STRESS STRAIN CURVE

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MECHANICS OF MATERIALSPRESENTATION

• STRESS AND STRAIN CURVE

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STUDENTSMUAZ ALI 15-ME-079ABDULLAH
15-ME-075ALI 15-ME-063M.
USAMA 15-ME-071 NAUMAN
15-ME-083
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STRSS

• When a material is loaded with a force, it
  produces a stress.
• The internal force per unit area is called
  stress.
• stress ?????????? ??????????
  ?????????????????? ????????
• The unit of stress are ( ?? ?? 2 ).

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• Normal(Tensile) stress
• stress perpendicular to material
• It is denoted by sigma ??.
• ?? ?? ??
• units ?? ?? 2
• Shear stress
• Force parallel to cross section called shear
  force.
• stress parallel to material
• It is denoted by tau ??.
• ?? ?? ??
• units ?? ?? 2

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• Thus can resolve stresses into tensile and shear
  components of forces
• Tensile stress (?)
• Shear stress (?)

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STRAIN

• Strain is the relative change in the shape or
  size of an object due to externally applied
  forces.
• Strain result of stress
• Deformation divided by original dimension.
• It is denoted by ?? .
• ?? ??h???????? ???? ??????????h ??????????????
  ??????????h ??? ??
• Unit less.

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• Normal strain
• A normal stress will cause a normal strain.
• When the size of material change due to applied
  normal stress called Normal strain.
• ?? ??h???????? ???? ??????????h ??????????????
  ??????????h ??? ??
• Unit less.
• Shear strain
• Shear strain is defined as the change in angle. 
• A shear stress will cause a shear strain.
• When the shape of material change due to applied
  shear stress called Shear strain.
• ?? ??? ?? ??Ø ??
• ?? ?? h ????????
• Unit less

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• ENGINEERING STRAIN
• It is also known as normal strain.
• ?? original length.
• L new length.
• Eng. Strain (L- ?? )/ ??

• TRUE STRAIN
• It is also known as logarithmic strain.
• ?? original length.
• L new length.
• True strain ?????? ?? ( ?? ?? )

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STRESS STRAIN RELATIONSHIP
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HOOKES LAW

• It states that when the material is loaded within
  the elastic limit the stress is directly
  proportional to strain.
• i.e. Stress a strain
• Stress Constant x Strain
• ????.??
• ????.??
• E can be derived from stress and strain graph.
  What is it?
• Similarly for G.

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Modulus

• The slope of the linear portion of the curve
  describes the modulus of
• the specimen.
• Youngs modulus (E) slope of stress-strain
  curve with sample in tension (aka Elastic
  modulus).
• Ratio of normal and strain.
• Shear modulus (G) - slope of stress-strain curve
  with sample in torsion or linear shear.
• Ratio of shear stress and strain.

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Poissons RatioIt is a
ratio of lateral and axial strain. ??
?? ?????????????? ?? ?????????? E is Modulus
of Elasticity.G is Modulus of Rigidity. ?? is
Poissons Ratio.
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Stress-Strain Diagram
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• Elastic Behaviour
• A straight line
• Stress is proportional to strain, i.e., linearly
  elastic
• elastic limit, or proportional limit spl
• If load is removed upon reaching elastic limit,
  specimen will return to its original shape
• Yielding
• Material deforms permanently yielding plastic
  deformation
• Once yield point reached, specimen continues to
  elongate (strain) without any increase in load
• Material is referred to as being perfectly
  plastic
• Yield point
• The point at which there is an appreciable
  elongation or yielding in the material without
  any increase in load.

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• Proportional Limit
• The Proportional Limit is the maximum stress at
  which stress
• and strain remain directly proportional.
• Elastic Limit
• The Elastic Limit is the maximum stress that the
  material can
• withstand without causing permanent deformation.

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• Strain hardening
• Strengthening of material by plastic deformation.
• Necking
• While specimen is elongating, its x-sectional
  area will decrease.
• Increase in length but decrease in diameter.
• UTS
• Ultimate tensile stress.
• Max stress that which a body withstand without
  fracture.
• At ultimate stress, cross-sectional area begins
  to decrease in a localized region of the
  specimen.
• Fracture
• The point after which material fractured.
• Specimen breaks at the fracture stress.

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Failure
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• Strain Energy
• Energy absorb up to elastic limit is called
  Strain Energy.
• Resilience
• Energy absorb up to yield point is called
  Resilience.
• Toughness energy
• Energy absorb from zero point to fracture point
  is called Toughness energy

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• PLASTIC REGION

• ELASTIC REGION

• In the plastic region, under plastic deformation,
  the material is permanently deformed/damaged as a
  result of the loading.
• In the plastic region, when the applied stress is
  removed, the material will not return to original
  shape
• The transition from the elastic region to the
  plastic region is called the yield point or
  elastic limit

• In the elastic region, ideally, if the stress is
  returned to zero then the strain returns to zero
  with no damage to the atomic/molecular structure,
  i.e. the deformation is completely reversed
• The material will return to its original shape
  after the material is unloaded( like a rubber
  band).
• The stress is directly proportional to the strain
  in this region

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• BRITTLE

• DUCTILE

• Ductile materials will withstand large strains
  before the specimen ruptures.
• Plastic deformation.
• Ductile materials often have relatively
  small Youngs moduli and ultimate stresses.
• Ductile materials exhibit large strains and
  yielding before they fail.
• Steel and aluminum usually fall in the class
  of Ductile Materials.
• Toughness energy is of ductile material is more
  because area under curve is more.

• Brittle materials fracture at much lower strains.
• No plastic deformation.
• Brittle materials often have relatively large
  Youngs moduli and ultimate stresses.
• Brittle materials fail suddenly and without much
  warning.
• Glass and cast iron fall in the class of  Brittle
  Materials.
• Toughness energy of brittle material is less
  because area under curve is low.

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