The thermal expansion of the directionally solidified AI-CuAI 2 eutectic
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equations for the thermal strains result:
THE
A1-CuAI 2 eutectic, when directionally solidified under conditions of high purity and high thermal gradients I has a regular lamellar microstructure of period X. This period is controlled by the rate R at which the melt is withdrawn from the furnace according to the relation: X2R = constant. The constant is dependent on material parameters which are held constant in this work. A universal law of composites proposed by Z. Hashin 2 is -'
+ K~
e,l c = O~longc2XT= 22c =
633c
f,oo.,0 OA,00 ~0
V =
Vi
~ ~
0
[1]
where V is the volume fraction, K is a physical property, the subscripts A and B refer to their respective phases, and C refers to the composite. This expression is independent of all microstructural parameters except volume fraction. Analogous formulae for electrical conductivity, dielectric constants, permeability, and heat conduction are known to be valid. B. PauP and R. Hill 4 have shown that the right-hand side holds for elasticity. The objective of this work was to measure the thermal expansion of the A1-CuA12 directionally solidified eutectic and determine whether the thermal expansion of the in-situ composite conforms to Hashin's universal law of composites and also to determine any anisotropy or lamellar spacing dependence of the thermal expansion. If the rule of mixtures is applied to an elastic model of the ideal microstructure (Fig. 1) with the constraint that no slip at the interface occurs ~,6,v the following DENNIS F. BAKER, Graduate Student Research Assistant, Department of Materials Science & Mineral Engineering, University of California, Berkeley, CA 94720 and R. H. BRAGG, Professor & Chairman, Department of Materials Science & Mineral Engineering, University of California, Berkeley, and Principal Investigator, Materials and Molecular Research Division, Lawrence Berkeley Laboratory. Manuscript submitted May 15, 1980. METALLURGICAL TRANSACTIONS A
[21
Ar
[3]
]AT
[4]
+
= a ..... Ic~ T = [C~AIVAI + a . . . . . 10go "~ L
Vo VA (EAI -- Eo) (2O A -- O lo.g0 -- a t r a . , 0 ) ]
(1 -- ~EA--~s
~ Kc
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