Skip to main content
SpringerLink
Log in

Micromechanical modeling of reinforcement fracture in particle-reinforced metal-matrix composites

  • Published:
Metallurgical and Materials Transactions A Aims and scope Submit manuscript

Abstract

Finite element analyses of the effect of particle fracture on the tensile response of particle-reinforced metal-matrix composites are carried out. The analyses are based on two-dimensional plane strain and axisymmetric unit cell models. The reinforcement is characterized as an isotropic elastic solid and the ductile matrix as an isotropically hardening viscoplastic solid. The reinforcement and matrix properties are taken to be those of an Al-3.5 wt pet Cu alloy reinforced with SiC particles. An initial crack, perpendicular to the tensile axis, is assumed to be present in the particles. Both stationary and quasi-statically growing cracks are analyzed. Resistance to crack growth in its initial plane and along the particle-matrix interface is modeled using a cohesive surface constitutive relation that allows for decohesion. Variations of crack size, shape, spatial distribution, and volume fraction of the particles and of the material and cohesive properties are explored. Conditions governing the onset of cracking within the particle, the evolution of field quantities as the crack advances within the particle to the particle-matrix interface, and the dependence of overall tensile stress-strain response during continued crack advance are analyzed.

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

Abbreviations

a:

crack length

Eij :

covariant components of Lagrangian strain

E:

Young’s modulus

fc :

volume fraction of fractured particles

L0 :

height of the unit cell

m:

strain rate hardening exponent of the matrix

N:

strain hardening exponent of the matrix

q, r:

cohesive constitutive parameters

r0 :

radius (or width) of the particle

R0 :

radius (or width) of the unit cell

S:

area

Ti :

nominal traction components

ui :

covariant components of the displacement vector

VR :

volume of the reinforcement

Vcell :

volume of the unit cell

δn, δr :

cohesive surface length parameters

Δi :

covariant components of the displacement jump across a cohesive surface

εave :

average axial strain rate

εave :

average axial strain

v:

Poisson’s ratio

ε:

effective strain

ε:

effective strain rate

σ0 :

yield strength of the matrix

σh :

hydrostatic stress

σ:

effective stress

∑ave :

overall average axial stress

∑R :

average axial stress in the reinforcement

σmax :

strength for normal separation of a cohesive surface

τmax :

strength for tangential separation of a cohesive surface

τ:

Kirchhoff stress

ϕ*:

Jaumann rate of Kirchhoff stress

σ′:

deviatoric Kirchhoff stress

ϕ:

cohesive surface potential

ϕn :

work of separation for normal decohesion

ϕi :

work of separation for tangential decohesion

*:

Unless explicitly specified the following conventions are adopted

( )R :

pertaining to the reinforcement

( )M :

pertaining to the matrix

( )int :

pertaining to the reinforcement matrix interface

( )n :

normal component of a vector

( )t :

tangential component of a vector

( ),i :

covariant differentiation in the reference frame

References

  1. Y.L. Shen, M. Finot, A. Needleman, and S. Suresh:Acta Metall. Mater., 1994, vol. 42, pp. 77–97.

    Article  CAS  Google Scholar 

  2. G. Bao:Acta Metall. Mater., 1992, vol. 40, pp. 2547–55.

    Article  Google Scholar 

  3. V. Tvergaard:J. Mech. Phys. Solids, 1993, vol. 41, pp. 1309–26.

    Article  MATH  ADS  CAS  Google Scholar 

  4. A. Needleman:J. Appl. Mech., 1987, vol. 54, pp. 525–31.

    Article  MATH  Google Scholar 

  5. A. Needleman:Ultramicroscopy, 1992, vol. 40, pp. 203–14.

    Article  MathSciNet  Google Scholar 

  6. V. Tvergaard:Int. J. Fract., 1982, vol. 18, pp. 237–52.

    Google Scholar 

  7. X. Xu and A. Needleman:Modelling Simul. Mater. Sci. Eng., 1993, vol. 1, pp. 111–32.

    Article  ADS  Google Scholar 

  8. J. Llorca, A. Needleman, and S. Suresh:Acta Metall. Mater., 1991, vol. 39, pp. 2317–35.

    Article  CAS  Google Scholar 

  9. J. Llorca, S. Suresh, and A. Needleman:Metall. Trans. A, 1992, vol. 23A, pp. 919–34.

    ADS  CAS  Google Scholar 

  10. S. Suresh, T. Christman, and Y. Sugimura:Scripta Metall, 1989, vol. 23, pp. 1599–1602.

    Article  CAS  Google Scholar 

  11. J.W. Hutchinson: inNumerical Solution of Nonlinear Structural Problems, R.F. Hartung, ed., ASME, New York, NY, 1973,p. 17.

