manufacturing process

1. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Types of Strain
Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
FIGURE 2.1 Types of strain. (a) Tensile. (b) Compressive. (c) Shear. All
deformation processes in manufacturing involve strains of these types.Tensile
strains are involved in stretching sheet metal to make car bodies,
compressive strains in forging metals to make turbine disks, and shear strains
in making holes by punching.
(c)(b)(a)
lo
l
lo
l
a
b
g
e =
l −lo
lo
γ =
a
b
Engineering Strain:
Shear Strain:

2. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Tensile-Test
FIGURE 2.2 (a) Original and final shape of
a standard tensile-test specimen. (b)
Outline of a tensile-test sequence showing
different stages in the elongation of the
specimen.
(a) (b)
Original
gage
length, lo
Fracture
lf
tan-1 E
PlasticElastic
Stress
UTS
Y
Fracture
Strain (for lo = 1)
l
eueo ef
0
Offset
Af
Ao
Uniform elongation
Neck
Total elongation
Y
Post-uniform elongation
lo
le
lu
lf

3. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Mechanical Properties
TABLE 2.1 Typical mechanical properties
of various materials at room temperature.
See also Tables 10.1, 10.4, 10.8, 11.3 and
11.7.
Elongation Poisson’s
E (GPa) Y (MPa) UTS (MPa) in 50 mm (%) Ratio (ν)
METALS (WROUGHT)
Aluminum and its alloys 69-79 35-550 90-600 45-5 0.31-0.34
Copper and its alloys 105-150 76-1100 140-1310 65-3 0.33-0.35
Lead and its alloys 14 14 20-55 50-9 0.43
Magnesium and its alloys 41-45 130-305 240-380 21-5 0.29-0.35
Molybdenum and its alloys 330-360 80-2070 90-2340 40-30 0.32
Nickel and its alloys 180-214 105-1200 345-1450 60-5 0.31
Steels 190-200 205-1725 415-1750 65-2 0.28-0.33
Stainless steels 190-200 240-480 480-760 60-20 0.28-0.30
Titanium and its alloys 80-130 344-1380 415-1450 25-7 0.31-0.34
Tungsten and its alloys 350-400 550-690 620-760 0 0.27
NONMETALLIC MATERIALS
Ceramics 70-1000 — 140-2600 0 0.2
Diamond 820-1050 — — — —
Glass and porcelain 70-80 — 140 0 0.24
Rubbers 0.01-0.1 — — — 0.5
Thermoplastics 1.4-3.4 — 7-80 1000-5 0.32-0.40
Thermoplastics, reinforced 2-50 — 20-120 10-1 —
Thermosets 3.5-17 — 35-170 0 0.34
Boron fibers 380 — 3500 0 —
Carbon fibers 275-415 — 2000-5300 1-2 —
Glass fibers (S, E) 73-85 — 3500-4600 5 —
Kevlar fibers (29, 49, 129) 70-113 — 3000-3400 3-4 —
Spectra fibers (900, 1000) 73-100 — 2400-2800 3 —
Note: In the upper table, the lowest values for E, Y , and UTS and the highest values for
elongation are for the pure metals. Multiply GPa by 145,000 to obtain psi, and MPa by
145 to obtain psi. For example 100 GPa = 14,500 ksi, and 100 MPa = 14,500 psi.

4. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Loading & Unloading; Elongation
FIGURE 2.3 Schematic illustration of
loading and unloading of a tensile-test
specimen. Note that during unloading the
curve follows a path parallel to the original
elastic slope.
Elastic recovery
Permanent
deformation
Strain
Unload
Load
Stress
FIGURE 2.4 Total elongation in a tensile
test as a function of original gage length for
various metals. Because necking is a local
phenomenon, elongation decreases with
gage length. Standard gage length is usually
2 in. (50 mm), although shorter ones can
be used if larger specimens are not
available.
0 1 2 3 4 5 6 87 9 10
80
70
60
50
40
30
20
10
0
0 50 100 150 200 250
Elongation(%)
Gage length (in.)
mm
1100-O Aluminum
Mild steelStructural silicon steel
Magnesium
Copper
High-purityalum
i
num
-annealed
Brass
Monel

5. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
True Stress and True Strain
TABLE 2.2 Comparison of engineering and
true strains in tension
e 0.01 0.05 0.1 0.2 0.5 1 2 5 10
0.01 0.049 0.095 0.18 0.4 0.69 1.1 1.8 2.4
True stress
True strain
σ =
P
A
ε = ln
l
lo
= ln
Ao
A
= ln
Do
D
2
= 2ln
Do
D

6. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
True Stress - True Strain Curve
FIGURE 2.5 (a) True stress--true strain
curve in tension. Note that, unlike in an
engineering stress-strain curve, the slope is
always positive and that the slope
decreases with increasing strain. Although
in the elastic range stress and strain are
proportional, the total curve can be
approximated by the power expression
shown. On this curve, Y is the yield stress
and Yf is the flow stress. (b) True stress-
true strain curve plotted on a log-log
scale. (c) True stress-true strain curve in
tension for 1100-O aluminum plotted on a
log-log scale. Note the large difference in
the slopes in the elastic and plastic ranges.
Source: After R. M. Caddell and R. Sowerby.
True strain ( )
Truestress
K
Yf
Y
0
0 1 1 f
= K n
Fracture
(a)
n
Log
Log
(b)
(c)
n = 0.25
K = 25,000
0.0001 0.001 0.01 0.1 1
1
10
100
Y
Truestress(psix103)
n
1
True strain ( )

7. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Power Law Flow Rule
TABLE 2.3 Typical values for K and n in
Eq. 2.11 at room temperature.
Material K (MPa) n
Aluminum, 1100-O 180 0.20
2024-T4 690 0.16
5052-O 210 0.13
6061-O 205 0.20
6061-T6 410 0.05
7075-O 400 0.17
Brass, 7030, annealed 895 0.49
85-15, cold rolled 580 0.34
Bronze (phosphor), annealed 720 0.46
Cobalt-base alloy, heat treated 2070 0.50
Copper, annealed 315 0.54
Molybdenum, annealed 725 0.13
Steel, low carbon, annealed 530 0.26
1045 hot rolled 965 0.14
1112 annealed 760 0.19
1112 cold rolled 760 0.08
4135 annealed 1015 0.17
4135 cold rolled 1100 0.14
4340 annealed 640 0.15
17-4 P-H, annealed 1200 0.05
52100, annealed 1450 0.07
304 stainless, annealed 1275 0.45
410 stainless, annealed 960 0.10
Note: 100 MPa = 14,500 psi.
Flow rule:
σ = Kεn
K = Strength coefficient
n = Strain hardening exponent

8. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
True Stress-True Strain forVarious Materials
FIGURE 2.6 True stress-true strain
curves in tension at room
temperature for various metals. The
point of intersection of each curve at
the ordinate is the yield stress Y; thus,
the elastic portions of the curves are
not indicated. When the K and n
values are determined from these
curves, they may not agree with those
given in Table 2.3 because of the
different sources from which they
were collected. Source: S. Kalpakjian.
Copper, annealed
2024-T36 Al
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
0
40
60
80
100
120
140
160
180
1200
1000
800
600
400
0
True strain ( )
Truestress(psix103
)
MPa
304 Stainless steel
70–30 Brass, as received
70–30 Brass, annealed
1020 Steel
1100-O Al
1100-H14 Al
6061-O Al
2024-O Al
8650 Steel
1112 CR Steel
4130 Steel
200
20

9. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Idealized Stress-Strain Curves
FIGURE 2.7 Schematic illustration of various types of idealized stress-
strain curves. (a) Perfectly elastic. (b) Rigid, perfectly plastic. (c)
Elastic, perfectly plastic. (d) Rigid, linearly strain hardening. (e) Elastic,
linearly strain hardening. The broken lines and arrows indicate
unloading and reloading during the test.
(b) (c)
=Y + Ep!
(e)
Y
Y + Ep( -Y/E )
Y
(d)
(a)
Y
= Y
tan-1 E
tan-1 Ep
Strain
Stress
= EP
Y
= Y
Y/E
=E
Y/E
E
FIGURE 2.8 The effect of strain-hardening
exponent n on the shape of true stress-
true strain curves. When n = 1, the
material is elastic, and when n = 0, it is
rigid and perfectly plastic.
= K n
n = 1
0<n<1
n = 0K
0 1
True strain (P)
Truestress

10. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Temperature and Strain Rate Effects
FIGURE 2.9 Effect of temperature on mechanical properties
of a carbon steel. Most materials display similar temperature
sensitivity for elastic modulus, yield strength, ultimate
strength, and ductility.
0 200 400 600
(°C)
0 200 400 600 800 1000 1200 1400
Temperature (°F)
Stress(psi3103)
120
80
40
0
Stress(MPa)
600
400
200
0
Elongation
Elastic modulus
200
150
100
50
0
Elasticmodulus(GPa)
Elongation(%)
0
20
40
60
Tensile strength
Yield strength
200
100
50
10
1
2
4
6
8
10
20
30
40
10-6 10-4 10-2 100 102 104 106
Strain rate (s-1)
Tensilestrength(psix103)
800°
600°
400°
200°
30°C
MPa
1000°
FIGURE 2.10 The effect of strain rate on the
ultimate tensile strength of aluminum. Note that as
temperature increases, the slope increases. Thus,
tensile strength becomes more and more sensitive
to strain rate as temperature increases. Source:
After J. H. Hollomon.

11. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Typical Strain Rates in Metalworking
Process True Strain Deformation Speed (m/s) Strain Rate (s−1)
Cold Working
Forging, rolling 0.1-0.5 0.1-100 1 − 103
Wire and tube drawing 0.05-0.5 0.1-100 1 − 104
Explosive forming 0.05-0.2 10-100 10 − 105
Hot working and warm working
Forging, rolling 0.1-0.5 0.1-30 1 − 103
Extrusion 2-5 0.1-1 10−1 − 102
Machining 1-10 0.1-100 103 − 106
Sheet-metal forming 0.1-0.5 0.05-2 1 − 102
Superplastic forming 0.2-3 10−4 − 10−2 10−4 − 10−2
TABLE 2.4 Typical ranges of strain, deformation speed, and strain rates in metalworking
processes.

12. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Effect on Homologous Temperature
FIGURE 2.11 Dependence of the strain-
rate sensitivity exponent m on the
homologous temperature T/Tm for various
materials. T is the testing temperature and
Tm is the melting point of the metal, both
on the absolute scale.The transition in the
slopes of the curve occurs at about the
recrystallization temperature of the
metals. Source: After F.W. Boulger.
0
0.2 0.4 0.6 0.8 1.00
0.05
0.10
0.15
0.25
0.20
Copper
Steel
Aluminum
304 Stainless
Titanium
Rene 41
Mo-T2C
Strainratesensitivityexponent(m)
T
Tm
Homologous temperature,

13. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Strain Rate Effects
C
Material Temperature, ◦C psi × 103 MPa m
Aluminum 200-500 12-2 82-14 0.07-0.23
Aluminum alloys 200-500 45-5 310-35 0-0.20
Copper 300-900 35-3 240-20 0.06-0.17
Copper alloys (brasses) 200-800 60-2 415-14 0.02-0.3
Lead 100-300 1.6-0.3 11-2 0.1-0.2
Magnesium 200-400 20-2 140-14 0.07-0.43
Steel
Low carbon 900-1200 24-7 165-48 0.08-0.22
Medium carbon 900-1200 23-7 160-48 0.07-0.24
Stainless 600-1200 60-5 415-35 0.02-0.4
Titanium 200-1000 135-2 930-14 0.04-0.3
Titanium alloys 200-1000 130-5 900-35 0.02-0.3
Ti-6Al-4V∗ 815-930 9.5-1.6 65-11 0.50-0.80
Zirconium 200-1000 120-4 830-27 0.04-0.4
∗ at a strain rate of 2 × 10−4 s−1.
Note: As temperature increases, C decreases and m increases. As strain
increases, C increases and m may increase or decrease, or it may become
negative within certain ranges of temperature and strain.
Source: After T. Altan and F.W. Boulger.
TABLE 2.5 Approximate range of values for C and m in
Eq. (2.16) for various annealed metals at true strains
ranging from 0.2 to 1.0.
m = Strain-rate sensitivity exponent
C = Strength coefficient
σ = C˙εm

14. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Effect of Strain Rate Sensitivity on
Elongation
FIGURE 2.12 (a) The effect of strain-rate sensitivity exponent m on the total elongation for various metals.
Note that elongation at high values of m approaches 1000%. Source: After D. Lee and W.A. Backofen. (b) The
effect of strain-rate sensitivity exponent m on the post uniform (after necking) elongation for various metals.
Source: After A.K. Ghosh.
0.20.1 0.3 0.4 0.5 0.6 0.70
10
102
103
Totalelongation(%)
m
Ti–5A1–2.5Sn
Ti–6A1–4V
Zircaloy–4
High- and ultra-high-
carbon steels
0
0.060.040.020
10
30
20
50
40
m
Post-uniformelongation(%)
A-K Steel
HSLA Steel
C.R. Aluminum (1100)
2036-T4 Aluminum
3003-O Aluminum
5182-O Aluminum
5182-O Al (150C)
70-30 Brass
Zn-Ti Alloy
(a) (b)

15. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Hydrostatic Pressure & Barreling
FIGURE 2.13 The effect of hydrostatic pressure on
true strain at fracture in tension for various metals.
Even cast iron becomes ductile under high pressure.
Source: After H.L.D. Pugh and D. Green.
5
4
3
2
1
0 300 600 900
MPa
0
0 20 40 60 80 100 120
Truestrainatfracture(f)
Zinc
Copper
Aluminum
Magnesium
Cast iron
Hydrostatic pressure (ksi)
FIGURE 2.14 Barreling in compressing a
round solid cylindrical specimen (7075-O
aluminum) between flat dies. Barreling is
caused by friction at the die-specimen
interfaces, which retards the free flow of
the material. See also Figs.6.1 and 6.2.
Source: K.M. Kulkarni and S. Kalpakjian.

16. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Plane-Strain Compression Test
FIGURE 2.15 Schematic illustration of the plane-strain
compression test. The dimensional relationships shown
should be satisfied for this test to be useful and
reproducible. This test gives the yield stress of the
material in plane strain, Y’. Source: After A. Nadai and H.
Ford.
b
w
h
w > 5h
w > 5b
b > 2h to 4h
Yield stress in plane strain:
Y =
2
√
3
Y = 1.15Y

17. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Tension & Compression; Baushinger
Effect
FIGURE 2.16 True stress-true strain curve
in tension and compression for aluminum.
For ductile metals, the curves for tension
and compression are identical. Source: After
A.H. Cottrell.
Tension
Compression
0
4
8
12
16
Truestress(ksi)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
True strain ( )
MPa
100
50
0
FIGURE 2.17 Schematic illustration of the Bauschinger
effect.Arrows show loading and unloading paths. Note the
decrease in the yield stress in compression after the
specimen has been subjected to tension.The same result is
obtained if compression is applied first, followed by
tension, whereby the yield stress in tension decreases.
Y
2Y
P
Tension
Compression

18. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Disk & Torsion Tests
FIGURE 2.18 Disk test on a brittle
material, showing the direction of loading
and the fracture path.This test is useful for
brittle materials, such as ceramics and
carbides.
Fracture
P
P
σ =
2P
πdt
FIGURE 2.19 A typical torsion-test specimen. It is
mounted between the two heads of a machine and is
twisted. Note the shear deformation of an element in the
reduced section.
l
l
r
r
r r
t
τ =
T
2πr2t
γ =
rφ
l

19. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Simple vs. Pure Shear
FIGURE 2.20 Comparison of (a) simple shear and (b) pure shear. Note
that simple shear is equivalent to pure shear plus a rotation.
3
1
3
3
1 = - 3
2
3
1
1
(a) (b)

20. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Three- and Four-Point Bend-Tests
FIGURE 2.21 Two bend-test methods for brittle materials: (a) three-
point bending; (b) four-point bending.The shaded areas on the beams
represent the bending-moment diagrams, described in texts on the
mechanics of solids. Note the region of constant maximum bending
moment in (b), whereas the maximum bending moment occurs only at
the center of the specimen in (a).
(a) (b)
Maximum
bending
moment
σ =
Mc
I

21. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Hardness Tests
FIGURE 2.22 General
characteristics of hardness
testing methods.The Knoop test
is known as a microhardness
test because of the light load and
small impressions. Source: After
H.W. Hayden, W.G. Moffatt, and
V.Wulff.
Load, P Hardness number
Shape of indentation
Side view Top viewTest Indenter
60 kg
150 kg
100 kg
100 kg
60 kg
150 kg
100 kg
500 kg
1500 kg
3000 kg
25 g–5 kg
1–120 kg
L136°
HK =
14.2P
L2
HV =
1.854P
L2
HB =
( D)(D - D2 - d2 )
2P
t = mm
t = mm
120°
L
b
t
L/b = 7.11
b/t = 4.00
dd
D
= 100 - 500t
HRA
HRC
HRD
E
Rockwell
Knoop
Brinell
Vickers
A
C
D
B
F
G
HRE
= 130 - 500t
HRB
HRF
HRG
Diamond cone
10-mm steel
or tungsten
carbide ball
Diamond pyramid
Diamond pyramid
- in. diameter16
1
steel ball
- in. diameter8
1
steel ball

22. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Hardness Test Considerations
FIGURE 2.23 Indentation geometry for Brinell
hardness testing: (a) annealed metal; (b) work-
hardened metal. Note the difference in metal
flow at the periphery of the impressions.
(a) (b)
d
d
FIGURE 2.25 Bulk deformation in mild steel under a
spherical indenter. Note that the depth of the
deformed zone is about one order of magnitude
larger than the depth of indentation. For a hardness
test to be valid, the material should be allowed to
fully develop this zone.This is why thinner specimens
require smaller indentations. Source: Courtesy of
M.C. Shaw and C.T.Yang.
FIGURE 2.24 Relation between Brinell hardness and yield
stress for aluminum and steels. For comparison, the Brinell
hardness (which is always measured in kg/mm2) is converted
to psi units on the left scale.
Carbon steels,
annealed 5.3
1
3.2
3.4
1
1
Aluminum, cold worked
Carbon steels,
cold worked
MPa
100 200 300 400 500
250
200
150
100
50
0
Hardness(psix103)
10 20 30 40 50 60 70 80
Yield stress (psi x 103)
Brinellhardness(kg/mm2)
150
100
50
0

23. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Fatigue
FIGURE 2.26 Typical S-N curves for two
metals. Note that, unlike steel, aluminum
does not have an endurance limit.
0
500
400
300
200
100
0
80
60
40
20
1045
Steel
Endurance limit
Number of cycles, N
(a) (b)
psix103
Number of cycles, N
Stressamplitude,S(MPa)
0 0
2
4
6
psix103
8
10
20
30
40
50
60
Diallyl-phthalate
Nylon (dry)
P
olycarbonate
PolysulfonePTFE
103 104 105 107106 108 109 1010 103 104 105 106 107
20
14-T6 Aluminum alloy
Phenolic
Epoxy
Stressamplitude,S(MPa)
FIGURE 2.27 Ratio of fatigue strength to tensile strength
for various metals, as a function of tensile strength.
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 50 200
0 200 400 600 800 1000 1200
MPa
Endurancelimit/tensilestrength
Titanium
Steels
Cast irons
Copper alloys
Aluminum alloys
Wrought
magnesium alloys
Cast
magnesium
alloys
Tensile strength (psi x 103)
100 150
0.1
0

24. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Creep & Impact
FIGURE 2.28 Schematic illustration of a typical
creep curve. The linear segment of the curve
(constant slope) is useful in designing
components for a specific creep life.
Primary
Time
Tertiary
Strain
Instantaneous
deformation
Rupture
Secondary
Specimen
(10 x 10 x 75 mm)
Pendulum
Pendulum
Notch
Specimen
(10 x 10 x 55 mm)
(a) (b)
FIGURE 2.29 Impact test specimens: (a) Charpy;
(b) lzod.

25. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Residual Stresses
FIGURE 2.30 Residual stresses developed in bending a beam made of an elastic, strain-hardening material.
Note that unloading is equivalent to applying an equal and opposite moment to the part, as shown in (b).
Because of nonuniform deformation, most parts made by plastic deformation processes contain residual
stresses. Note that the forces and moments due to residual stresses must be internally balanced.
Tensile
Compressive
(a)
(b)
(c)
(d)
a b c
o
a
d
o
e
f

26. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Distortion due to Residual Stress
FIGURE 2.31 Distortion of parts with residual stresses after cutting or slitting: (a) rolled sheet or plate; (b)
drawn rod; (c) thin-walled tubing. Because of the presence of residual stresses on the surfaces of parts, a
round drill may produce an oval-shaped hole because of relaxation of stresses when a portion is removed.
(c)
(a)
Before After
Before After
Before After
(b)

27. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Elimination of Residual Stresses
FIGURE 2.32 Elimination of residual stresses by stretching. Residual stresses can be also reduced or
eliminated by thermal treatments, such as stress relieving or annealing.
Stress
(a) (b)
CompressiveTensile
t
c
(c)
Y
t
c
!t
!c
Tension
Y
(d)
Compression
2Y

28. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
State of Stress in Metalworking
FIGURE 2.33 The state of stress in various metalworking
operations. (a) Expansion of a thin-walled spherical shell under
internal pressure. (b) Drawing of round rod or wire through a
conical die to reduce its diameter; see Section 6.5 (c) Deep
drawing of sheet metal with a punch and die to make a cup; see
Section 7.6.
(a)
(b)
(c)
!1
!1
!1 !1
!1 !1
!3
!3
!3
!3
!3
!3
!2
!2
!2
!2

29. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Strain State in Necking
FIGURE 2.34 Stress distribution in the
necked region of a tension-test specimen.
a
Distribution of
axial stress
Distribution of
radial or
tangential stress
Maximum axial stress
Average axial true stress
= True stress in
uniaxial tension
R
1
2
3 Correction factor due to Bridgman:
σ
σav
=
1
1+
2R
a
1+
a
2R

30. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
States of Stress
FIGURE 2.35 Examples of states of stress:
(a) plane stress in sheet stretching; there
are no stresses acting on the surfaces of
the sheet. (b) plane stress in compression;
there are no stresses acting on the sides of
the specimen being compressed. (c) plane
strain in tension; the width of the sheet
remains constant while being stretched. (d)
plane strain in compression (see also Fig.
2.15); the width of the specimen remains
constant due to the restraint by the
groove. (e) Triaxial tensile stresses acting
on an element. (f) Hydrostatic
compression of an element. Note also that
an element on the cylindrical portion of a
thin-walled tube in torsion is in the
condition of both plane stress and plane
strain (see also Section 2.11.7).
(a)
(c)
(e)
(b)
(f)
(d)
p
p
p
p
p
p
!1
!1
!3
!1
!1
!3
!2
!2
!1 !3
!3
!3
!3
!1
!1
!3
!1
!3

31. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Yield Criteria
Tension
Y
Compression
Maximum-shear
stress criterion
Distortion-energy
criterion
Tension
Compression
Y
!1 !1
!1
!3
!3
!3 !1
!3
!3
!1
!1
!1 !1
!1
!3
!3
!3
!3
FIGURE 2.36 Plane-stress diagrams for maximum
-shear-stress and distortion-energy criteria.
Note that 2 = 0.
Maximum-shear-stress criterion:
Distortion-energy criterion:
σmax −σmin = Y
(σ1 −σ2)2
+(σ2 −σ3)2
+(σ3 −σ1)2
= 2Y2

32. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Flow Stress and Work of Deformation
FIGURE 2.37 Schematic illustration of
true stress-true strain curve showing yield
stress Y, average flow stress, specific
energy u1 and flow stress Yf.
Yf
Y
Y
Truestress
u1
True strain (!)
!10
0
Flow stress:
Specific energy
¯Y =
Kεn
1
n+1
u =
Z ε
0
¯σd¯ε

33. Manufacturing Processes for Engineering Materials, 5th ed.
Kalpakjian • Schmid
© 2008, Pearson Education
ISBN No. 0-13-227271-7
Ideal & Redundant Work
FIGURE 2.38 Deformation of grid patterns in a
workpiece: (a) original pattern; (b) after ideal
deformation; (c) after inhomogeneous deformation,
requiring redundant work of deformation. Note that
(c) is basically (b) with additional shearing, especially
at the outer layers.Thus (c) requires greater work of
deformation than (b). See also Figs. 6.3 and 6.49.
(a)
(b)
(c)
Total specific energy:
Efficiency:
utotal = uideal +ufriction +uredundant
η =
uideal
utotal