Chapter 6 - 1 • Stress and strain: What are they and why are they used instead of load and deformation? Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? • Plastic behavior: At what point does permanent deformation occur? What materials are most resistant to permanent deformation? • Toughness and ductility: What are they and how do we measure them? Mechanical Properties • Hardness: What is hardness of a material and how do we measure it?
Transcript
Chapter 6 - 1
• Stress and strain: What are they and why are they used instead of load and deformation?
• Elastic behavior: When loads are small, how much deformation occurs? What materials deform least?
• Plastic behavior: At what point does permanent deformation occur? What materials are most resistant to permanent deformation?
• Toughness and ductility: What are they and how do we measure them?
Mechanical Properties
• Hardness: What is hardness of a material and how do we measure it?
Chapter 6 -2
How materials deform as a function of applied load Testing methods and language for mechanical properties of materials.
Str
es
s,
(M
Pa
)
Strain, (mm / mm)
Chapter 6 - 3
Elastic means reversible!
Elastic Deformation
1. Initial 2. Small load 3. Unload
F
bonds stretch
return to initial
F
Linear- elastic
Non-Linear-elastic
Chapter 6 - 4
Plastic means permanent!
Plastic Deformation (Metals)
F
linear elastic
linear elastic
plastic
1. Initial 2. Small load 3. Unload
p lanes still sheared
F
elastic + plastic
bonds stretch & planes shear
plastic
Chapter 6 -
Forces and Responses
• Tensile – applied loads “pull” the sample
Chapter 6 - 6
Linear Elastic Properties
• Modulus of Elasticity, E: (also known as Young's modulus)
• Hooke's Law:
= E
Linear- elastic
E
F
Fsimple tension
test
Chapter 6 -
Tensile Forces
¾ inch
½ inch
8 ½ inches
Failure ZoneGripping Zone
Gripping Zone
Chapter 6 -
Forces and Responses
Compression: applied loads “squeeze” the sample
Chapter 6 - 9
Mechanical Properties• Slope of stress strain plot (which is proportional to the
elastic modulus) depends on bond strength of metal
Adapted from Fig. 6.7, Callister 7e.
Chapter 6 - 10
• Elastic Shear modulus, G:
G
= G
Other Elastic Properties
• Special relation for isotropic materials:
2(1 )EG
Chapter 6 - 11
Poisson's ratio,
• Poisson's ratio, :
Units:E: [GPa] or [psi]: dimensionless
L
-
L
metals: ~ 0.33ceramics: ~ 0.25polymers: ~ 0.40
Chapter 6 -
Plastic Deformation
Chapter 6 - 13
(Ultimate) Tensile Strength, TS
Adapted from Fig. 6.11, Callister 7e.
y
strain
Typical response of a metal
F = fracture or
ultimate
strength
Neck – acts as stress concentrator
eng
inee
ring
TS s
tres
s
engineering strain
• Maximum stress on engineering stress-strain curve.
Chapter 6 -
Ductility
Measures how much the material can be stretched before fracture
• The ability to absorb energy up to fracture =the total area under the strain-stress curve up to fractureUnits: the energy per unit volume, e.g. J/m3
Toughness
Brittle fracture: elastic energyDuctile fracture: elastic + plastic energy
very small toughness (unreinforced polymers)
Engineering tensile strain,
E ngineering
tensile
stress,
small toughness (ceramics)
large toughness (metals)
Adapted from Fig. 6.13, Callister 7e.
Chapter 6 -
Toughness
• Impact (toughness) – applied loads “hit” the sample
• Impact (charpy, dart)
Chapter 6 - 18
Resilience, Ur• Ability of a material to store energy
– Energy stored best in elastic region
If we assume a linear stress-strain curve this simplifies to
Adapted from Fig. 6.15, Callister 7e.
yyr2
1U
y dUr 0
Chapter 6 - 19
True Stress & Strain
• True stress
• True Strain
iT AF
oiT ln
1ln
1
T
T
Adapted from Fig. 6.16, Callister 7e.
Chapter 6 -
Elastic Solid
• Stress-strain• What happens when force is removed?
– Recovery
Chapter 6 - 21
Elastic Strain Recovery
Adapted from Fig. 6.17, Callister 7e.
Chapter 6 - 22
Hardening
• Curve fit to the stress-strain response:
T K T n
“true” stress (F/A) “true” strain: ln(L/Lo)
hardening exponent:n = 0.15 (some steels) to n = 0.5 (some coppers)
• An increase in y due to plastic deformation.
large hardening
small hardeningy 0
y 1
Chapter 6 -
Stress-Strain Diagram
Strain ( ) (L/Lo)
41
2
3
5
Str
ess
(F
/A)
Elastic Region
PlasticRegion
StrainHardening Fracture
ultimatetensile strength
Slo
pe=
E
Elastic region slope =Young’s (elastic) modulus yield strengthPlastic region ultimate tensile strength strain hardening fracture
necking
yieldstrength
UTS
y
εEσ
ε
σE
12
y
ε ε
σE
Chapter 6 - 24
Hardness• Resistance to permanently indenting the surface.• Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties.
e.g., 10 mm sphere
apply known force measure size of indent after removing load
dDSmaller indents mean larger hardness.
increasing hardness
most plastics
brasses Al alloys
easy to machine steels file hard
cutting tools
nitrided steels diamond
Adapted from Fig. 7.18.
Chapter 6 - 25
Hardness Testers
Chapter 6 - 26
Hardness: Measurement
• Rockwell– No major sample damage– Each scale runs to 130 but only useful in range
20-100. – Minor load 10 kg– Major load 60 (A), 100 (B) & 150 (C) kg
• A = diamond, B = 1/16 in. ball, C = diamond
• HB = Brinell Hardness– TS (MPa) = 3.45 x HB– TS (psi) = 500 x HB
Chapter 6 - 27
Conversion of Hardness Scales
Also see: ASTM E140 - 07 Volume 03.01Standard Hardness Conversion Tables for Metals Relationship Among Brinell Hardness, Vickers Hardness, Rockwell Hardness, Superficial Hardness, Knoop Hardness, and Scleroscope Hardness
Chapter 6 -
Chapter 6 - 29
Variability in Material Properties
• Elastic modulus is material property• Critical properties depend largely on sample flaws
(defects, etc.). Large sample to sample variability. • Statistics
– Mean
– Standard Deviation 2
1
2
1
n
xxs i
n
n
xx n
n
where n is the number of data points
Chapter 6 -
Property Variability and Design/Safety FactorsAverage and standard deviation
Chapter 6 - 31
• Design uncertainties mean we do not push the limit.• Factor of safety, N
Ny
working
Often N isbetween1.2 and 4
• Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 5.
Design or Safety Factors
4
0002202 /d
N,
5
Ny
working
1045 plain
carbon steel: y = 310 MPa
TS = 565 MPa
F = 220,000N
d
Lo
d = 0.067 m = 6.7 cm
Chapter 6 - 32
• Stress and strain: These are size-independent measures of load and displacement, respectively.
• Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G).
• Toughness: The energy needed to break a unit volume of material.
• Ductility: The plastic strain at failure.
Summary
• Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches y.
