Bruce Mayer, PE
Registered Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-45: Materials of Engineering
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt

 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-14_Metal_MechProp-1.ppt

 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-14_Metal_MechProp-1.ppt

 In The USA the American Society for
Testing and Materials (ASTM) Sets
Many, Many Materials-Test Standards

Founded in 1898, ASTM International is a not-for-profit organization that provides a global forum for the development and publication of voluntary consensus standards for materials, products, systems, and services.
Over 30,000 individuals from 100 nations are the members of ASTM International, who are producers, users, consumers, and representatives of government and academia. In over 130 varied industry areas, ASTM standards serve as the basis for manufacturing, procurement, and regulatory activities. Formerly known as the American Society for Testing and Materials,
ASTM International provides standards that are accepted and used in research and development, product testing, quality systems, and commercial transactions around the globe.
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt

 Apply/Remove a SMALL Force Load to a Specimen
1. Initial 2. SMALL load 3. Unload bonds stretch return to initial
5
• F 
Force Load d
(lb or N)
• d 
Deformation in
Response to the
Load (in or m)
Engineering-45: Materials of Engineering
F
F
Linearelastic
ELASTIC means
REVERSIBLE
Non-Lineard elastic
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt

 Apply/Remove a LARGE Force Load to a Specimen
1. Initial 2. LARGE load bonds stretch
& planes shear
3. Unload
Planes
Still
Sheared
PLASTIC means
PERMANENT
Engineering-45: Materials of Engineering
6 d elastic+plastic F
F d plastic linear elastic linear elastic d plastic
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt
d


 Normalize Applied-Force to Supporting Area
 TENSILE Stress,
Ft
σ  SHEAR Stress,

Ft F
Area, A
Area, A Fs
 =
F t
A o original area before loading
Engineering-45: Materials of Engineering
7
Fs
Ft
F
• Engineering Stress Units →
N/m 2 (Pa) or lb/in 2 (psi)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt
Ft

• Simple tension: cable
F
Ao= cross sectional
Area (when unloaded)
 =
F
A o
F
• Simple shear: drive shaft
A c
M Fs
A o
Ski lift
(photo courtesy P.M. Anderson)
 =
Fs
A o
M
2R
Engineering-45: Materials of Engineering
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Note:  = M/ A o
R here.
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt
5

• Simple COMPRESSION:
A o
Balanced Rock, Arches
National Park
(photo courtesy P.M. Anderson)
Engineering-45: Materials of Engineering
9
Canyon Bridge, Los Alamos, NM
(photo courtesy P.M. Anderson)
Note: These are
COMPRESSIVE structural members
( σ < 0; i.e., a NEGATIVE number)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt
6

 BIAXIAL Tension  HYDROSTATIC Compression
Tank Surface
Pressurized tank
(photo courtesy
P.M. Anderson)
Surface
Element
 > 0
 z > 0
Engineering-45: Materials of Engineering
10
Fish under water
(photo courtesy
P.M. Anderson)
 h
< 0
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt


 TENSILE Strain d /2
 LATERAL Strain d
L
/2 w o
L d /2 d
L
/2 o
 SHEAR Strain
Engineering-45: Materials of Engineering
11 g
=
 x / y = tan

 x

 Engineering STRAIN Units
→ NONE (Dimensionless)
• To Save Writing Exponents
– µ-in/in
– µm/m y
90 º
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt
90 º 

 Std Specimen
 Tension Tester
 Other Tests
• Compression Test for
Brittle Materials
– e.g.; Concrete → GREAT in
Compression, Fractures in
Tension/Shear
• Torsion (twist) Test
– Drive Shafts, Torsion Bars for Vehicle Suspension
Engineering-45: Materials of Engineering
12
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt

13
 Consider a Tension Test With SMALL loads; Plotting σ vs. ε Find

 The Data Plots as a
E
Line Through the
Origin
• Thus σ  ε
1
Linearelastic

– The Constant of Proportionality is the Slope, E
 E is the “Modulus of Elasticity”, or
“Young’s Modulus”
• Linear Elastic Materials are said to follow
Hooke’s (spring) Law  =
E
 
Bruce Mayer, PE Engineering-45: Materials of Engineering
F simple tension test
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt
F

 During a Pull-Test the Material
CONTRACTS Laterally, ε
L
, as it

Extends Longitudinally, ε. Plotting

This Data Also Plots
L as a Line
• Thus ε
L
 ε
– The Constant of
Proportionality is the Slope,


  is “Poisson’s Ratio” as Defined by
 =  
L

1

F simple tension test
F
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt


 Data From
 vs. g
Shear
Stress Test

G
1 g g
 =
G g g
 Leads to Hooke’s
=
Law in Pure Shear arctan
   = arctan
• Where
– G 
Modulus of
Rigidity (Shear Modulus) http://www.efunda.com/materials/common_matl/Common_Matl.cfm?MatlPhase=Solid&MatlProp=M echanical#Mechanical
Engineering-45: Materials of Engineering
15
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt

P
 Data From
P vs.

