6 The physical basis of Youngs modulus

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6 - The physical basis of Youngs modulus

• Key points
• Bond stiffness and deformation in homogeneous
  materials
• Definition of Youngs modulus
• Effective moduli for composite materials

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Youngs modulus reflects the bond stiffness and
area density of bonds
For a spring F - k x
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Estimating Youngs Modulus(The Math)
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For an ionic material
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Hierarchy of bond stiffnesses
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Factors Governing Moduli in Lightly Cross Linked
Polymers (e.g. rubber) are Different from those
in Crystalline Materials

• At low temperatures, polymers behave more or less
  as expected
• 2 Gpa lt E lt 4 GPa
• At higher temperatures, the moduli can be much
  lower than predicted on the basis of Van der
  Waals bonding
• On the order of 10-2 GPa
• At these temperatures, Van der Waals bonds
  melt, and E is governed by much lower stresses
  required to untangle individual polymer chains
• Strong covalent cross linking keeps the overall
  structure from melting, the doesnt contribute
  much to the modulus

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The Temperature at which Van der Waals Bonds
Melt is called the Glass Transition
Temperature, TG

• Polymers with no cross linking become viscous
  liquids above TG
• Those with some cross linking become leathery
• Highly cross-linked polymers have moduli
  comparable to aluminum

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Composites Allow Materials Engineers to Tailor
Properties
Particle Reinforced
Fiber Reinforced
Laminar (Layered)
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Fiber Reinforced CompositesLoaded Parallel to
the Fibers
Upper Limit
We assume that the longitudinal strain in the
fibers and the matrix are the same
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Fiber Reinforced CompositesLoaded Normal to the
Fibers
Lower Limit
We assume that the stresses in the fibers and the
matrix are the same
s
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Other Composites Have Moduli That Fall Between
the Upper and Lower Limits for Fibrous Composites

• Particulate composites have moduli that are near
  the lower limit
• isotropic