Engineering 45
Mechanical
Properties of
Metals (2)
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-45: Materials of Engineering
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Learning Goals.1 – Mech Props
 STRESS and STRAIN:
• What they are and why they are they used
instead of LOAD and DEFORMATION
 ELASTIC Behavior
• How much deformation occurs when Loads
are SMALL?
• Which materials deform least
Engineering-45: Materials of Engineering
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Learning Goals.2 – Mech Props
 PLASTIC Behavior
• Determine the point at which Dislocations
cause PERMANENT deformation
• Which materials are most resistant to
Permanent Deformation
 TOUGHNESS and DUCTILITY
• What they are
• How to Measure them
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Properties of Solid Materials
 Mechanical: Characteristics of
materials displayed when forces and/or
torques are applied to them.
 Physical: Characteristics of materials
that relate to the interaction of materials
with various forms of energy.
 Chemical: Material characteristics that
relate to the structure of a material.
 Dimensional: Size, shape, and finish
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Material Properties
Chemical
Physical
Mechanical
Dimensional
Composition
Melting Point
Tensile properties
Standard Shapes
Microstructure
Thermal
Toughness
Standard Sizes
Phases
Magnetic
Ductility
Surface Texture
Grain Size
Corrosion
Crystallinity
Molecular Weight
Electrical
Optical
Acoustic
Gravimetric
Fatigue
Hardness
Creep
Compression
Stability
Mfg. Tolerances
Flammability
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Recall ELASTIC Deformation
 Apply/Remove a SMALL Force-Load to a Specimen
1. Initial
3. Unload
2. SMALL load
bonds
stretch
return to
initial
d
• F  Force Load
(lb or N)
• d  Deformation in
Response to the
Load (in or m)
Engineering-45: Materials of Engineering
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F
F
Linear- ELASTIC means
elastic REVERSIBLE
Non-Linearelastic
d
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Recall PLASTIC Deformation
 Apply/Remove a LARGE Force Load to a Specimen
1. Initial
2. LARGE load
bonds
stretch
& planes
shear
delastic+plastic
PLASTIC means
PERMANENT
Engineering-45: Materials of Engineering
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F
3. Unload
Planes
Still
Sheared
dplastic
F
linear
elastic
linear
elastic
dplastic
d
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Plastic Deformation -
 Simple Tension Test (Temperature <Tmelt/3)
Elastic+Plastic
at larger stress
Tensile
Stress,
Elastic
initially
P
Engineering-45: Materials of Engineering
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Elastic Recovery
permanent (plastic)
after load is removed
engineering strain, 
plastic strain
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
YIELD Strength, y
 Define YIELD Strength as the Stress at Which
NOTICEABLE Plastic Deformation Occurs
• Define NOTICEABLE as 0.2% → P = 0.002 (0.2%)
• For Matl’s WithOUt a
well Defined Yield Pt
σy = σ(ε = 0.2%)
 For a 2” gage-length
• ΔL = 2”•0.002
= 0.004” (0.1 mm)
Engineering-45: Materials of Engineering
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y
tensile stress, 
 σy ≡ Yield Strength
engineering strain, 
P = 0.002
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Yield Strength: Comparison
y,ceramics >>
y,metals >>
y,polymers
Room T values
Based on data in Table B4,
Callister 6e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
Engineering-45: Materials of Engineering
10
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
TENSILE/ULTIMATE Strength
 Define TENSILE/ULTIMATE Strength (TS/σu)
as the MAX-σ Point on the σ-ε Curve
• Metals: occurs when
noticeable
NECKING starts
• Ceramics: occurs when
CRACK PROPAGATION
starts
• Polymers: occurs when
POLYMER BACKBONES
are aligned and about to
break
engineering stress
TS
y
engineering strain
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Tensile Strength: Comparison
TSceramics 
TSmetals 
TScomp >>
TSpolymers
Room T values
Engineering-45: Materials of Engineering
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Based on data in Table B4,
Callister 6e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
AFRE, GFRE, & CFRE =
aramid, glass, & carbon
fiber-reinforced epoxy
composites, with 60 vol%
fibers. Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Ductility → Strain at Fracture
 At Tensile Fracture Define Ductility
in Terms of ELONGATION
Engineering
tensile
stress, 
smaller %EL
(brittle if %EL<5%)
Larger %EL
(ductile if
%EL>5%)
Lo
Ao
Af
Engineering tensile strain, 
 Plastic Strain At
Tensile Failure
Engineering-45: Materials of Engineering
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% EL 
L f  Lo
Lo
100
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Lf
Ductility → Strain at Fracture
 Alternative Definition  Note: %RA and %EL
is Reduction of Area
Tend to Be Quite
Comparable
Lo
Ao
Af
Lf
 RA Ductility
% RA 
Ao  A f
Ao
Engineering-45: Materials of Engineering
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100
• Reason: crystal slip
does not change
material VOLUME.
• %RA < %EL possible
if internal voids form
in neck.
• %EL is More
Common Than
%RA
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Desirable Mechanical Properties
 Without
Considering Such
Factors Cost,
Weight, Weldability,
etc., The Typically
Desired
Combination of
Strength and
Ductility
• HIGH σy
 σy, is the Mechanical
DESIGN
PARAMETER, not
The Ultimate
Strength
• YIELDING
permanently deforms
(bends) Structures;
typically rendering
them NON-functional
• HIGH %EL
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Resilience → Energy Storage
 Consider the σ·ε
Product
F dL F  dL
  

A L
A L
 Next Consider the
σ-ε Curve in the
Elastic Range
dU 
 Now
• F•δL has Units of
ENERGY (J)
  d
• A•L has Units of
Volume (cu-m)
 Let U → J/m3
Engineering-45: Materials of Engineering
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dε
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Resilience cont.
y

