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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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
Y.L. Shen, M. Finot, A. Needleman, and S. Suresh:Acta Metall. Mater., 1994, vol. 42, pp. 77–97.
G. Bao:Acta Metall. Mater., 1992, vol. 40, pp. 2547–55.
V. Tvergaard:J. Mech. Phys. Solids, 1993, vol. 41, pp. 1309–26.
A. Needleman:J. Appl. Mech., 1987, vol. 54, pp. 525–31.
A. Needleman:Ultramicroscopy, 1992, vol. 40, pp. 203–14.
V. Tvergaard:Int. J. Fract., 1982, vol. 18, pp. 237–52.
X. Xu and A. Needleman:Modelling Simul. Mater. Sci. Eng., 1993, vol. 1, pp. 111–32.
J. Llorca, A. Needleman, and S. Suresh:Acta Metall. Mater., 1991, vol. 39, pp. 2317–35.
J. Llorca, S. Suresh, and A. Needleman:Metall. Trans. A, 1992, vol. 23A, pp. 919–34.
S. Suresh, T. Christman, and Y. Sugimura:Scripta Metall, 1989, vol. 23, pp. 1599–1602.
J.W. Hutchinson: inNumerical Solution of Nonlinear Structural Problems, R.F. Hartung, ed., ASME, New York, NY, 1973,p. 17.
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.
V. Tvergaard:J. Mech. Phys. Solids, 1976, vol. 24, pp. 291–304.
D. Peirce, C.F. Shih, and A. Needleman:Comp. Struct., 1984, vol. 18, pp. 857–87.
J. Yang, C. Cady, M.S. Hu, I. Zok, R. Mehrabium, and A.G. Evans:Acta Metall. Mater., 1990, vol. 38, pp. 261–19.
Y. Brechet, J.D. Embury, S. Tao, and L. Luo:Acta Metall. Mater., 1991, vol. 39, pp. 1781–86.
T. Mochida, M. Taya, and D. Lloyd:Mater. Trans. JIM, 1991, vol. 32, pp. 931–42.
P.M. Mummery, P. Anderson, G. Davis, B. Derby, and J.C. Elliott:Scripta Metall. Mater., 1993, vol. 29, pp. 1457–62.
P.M. Mummery, B. Derby, and C.B. Scruby:Acta Metall. Mater., 1993, vol. 41, pp. 1431–45.
J. Bonnen, J. Allison, and J.W. Jones:Metall. Trans. A, 1991, vol. 22A, pp. 1007–19.
C.L. Horn:J. Mech. Phys. Solids, 1992, vol. 20, pp. 991–1008.
M.S. Hu:Scripta Metall. Mater., 1991, vol. 25, pp. 695–700.
G.M. Newaz and B.S. Majumdar:J. Mater. Sci. Lett., 1993, vol. 12, pp. 551–52.
W.H. Hunt, , J.R. Brockenbrough, and P.E. Magnusen:Scripta Metall. Mater., 1991, vol. 25, pp. 15–20.
H. Ribes, R. Da Silva, M. Suéry, and T. Bretheau:Mater. Sci. Technol., 1990, vol. 6, pp. 621–28.
Y. Brechet, J. Newell, S. Tao, and J.D. Embury:Scripta Metall. Mater., 1993, vol. 28, pp. 47–52.
J.R. Rice:J. Appl. Mech., 1968, vol. 35, pp. 379–86.
Y.-L. Shen, M. Finot, A. Needleman, and S. Suresh: Brown University, Providence, RI, unpublished research, 1994.
Author information
Authors and Affiliations
Additional information
Formerly Graduate Research Assistants, Brown University
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02648860