Determination of elastic modulii (tension and torsion tests)

[svishal03]

I’ve been struggling with this for quite some time and will be grateful if someone can help me.

I have got the data for some tension and torsion tests performed on standard specimen- the tests were done by someone else- not me.

I’m trying to do a material modelling based on the tests carried out.

I computed the elastic modulus of from the tension tests by fitting a straight line to initial points on the curve of true stress vs true strain (see attached jpg file- modulus_of_elasticity)

I now want to compute the shear modulus (modulus of rigidity) by results of torsion test.

And I ought to be satisfying the relationship between elastic constants as well (just to make sure that I’ve done things correctly) that is:

G = E / 2 (1+mu)

Where;

G = shear modulus
E = modulus of elasticity
mu = Poisson’s ratio.

Actually, just like tension test, for torsion test too, I plotted shear stress vs shear strain - shear strain being = gamma /2 where gamma = angle of twist (in radians) * radius of the specimen / gauge length.

I did this but could not satify the relation (difference being over 50!) G = E / 2 (1+mu)

Before going into the details of the shear stress vs shear strain curve, I’m attaching the load set data for torsion test (refer file load_set.xls)given by the experimentologist and shall be grateful if someone shows me the computation of shear stress, angle of twist for just one reading of this set. I feel that I’m missing something here.

 

[afreiden]

I see you have no replies..
My thoughts..

1) There appears to be damage (plasticity?) occurring in your tension test. None of the equations that you posted apply to plasticity.

2) If you are only considering the elastic portion, which does appear to be linear and small ("infinitesimal") strain, then you are correct: your check on the value of G should match.

You mention shear stress.. but in your Excel file you have torque and angle of twist.. You could write G as a function of the torque and angle of twist, right? Otherwise, how are you obtaining shear stress?