Chap 16 Solns-6E

# Chap 16 Solns-6E - CHAPTER 16 COMPOSITES PROBLEM SOLUTIONS...

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CHAPTER 16 COMPOSITES PROBLEM SOLUTIONS 16.1 The major difference in strengthening mechanism between large-particle and dispersion- strengthened particle-reinforced composites is that for large-particle the particle-matrix interactions are not treated on the molecular level, whereas, for dispersion-strengthening these interactions are treated on the molecular level. 16.2 The similarity between precipitation hardening and dispersion strengthening is the strengthening mechanism--i.e., the precipitates/particles effectively hinder dislocation motion. The two differences are: 1) the hardening/strengthening effect is not retained at elevated temperatures for precipitation hardening--however, it is retained for dispersion strengthening; and 2) the strength is developed by a heat treatment for precipitation hardening--such is not the case for dispersion strengthening. 16.3 The elastic modulus versus volume percent of WC is shown below, on which is included both upper and lower bound curves; these curves were generated using Equations (16.1) and (16.2), respectively, as well as the moduli of elasticity for cobalt and WC given in the problem statement. 1

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16.4 This problem asks for the maximum and minimum thermal conductivity values for a TiC-Co cermet. Using a modified form of Equation (16.1) the maximum thermal conductivity k max is calculated as k max = k m V m + k p V p Co V Co TiC V TiC = (69 W/m- K)(0.15) + (27 W/m-K)(0.85) = 33.3 W/m-K And, from a modified form of Equation (16.2), the minimum thermal conductivity k min is k min = k Co k TiC V Co k TiC + V TiC k Co = (69 W /m-K)(27 W /m-K) (0.15)(27 W /m-K) + (0.85)(69 W /m -K) = 29.7 W/m-K 16.5 Given the elastic moduli and specific gravities for copper and tungsten we are asked to estimate the upper limit for specific stiffness when the volume fractions of tungsten and copper are 0.70 and 0.30, respectively. There are two approaches that may be applied to solve this problem. The first is to estimate both the upper limits of elastic modulus [ E c (u) ] and specific gravity ( ρ c ) for the composite, using equations of the form of Equation (16.1), and then take their ratio. Using this approach E c (u) = E Cu V Cu + E W V W = (110 GPa)(0.30) + (407 GPa)(0.70) = 318 GPa And ρ c ρ Cu V Cu + ρ W V W = (8.9)(0.30) + (19.3)(0.70) = 16.18 Therefore 2
Specific Stiffness = E c (u) ρ c = 318 GPa 16.18 = 19.65 GPa With the alternate approach, the specific stiffness is calculated, again employing a modification of Equation (16.1), but using the specific stiffness-volume fraction product for both metals, as follows: Specific Stiffness = E Cu ρ Cu V Cu + E W ρ W V W = 110 GPa 8.9 (0.30) + 407 GPa 19.3 (0.70) = 18.47 GPa 16.6 (a) The matrix phase is a continuous phase that surrounds the noncontinuous dispersed phase. (b) In general, the matrix phase is relatively weak, has a low elastic modulus, but is quite ductile. On the other hand, the fiber phase is normally quite strong, stiff, and brittle.

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## This homework help was uploaded on 02/07/2008 for the course MATENG MAT201 taught by Professor Na during the Spring '08 term at Wisconsin Milwaukee.

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Chap 16 Solns-6E - CHAPTER 16 COMPOSITES PROBLEM SOLUTIONS...

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