 In The Elastic Range U 
d
r
0.002
the Material
Stretches and then
 In the Elastic Range
Returns to the
  E   &  y 0.002 so
Original Size
 y  y E & d  d E
 Thus Define
Resilience, Ur, as the  Then the Ur Integral
2 y
REVERSIBLE
y
 
U r  E  d  E  
Energy Storage
0
2 0

• U → Area under σ·ε
r
curve in elastic Rng
Engineering-45: Materials of Engineering
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Ur  
2
y
2E
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
E
Toughness
 An Extension of RESILIENCE Beyond the
Elastic Range to Plastic-Flow & Fracture
 A Measure of the TOTAL Energy-per-Vol
Absorbance Capability of a Material
•  to the Total Plastic-Def. Area under the σ-ε curve
, Engineering
Tensile Stress
smaller toughness (ceramics)
larger toughness
(metals, some composites)
smaller toughnessunreinforced
polymers
Engineering tensile strain, 
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
TRUE Stress & Strain
 Engineering Stress
  F Ao
• F  Applied Pull
• Ao  Original Area
 But the Specimen
NECKS-DOWN,
Reducing the Area
• So the TRUE Stress
 T  F Ai
• Ai  Instantaneous
Area = f(σ) or f(ε)
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
TRUE Stress & Strain cont
 Engineering Strain
Original
(UnLoaded)
L0
  L Lo
 In the Instantaneous
Case (see Rt)
Load at
Instant “i”
d i  dx' x'Pt P '
• Integrating

T
0
Li
Li
d i   dx' x'
Lo
 T  ln x'
Li
L0
Engineering-45: Materials of Engineering
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 Thus
 T  ln Li   ln Lo 
 T  ln Li Lo 
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Engineering/True Stress/Strain
 For Strain
 T  ln Li Lo 
Ao Lo
F
 T  ; but Ai 
Ai
Li
 Lo  L 
FLi
Li
F Li


;
  T 
 ln 
Ao Lo Ao Lo
Lo
 Lo 
and Li  Lo  L;
 T  ln 1   
 Now Assume
Constant Material
VOLUME
Ao Lo  Ai Li
Engineering-45: Materials of Engineering
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Li Lo  L

 (1   )
Lo
Lo
 T   (1   )
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Plastic Behavior → -
Stress
True Stress - Strain
Curve
Fracture
Ultimate Tensile Strength
Engineering
Stress - Strain
Curve
Fracture
Strain
Typical Metal
Engineering-45: Materials of Engineering
22
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Typ. Work-Hardening Parameters
 For Most Metals, True Stress Increases
in the Plastic Range (not ElastoPlastic)
Log(true stress, T) MPa
• The Material “Hardens” as it is WORKED
K
 T , plas
Note : Log (1)  0
 K 

 yintercept  K
fracture
n
T , plas
n  slope
necking
0.0010
0.010
0.10
Log (true plastic strain, T)
Engineering-45: Materials of Engineering
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1.0
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Strain-Hardening
 K  Work-Hardening Prefactor in MPa or Ksi
 n  Work-Hardening Exponent (unitless)
Material
1020 Steel
4340 Steel
2024 Al Alloy
304 Stainless Steel
70/30 Brass
Yield Stress
(MPa)
300
400
350
210
75
Engineering-45: Materials of Engineering
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Ultimate
Stress (MPa)
420
600
400
550
300
Elastic
Modulus
(MPa)
207000
207000
72000
185000
110000
K
(MPa)
n
530
640
690
1275
900
0.26
0.15
0.16
0.45
0.49
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Elastic Recovery
 When a material is
released prior to
fracture:
• Some of the total
energy is stored
elastically
• Some is absorbed by
the plastic
deformation
• The plastic
deformation energy
represents the lattice
strains.
Engineering-45: Materials of Engineering
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 The elastic energy will
be recovered once the
material is released
• i.e., the material
will unstretch
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Elastic Recovery cont.

To determine the
amount that the
material recovers:
1. draw a line
PARALLEL to the
elastic modulus line
that goes back to
the strain axis
2. The difference in
strains provides the
recovered length
3. The area under this
line is the
recovered energy
Engineering-45: Materials of Engineering
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3
1
Elastic
Energy, Ur
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Hardness
 Short Definition = Resistance to
Penetration
 Metals HandBook
"Resistance of metal to plastic deformation, usually by
indentation. However, the term may also refer to
stiffness or temper, or to resistance to scratching,
abrasion, or cutting. It is the property of a metal, which
gives it the ability to resist being permanently, deformed
(bent, broken, or have its shape changed), when a load
is applied. The greater the hardness of the metal, the
greater resistance it has to deformation.
Engineering-45: Materials of Engineering
27
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Hardness, cont.
 Hardness  Resistance to Plastic Indentation
 LARGE Hardness Indicates Properties:
• Resistance to plastic deformation or cracking
when loaded in COMPRESSION
• Better Wear Resistance
e.g.,
10mm sphere
apply known force
(1 to 1000 kg)
Smaller indents
mean larger
hardness
d
D
most
plastics
measure size
of indent after
removing load
brasses easy to machine
Al alloys steels
file hard
cutting
tools
nitrided
steels
diamond
increasing hardness
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
WhiteBoard Work
Engineering-45: Materials of Engineering
29
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt
Elastic Strain RECOVERY
Parallel
Lines
Ur
Engineering-45: Materials of Engineering
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 When a PostYield Load is
Removed the
Material
Recovers along
a Line
PARALLEL to
the initial
ELASTIC
extension Line
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-15_Metal_MechProp-2.ppt