Good Manufacturing Practices (GMP), Good Laboratory Practices ...
ME383 Modern Manufacturing Practices
32
1 ME 383 Modern Manufacturing Practices Lecture Note #3 Stress-Strain & Yield Criteria Dr. Y.B. Guo Mechanical Engineering The University of Alabama
-
Upload
colin-vega -
Category
Documents
-
view
44 -
download
0
description
ME383 Modern Manufacturing Practices. Lecture Note #3 Stress-Strain & Yield Criteria Dr. Y.B. Guo Mechanical Engineering The University of Alabama. Today’s Lecture. Engineering Stress & Strain True Stress & Strain Engineering Stress/Strain vs. True Stress/Strain Stress – Strain Curves. - PowerPoint PPT Presentation
Transcript of ME383 Modern Manufacturing Practices
1
ME 383
Modern Manufacturing Practices
Lecture Note #3
Stress-Strain & Yield Criteria
Dr. Y.B. GuoMechanical Engineering
The University of Alabama
2
Today’s Lecture
• Engineering Stress & Strain• True Stress & Strain• Engineering Stress/Strain vs. True Stress/Strain• Stress – Strain Curves
3
Deformation Mode
• Basic Deformation Mode
Tension or Compression
Torsion
4
Tensile Test Simulation
5
Tensile Test Simulation
6
Engineering Stress & Strain - Tension
• Engineering Stress
• Engineering Strain (compression vs. tension)
P
P
l 0l
A
0A
x
y
)(min 0
psiA
P
AreaalNor
Force
(%)min 0
0
0 l
ll
l
l
LengthalNor
ChangeLengthe
7
Engineering Stress & Strain - Tension
• Elongation
• Ductility (Reduction of Area)
P
P
fl 0l
fA
0A
x
y
1000
0
l
llElongation f
100Re0
0
A
AAareaofduction f
8
Engineering Stress & Strain - Tension
• Poisson’s Ratio ( ~ 0.3)
P
P
fl 0l
fA
0A
x
y
y
x
9
Shear Stress & Strain
• Shear Stress
• Shear Strain
F
FAA
F
a
b tanb
a
10
True Stress & Strain
• More Accurate Measurement
• True Stress
• True Strain
P
P
l 0l
A
0A
x
y
A
P
AreaeousIns
Force
tantan
D
D
D
D
A
A
l
l 0
2
00
0
ln2lnlnln
11
Engineering Stress/Strain vs. True Stress/Strain
• True Stress & Engineering Stress (Up to necking)
• True Strain & Engineering Strain (Up to necking)
el
l
l
ll
l
l
A
P
l
lAP
A
P
11 00
00
00
0000
el
ll
l
l
1lnlnln
0
0
0
12
Engineering Stress-Strain Curve
X
0l
el
ul
fl
0e ue fe
Neck
Y
UTS
Fracture
PlasticElastic
E
Y
Offset, 0.2%
l
13
Engineering Stress-Strain Curve (Cont’d)
• Young’s Modulus : slope of the of the elastic range
• Yield Strength : stress required to generate permanent deformation
• Tensile Strength : maximum stress
• Flow Stress: stress causes continuous deformation after yielding
• Failure Stress: stress when the material fractures
E
Y
UTS
14
True Stress-Strain Curve
• Constitutive Eq.
(plastic range)
• :strength coefficient
(true stress at unit true strain)
• :strain hardening exponent
nK
K
n
logloglog nK
Log
log
Klogn
1
True
Eng.
f
15
True Stress-Strain Curve (Cont’d)
• True Strain Equals to the “n” Value at Necking, i.e., Max Load (only occurs in tension)
• Proof
eAAA
A0
0ln
ee
d
dA
d
dPeAAP 00
nKd
ddPneckingAt
,0,
nKnK nn 1
P
16
Example 1
• A strip of metal of 1.5m long is stretched in three steps: to length of 2.0m, then to 2.5m, finally to 3.0m. Calculate engineering and true strain.
• Solution:
Engineering Strain
totaltotalf
total
total
eel
lle
eeee
l
lle
l
lle
l
lle
15.1
5.10.3
783.0
200.05.2
5.20.3
250.00.2
0.25.2
333.05.1
5.10.2
0
0
321
2
233
1
122
0
011
17
Example 1 (Cont’d)
• True Strain
totaltotalf
total
total
eel
l
l
l
l
l
l
l
693.05.1
0.3lnln
693.0
182.05.2
0.3lnln
223.00.2
5.2lnln
288.05.1
0.2lnln
0
321
2
33
1
22
0
11
18
Example 2
• Calculate True and Engineering
• at necking
psi5.0000,100 UTS
n
psiA
P
AP
eAAP
eAAnA
A
Kn
UTS
neckneck
n
850,42
850,42
5.0ln
707105.0000,001
0
0
5.00
5.00
0
5.0
19
End
• Questions ?
20
Today’s Lecture
• Stress-Strain State:• Hooke’s Law• Yield Criteria:
1) Tresca 2) von Mises
• Effective Stress and Strain• Work of Deformation and Temperature
• Case Studies
21
Stress State - Triaxial Stress
• Equilibrium:
• Principal Stress
0iF
0iM
1
2
3321
22
Strain State - Triaxial Strain
• Principal Strain
1
2
3
321
23
Stress-Strain Relationship in Triaxial State
• Generalized Hooke’s Law
• Example: In Tension,
2133
3122
3211
1
1
1
E
E
E
032
E
E
132
11
24
Yield Criteria
• Tresca• von Mises
• Difference < 15%• Ductile Mat’s Breaks at Max. Shear Stress,
while Brittle at Max. Normal Stress
y ),,max( 313221
2231
232
221 2 y
25
Effective Stress and Effective Strain
• Convenient Way of Expressing the Stress State
• Effective Stress - based on principal stress
• Effective Stress - based on normal stress
21231
232
221
31
2
1
5.0222222 62
1xzyzxyzxzyyx
26
Effective Stress and Effective Strain
• Convenient Way of Expressing the Strain State
• Effective Strain (Tresca)
(von Mises)
313
2
21231
232
2213
2
27
Work of Deformation & Temp.
• Specific Energy (deformation work per unit volume)
• Work
• Temperature
332211 ddddu
0
du
volumeuW
c
uT
28
Example 1 - Stress State & yield
Q: P?
Tresca:
Von Mises:
t
r21
l
stressplaneshellthin
t
pr
rt
rp
A
FFrp
t
pr
tl
rlp
A
FFrlp
,0
22
2
22
3
2
2
222
2
1
111
r
tp
r
tp
t
pr
y
y
yyy
3
2
2 2231
232
221
31
29
Example 2 - Stress State & yield
Q: P?
0
22
22
3
2
2
222
2
2
1
111
2
t
pr
rt
rp
A
FFrp
t
pr
rt
rp
A
FFrp
r
tp
r
tp
t
pr
y
y
yy
yy
2
2
2
222
312
322
21
2131
Tresca:
Von Mises:
t
r2
1
30
Example 3 - Work and Temp.
Q: W and T?
0
22
22
3
2
2
222
2
2
1
111
2
t
pr
rt
rp
A
FFrp
t
pr
rt
rp
A
FFrp
t
r21
fr
011
2211
0
22
0
11
0021
ln22
ln2
2ln
21
r
r
ddu
r
r
r
r
fy
ff
31
Example 3 - Work and Temp.
c
r
r
c
uT
r
rtr
trr
r
VolumeuW
fy
fy
fy
0
00
20
02
00
ln2
ln8
)4()ln2(
32
End
• Questions ?
