CHE 333 Class 14

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CHE 333 Class 14

• True Stress True Strain
• Crystalline Processes During Deformation.

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Typical Data - Metals
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Polymer Stress V Strain
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Typical Data-Polymers
Iron Modulus is 282 Gpa on same scale
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Typical Data - Ceramics
Iron 41 Al 11
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True Stress and Strain

• Engineering stress and strain calculations
• do not account for the decrease in cross
• sectional area that occurs in the plastic
  region.
• True stress and strain do take into acccount
• the cross sectional area changes and so
• change the shape of stress strain data in
• the plastic deformation region.
• st F / Ai
• st True stress
• F Force
• Ai instantaneous cross section.
• et ln li/lo
• et true strain
• li instantaneous length
• lo original length
• Assumes constant volume.

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Work or Strain Hardening

• From the true stress strain data, one important
  feature is the difference to the
• engineering stress strain data. A UTS before
  failure is absent for the true stress strain
• case. It can be said that the material requires
  an increase in stress to continually
• increase the strain. This is called Work
  Hardening for metals. Analysis shows that
• if a metal is work hardened that the stress
  required to cause more plastic deformation
• is increased. If the material is loaded
• to point 1, then unloaded it will
• be plastically deformed and
• will have a permanent shape
• change. On loading again,
• the yield stress will no longer
• be point 2, but point 1, which
• effectively increases the
• service load before
• plastic deformation.

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Load unload load path
2
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True Stress Strain Relations
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Upper and Lower Yield Stress

• Steels show a stress strain curve around the
• yield point which exhibit a decrease in stress
• as strain increases, followed by a yield
• point elongation before the usual plastic
• deformation occurs. The 0.2 yield stress
• construction is used in this case.

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Deformation Mechanisms

• Elastic deformation.
• Metals stretching of bonds between
• the atoms.
• Polymer same
• Ceramics same.
• As bond strength increases, so does the
• elastic modulus, proportional to the slope
• of the Force distance curve at 0 force.