V
Tests -K
1
 Leads to Hooke’s
Law in Pure
HydroStatic
Compression

V
P
= 
K
V
O
Engineering-45: Materials of Engineering
16
 V
Vo
P
P
P
Pressure
Test:
Init. vol =V o
.
Vol chg. =  V
• Where
– K 
Modulus of
Compression
(Bulk Modulus) in GPa or Mpsi
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt
P

 Uniaxial Tension
 =
• Also Poisson’s Ratio
 =  
L

 Pure Shear
 =
G g
17
 All-Over
Compression
P
= 
K

V
V
O
Engineering-45: Materials of Engineering
 Isotropic Material
“Modulus Relations”
G
K
=
E
=
E 3
2


1
1

 
2



 Steel Properties
• E = 190-210 GPa
• G = 75-80 GPa
• K = 150-160 GPa
• 
= 0.27-0.3
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt

18
Metal
Young's Modulus
E (Mpsi)
Shear modulus,
G (Mpsi)
Bulk Modulus,
K (Mpsi)
Poisson's ratio, 
0.3
Aluminum 10.2
3.8
10.9
Brass, 30 Zn
Chromium
Copper
Iron (soft)
Iron (cast)
Lead
Magnesium
Molybdenum
Nickel (soft)
Nickel (hard)
Nickel-silver, 55CU-18Ni-27Zn
Niobium
Silver
Steel, mild
Steel, 0.75 C
Steel, 0.75 C, hardened
Steel, tool
Steel, tool, hardened
Steel, stainless, 2Ni-18Cr
Tantalum
Tin
Titanium
Tungsten
Vanadium
Zinc
30.5
29.2
30.7
29.5
31.2
26.9
7.2
17.4
59.6
18.5
15.2
47.1
28.9
31.8
19.2
15.2
12.0
30.7
14.6
40.5
18.8
30.7
22.1
2.3
6.5
11.8
11.3
11.9
11.4
12.2
10.0
2.7
6.6
23.3
6.8
6.1
18.2
11.0
12.2
5.0
5.4
4.4
11.9
5.4
16.7
7.0
11.8
8.7
0.8
2.5
24.5
23.9
24.0
24.0
24.1
28.5
8.4
15.7
45.1
22.9
10.1
37.9
25.7
27.2
19.1
24.7
15.0
24.5
16.2
23.2
20.0
24.6
15.9
6.6
5.2
0.4
0.3
0.4
0.2
0.3
0.3
0.3
0.3
0.3
0.3
0.4
0.3
0.3
0.3
0.3
0.4
0.4
0.3
0.4
0.2
0.3
0.3
0.3
0.4
0.3
Bruce Mayer, PE Engineering-45: Materials of Engineering
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt

Metals
Alloys
Graphite
Ceramics
Semicond
Polymers
Composites
/fibers
1200
1000
800
600
400
E (GPa)
200
100
80
60
40
Diamond
Tungsten
Molybdenum
Steel, Ni
Tantalum
Platinum
Cu alloys
Zinc, Ti
Silver, Gold
Aluminum
Magnesium,
Tin
Si carbide
Al oxide
Si nitride
<111>
Si crystal
<100>
Glass -soda
Concrete
Carbon fibers only
CFRE(|| fibers)*
Aramid fibers only
A FRE(|| fibers)*
Glass fibers only
GFRE(|| fibers)*
E ceramics
E metals
>
>>
E polymers
10 9 Pa
20
10
8
6
4
2
1
0.8
0.6
0.4
Graphite
0.2
Engineering-45: Materials of Engineering
19
Polyester
PET
PS
PC
PP
HDP E
PTFE
LDPE
GFRE*
CFRE*
GFRE( fibers)*
CFRE( fibers) *
AFRE( fibers) *
Epoxy only
Wood( grain)
Based on data in Table B2,
Callister 7e .
Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers.
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt

 Affect of Temperature on an Aluminum Alloy
 In General for Increasing T
20
• E↓
• d
L
↑ at Fracture
•  ↓ at Fracture
Engineering-45: Materials of Engineering Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt

 UniAxial Tension
F d
/2
 Simple Torsion, Solid
Cylinder
M=moment
 =angle of twist
Ao
L o
Lo w o
 =
2 ML o p r
4 o
G d
L
/2
2ro d = FL o
E A o d
L
=   Fw o
E A o
– Material, geometric, and loading parameters contribute to deflection
– Larger elastic moduli minimize elastic deflection
Engineering-45: Materials of Engineering
21
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt

6.66 kN
 Consider this Situation:
 Given for Cu
• E = 110 GPa (16 Mpsi)
•  y
= 240 MPa (35 ksi)
 Find PreLoad/PreStrain
Diameter, d , for a
PostLoad/PostStrain
Axial Extension δ = 0.5 mm
Cu d
6.66 kN
380 mm
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-14_Metal_MechProp-1.ppt