Page 278 - Materials Science and Engineering An Introduction

250 • Chapter 7 / Dislocations and Strengthening Mechanisms

Spreadsheet Problem 7.D7 A cylindrical brass rod having a minimum ten-
7.1SS For crystals having cubic symmetry, generate a sile strength of 450 MPa (65,000 psi), a ductility
spreadsheet that allows the user to determine the of at least 13%EL, and a final diameter of 12.7
angle between two crystallographic directions, mm (0.50 in.) is desired. Some brass stock of
given their directional indices. diameter 19.0 mm (0.75 in.) that has been cold
worked 35% is available. Describe the procedure
you would follow to obtain this material. Assume
DESIGN PROBLEMS that brass experiences cracking at 65%CW.
Strain Hardening 7.D8 Consider the brass alloy discussed in Problem 7.41.
Recrystallization Given the following yield strengths for the two spec-
7.D1 Determine whether it is possible to cold work imens, compute the heat treatment time required at
steel so as to give a minimum Brinell hardness 650 C to give a yield strength of 90 MPa. Assume a
of 240 and at the same time have a ductility of at value of 2 for n, the grain diameter exponent.
least 15%EL. Justify your answer.
Time (min) Yield Strength (MPa)
7.D2 Determine whether it is possible to cold work
brass so as to give a minimum Brinell hardness 40 80
of 150 and at the same time have a ductility of at 100 70
least 20%EL. Justify your answer.
7.D3 A cylindrical specimen of cold-worked steel has FUNDAMENTALS OF ENGINEERING
a Brinell hardness of 240. QUESTIONS AND PROBLEMS
(a) Estimate its ductility in percent elongation. 7.1FE Plastically deforming a metal specimen near
(b) If the specimen remained cylindrical during room temperature generally leads to which of the
deformation and its original radius was 10 mm following property changes?
(0.40 in.), determine its radius after deformation. (A) An increased tensile strength and a
7.D4 It is necessary to select a metal alloy for an ap- decreased ductility
plication that requires a yield strength of at least (B) A decreased tensile strength and an increased
310 MPa (45,000 psi) while maintaining a mini- ductility
mum ductility (%EL) of 27%. If the metal may (C) An increased tensile strength and an increased
be cold worked, decide which of the following are ductility
candidates: copper, brass, or a 1040 steel. Why?
(D) A decreased tensile strength and a decreased
7.D5 A cylindrical rod of 1040 steel originally ductility
11.4 mm (0.45 in.) in diameter is to be cold
worked by drawing; the circular cross section 7.2FE A dislocation formed by adding an extra half-
will be maintained during deformation. A cold- plane of atoms to a crystal is referred to as a (an)
worked tensile strength in excess of 825 MPa (A) screw dislocation
(120,000 psi) and a ductility of at least 12%EL
are desired. Furthermore, the final diameter (B) vacancy dislocation
must be 8.9 mm (0.35 in.). Explain how this may (C) interstitial dislocation
be accomplished. (D) edge dislocation

7.D6 A cylindrical rod of brass originally 10.2 mm 7.3FE The atoms surrounding a screw dislocation
(0.40 in.) in diameter is to be cold worked experience which kinds of strains?
by drawing; the circular cross section will be
maintained during deformation. A cold-worked (A) Tensile strains
yield strength in excess of 380 MPa (55,000 psi) (B) Shear strains
and a ductility of at least 15%EL are desired. (C) Compressive strains
Furthermore, the final diameter must be 7.6 mm
(0.30 in.). Explain how this may be accomplished. (D) Both B and C