Metal-lnduced embrittlement of low-carbon steel by indium in association with tellurium
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K~
=
/~l E¢(1
~ f )K ~
E.,
+ xfE~o'oao
where Ec and E,, are elastic moduli o f the composite and the intermetallic matrix, respectively, K,, is the matrix toughness, and f, o'o, and ao are the volume fraction, unconstrained yield strength, and radius o f the ductile phase, respectively. The parameter X is the normalized work o f rupture o f the ductile particle undergoing deformation and fracture within the constraint imposed by the surrounding elastic matrix. This value was calculated using the previous equation, taking experimental values o f all the variables. The values o f Kc, f, and ao are 12.8 MPa, 0.345, and 2 /xm, respectively, from the present investigation. Values for Kin, O'o, and Em w e r e taken from previous studies, [4"61 as 3 MPaV/-m, 386 MPa, and 327 GPa, respectively. Using the rule o f mixtures, the composite modulus, Ec, is calculated to be 195 GPa. Collectively, this leads to the calculated value o f parameter X equal to 1.75. The value o f normalized work o f rupture parameter X is system specific and strongly depends upon the properties o f the interface between the ductile particles and the surrounding constraining elastic matrix,tg~ If the interface is very strong, then very high constraint is imposed upon the deforming phase, thereby promoting cleavage failure, resulting in a decreased value o f X. A1tematively, if the constraint is too low o r virtually absent, then this parameter can also decrease appreciably, preventing load transfer to the particles. An earlier study has shown that for a large n u m b e r o f two-phase systems, the increment o f toughening due to ductile-phase bridging can be predicted reasonably well by taking X ~ 4-t~°] This value is higher than that obtained in the present investigation. This may be due to the possibility that the small Nb particles in the present alloy do not experience much constraint. Note that the toughening data previously reported on wrought Nb-10Si alloy also gave X 504--VOLUME 24A, FEBRUARY 1993
1.6. For both cases, ductile-particle c r a c k bridging was assumed to be the main mode o f toughening. O t h e r mechanisms, such as c r a c k deflection, microcracking, and c r a c k blunting, may also be operative. The magnitude o f their contribution to toughening is a subject o f continuing research. REFERENCES 1 . M.G. Mendiratta and D.M. Dimiduk: Mater. Res. Soc. Syrup. Proc., 1 9 8 9 , vol. 1 3 3 , p p . 441-46. 2 . M.G. Mendiratta and D.M. Dimiduk: Scripta Metall., 1 9 9 1 , vol. 2 5 , p p . 237-42. 3 . J.J. Lewandowski, D. Dimiduk, W.R. Kerr, and M.G. Mendiratta: Mater. Res. Soc. S y m p . Proc., 1 9 9 0 , vol. 120, p p . 103-08. 4 . Madan G. Mendiratta, John J. Lewandowski, and Dennis M . Dimiduk: Metall. Trans. A, 1 9 9 1 , vol. 22A, p p . 1573-83. 5 . P.R. Subramanian and M.G. Mendiratta: UES, Inc., Dayton, OH, unpublished research, 1 9 9 2 . 6 . Rama K. Nekkanti and Dennis M . Dimiduk: Mater. Res. Soc. S y m p . Proc., 1 9 9 0 , vol. 1 9 4 , p p . 175-82. 7 . J.J. Lewandowski and J. Rigney: Proc. 2ndlnt. Ceramic Science and Tec
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