Effect of Inclusions on Shrinkage
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EFFECT OF INCLUSIONS ON SHRINKAGE GEORGE W. SCHERER E.I. DuPont de Nemours & Co., Central R & D Department, P.O. Box 80356, Wilmington, DE 19880-0356 USA ABSTRACT The effects of inclusions on densification are discussed, including their influence on the development of stresses during drying, and on the kinetics of sintering. Special attention is given to the problem of crystallization during sintering. INTRODUCTION Inclusions, such as particles or whiskers, are often introduced into gels to provide toughness to the sintered body. In other cases, inclusions appear spontaneously, as the glassy matrix crystallizes during aging or sintering. Whatever their origin, inclusions inhibit shrinkage of the body and thereby influence the development of stresses during drying and the rate of densification during sintering. In this paper, we examine these effects. DRYING Stresses arise during drying because of a gradient in the capillary tension in the liquid phase [1,2]. For a plate of thickness 2L drying from both faces, the drying stress is a. =CNHG (-ý)
[acOsh(oZ
/
Ssinh(a)
L)
1 I(
1)
where the constant C. - 1, HG is the viscosity of the solid network, I'E is the evaporation rate, z is the coordinate normal to the drying surface, and the parameter a is 2
a
L
L
FDHG
(2)
where D is the permeability and 77L is the viscosity of the liquid in the pores. Inclusions stiffen the matrix, so they increase HG; this reduces a and that leads to smaller drying stresses. That is, an increase in the macroscopic rigidity of the body tends to flatten the pressure gradient and reduce the macroscopic stresses. However, the local stresses might increase, because if the gel is trapped in the interstices of a relatively rigid network of particles, it cannot shrink, and the stresses may be even greater than in a film (which is constrained in only two directions). When a is small, eq. (1) reduces to 6
LflLVE (z2 2
2D
L
1
3)
(3)
so the stress is inversely proportional to the permeability. In a composite, the permeability will be sensitive to the degree of wetting of the inclusions by the matrix. For instance, if hydrophobic whiskers were introduced into a hydrophilic gel, the gel would not adhere to the Mat. Res. Soc. Symp. Proc. Vol. 180. 01990 Materials Research Society
504
whiskers, so open channels could form along the whiskers. Whiskers percolate readily (for example, whiskers with an aspect ratio of 10 to 1 have a percolation threshold, Pc, of only -9 vol% [3]), so such channels could provide an easy path for fluid flow through the body, and this would substantially lower the drying stresses. However, those channels would probably open further during sintering and act as mechanical flaws in the resulting body. Finally, inclusions toughen the matrix by interrupting crack growth, so the body could retain its macroscopic integrity, but be full of microcracks produced by local drying stresses. Such flaws could grow during sintering, and prevent complete densification. SINTERING
Inclusions retard sintering, because the matrix
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