Page 235 - Materials Science and Engineering An Introduction

Questions and Problems • 207

REFERENCES

ASM Handbook, Vol. 8, Mechanical Testing and Evaluation, Dieter, G. E., Mechanical Metallurgy, 3rd edition, McGraw-
ASM International, Materials Park, OH, 2000. Hill, New York, 1986.
Bowman, K., Mechanical Behavior of Materials, Wiley, Dowling, N. E., Mechanical Behavior of Materials, 3rd edition,
Hoboken, NJ, 2004. Prentice Hall (Pearson Education), Upper Saddle River,
Boyer, H. E. (Editor), Atlas of Stress–Strain Curves, 2nd edi- NJ, 2007.
tion, ASM International, Materials Park, OH, 2002. Hosford, W. F., Mechanical Behavior of Materials, Cambridge
Chandler, H. (Editor), Hardness Testing, 2nd edition, ASM University Press, New York, 2005.
International, Materials Park, OH, 2000. Meyers, M. A., and K. K. Chawla, Mechanical Behavior of
Courtney, T. H., Mechanical Behavior of Materials, 2nd edition, Materials, 2nd edition, Cambridge University Press, New
Waveland Press, Long Grove, IL, 2005. York, 2009.
Davis, J. R. (Editor), Tensile Testing, 2nd edition, ASM
International, Materials Park, OH, 2004.
QUESTIONS AND PROBLEMS

Problem available (at instructor’s discretion) in WileyPLUS
Concepts of Stress and Strain 6.6 Consider a cylindrical nickel wire 2.0 mm
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6.1 Using mechanics-of-materials principles (i.e., equa- (0.08 in.) in diameter and 3 * 10 mm (1200 in.)
tions of mechanical equilibrium applied to a free- long. Calculate its elongation when a load of
body diagram), derive Equations 6.4a and 6.4b. 300 N (67 lb f ) is applied. Assume that the defor-
mation is totally elastic.
6.2 (a) Equations 6.4a and 6.4b are expressions for
normal (s¿) and shear (t¿) stresses, respectively, 6.7 For a brass alloy, the stress at which plastic de-
as a function of the applied tensile stress (s) and formation begins is 345 MPa (50,000 psi), and the
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the inclination angle of the plane on which these modulus of elasticity is 103 GPa (15.0 * 10 psi).
stresses are taken (u of Figure 6.4). Make a plot (a) What is the maximum load that can be ap-
showing the orientation parameters of these ex- plied to a specimen with a cross-sectional area of
2
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pressions (i.e., cos u and sin u cos u) versus u. 130 mm (0.2 in. ) without plastic deformation?
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(b) From this plot, at what angle of inclination is (b) If the original specimen length is 76 mm (3.0
the normal stress a maximum? in.), what is the maximum length to which it can
(c) At what inclination angle is the shear stress a be stretched without causing plastic deformation?
maximum? 6.8 A cylindrical rod of steel (E = 207 GPa, 30 * 10
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psi) having a yield strength of 310 MPa (45,000
Stress–Strain Behavior psi) is to be subjected to a load of 11,100 N (2500
6.3 A specimen of copper having a rectangular cross lb f ). If the length of the rod is 500 mm (20.0 in.),
section 15.2 mm * 19.1 mm (0.60 in. * 0.75 in.) is what must be the diameter to allow an elongation
pulled in tension with 44,500 N (10,000 lb f ) force, of 0.38 mm (0.015 in.)?
producing only elastic deformation. Calculate the 6.9 Compute the elastic moduli for the following
resulting strain. metal alloys, whose stress–strain behaviors may
6.4 A cylindrical specimen of a nickel alloy having an be observed in the Tensile Tests module of Virtual
elastic modulus of 207 GPa (30 * 10 6 psi) and an Materials Science and Engineering (VMSE): (a)
original diameter of 10.2 mm (0.40 in.) experiences titanium, (b) tempered steel, (c) aluminum, and (d)
only elastic deformation when a tensile load of carbon steel. How do these values compare with
8900 N (2000 lb f ) is applied. Compute the maxi- those presented in Table 6.1 for the same metals?
mum length of the specimen before deformation 6.10 Consider a cylindrical specimen of a steel alloy
if the maximum allowable elongation is 0.25 mm (Figure 6.22) 8.5 mm (0.33 in.) in diameter and
(0.010 in.). 80 mm (3.15 in.) long that is pulled in tension.
6.5 An aluminum bar 125 mm (5.0 in.) long and hav- Determine its elongation when a load of 65,250 N
ing a square cross section 16.5 mm (0.65 in.) on (14,500 lb f ) is applied.
an edge is pulled in tension with a load of 66,700 6.11 Figure 6.23 shows the tensile engineering stress–
N (15,000 lb f ) and experiences an elongation of strain curve in the elastic region for a gray cast
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0.43 mm (1.7 * 10 in.). Assuming that the defor- iron. Determine (a) the tangent modulus at 25 MPa
mation is entirely elastic, calculate the modulus of (3625 psi) and (b) the secant modulus taken to
elasticity of the aluminum. 35 MPa (5000 psi).