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Chapter 11
MECHANICAL
PROPERTIES
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Important Mechanical Properties
from a Tensile Test
Young's Modulus: This is the slope of the linearportion of the stress-strain curve, it is usuallyspecific to each material; a constant, known value.
Yield Strength: This is the value of stress at the
yield point, calculated by plotting young's modulusat a specified percent of offset (usually offset =0.2%).
Ultimate Tensile Strength: This is the highest
value of stress on the stress-strain curve. Percent Elongation: This is the change in gauge
length divided by the original gauge length.
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Terminology
Load - The force applied to a material duringtesting.
Strain gage or Extensometer- A device used for
measuring change in length (strain).
Engineering stress - The applied load, or force,
divided by the original cross-sectional area of the
material.
Engineering strain - The amount that a material
deforms per unit length in a tensile test.
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F
bonds
stretch
return to
initial
1. Initial 2. Small load 3. Unload
Elastic means reversible.
Elastic Deformation
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1. Initial 2. Small load 3. Unload
Plastic means permanent.
F
linear
elasticlinear
elastic
plastic
Plastic Deformation (Metals)
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Typical stress-strain
behavior for a metal
showing elastic andplastic deformations,
the proportional limit P
and the yield strengthy, as determined
using the 0.002 strain
offset method(where there
is noticeable plastic deformation).
P is the gradual elastic
to plastic transition.
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Plastic Deformation (permanent)
From an atomic perspective, plasticdeformation corresponds to the breaking of
bonds with original atom neighbors and
then reforming bonds with new neighbors. After removal of the stress, the large
number of atoms that have relocated, do
not return to original position. Yield strength is a measure ofresistance
to plastic deformation.
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(c)2003 Brooks/Co le, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license.
Localized deformation of a ductile material during a
tensile test produces a necked region.
The image shows necked region in a fractured sample
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Permanent Deformation
Permanent deformation for metals isaccomplished by means of a process called
slip, which involves the motion of
dislocations.
Most structures are designed to ensure that
only elastic deformation results when stress
is applied.
A structure that has plastically deformed, or
experienced a permanent change in shape,
may not be capable of functioning as
intended.
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tensile stress,
engineering strain,
y
p = 0.002
Yield Strength, y
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Stress-Strain Diagram
Strain ( ) (DL/Lo)4
1
2
3
5
Elastic
Region
Plastic
Region
Strain
Hardening Fracture
ultimatetensile
strength
Elastic region
slope =Youngs (elastic) modulus
yield strength
Plastic regionultimate tensile strength
strain hardening
fracture
necking
yieldstrength
UTS
y
E
E
12
y
E
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Stress-Strain Diagram (cont)
Elastic Region (Point 12)
- The material will return to its original shape
after the material is unloaded( like a rubber band).
- The stress is linearly proportional to the strain in
this region.
E : Stress(psi)
E : Elastic modulus(Youngs Modulus) (psi)
: Strain (in/in)
- Point 2 : Yield Strength : a point where permanent
deformation occurs. ( If it is passed, the material will
no longer return to its original length.)
E or
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Strain Hardening
- If the material is loaded again from Point 4, the
curve will follow back to Point 3 with the same
Elastic Modulus (slope).- The material now has a higher yield strength of
Point 4.
- Raising the yield strength by permanently strainingthe material is called Strain Hardening.
Stress-Strain Diagram (cont)
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Tensile Strength (Point 3)- The largest value of stress on the diagram is called
Tensile Strength(TS) or Ultimate Tensile Strength
(UTS)
- It is the maximum stress which the material can
support without breaking.
Fracture (Point 5)
- If the material is stretched beyond Point 3, the stressdecreases as necking and non-uniform deformation
occur.
- Fracture will finally occur at Point 5.
Stress-Strain Diagram (cont)
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(c)2003 Brooks/Co le, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license.
The stress-strain curve for an aluminum alloy.
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After yielding, the stress necessary to
continue plastic deformation in metals
increases to a maximum point (M) andthen decreases to the eventual fracture
point (F).
All deformation up to the maximum
stress is uniform throughout the tensile
sample. However, at max stress, a small
constriction or neck begins to form.
Subsequent deformation will be
confined to this neck area.
Fracture strength corresponds to thestress at fracture.
Region between M and F:
Metals: occurs when noticeable necking starts.
Ceramics: occurs when crack propagation starts.
Polymers: occurs when polymer backbones are aligned and about to break.
Tensile Strength, TS
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Tensile stress, : Shearstress, t:
Ft
Aooriginal area
before loading
Stress has units: N/m2 or lb/in2
Engineering Stress
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Another ductility measure: 100% xAAAARo
fo
Ductility may be expressed as eitherpercent elongation (%
plastic strain at fracture) orpercent reduction in area.
%AR > %EL is possible if internal voids form in neck.
100% xl
ll
ELo
of
Ductility, %EL
Ductility is a measure of the
plastic deformation that hasbeen sustained at fracture:
A material that
suffers very
little plastic
deformation is
brittle.
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Toughness
Lower toughness: ceramics
Higher toughness: metals
Toughness is
the ability to
absorb
energy up tofracture (energyper unit volume of
material).
A toughmaterial has
strength and
ductility.
Approximated
by the area
under the
stress-strain
curve.
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Energy to break a unit volume of material
Approximate by the area under the stress-strain
curve.
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smaller toughness-
unreinforced
polymers
Engineering tensile strain,
Engineering
tensile
stress,
smaller toughness (ceramics)
larg er toughness(metals, PMCs)
Toughness
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Linear Elastic Properties
Modulus of Elasticity, E:
(Young's modulus)
Hooke's Law:
= E
Poisson's ratio:metals: n ~ 0.33
ceramics:n
~0.25polymers: n~0.40
Units:
E: [GPa] or [psi]
n: dimensionless
n x/y
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Engineering Strain
Strain is dimensionless.
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Stress and strain: These are size-independentmeasures 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). Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive)
uniaxial stress reaches y.
Toughness: The energy needed to break a unitvolume of material.
Ductility: The plastic strain at failure.
Summary