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Unformatted text preview: ME 382 Fall 2007 Midterm 2
Mouday, November 19, 2007 This is a closed book exam, students are allowed to use an unmarked copy ofthe
ME382 data book.
Answer of! questions.
Show ail caleuiotions (on this atom) for full credit.
There are a total of 1 0 pages to this exam. Use a mier/ straight edge to read from graphs for full credit Name: SO’U é‘Oh g
Section: _/ I Honor Pledge: Question 1 (a) You are part of a design team charged with designing a thinwalled spherical
pressure vessel that will have a radius of 2.00 m. The pressure vessel will
have to survive 1000 cycles of being pressurized between 4.00 MPa and
0.00 MPa. The pump cannot maintain pressure once there is a leak in the wall
of the vessel. Any crack in the pressure vessel may be assumed to originate from the surface and to be semicircular with a radius of a. The modeI stress intensity factor is given by XI, = can/m, where the stress is the stress normal to the
crack.
The pressure vessel is to be made out a steel that has a fracture toughness of 130 MPaJ—n: , a yield stress of 750 MPa, and exhibits a Paris Law for crack growth of the form (it? _ 1.46 —=2.12x10”a1< ' , dN ( ’)
where AK, is in MPa Jm. One of your colleagues, who graduated from Ohio State, designed the'
pressure vessel according to a "leakbefore—break" criterion, with a wall thickness of 5.00 mm. What is the safety factor on wall thickness for this design?
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re Weight Percent 'I'In Sn You are considering an alloy of iron and tin for structural purposes. The phase diagram is given above. (yFe) is an f.c.c. phase, (uFe) is a b.c.c,
phase, (Sn) is an f.c.c. phase, FeESnB, Fe3Sn2, FeSn, FeSn2 are all
intermetallic compounds. (The two liquid phases L1 and L2 are distinct
phases below 1505 °C; 1'.e., there is a miscibility gap.) (a) Over what range of compositions might it be possible to form martensite. Explain your answer. W Can/w lam/La, 1"“ ﬁlm Dz a;
.CC. 013x111]. WW For m (9/wa cull/035'; U’VV‘ WMM.U?W :yF£HK'F£ WWWﬂDOC {564’ 5 AS 6.6.15.7 (b) What is the maximum concentration of tin you could use, if you wanted to
explore the possibility of using only solidsolution hardening at room temperature? Explain you answer. (Assume the solubilities and phases at room temperature are identical to those at 200 0c.)
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: r WW MW. (d) Assume that (aFe) precipitates out of the liquid phase L1 as cylindrical
precipitates with a length 5 times the diameter. If the energy of the interfaces between the (aFe) and liquid phases L1 is 1.0 J/mz, and the decrease in the Gibbs' free energy associated with precipitating 1.0 m3 of (ed7e) is 200 M], calculate the critical nucleation size of an (aFe) precipitate. v: {(51921 = 7r(g§)i".5‘at :35} 1‘ r, s
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(a) Explain why brittle materials that follow a Weibull distribution of strengths also Show a Weibuil distribution of lifetimes during stress corrosion cracking. Err/71¢? mmrdri'aI'S tiff/2623f fro/Jim :21 meuﬂ A’th'bwﬁml
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by (1 ]‘J€abblf df'3“fwiz¢tf")¢1ii./5_ (b) The top and bottom plates of a beam, shown below, are fabricated from a
material with a Weibull modulus of m = 6.0 and SD = 175 MPa for a VG of
1000 mma. What is the maximum force F that can be supported if a
survival probability of 99.0% is required? The plates have a thickness of
1.0 mm and a width of 20.0 mm. The cross—section of the beam has a
moment of inertia I = 4000 ram“ . (You may assume the plates are thin enough to neglect the variation of stress through the thickness of the plates, and that shear stresses in the plates may be neglected). (This page is left blank in case you need more space) WQJ‘EUH all'sf'rﬁ'buﬁen; ‘ _. V— = 7116!.) _ Z PX MEL (4’ in \Q‘K, Km mm) AV: AA'K = (ZOmmYlmm >611
LL, J50? {Mi 1:; 'm gnaw 2 ijw 491531 ‘15 in CcvaeSSRUVL. 1[(32'521‘1‘4mm Z (Z Px>é(gomML> AX ¥ ‘7‘ (000mm‘
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KOOOMME’ V175" O, W : (zomrﬂﬂ< 23“) Q7 ‘ 0 000mm) Cf P: 0.05% w = MN” 10 ...
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 Winter '08
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