CHE 333 Class 14 True Stress True Strain Crystalline Processes During Deformation.
Typical Data - Metals
Polymer Stress V Strain
Typical Data-Polymers Iron Modulus is 282 Gpa on same scale
Typical Data - Ceramics Iron 41 Al 11
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. t = F / Ai t = True stress F = Force Ai = instantaneous cross section. t = ln li/lo t = true strain li = instantaneous length lo = original length Assumes constant volume.
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. Load – unload – load path 1 2
True Stress Strain Relations
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.
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.