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Objectives
1. Define stress & strain.2. Utilize Hooke’s Law to calculate
unknown stresses and strains.
3. Determine material parameters from a
stress-strain curve.
4. Recognize elastic and plastic
components of deformation in a
material.5. Identify the regions of behavior on a
stress-strain diagram.
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Stress
Intensity of ForceStress = ____ /____
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Types of Stress
Normal : load perpendicularto area
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Types of Stress
a) Normal
b) Shear : load parallel to area
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Types of Stress
a) Normal
b) Shear
c) Hydrostatic (uniform pressure)
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Strain: Intensity of Deformation
e = ____/_____ =dl / lo
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Types of Strain
Normal : deformation in thethe direction of length
Longitudinal Strain
e = u / l
Transverse Strain
e = v / l
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Transverse Strain
Materials tend to expand/contractin the directions perpendicular to
the load application.
Poisson’s Ratio
= - _____________axial strain
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Why Poisson’s Ratio ?
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Poissons Ratio Values
= 0.5 constant volume
= 0.3 good guess for most materials
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Types of Strain
Normal
Shear : deformation normal to length
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Types of Strain
Normal
Shear
Dilatational (volume change)
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Relating Stress and Strain
Called a “Constitutive Model”
Simple Linear Model: “Hooke’s Law”
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Relating Stress and Strain
NormalS = E e
Stress = Young’s modulus x strain
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Relating Stress and Strain
ShearHooke’s Law
= G
Shear Modulus
G = E / [2 (1+ )]
= shear stress
G = shear modulus = shear strain
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Relating Stress and Strain
Dilatational (hydrostatic)
Hooke’s Law
P = K
K= E/3(1-2)
P = pressure
K = bulk
modulus
= V/ Vo
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Real Material Behavior -Hookean to a limiting strain
-Proportional limit : Deviationfrom linear
-After PL*Linear
*Flat
*Non linear
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Tensile Test
Callister, Materials Science & Engineering
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What is Elastic Deformation?
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*Recoverable strain (elastic)
*Nonrecoverable strain (plastic)
Real Material Behavior
S
e
ElasticElastic /plastic
Plastic Elastic
Sl f R Li
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Slope of Recovery Line
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Unload/Reload
Callister, Materials Science & Engineering
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Yield Strength from S-e Curve
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Everything Together
Wh t i Vi l ti
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What is Viscoelastic
Deformation?
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Creep Test Viscoelasticity
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Deformation TypesName Math Model Time Dependency Type
Elastic Linear/Nonlinear None Recoverable
Plastic Linear/Nonlinear None Nonrecoverable
Viscoelastic Linear/Nonlinear Strong Recoverable
Viscoplastic Nonlinear Strong Nonrecoverable
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Representative Modulii
Material Modulus (psi)
Aluminum 10x10^6
Steel 30x10^6
Polycarbonate 300 x 10^3