Abstract
The addition of a dispersed ductile phase in a brittle ceramic can result in an increased fracture toughness, mainly due to plastic dissipation during crack bridging. The large elastic-plastic deformations of a ductile particle intercepted by a brittle matrix crack are here analysed numerically with main focus on the effect of the growth of a single void in the particle centre, as has been observed experimentally. Particle-matrix debonding is incorporated in the numerical model, represented in terms of a cohesive zone formulation, and so is the effect of initial residual stresses induced by the thermal contraction mismatch during cooling from the processing temperature. The bridging behaviour is studied for different combinations of material parameters, and the void growth behaviour is related to previous results for cavitation instabilities in elastic-plastic solids.
Similar content being viewed by others
References
B. Budiansky, J.W. Hutchinson and A.G. Evans, Journal of the Mechanics and Physics of Solids 34 (1986) 167–189.
R.M. McMeeking and A.G. Evans, Journal of the American Ceramics Society 65 (1982) 242–246.
J.W. Hutchinson, Acta Metallurgica 35 (1987) 1605.
L.S. Sigl, P.A. Mataga, B.J. Dalgleish, R.M. McMeeking and A.G. Evans, Acta Metallurgica 36 (1988) 945–953.
J.W. Hutchinson, M.E. Mear and J.R. Rice, Journal Applied Mechanics 54 (1987) 828–832.
F. Erdogan and K. Arin, International Journal of Fracture 11 (1975) 191–204.
B. Budiansky, J.C. Amazigo and A.G. Evans, Journal of the Mechanics and Physics of Solids 36 (1988) 167–187.
P.A. Mataga, Acta Metallurgica 37 (1989) 3349–3359.
V. Tvergaard, International Journal of Mechanical Science 34 (1992) 635–649.
G. Bao and C.-Y. Hui, International Journal of Solids and Structures 26 (1990) 631–642.
B. Flinn, M. Rühle and A.G. Evans, Toughening in composites of Al2O3 reinforced with Al, University of California, Santa Barbara, Materials Department Report (1989).
M.F. Ashby, F.J. Blunt and M. Bannister, Acta Metallurgica 37 (1989) 1857.
Y. Huang, J.W. Hutchinson and V. Tvergaard, Journal of the Mechanics and Physics of Solids 39 (1991) 223–241.
V. Tvergaard, Y. Huang and J.W. Hutchinson, European Journal of Mechanics, A/Solids 11 (1992) 215–231.
V. Tvergaard, Materials Science Engineering A 125 (1990) 203–213.
A. Needleman, Journal of Applied Mechanics 54 (1987) 525–531.
V. Tvergaard, in Advances in Applied Mechanics 27, J.W. Hutchinson and T.Y. Wu (eds.), Academic Press, New York (1990) 83–151.
S. Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill, New York (1951).
V. Tvergaard, Journal of the Mechanics and Physics of Solids 24 (1976) 291–304.
B. Budiansky, J.W. Hutchinson and S. Slutsky, in Mechanics of Solids, The Rodney Hill 60th Anniversary Volume, H.G. Hopkins and M.J. Sewell (eds.), Pergamon Press (1988) 13–45.
A. Bagchi and A.G. Evans, Measurements of the debond energy for thin metallization lines on dielectrics, University of California, Santa Barbara, Materials Department Report (1994).
V. Tvergaard and J.W. Hutchinson, Journal of the Mechanics and Physics of Solids 41 (1993) 1119–1135.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tvergaard, V. Cavity growth in ductile particles bridging a brittle matrix crack. Int J Fract 72, 277–292 (1995). https://doi.org/10.1007/BF00037315
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00037315