Small-scale crack bridging and the fracture toughness of particulate-reinforced ceramics
Abstract
Theoreticalanalyses of small-scale bridging of crack surfaces by elastic-ideally plastic springs are presented and applied to the study of the fracture toughness of ceramics reinforced by small particles. The dependence of toughening on particle size, concentration, strength, and ductility is explored, and relations between toughening and bridge length at fracture are given. Available experimental information is examined in the light of the analyses.
References (9)
- B. Budiansky
J. Mech. Phys. Solids
(1965) - R. Hill
J. Mech. Phys. Solids
(1965) - L.R.F. Rose
J. Mech. Phys. Solids
(1987) - B. Budiansky
Proc. Tenth U.S. Nat. Congr. Appl. Mech., Austin, Texas, June 16–20, 1986
(1986)
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On Sabbatical Leave from the Department of Mathematics, University of Nigeria, Nsukka, Nigeria.