Material Sciences and Engineering, MatE271 1
Material Sciences and Engineering MatE271 1Week9
Mechanical Behavior
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Mechanical Behavior
Application
1. Support load - Applied vs. dead weight- Static vs. dynamic
2. Controlled deformation-Small vs. large
3. Reliability
• How microstructure affects mechanical properties
• Tailored microstructure for mechanical properties
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Goals for this unit (Ch. 6)
�Detailed coverage of basic mechanical properties- Describe the concepts of stress and strain
- Differentiate between elastic and plastic deformation
- Quantify elastic properties of materials
- Describe measures of hardness, ductility,
toughness and strength
- Understand fracture, fatigue and creep failures
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6.1 Stress vs. Strain
load
Displacement (�L)
Area(Ao)
Length(Lo) � = P/ Ao (N/m2 )
� = �L/ Lo
Stress
Strain
Engineering Stress - load/original cross sectional area
There are also shear and torsional stresses
For tensile or compressive stresses
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Stress vs. Strain: units
�Stress����F/Ao (where Ao is the original cross-sectional
area)psi (pounds force per square inch)MPa (Mega Pascals = 106 N/m2 )
�Strain� = �L/Lo (where Lo is the original length)
unitless-sometimes expressed as a percentage
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x
z
y
�Ps
Lo
�y
����Ps ���s ����tan ��� �y �Lo
�
Shear Stress vs. Shear Strain
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Application of Loads
Tension Compression
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Application of Loads
Shear
Torsional
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• One of the most common stress-strain
tests performed is tensile testing
• There are standards for the shape and size
and finish of test specimens
• Tensile testing equipment elongates a
specimen at a constant rate and measures:
– Load (load cell)
– Elongation (extensometer)
Tensile testing
Load cell
Gage length
Crosshead
Specimen
Grip
Grip
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Tensile testing
Load cell
Gage length
Crosshead
Specimen
Grip
Grip
Stre
ss
Elastic Plastic
Yield strength
Tensile strength
Fracture
Strain
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Elastic Deformation
�Definition• When stress and strain are proportional
• Non-permanent
• When stress is removed, strain disappears
• i.e. the sample returns to it’s original shape
�What is happening?• small changes in inter-atomic spacing
• bonds are stretching but not breaking
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Modulus of elasticity depends on bond strength!
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Modulus of Elasticity
Elastic modulus is the slope of the atom forcevs distance curve at
equilibrium spacing
• Slope of stress-strain curve in
elastic region
��= (E)(�� �Hooke’s Law)
E - modulus of elasticity
(Young’s modulus)Material E (GPa)
Steel 207
Aluminum 69
Al2O3 370
SiC 470
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Elastic Stress - Strain Behavior
�Shear stress and strain are also proportional to each other in the elastic region:
� = G�����shear stress����shear strain G ��shear modulus
Compare to� = E�
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Example Problem
�A tensile force of 2000N is applied along the axis of an aluminum cylindrical specimen (E = 70 GPa, 1 m long, radius 0.01 m). Assuming the deformation is elastic, estimate the elongation.
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Poisson’s Ratio
�Q. When a specimen is elongated in one direction - what happens in the other two directions?
�A. Usually, they contract.�The ratio of lateral to axial strains is
called Poisson’s ratio
� � �
� x� z
� �
� y
� z
The - sign assures �will be positive
z
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Poisson’s Ratio
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Poisson’s Ratio
�Q. What is Poisson’s ratio for an isotropic material?
�A. If the properties are the same in all directions, then � = 0.25
�Most metals have a � = 0.25 to 0.35
�Admissible range -1 � � � 0.5• for no volume change � � 0.5
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Poisson’s Ratio
�Shear and elastic moduli are related:
E = 2G(1+�)
�Most materials are elastically anisotropic• E varies with crystallographic direction
• most polycrystalline materials may be considered to be isotropic
�Most engineering materials are polycrystalline
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Plastic Deformation� There is a limit to
how much a metalcan be deformed before it will notreturn to its originalshape when the stressis removed
� After reaching elasticlimit, deformation is plastic (in metals dislocation movement).
(in ceramics micro-cracking)
Stre
ss
Elastic Plastic
Yield strength
Tensile strength
Fracture
Strain
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Plastic Deformation
� In metals: Plastic deformation corresponds to the breakingof bonds with atom neighbors and reformingbonds with new neighbors
- (dislocation motion)�Beyond Yield point,
stress is notnot proportional to strain (Hooke’s law is not valid)
PlasticElastic
Strain
Stre
ss �y
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• During plastic deformation, shear stresses cause dislocation
movement resulting in slip.
