Elastic Deformation
1. Initial
2. Small load
3. Unload
bonds
stretch
return to
initial
δ
F
F
Linearelastic
δ
Chapter 6: Mechanical properties of metals
Non-Linearelastic
MAE 20
1
Plastic Deformation (Metals)
1. Initial
2. Small load
bonds
stretch
& planes
shear
δelastic + plastic
3. Unload
planes
still
sheared
δplastic
F
F
linear
elastic
linear
elastic
δplastic
Chapter 6: Mechanical properties of metals
MAE 20
δ
2
1
Tension and compression tests
Chapter 6: Mechanical properties of metals
MAE 20
3
Shear test
F
Ao
θ
F
Chapter 6: Mechanical properties of metals
MAE 20
4
2
Linear Elastic Properties
σ
E
ε
Linearelastic
F
F
simple
tension
test
Chapter 6: Mechanical properties of metals
MAE 20
5
Poisson’s ratio
εz
εx
εy
εx
εy
εz
Chapter 6: Mechanical properties of metals
MAE 20
6
3
Other Elastic Properties
τ
M
G
M
P
K
Chapter 6: Mechanical properties of metals
simple
torsion
test
γ
P
ΔV P
Vo
MAE 20
P
pressure
test: Init.
vol =Vo.
Vol chg.
= ΔV
7
Useful linear elastic relationships
F
Ao
wo
Lo
Chapter 6: Mechanical properties of metals
MAE 20
8
4
Plastic deformation
Chapter 6: Mechanical properties of metals
MAE 20
9
Yield strength
σy
elastic
plastic
0.002
Chapter 6: Mechanical properties of metals
MAE 20
10
5
engineering
stress
Tensile strength, TS
Typical response of a metal
strain
engineering strain
Chapter 6: Mechanical properties of metals
MAE 20
11
Ductility
Engineering
tensile
stress, σ
smaller %EL
larger %EL
Lo
Ao
Af
Lf
Engineering tensile strain, ε
Chapter 6: Mechanical properties of metals
MAE 20
12
6
Toughness
Engineering
tensile
stress, σ
Engineering tensile strain,
Chapter 6: Mechanical properties of metals
ε
MAE 20
13
Resilience
σy
0.002
Chapter 6: Mechanical properties of metals
MAE 20
εy
14
7
Elastic Strain Recovery
Stress
D
Strain
Chapter 6: Mechanical properties of metals
MAE 20
15
True stress and true strain
Ao
Ai
Chapter 6: Mechanical properties of metals
MAE 20
16
8
True stress and true strain
TS
Chapter 6: Mechanical properties of metals
MAE 20
17
Strain hardening
failure
σ
true
corrected
TS
engineering
failure
ε
Chapter 6: Mechanical properties of metals
MAE 20
18
9
log (true plastic stress, σPT)
log-log plot to determine K, n
0.0010
0.010
0.10
1.0
log (true plastic strain, εPT)
Chapter 6: Mechanical properties of metals
MAE 20
19
Hardness
e.g.,
10 mm sphere
apply known force
brasses
Al alloys
Smaller indents
mean larger
hardness.
d
D
most
plastics
measure size
of indent after
removing load
easy to machine
steels
file hard
cutting
tools
nitrided
steels
diamond
increasing hardness
Chapter 6: Mechanical properties of metals
MAE 20
20
10
Hardness scales
Chapter 6: Mechanical properties of metals
MAE 20
21
Relationship between
hardness and tensile
strength for some
metals
Chapter 6: Mechanical properties of metals
MAE 20
22
11