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 Initially, thermoplastic
polymer tensile sample,
polymer chains are
randomly oriented
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 The neck continues to
grow until the chains in
the entire gage length
have aligned
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 A “tough” material has strength and ductility
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% EL 

l f  lo
lo

x100

% AR 

Ao  A f
Ao

x100

• Ductility may be expressed as percentage of elongation
percentage area reduction
...
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Types of Modulus
Modulus: Slope of the
stress-strain curve
Initial Modulus
slope of the curve drawn at the
origin
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Secant Modulus
Ratio of stress to strain at any
point on curve in a stress-strain
diagram
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Initial Modulus
Tangent Modulus

Stress



Secant Modulus

Strain



True Stress and True Strain
 True stress : The load divided by the actual crosssectional area of the specimen at that load
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Linear Elastic Properties
Hooke's Law:

=E

Units:
E: [GPa] or [psi]
n: dimensionless

Modulus of Elasticity, E:
(Young's modulus)

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Engineering Stress
• Tensile stress, :

• Shear stress, t:

Ft

Ao
original area
before loading

Stress has units: N/m2 or lb/in2

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Stress () for tension and
compression

F

Ao
Strain () for tension and
compression
Tensile load

Compressive load
Shear stress

Fs
t 
Ao
Shear strain
g = tan q

Torsional deformation
angle of twist, f

ENGINEERING STRAIN
• Tensile strain:

• Lateral strain:

/2

wo
• Shear strain:

L/2

Lo
/2
L/2

q/2

g = tan q
/2 - q
/2

Strain is always
dimensionless
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 X & Y direction
Contractions
hence –ve negative
strain

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Engineering Strain

Poisson's ratio:
n  x/z

metals: n ~ 0
...
25
polymers: n ~0
...

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But is always expressed in percentage

Bending (Flexural)
 Standard test – Rectangular cross section and 3 point bending
 Practice – cross section and bending mode may differ
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Note :
k, I, Z and n can be found from standard tables (see table on next slide)
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15

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Example

Consider a rectangular cross section
beam deflected in the centre of a 3 point
ends free bending mode
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Outcome of test:
Flexural strength or modulus
of rupture that is the stress
required to fracture a specimen
in a bend test
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Quantitative hardness techniques where a small
indenter is forced into the surface of a material
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The softer the material, the larger and deeper the
indentation (and lower hardness number)
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• Elastic behavior: This reversible behavior often
shows a linear relation between stress and strain
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• Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive)
uniaxial stress reaches y
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• Ductility: The plastic strain at failure

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