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Unformatted text preview: bril'ci SHAH—E Materials Science and Engineering 564 UNIVERSIW Mechenieal behavger wch micmszrzgezwe
Winter 2007 Final Exam March 13, 2007 Instructions: Enter your 4digit course code here for identiﬁcation: WE ' You have approximately 1:50 to complete this exam.
' Answer all questions.
' Write your answers in the space provided.
0 Show all work in order for partial credit to be considered.
 You may use your twosided sheet of personal notes, a calculator, and a ruler.
' The point values for each question are given below.
Good luck! 1: ___/10
2: __/1()
3: ____/10
4: ___/10
5: ___/10
6' ___/10
7 ___/15
8 ___/15
9: ‘__/10
10: _/10
11: /30 TOTAL: / 140 1/9 1. MSE 564 Final Mar. 13, 2007 Yield strength of a polycrystal (10 points)
A polycrystalline metal rod is loaded in simultaneous tension oxx and torsion oxy = oyx. The ratio of applied tensile to shear stress is 2:1. Yield is observed when oxy
reaches 100 MPa. Estimate the yield strength of the material in simple tension. + (QC‘thk‘Cvik «— (amtk boutf'T‘L . U H
3
“c7
.2 \ =ﬂl00 M173 Catk jcQié,
= 7.05 MP2; cv‘r «nub Answer (10 points): tensile yield strength = Response of a polycrystalline metal with nanometer grain size (10 points)
State whether the room temperature yield strength and elevated temperature creep
rate are expected to increase, decrease, or remain unchanged as grain size is
decreased from 50 rim to 50 nm. For each property, circle the appropriate response and then provide a short explanation that states the explicit dependence on grain
size. a. room T yield strength (circle one): decrease unchanged Explanation: éggggrgéﬂgé in gchg EgmH— EJ. ﬁ
~ 5‘ , \ {M (“can ir‘ 5A4. page 2 / 9pages total MSE 564 Final Mar. 13, 2007 Creep rupture lifetime (10 points)
Based on the LarsonMiller plot below, does cutting the stress in half lead to more
than or less than double the lifetime, when T = 1000K? Provide a reason for your a f nswer and show any calculations, if needed. T(2O + log n x 103(‘R—hr) etch QM <7: (000 M91, TCZO +103 bf] : l"!  103
K'ngv 60 W6 gar GT: 306 M99}
'40 TEzo +£u3kr1: leogmqt Stress (MPa) —20E T": (COOK)
‘tr ~—
I lézkr‘ @ @300 M91,
so°w @ ’beomfk u
.— Cluvisf > {Ir M’ "SM MP, {g Mark Rxews ﬂuxth
“(wic otl (poo Miza... me + log n x 103(°K—hr) FIGURE 5.25 LarsonMiller plot showing 8590 ironbased alloy data presented in
Fig. 53. mm R.W. Hertzberg Less than double the lifetime Make sure to show your reasoning. page 3 / 9pages total MSE 564 Final Mar. 13, 2007 Effect of yield strength on critical flaw size (10 points) The Point Pleasant Bridge design discussed in class called for steel with a yield
strength of 50 ksi. Instead, steel with a yield strength of 75 ksi was used. State
whether this deviation from the design specification is expected to increase,
decrease, or not change the critical flaw size for fracture. Provide an explanation
below. Answer (circle one): . _
Increase Decrease Not change Explanation: page 4/ 9pages total MSE 564 Final Mar. 13, 2007 Controlled and inherent flaw testing (10 points) Griffith performed a set of experiments in which a crack of known size was put into
a glass sample and then stressed to fracture. Below are two sets of measurements
for some sodalime glass. flaw size (mm) fracture stress (MPa)
5 mm 3.55
7.5 mm 2.90 A sample of glass in "as—is" condition fractures at 100 MPa. Based on the
information given, estimate the size of the ﬂaw that fractured the "as—is" sample. newLad
5:; W‘ 9‘ CW§+M+ a.
Cgﬁam W‘oﬂ. > k vQMt.
