1. True Stress True Strain Crystalline Processes During Deformation.
CHE 333 Class 12
True Stress True Strain
Crystalline Processes During Deformation.

2. Typical Data - Metals

3. Polymer Stress V Strain

4. Typical Data-Polymers
Iron Modulus is 282 Gpa on same scale

5. Typical Data - Ceramics
Iron Al

6. 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.

7. 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. 1 2
Load – unload – load path

8. True Stress Strain Relations

9. 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.

10. 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.