    Google Scholar 

  12. A. Needleman: inPlasticity of Metals at Final Strain: Theory, Experiment and Computation, E.H. Lee and R.L. Mallett, eds., RPI press, Troy, NY, 1982, pp. 387–436.

    Google Scholar 

  13. V. Tvergaard:J. Mech. Phys. Solids, 1976, vol. 24, pp. 291–304.

    Article  ADS  Google Scholar 

  14. D. Peirce, C.F. Shih, and A. Needleman:Comp. Struct., 1984, vol. 18, pp. 857–87.

    Article  Google Scholar 

  15. J. Yang, C. Cady, M.S. Hu, I. Zok, R. Mehrabium, and A.G. Evans:Acta Metall. Mater., 1990, vol. 38, pp. 261–19.

    Google Scholar 

  16. Y. Brechet, J.D. Embury, S. Tao, and L. Luo:Acta Metall. Mater., 1991, vol. 39, pp. 1781–86.

    Article  CAS  Google Scholar 

  17. T. Mochida, M. Taya, and D. Lloyd:Mater. Trans. JIM, 1991, vol. 32, pp. 931–42.

    CAS  Google Scholar 

  18. P.M. Mummery, P. Anderson, G. Davis, B. Derby, and J.C. Elliott:Scripta Metall. Mater., 1993, vol. 29, pp. 1457–62.

    Article  Google Scholar 

  19. P.M. Mummery, B. Derby, and C.B. Scruby:Acta Metall. Mater., 1993, vol. 41, pp. 1431–45.

    Article  CAS  Google Scholar 

  20. J. Bonnen, J. Allison, and J.W. Jones:Metall. Trans. A, 1991, vol. 22A, pp. 1007–19.

    ADS  CAS  Google Scholar 

  21. C.L. Horn:J. Mech. Phys. Solids, 1992, vol. 20, pp. 991–1008.

    ADS  Google Scholar 

  22. M.S. Hu:Scripta Metall. Mater., 1991, vol. 25, pp. 695–700.

    Article  CAS  Google Scholar 

  23. G.M. Newaz and B.S. Majumdar:J. Mater. Sci. Lett., 1993, vol. 12, pp. 551–52.

    CAS  Google Scholar 

  24. W.H. Hunt, , J.R. Brockenbrough, and P.E. Magnusen:Scripta Metall. Mater., 1991, vol. 25, pp. 15–20.

    Article  CAS  Google Scholar 

  25. H. Ribes, R. Da Silva, M. Suéry, and T. Bretheau:Mater. Sci. Technol., 1990, vol. 6, pp. 621–28.

    CAS  Google Scholar 

  26. Y. Brechet, J. Newell, S. Tao, and J.D. Embury:Scripta Metall. Mater., 1993, vol. 28, pp. 47–52.

    Article  CAS  Google Scholar 

  27. J.R. Rice:J. Appl. Mech., 1968, vol. 35, pp. 379–86.

    Google Scholar 

  28. Y.-L. Shen, M. Finot, A. Needleman, and S. Suresh: Brown University, Providence, RI, unpublished research, 1994.

Download references

Author information

Authors and Affiliations

  1. Department of Materials Science and Engineering, Massachusetts Institute of Technology, 02139, Cambridge, MA

    M. Finot (Graduate Research Assistant) & Y. L. Shen (Postdoctoral Research Associate)

  2. Division of Engineering, Brown University, 02912, Providence, RI

    A. Needleman (Professor of Engineering)

  3. Massachusetts Institute of Technology, 02139, Cambridge, MA

    S. Suresh (Richard P. Simmons Professor of Materials Science and Engineering and Professor of Mechanical Engineering)

Authors
  1. M. Finot
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. L. Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Needleman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Suresh
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Formerly Graduate Research Assistants, Brown University

Rights and permissions

Reprints and permissions

About this article

Cite this article

Finot, M., Shen, Y.L., Needleman, A. et al. Micromechanical modeling of reinforcement fracture in particle-reinforced metal-matrix composites. Metall Mater Trans A 25, 2403–2420 (1994). https://doi.org/10.1007/BF02648860

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02648860

Keywords

Search

Navigation