers, Dordrecht

    Google Scholar 

  • Needleman A (1987) A continuum model for void nucleation by inclusion debonding. J Appl Mech 54:525–531

    Article  Google Scholar 

  • Samudrala O, Huang Y, Rosakis AJ (2002) Subsonic and intersonic mode II crack propagation with a rate-dependent cohesive zone. J Mech Phys Solids 50:1231–1268

    Article  Google Scholar 

  • Samudrala O, Rosakis AJ (2003) Effect of loading and geometry on the subsonic/intersonic transition of a bimaterial interface crack. Eng Fract Mech 70:309–337

    Article  Google Scholar 

  • Skidmore CB, Phillips DS, Son SF, Asay BW (1997) Characterization of HMX particles in PBX 9501. In: Proceedings of the topical conference on shock compression of condensed matter, Los Alamos, New Mexico, American Institute of Physics, pp 112–119

  • Tan H, Huang Y, Liu C, Geubelle PH (2005a) The Mori–Tanaka method for composite materials with nonlinear interface debonding. Int J Plasticity 21:1890–1918

    Article  CAS  Google Scholar 

  • Tan H, Liu C, Huang Y, Geubelle PH (2005b) The cohesive law for the particle/matrix interfaces in high explosives. J Mech Phys Solids 53:1892–1917

    Article  CAS  Google Scholar 

  • Tan H, Huang Y, Liu C, Geubelle PH (2006) Effect of nonlinear interface debonding on the constitutive model of composite materials. Int J Multiscale Comput Eng 4:147–167

    Article  CAS  Google Scholar 

  • Tan H, Huang Y, Liu C, Ravichandran G, Inglis HM, Geubelle PH (2007) The uniaxial tension of particle-reinforced composite materials with nonlinear interface debonding. Int J Solids Struct 44:1809–1822

    Article  Google Scholar 

  • Thiagarajan G, Hsia KJ, Huang Y (2004a) Finite element implementation of Virtual Internal Bond model for crack behavior simulation. Eng Fract Mech 71:401–423

    Article  Google Scholar 

  • Thiagarajan G, Huang Y, Hsia KJ (2004b) Fracture simulation using an elasto-viscoplastic virtual internal bond model with finite elements. J Appl Mech 71:796–804

    Article  Google Scholar 

  • Tvergaard V, Hutchinson JW (1992) The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. J Mech Phys Solids 40: 1377–1397

    Article  Google Scholar 

  • Tvergaard V, Hutchinson JW (1993) The influence of plasticity on mixed-mode interface toughness. J Mech Phys Solids 41:1119–1135

    Article  Google Scholar 

  • Weng GJ (1984) Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions. Int J Eng Sci 22:845–856

    Article  Google Scholar 

  • Xu XP, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42:1397–1434

    Article  Google Scholar 

  • Zaug JM (1998) Elastic constants of β-HMX and tantalum, equations of state of supercritical fluids and fluid mixtures and thermal transport determinations. In: Proceedings of 11th international detonation symposium, Snowmass, Colorado, p 498

  • Zhang P, Klein PA, Huang Y, Gao H, Wu PD (2002) Numerical simulation of cohesive fracture by the Virtual-Internal-Bond model. Comput Modeling Eng Sci 3:263–278

    Google Scholar 

  • Zhong XA, Knauss WG (1997) Analysis of interfacial failure in particle-filled elastomers. J Eng Mater Technol 119:198–204

    CAS  Google Scholar 

  • Zhong XA, Knauss WG (1999) On the stability of phase separation in a finite solid with interfaces. Mech Compos Mater Struct 6:1–7

    Article  CAS  Google Scholar 

  • Zhong XA, Knauss WG (2000) Effects of particle interaction and size variation on damage evolution in filled elastomers. Mech Comput Mater Struct 7:35–53

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester, M60 1QD, UK

    Henry Tan

  2. Departments of Civil and Environmental Engineering and Mechanical Engineering, Northwestern University, Evanston, IL, 60208, USA

    Young Huang

  3. Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Cheng Liu

  4. Graduate Aeronautical Laboratory, California Institute of Technology, Pasadena, CA, 91125, USA

    Guruswami Ravichandran

  5. Department of Civil and Environmental Engineering, University of Illinois, Urbana, IL, 61801, USA

    Glaucio H. Paulino

Authors
  1. Henry Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Young Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cheng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guruswami Ravichandran
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Glaucio H. Paulino
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Henry Tan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tan, H., Huang, Y., Liu, C. et al. Constitutive behaviors of composites with interface debonding: the extended Mori–Tanaka method for uniaxial tension. Int J Fract 146, 139–148 (2007). https://doi.org/10.1007/s10704-007-9155-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-007-9155-5

Keywords

Search

Navigation