CHE 333 Class 11

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CHE 333 Class 11

• Mechanical Behavior of Materials

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Elastic Deformation.

• Consider a metal rod fixed at one end.
• At the other end a load can be applied
• by some manner. When a small amount
• of load is applied, if the length of the metal
• rod was measured it would be longer. If the
• load is removed, and the rod measured
• again, it would return to the original
• length. It is said that the deformation
• was recovered. This type of deformation
• is ELASTIC, that is all recovered on load
  removal.
• It was also found that the extension of the rod
• was directly proportional to the load applied.
• Load extension data would be as shown
• in the diagram.
• Service loads should be ELASTIC

Load
Extension
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Plastic Deformation
Load

• Following elastic deformation, the load
• extension curve is no longer linear,
• as shown in the diagram. After the linear
• elastic portion, a non linear region starts
• which indicates the start of PLASTIC
• deformation. If the load is removed at
• a point after plastic deformation is initiated
• the metal rod will not return to the same
• length as the initial length. It will be longer
• by the amount of plastic deformation. The
• new increase length is the plastic
• deformation. In this case all the deformation
• was not recovered. The elastic portion is
• recovered but not the plastic deformation.
• The load removal curve decreases parallel
• to the elastic deformation line.

Load Removal
Final length after load removal
Extension
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Stress Strain Curves
Stress

• The load extension data can be transformed
• into Stress Strain data by normalising
• with respect to material dimensions.
• The stress is the load divided by the
• original cross sectional area.
• s L/A
• s stress , units MPa, or psi or ksi
• L load applied
• A original cross sectional area
• The strain is the increase in length
• normalised by the original length.
• e Dl/l
• e strain dimensionless (in/in)
• Dl increase in length
• l original length
• Strain is often given in percent so x100
• As the normalisations are by constants

Strain
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Hookes Law and Youngs Modulus
Stress
Hookes Law is concerned with Elasticity. s
Ee Stress is proportional to strain, But only in
the elastic region. This is the elasticity or
elastic Modulus of materials, sometimes Called
Youngs Modulus. Metal Youngs
Mod 106psi Aluminum 11 Gold 16 Copper 28 Iro
n (BCC) 41
Yield Stress
Strain
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Yield Stress Ultimate Tensile Stress
The Yield Stress is at the onset of plastic
deformation. The Ultimate Tensile Stress is the
maximum stress during the stress strain
test. Manufacturing between YS and UTS The strain
to failure can be measured from the stress
strain data, The 0.2 yield stress is used
for materials such as steel as the yield point
is sometimes difficult to determine. At 0.2
strain a line is drawn parallel to the
elastic portion of the data until it
intersects the plastic portion of the data.
The stress level at this point is the 0.2 yield
stress. (0.002 strain)
Stress
Ultimate Tensile Stress
0.2 YS
Yield Stress
Strain at Failure
Strain
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Brittle Behavior
Stress
Failure at this stress
Brittle materials exhibit little on no plastic
deformation region. Only elastic deformation is
found. The energy of failure is then the area
under the stress stain curve, which for a brittle
material is the area of a right angel
triangle, or half base multiplied by the
height. Or half the strain at failure
multiplied by the stress at failure. Plastic
deformation adds a considerable amount of energy
to the failure process. Ceramics and martensitic
steels show this behavior. Energy of failure is
the area under the stress strain curve. For
brittle materials it is half the strain
multiplied by the failure stress.
Strain
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Reduction of Area
At the UTS, for metals local deformation starts,
and thereafter the deformation is
concentrated locally. This causes a NECK to
occur shown above along with the crack at
failure.The cross section is reduced at the
failure point compared to the region outside the
neck. One measure of DUCTILITY besides
elongation at failure is reduction of area ROA
final cross sectional area/ original cross
sectional area
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Cup and Cone Failure
Final failure in round bar is often characterized
for a ductile material as a Cup and Cone
failure. An example is shown. The fracture
starts in the interior of the material and
spreads internally until only a small annulus of
material remains. This then shears at 45o to the
applied stress. The more ductile the
material the larger the shear lip.
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Sheet Tensile Sample
A sheet material tensile sample is shown above.
ASTM has standard dimensions. At either end is a
grip area, and in the center is the gauge length
which is a narrower section to ensure failure
outside the grip area effects. The thickness and
width of the sample need to be known to
calculate the stress data and the original length
to calculate the strain at failure.
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Failed Sample Metal
A failed sample is compared to a new untested
sample. Note the failure is at 45o to the
applied stress. The local deformation in this
case is very near the failure point. ROA Data
would be very difficult in this case. Elongation
at failure would be more useful
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Failed Sample - Polymer
A failed polymer sample has a large elongation at
failure in comparison to the metal sample. Sample
is 0.5 in wide to provide a scale.
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Polymer Stress Strain Curve
Stress
Strain
Polymers generally have low elastic modulus and
long elongations to failure compared to Metals.
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Homework

• Draw a stress strain curve for a ductile material
  indicating yield stress, UTS, strain to failure.
• Draw the stress strain curve for a brittle
  material.
• Briefly describe strain rate sensitivity.