Page 241 - Materials Science and Engineering An Introduction

Questions and Problems • 213

(b) Compute the final specimen length when the 47.3 48.7 47.1
load is increased to 23,500 N (5280 lb f ) and then 52.1 50.0 50.4
released.
45.6 46.2 45.9
6.53 A steel alloy specimen having a rectangular 49.9 48.3 46.4
cross section of dimensions 19 mm * 3.2 mm
3
1
( in. * in.) has the stress–strain behavior shown 47.6 51.1 48.5
4
8
in Figure 6.22. This specimen is subjected to a ten- 50.4 46.7 49.7
sile force of 110,000 N (25,000 lb f ).
(a) Determine the elastic and plastic strain values. 6.61 The following table gives a number of yield
strength values (in MPa) that were measured on
(b) If its original length is 610 mm (24.0 in.), what the same aluminum alloy. Compute average and
will be its final length after the load in part (a) is standard-deviation yield strength values.
applied and then released?
274.3 277.1 263.8
Hardness 267.5 258.6 271.2
6.54 (a) A 10-mm-diameter Brinell hardness indenter 255.4 266.9 257.6
produced an indentation 2.50 mm in diameter in 270.8 260.1 264.3
a steel alloy when a load of 1000 kg was used.
Compute the HB of this material. 261.7 279.4 260.5
(b) What will be the diameter of an indentation
to yield a hardness of 300 HB when a 500-kg load Design/Safety Factors
is used? 6.62 Upon what three criteria are factors of safety
6.55 (a) Calculate the Knoop hardness when a 500-g based?
load yields an indentation diagonal length of 6.63 Determine working stresses for the two alloys
100 m. that have the stress–strain behaviors shown in

(b) The measured HK of some material is 200. Figures 6.12 and 6.22.
Compute the applied load if the indentation di-
agonal length is 0.25 mm. Spreadsheet Problem
6.56 (a) What is the indentation diagonal length when 6.1SS For a cylindrical metal specimen loaded in
a load of 0.60 kg produces a Vickers HV of 400? tension to fracture, given a set of load and
(b) Calculate the Vickers hardness when a 700-g corresponding length data, as well as the pre-
load yields an indentation diagonal length of deformation diameter and length, generate a
0.050 mm. spreadsheet that allows the user to plot (a) en-
gineering stress versus engineering strain, and
6.57 Estimate the Brinell and Rockwell hardnesses (b) true stress versus true strain to the point of
for the following:
necking.
(a) The naval brass for which the stress–strain
behavior is shown in Figure 6.12.
(b) The steel alloy for which the stress–strain DESIGN PROBLEMS
behavior is shown in Figure 6.22. 6.D1 A large tower is to be supported by a series of
6.58 Using the data represented in Figure 6.19, spec- steel wires; it is estimated that the load on each
ify equations relating tensile strength and Brinell wire will be 13,300 N (3000 lb f ). Determine the
hardness for brass and nodular cast iron, similar to minimum required wire diameter, assuming a fac-
Equations 6.20a and 6.20b for steels. tor of safety of 2.0 and a yield strength of 860 MPa
(125,000 psi) for the steel.
Variability of Material Properties 6.D2 (a) Consider a thin-walled cylindrical tube
6.59 Cite five factors that lead to scatter in measured having a radius of 65 mm that is to be used to
transport pressurized gas. If inside and outside
material properties. tube pressures are 100 and 2.0 atm (10.13 and
6.60 The following table gives a number of Rockwell 0.2026 MPa), respectively, compute the mini-
G hardness values that were measured on a single mum required thickness for each of the fol-
steel specimen. Compute average and standard- lowing metal alloys. Assume a factor of safety
deviation hardness values. of 3.5.