Page 242 - Materials Science and Engineering An Introduction

214 • Chapter 6 / Mechanical Properties of Metals

(b) A tube constructed of which of the alloys will cost (d) If this thickness is found to be suitable, com-
the least amount? pute the minimum thickness that could be used
without any deformation of the tube walls. How
Yield Unit Mass much would the diffusion flux increase with this
Strength, Density, Cost, c reduction in thickness? However, if the thickness
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Alloy S y (MPa) R (g/cm ) ($US/kg) determined in part (c) is found to be unsuitable,
Steel (plain) 375 7.8 1.65 then specify a minimum thickness that you would
Steel (alloy) 1000 7.8 4.00 use. In this case, how much of a decrease in diffu-
sion flux would result?
Cast iron 225 7.1 2.50 6.D4 Consider the steady-state diffusion of hydrogen
Aluminum 275 2.7 7.50 through the walls of a cylindrical nickel tube as
Magnesium 175 1.80 15.00 described in Problem 6.D3. One design calls for a
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diffusion flux of 2.5 * 10 mol/m 2 # s, a tube radius
6.D3 (a) Gaseous hydrogen at a constant pressure of of 0.100 m, and inside and outside pressures of
0.658 MPa (5 atm) is to flow within the inside of a 1.015 MPa (10 atm) and 0.01015 MPa (0.1 atm),
thin-walled cylindrical tube of nickel that has a ra- respectively; the maximum allowable temperature
dius of 0.125 m. The temperature of the tube is to is 300 C. Specify a suitable temperature and wall
be 350 C and the pressure of hydrogen outside of thickness to give this diffusion flux and yet ensure
the tube will be maintained at 0.0127 MPa (0.125 that the tube walls will not experience any perma-
atm). Calculate the minimum wall thickness if the nent deformation.
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diffusion flux is to be no greater than 1.25 * 10
mol/m 2 # s. The concentration of hydrogen in the FUNDAMENTALS OF ENGINEERING
nickel, C H (in moles hydrogen per cubic meter of
(in QUESTIONS AND PROBLEMS
Ni), is a function of hydrogen pressure, P H 2
MPa), and absolute temperature T according to 6.1FE A steel rod is pulled in tension with a stress
that is less than the yield strength. The modulus
12,300 J>mol of elasticity may be calculated as
exp a - b (6.34)
RT (A) Axial stress divided by axial strain
C H = 30.81p H 2
Furthermore, the diffusion coefficient for the dif- (B) Axial stress divided by change in length
fusion of H in Ni depends on temperature as
(C) Axial stress times axial strain
39,560 J>mol (D) Axial load divided by change in length
2
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D H (m >s) = 4.76 * 10 exp a - b
RT 6.2FE A cylindrical specimen of brass that has a diam-
(6.35) eter of 20 mm, a tensile modulus of 110 GPa, and
(b) For thin-walled cylindrical tubes that are a Poisson’s ratio of 0.35 is pulled in tension with
pressurized, the circumferential stress is a func- force of 40,000 N. If the deformation is totally elas-
tion of the pressure difference across the wall tic, what is the strain experienced by the specimen?
(≤p), cylinder radius (r), and tube thickness (≤x) (A) 0.00116 (C) 0.00463
according to Equation 6.25—that is,
(B) 0.00029 (D) 0.01350
r p
s = (6.25a) 6.3FE The following figure shows the tensile stress–
x strain curve for a plain-carbon steel.
Compute the circumferential stress to which the (a) What is this alloy’s tensile strength?
walls of this pressurized cylinder are exposed.
(Note: The symbol t is used for cylinder wall thick- (A) 650 MPa (C) 570 MPa
ness in Equation 6.25 found in Design Example (B) 300 MPa (D) 3,000 MPa
6.2; in this version of Equation 6.25 (i.e., 6.25a) we (b) What is its modulus of elasticity?
denote wall thickness by ≤x.) (A) 320 GPa (C) 500 GPa
(c) The room-temperature yield strength of Ni is
100 MPa (15,000 psi), and s y diminishes about 5 (B) 400 GPa (D) 215 GPa
MPa for every 50 C rise in temperature. Would (c) What is the yield strength?
you expect the wall thickness computed in part (A) 550 MPa (C) 600 MPa
(b) to be suitable for this Ni cylinder at 350 C?
Why or why not? (B) 420 MPa (D) 1000 MPa