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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