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Unformatted text preview: Materials Science and Engineering 644
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Midterm Exam February 9, 2003 " Instructions: Enter your 4 digit course code here: Kg I You have approximately 50 minutes to compiete this exam. Answer all 6 questlo
Write your answers in the spaces provided. You may use your one—sided sheet of
persona11 notes and a calculator. The point values for each question are given below.
Good luck! /10 /10 1
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6 /10 TOTAL: / 100 U7 MSE 644 Midterm Feb. 9, 2004 Properties of Matrix Materials (10 points) Composite materials provide improvement over inherently poor matrix properties.
State the relevant properties next to each matrix below. Make sure your answers
are complete. Answer: CERAMIC METAL POLYMER
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Tmpp’t ‘ c. (cop'H‘mll Relative properties of a metal matrix and ceramic fiber (10 points) Sketch on the stress«strain plot below the relative tensile response of an aluminum
matrix and an alumina fiber. On your plot, be sure to indicate the reiative
differences in elastic modulus, strength, and ductility. Answer: M
tensﬁe areas (Pa)
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Jr a 7;, tenstie strain page 2 f 7pages total MSE 644 Midterm Feb. 9, 2004 Conditions for a iightweight, bucklingresistant rod (30 points)
Consider a rod having a circular cross section of radius r. The rod length I must equal lm and when loaded axially with a force F = 100 N, the rod must not buckle.
The buckling force for a circular rod of length l is
3 4
Jr‘ Er Fzmckle = (a) Using the above information, derive an expression for the minimum radius r
required to satisfy the buckling condition mentioned above. Your answer should be
stated in terms of Young’s modulus E and any other necessary parameters. _ i— : 13 ~_ Lt ‘
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.L— Eub§¥' m no. 113E \Mo glad Maw?!" Answer to part (a): r
rmin: (boo “'1‘? \le ﬁg 11' 3 am J it,“ (b) Derive an expression for the weight of a beam that will satisfy the deﬂection
condition mentioned in part (a). Express your answer in terms of the density, p, and E, as well as other necessary parameters. in: writing (m
: “3/ (moo “.mi “2
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E." ‘T weight: 40 ’2 ‘ m  NHL \FTF i E 47 Answer to part (b): page 3 r’ 7pages total MSE 644 Midterm Feb. 9, 2004 Problem 3 cont’d (c) Label on the diagram below the specific point(s) at which the rod will have
minimum weight and still satisfy the buckling requirement. l Answer to part (c): 1000 «x Density. 9 (Morm’l new 3"“? 0“ . m w Infiltration Pressure (10 points) The pressure to infiltrate a preform of continuous, unidirectional glass fibers is 100
Pa, when the spacing from fiber—to—ﬁber center is 40 um and the fiber radius is 10
um. Based on this information, determine the pressure necessary to infiltrate a
similar preform with having 35% volume fraction of the same glass fibers. (P: 253;?! JAS SolQQ’c S
m of; r7; 4? ‘{DBW 7.008512%) = 108w
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/ :Zobwﬂ .lovmii 10E.“ d Answer: :3 “15.30 7% © page 4 / Tpages total MSE 644 Midterm Feb. 9, 2004 Stressstrain behavior for a CMC (10 points) Provide qualitative sketches of the tensile stress strain curves for the following: (I) monolithic lithium alumino silicate (LAS) matrix (2) LAS reinforced with unidirectional SiC ﬁbers (3) LAS with the same volume fraction of SiC ﬁbers, but in a 0/90“ layup (4) LAS with the same volume fraction of SiC fibers, but in a 3D braid. Put all curves on the plot below. There is no need to indicate numerical values of
Stress or strain. However, make sure that your answer reﬂects proper relative trends
in elastic moduli, tensile strength, and ductility. {attains strain page 5 f Tpages total 6. MSE 644 Midterm F eb. 9, 2004 Optimal Properties in a layered composite (38 points)
You are considering a layered composite material comprised of alternating layers of
aluminum and alumina. The relevant constituent properties are: Aluminum Alumina
E = 69 GPa E = 380 GPa
k = 222 meK k = 39 me~K Note that the thermal conductivity k relates the heat ﬂux q (in me2) parallel to a temperature gradient de’dx (in Kim) according to: 3°10 6{75
dT
= — k—
q dx (a) Draw on the plot below an estimate of the elastic m a
parallel to the layers, as a function of volume fraction u ' the composite Answer to part (a): Econmm {$93} Walrch a $32 0,4 0.6 {1.8 1
wlma am aluminaas wiklzﬂg) (b) Determine the numerical range of volume fraction of alumina over which the
elastic modulus of the composite parallel to the layers is greater than l60 GPa. £9) E“: (clearQ l 3°50»? >tcoo
3H 1U} > all N} > 23°76, Answer to part (b): AV; > ‘za valve @_ "' 2 [£ 164,999.13? ae6fl'aestotal . ,
p g p g were M d3.th MSE 644 Midterm Feb. 9, 2004 Question 6 continued... (c) Draw on the plot below an estimate of the composite thermal conductivity
perpendicular to the layers, as a function of volume fraction of alumina. Answer to part (c):
'7 JCI>"‘”Q  kcomposite (WMK) 0 0.2 0.4 0.6 0.8 1
volume fraction alumina, v(Al203) ((1) Determine the numerical range of volume fraction of alumina over which the
thermal conductivity of the composite perpendicular to the layers is greater than 92 meK. {z
a“? 7 El: W/M—K
_‘_ <_ J—
ezan ‘iz. I U #212  l 4 2H2: _ 0‘ 0
Answer to part ((1): Afr < 30vol7° @ Elﬁn " Z i L “31 ﬁamAKC‘g«tj
Page 7 f Tpages total "to"? _ we CLQQOLMA. ...
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 Winter '05
 Anderson
 Aluminium, Tensile strength, elastic modulus, Composite material

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