Determination of elastic modulii (tension and torsion tests)

• svishal03
In summary, the speaker is seeking help with material modeling based on tension and torsion tests. They have computed the elastic modulus from the tension test and now want to compute the shear modulus and check the relationship between elastic constants. They are also struggling with understanding the shear stress vs shear strain curve from the torsion test. They are looking for someone to help them with the computation of shear stress and angle of twist for one reading from the load set data provided. They are concerned about potential plasticity in the tension test and want to ensure they are correctly interpreting the results.
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.

Attachments

• modulus_of_elasticity.jpg
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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?

What is the purpose of determining elastic modulii through tension and torsion tests?

The purpose of determining elastic modulii through tension and torsion tests is to measure the strength and stiffness of a material. This information is important for engineers and designers to ensure that the material can withstand the required loads and stresses in a given application.

What is the difference between tension and torsion tests?

Tension tests involve applying a pulling force to a material, while torsion tests involve twisting the material. Tension tests are used to measure the material's resistance to stretching or elongation, while torsion tests measure its resistance to twisting.

What are the common materials used for tension and torsion tests?

Common materials used for tension and torsion tests include metals, such as steel and aluminum, as well as polymers and composites. These materials are widely used in various industries and have different elastic properties.

How is the elastic modulus calculated from tension and torsion test data?

The elastic modulus, also known as Young's modulus, is calculated by dividing the stress by the strain in a material. In tension tests, the stress is the force applied divided by the cross-sectional area of the material, and strain is the change in length divided by the original length. In torsion tests, the stress is the torque applied divided by the polar moment of inertia, and the strain is the angle of twist divided by the original length.

What are the limitations of tension and torsion tests in determining elastic modulii?

Some limitations of tension and torsion tests include the assumption of linear elastic behavior, which may not hold true for some materials at high stresses. Additionally, the shape and size of the test specimen can also affect the results. Finally, the tests may not accurately represent the behavior of the material in real-life applications due to factors such as temperature, humidity, and loading conditions.

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