• This deformation is permanent (not recovered when stress is removed.)
Slip produces plastic deformation
Check week 5 slides 20-33
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Yielding and Yield Strength
�Most structures are designed such that only elastic deformation occurs when a stress is applied
�The point at which plastic deformation occurs must be known (what stress level will bend the metal permanently?)
� Phenomenon is called yielding� For metals that experience a gradual transition, the
point is called the proportional limit
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Proportional Limit
�How do you know where �y is?
�By convention, a specified strain offset of 0.002 is used to identify the yield strength, �y.
PlasticElastic
Strain
Stre
ss
�y
0.0020.2%
P
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Elastic recovery after plastic deformation
Strain (mm/mm)
Stre
ss (M
Pa)
Elastic Recovery
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• Process of plastic deformation (slip)multiplies the number of dislocations
• As each increment of plastic deformation occurs, dislocations findit harder and harder to move because of “entanglement” with ever increasingnumber of dislocations
• Result is that yield strength increases afterplastic deformation (“strain hardening”)
Work Hardening (Strain Hardening)
Strain
Stre
ss
Yield point
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Yield Point Phenomenon
� Some steels show a yield point which occurs abruptly
� Yield point is taken as the average stress of the lower yield point
� Yield points for steels vary from 5,000 to 200,000 psi!
Strain
Stre
ss
�y
UpperYield Pt.
LowerYield Pt.
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Tensile Strength
� After yielding, stress increasesto a maximum, then decreases,and eventually the material
fractures� Tensile strength is the stress
at the maximum of the engineering stress vs strain curve.
� Deformation up to this point is uniformthroughout the sample
� After maximum stress, necking occurs
Stre
ss
Elastic Plastic
Yield strength
Tensile strength
Fracture
Strain
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True vs. Engineering Stress and Strain• Does material actually get
weaker after TS has been
exceeded?
• No, that is an “artifact” of
using engineering stress
instead of true stress in the plot.
• X-sectional area is decreasing,
and especially after necking
starts.
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True Stress and Strain
True Stress = P/A (A: is the current area)True Strain = �L/L (L:current length)
Vol= AL =Ao Lo
�true�P LAo Lo
• When strength of a metal is cited, for design purposes, the yield strength is used.
• The fracture strength is the stress at fracture
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Definition - Ductility
�Measure of degree of plastic deformation that has been sustained before fracture
� If there is little plastic deformation before fracture --- called brittle
�Ductility = percent elongation
%EL �
(l f � lo )lo
x 100
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Ductility
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Ductility
Why is ductility important?� Specifies how much a structure will deform before
fracture� Specifies how much deformation is allowable
during fabrication�Ductility is strongly temperature dependent
– i.e., ductile-to-brittle transitions
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Toughness�Capacity to absorb energy when deformed, up to
fracture�Given by area under curve�Describes the combination of strength and ductility
tougher
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Charpy Impact Test of ToughnessSeldom have complete stess-strain curve, so an impact test is usually used to measure toughness
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Comparison of Mechanical Characteristics
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Hardness
Hardness: surface resistance to indentation
H= F/Aprojected
F
�
Ap
- Quantitative means use a small indenterforced into the surface
- Indenter: round (ball)pointed (cone or pyramid)
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Hardness Tests
� There is a correlation between tensile strength
and hardness
� Hardness tests are simple and inexpensive
� Hardness tests are nondestructive (you still have a
usable sample when you are done)
�Other properties can be estimated from hardness
information.
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Tensile Strength often scales with Hardness
Stre
ngth
, MPa
Hardness, BHN
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Hardness Tests
�Although the scales are quantitative, the numbers are only relative (rather than absolute values)
�Only compare hardness values obtained using the same method
�Methods of testing• Rockwell Hardness
• Brinell Hardness
• Knoop and Vickers Microhardness
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Rockwell Hardness
�Most common method�Indenters are hardened steel balls of various
diameters�The hardness is determined by the
difference in depth of the indentation of two different loads
�Modern instruments are automated
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Brinell Hardness
�Hard, spherical indenter is forced into the surface (like for Rockwell)
�The indentor is steel or WC (tungsten carbide)
� Standard loads are used
�The load is maintained for a specified amount of time
�The diameter of the indentation is measured with a microscope
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Knoop and Vickers
�Very small diamond indenter with a pyramid geometry is forced into the specimen.
�The resulting impression is measured�Knoop is frequently used for ceramics
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Summary of Standard Hardness Tests