(m M17; 3 (5.55 M03 x! 0:00 5m We, 6:; 430M) MM :ogsMpafKA '1'. 0.7—5 MPZ J; Mirrormist—hackle features (10 points) A fractured sapphire rod has a fracture surface with a mirror boundary located 1 mm from the defect origin. Another sapphire rod is fractured at a tensile stress of
200 MPa and a mirror boundary is observed to be 0.5 mm from the defect origin.
Estimate the tensile fracture stress for the ﬁrst sample. page 5 / 9pages total MSE 564 Final Mar. 13, 2007 Weibull statistics for an inhomogeneously stressed rod (15 points)
A volume V0 of alumina rod is determined to have Weibull parameters 00 = 250 MPa and m = 10, with the threshold stress ou = 0. Your application calls for an
alumina rod of volume 2.5 V0. When loaded with an axial force F = 100 N, a
section of volume 1.5 V0 has a uniform stress of 200 MPa and another portion of
volume 1.0 V0 has a uniform stress of 225 MPa. Estimate the following: a. The probability of survival of the section with volume 1.5 V0. .\1 E)“
V a"
scam € ° ° gm w
“*5 5'90
SC’LOOMWa.)l5Vp>= e = (1°35
Answer: 0.8.5 b. The probability of survival of the section with volume 1.0 V0. 215 ‘0
“' < 270 SCZZWPA)\VO)= Q. : om A : c. The probability of survival of the entire rod of volume 2.5 V0. 3 13 'S “W l'SVO “Ova ll 0.85' 03H : ago Answer: O.QO page 6/ 9pages total MSE 564 Final Mar. 13, 2007 Mechanical analog to a polymer (15 points) You decide to model a visco—elastic polymer using a 4—element viscoelastic
construction. 21. Draw a sketch of this analog and assign next to each element an elastic
modulus or viscosity as appropriate. b. The springs in the model have an elastic modulus of 500 MPa and the
dashpots have a viscosity of 50 GPa—s. Estimate the permanent strain if a
stress of 100 MPa is applied for 125 3. PM wad" Q 1 g .E = rOOMPa .ﬂSs... 0.25“
“’11, So~to3M‘Pa'9 c. A stress of 100 MPa is applied for 125 s and then removed. Estimate the
strain after 150 s. Dill/u,“ c5“ (5 appkmd 0A k:0, QCG'Ié’l: *3; (l— Q ) Jr gf T*'ﬂ}:\oo;
" 7' "'73 52 We WW. Sr‘y Su‘Lu/mkko\u ISG
60255) : twp; +_ locum} (r... e it) + (COMP; “5015 ’5
+ t—‘gWah 03.2%) (LES/9+ GEM) “5
:Joomm (e—IEO/T— Q 19w} +_ IOOMPB (2:3 __ 0,39 503ml?  _. Mr? "
Answer: page 7 / 9pages total MSE 564 Final Mar. 13, 2007 Critical tension to fracture {111} planes (10 points) A crystal of diamond is loaded in tension along a <100> direction. A crack is
situated on a {111} plane and it will propagate when the tensile stress normal to the
{111} plane reaches 100 MPa. At what value of tension along a <100> direction
will the crack propagate? Note that diamond has a cubic crystal structure. \ﬁ‘U‘
6;!“ :. 0’” COS 9m C03 9‘”  ﬂ“,
: ‘57! —‘ Jo  01¢ i V3 V3 3 Answer: .300 M?& page 8 / 9pages total 10. 11. MSE 564 Final Mar. 13, 2007 Fracture surface features and crack growth directions (10 points) State one room temperature fracture surface feature in a metal alloy that can help
determine the direction of crack growth and therefore origin of fracture. Sketch the
feature and indicate the direction of crack _ _ ation. Answer: Q) OWL/um MWS @ Gamma.» rtDMgMQs @ “Taégowl' True or False (3 points each = 30 points total)
Circle True or False as appropriate for each statement below. a. The amount of slant fracture in a carbon steel part is likely to decrease with
increasing rate of loading. False b. The tensile strength of a thermoplastic polymer increases with crystallinity. False c. The maximum damping for an amorphous the oplastic polymer occurs in the
vicinity of the glass transition temperature. False (1. Given: In principle, fracture toughness can be measured for slant fracture vs
flat fracture. In practice, the convention is to report the value associated with
ﬂat fracture.
etion: To achieve this, thicker rather than thinner samples should be used. alse e. Cold drawing of a polymer refers to s tching of a polymer well below the
glass transition temperature. True f. A mater' a . ith a large Weibull modulus essentially has negligible flaws in it.
True g. Increasing MW will increase relaxatio odulus primarily at shorter times, with
little change at longer times. True h. Thermoplastic and thermosetting polymers usually are ducti .7 nough to have
room temperature failure strains greater than 10%. True i. Notch strengthening suggests that a bar with notches cut into it will r uire a
larger stress to fail it than the same bar without any notches. True j. The probability of survival of a glass rod of volume V0 typically shoul be aller than that for a cable of individual glass fibers with total volume V0. False END OF EXAM! page 9/ 9pages total ...
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 Winter '08
 Anderson
 Tensile strength, Final Mar., 9pages total MSE

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