Manufacturing Processes

Dr Simin Nasseri
Groover’s Chapter 3 Problems:
3.20

A metal alloy has been tested in a tensile test with the following results for the flow curve
parameters: strength coefficient = 620.5 MPa and strain

hardening exponent = 0.26.
The same metal
is now tested in a compression test in which the starting height of the specimen = 62.5 mm and its
diameter = 25 mm. Assuming that the cross section increases uniformly, determine the load
required to compress the specimen to a height of (a
) 50 mm and (b) 37.5 mm.
Solution
: Starting volume of test specimen
V
= π
hD
o
2
/4 = 62.5π(25)
2
/4 = 30679.6 mm
3
.
(a) At
h
= 50 mm, ε = ln(62.5/50) = ln(1.25) = 0.223
Y
f
= 620.5(.223)
.26
= 420.1 MPa
A
=
V
/
L
= 30679.6/50 = 613.6 mm
2
F
= 420.1(613.6) =
257,7
70 N
(b) At
h
= 37.5 mm, ε = ln(62.5/37.5) = ln(1.667) = 0.511
Y
f
= 620.5(0.511)
.26
= 521.1 MPa
A
= V/L = 30679.6 /37.5 = 818.1 mm
2
F
= 521.1(818.1) =
426,312 N
3.23
A bend test is used for a certain hard material. If the transverse rupture strengt
h of the material
is
known to be 1000 MPa, what is the anticipated load at which the specimen is likely to fail, given
that
its dimensions are: width of cross section = 15 mm, thickness of cross section = 10 mm, and
length =
60 mm?
Solution
:
F
= (
TRS
)(
bt
2
)/1.5
L
= 1000(15 x 10
2
)/(1.5 x 60) =
16,667 N.
3.30
In a Brinell hardness test, a 1500 kg load is pressed into a specimen using a 10 mm diameter
hardened steel ball. The resulting indentation has a diameter = 3.2 mm. Determine the Brinell
hardness number for the metal.
Solution
:
HB
= 2(1500)/(10π(10

(10
2

3.2
2
)
.5
) = 3000/(10π x 0.5258) =
182 BHN
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