## Description

**Torsion test**

**Lab objectives & introduction:**

Torsion test is a good phenomenon to determine the modulus of elasticity in shear, torsion yield strength and modulus of rupture of a material. Torsion test is not widely accepted as much as the tensile test. This test is often used on brittle materials and can be tested in full sized parts. Also, the elastic properties in torsion test can be obtained by using the torque at the proportional limit. State of stress in torsion is found on the surface of a bar on two mutually perpendicular planes. However, there are two types of torsion failures. The first one is, the shear (ductile) Failure and which is along the maximum shear plane. On the other hand, tensile (brittle) failures are those perpendicular to the maximum tensile stress. The transformation equations for a plane stress can be represented in graphical form by plot known Mohr’s circle.

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**Methodology:**

Like any other experiment, before we start our procedures, we noted down our measurable variables. Such as, noting down our specimen’s length and the cross sectional diameter to find our area. However, we are going to continue next, on the torsion machine that should be calibrated by applying different loads to our specimen. This is all done respectively to our torque. Anyways, we then center our specimen in between four jaws then turn on the machine to give us some torque. From our rotational angle of twist and torque we can continue and use our equations to determine all of our calculations

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**Known variables and equations:**

Where τ_{max} is the maximum shear stress, G is the modulus of rigidity, D is the representation of our diameter, L is our length, J polar moment of inertia and M_{T} is the torsional moment.

In order to convert the plot from T-θ into τ-γ (shear stress-shear strain, respectively), the following equations can be utilized:

-In the elastic region of the T-θ curve, τ=2T/π

-In the plastic region of the T-θ curve, τ=(1/2π)(θ + 3T)

-And finally, γ= where L=the length of the member being tested (valid for plastic or elastic range).

Once the τ-γ has been plotted, the modulus of rigidity (G) is the slope of the elastic region of said curve. It is similar to Young’s Modulus (E) for members in tension. If the Poisson’s ratio (ν) of the material is known, G can be found with the

Similarly, in the elastic region: τ=Gγ. Using these methods, the torsion test can be used to calculate many important engineering properties of a given material.