Theory Lecture 5
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Transcript of Theory Lecture 5
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PREVIOUS LECTURE
Stress on Oblique Planes
Design and Factor of Safety
Strain
Stress – Strain curve
Necking
Brittle vs Ductile materials
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STRESS-STRAIN DIAGRAM
Plotting the stress σ = 𝑃𝐴 against
the strain ε = δ𝐿 , generates the
stress-strain curve.
Characteristic of the property of
every material, irrespective of the
dimensions of the material.
Tensile Testing is done to check for the stress-strain properties of a material.
Materials can be broadly classified into brittle and ductile on the basis of stress-strain diagram.
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DUCTILE MATERIALS
Ductile materials are classified with their ability to yield
at normal temperatures.
• Yield strength
• Ultimate Strength
• Breaking Strength
• Strain Hardening?
• Examples?
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BRITTLE MATERIALS
Rupture occurs without prior change in the rate of elongation.
Absence of necking.
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DUCTILE MATERIALS
Yield point is not clear for some ductile materials i.e.
aluminum
Yield strength can be defined by using the offset
method.
For example 0.2% offset
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DUCTILE MATERIALS : MEASURE
A standard measure of ductility of a material is Percent
Elongation, defined as :
Percent Elongation = 100 𝑳𝑩−𝑳𝟎
𝑳𝟎
Where L0 = initial length of the test material
And LB = final length at the rupture
Another measure is Percent Reduction in Area , defined as:
Percent Reduction in Area = 100 𝑨𝟎−𝑨𝑩
𝑨𝟎
Where A0 = initial cross-section of the test material
And AB = final cross-section at the rupture
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COMPRESSIVE LOADING
For ductile materials, stress-stress curve would be
similar, up till the strain hardening.
Necking cannot occur in the compression.
For brittle materials ultimate strength in compression is
much larger.
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TRUE STRESS AND TRUE STRAIN
The stress taken so far is
also known as
engineering stress.
True stress is obtained
by dividing the applied
force by the deformed area. σ = P/A.
Similarly, ‘True Strain’ is
obtained by adding
successive values of
strain:
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HOOKE’S LAW; MODULUS OF ELASTICITY
Who? Cap’n hook?
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HOOKE’S LAW
For the initial straight line portion of the stress-strain
diagram, the stress is directly proportional to strain:
The relation is known as ‘Hooke’s Law’.
The coefficient ‘E’ is known as ‘modulus of
elasticity’ of ‘Young’s modulus’ . Units?
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HOOKE’S LAW
The largest value of stress for which the Hooke’s law
can be used is known as the ‘proportional limit’.
Isotropic materials : properties like modulus of
elasticity, stress, strain are independent of the force
applied.
Anisotropic materials: properties like modulus of elasticity, stress and strain are dependent on the direction of the force applied.
Examples of anisotropic materials?
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ELASIC vs PLASTIC BEHAVIOR
If the strain disappears when the force applied is
removed, the material is said to be behaving
‘elastically’.
The largest value of stress for which a material
behaves elastically is known as ‘elastic limit’.
If the deformation is permanent, the material is
said to have undergone ‘plastic deformation’.
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ELASIC vs PLASTIC BEHAVIOR
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FATIGUE AND REPEATED LOADING
If an object is loaded and unloaded many times,
failure occurs even when the loading is within elastic
limits.
This phenomenon is known as ‘fatigue’.
Fatigue must be considered in design of all
structures.
Examples of cyclic loading?
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FATIGUE AND REPEATED LOADING
The number of loading
and unloading cycles
required before the
object fails can be
found experimentally.
The maximum stress is
plotted as abscissa and
the number of cycles
as ordinate to obtain a ‘σ-n’ curve:
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Reference :
Chapter no 2 : Stress and Strain – Axial Loading
Mechanics of materials by Beer & Johnston
MecMovies.net
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ANY QUESTIONS?
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BONUS QUESTION
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SOLUTION