Experimantal data; true/engineering stress and strain
I am a PhD-student specialized on numeric methods in mechanics of solids.
Currently in my wor I try to find the exact solution for tension of hollow cylinder from incompressible material with non-linear deformations.
I use some theoretical models and want to find approximations of coefficients from this models by using experimental data.
At that great site I found some experimental data for uniaxial tension - it can be greatly used to approximate my graphs.
But there are some things I don't understand, it is the kind of terminological questions.
There are 2 kind of experimental data for polymers on this site: true strain/true stress diagram and engineering strain/engineering stress diagram.
So, suppose I use a specimen with lenght L0. The lenght of specimen after tension will became L. So as I understand the engineering strain it is exactly
e = L/L0
So how could I interpret the true strain in such terminology ?
The one thing I found is that true strain is something like E=ln(e+1), where "e" defined above. Is it correct?
So, what about true/engineering stresses.
Of course I found the components of Cauchy stress tensor(and Piola stress tensor of course). So I can calculate the actual load(force). As I understand, the necessary component of Cauchy stress tensor is the true strain, isn't it ?
How can I calculate the engineering stress by using components of Cauchy stress tensor and geometry of uniaxial speciment ?
Great thanks for all answers!
The engineering strain is defined by:
strain_eng = (L-L0) / L0
The true strain is defined by:
strain_true = ln( L/L0 ) = ln(1 + strain_eng)
The true stress is here converted from engineering stress assuming incompressibility, hence:
stress_eng = F / A0,
stress_true = (L/L0) * stress_eng
for a uniaxial test.
Great thanks for your answer! It is exactly what I need.