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 41Al 11

True Stress and StrainEngineering 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.