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MSE 200
MSE 200 Test2 S. S. Number:
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View Full Document1 (a) Two specimens are deformed. One from an area of cross section
of Ao to 3Ao and another from an original length lo to 3lo. In both
cases the initial length is lo and the initial area of crsssection is Ao.
Show that these are equivalent in terms of true strain but are different
in terms of engineering strain.
(b) Calculate the ratio of true stress to engineering stress for the two
specimens. points:10
Ao to 3Ao is lo to lo/3. True strain=ln(1/3)=ln(3)
lo to 3 lo gives a true strain= ln(3)
These are equivalent since one is in compression and the other
tension but magnitudes are equal.
True stress/Engineering strain = 1+engineering strain.
Calculate engineering strain as (lolo/3)=2lo/3
Also (3lolo)/lo=2
Thus engineering strains are not equal.
Calculate ratio of true to engineering stress from the above.
2. In a steady state creep experiments of silver, a strain rate of 0.001
sec1 is observed at 500o C and a strain rate of 0.010 sec1 is
observed at 600o C. Determine the creep rate at 400 o C. points:6
e2/e1=exp{(Q/k)[1/T21/T1]}
Use e2=0.001 at T=773 K, e1=0.01 at T=873 and calculate Q/k
Use Q/k and T=673 K to determine e3 using either e2 or e1.
3. (a) A titanium alloy used for air craft frames has a critical fracture
toughness of 68,000 Psi.inch1/2. If the fracture strength is 40,000 psi,
determine the surface crack size. If the fracture toughness is increased
by a factor of 1.5 after reducing the grain size, what will be the crack
size for the same fracture strength.
(b) The yield strength of an alloy above the lattice frictional stress at
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 Spring '08
 wholedepartment

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