Conduct Torsion test to find out Modulus of rigidity

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AIM :- Torsion test on mild steel rod.
OBJECT :-To conduct torsion test on mild steel or cast iron specimens to find out modulus of rigidity.
APPARATUS:-

1. A torsion testing machine.
2. A steel rule and Vernier Caliper or micrometer.
3. Test Specimen size as per machine requirement(The specimen should be of such size as to permit the desired strain measurement to be made with sufficient accuracy. It should be of such properties that the stress due to gripping ends does not affect the portion of the specimen on which measurements are made. The ends of the specimen should be such that they can be securely gripped without any local failure at the grips).

THEORY:-
A torsion test is quite instrumental in determining the value of Modulus of rigidity of a metallic specimen.The value of modulus of rigidity can be found out thought observations made during the experiment by using the torsion equation
\[\frac{T}{J}=\frac{{{f}_{s} (or) \tau }}{R}=\frac{G\theta }{L}\]
Where
T = Torque in N-mm
${{I}_{p}}$ = Polar moment of inertia of specimen in ${{mm}^{4}}$
${{f}_{s}}$ = Shear stress at Radius R of the Specimen $\frac{N}{m{{m}^{2}}}$
R = Radius of the shaft in mm
G = Modulus of rigidity in $\frac{N}{mm^2}$N/mm2
$\theta $ = Angle of twist in radians (1 degree = 0.01745 rad)
L = Length of the shaft in mm
Hence \[G=\frac{T}{{{I}_{p}}}X\frac{L}{\theta }\]
For solid circular diameter 'd' \[{{I}_{p}}=\frac{\pi {{d}^{4}}}{32}\]
For circular shaft of external diameter D and internal diameter d, \[{{I}_{p}}=\frac{\pi {{D}^{4}-{d}^{4}}}{32}\]
Procedure

1. Measure the diameter of test specimen using vernier calipers
2. Measure the gauge length of the specimen.
3. Hold the specimen in between the plates with a dog holder.
4. Adjust the circular min scale with zero of the vernier scale and also ensure that torque reading show the value in digital indicator.
5. Apply an increasing torque to the specimen in suitable increments by using automatic control.
6. Continue the test and record the corresponding readings of torque and angle of twist, until fracture occurs.
7. Plot a graph of torque vs angle of twist and determine the Modulus of Rigidity.

Observations
Diameter of the specimen 'd' =
Gauge length 'L'=
Polar moment of inertia '$I_p$' =

S.No	Angle of twist $\theta $ in degrees	Angle of twist $\theta $ in radians (1 degree = 0.01745 rad)	Torque(T) Kg-cm
1
2
3
4

Precautions

1. The test piece should, as far as possible, be straight and of sufficient length to provide the 'desired length between the grips.
2. Any straitening should be done by hand without damaging the test piece.
3. The free length between the grips should be provided strictly to IS -1 717.
4. If the failure of the specimen takes place with in twice the diameter of the grips, the test should be considered as invalid and should be repeated.
5. The surface of the test piece after failure should be examined so that it is free from cracks.

Result
Modulus of rigidity of given specimen= _____________ $\frac{N}{mm^2}$.

Discussion
Compare the experimental results with the theoretical values for test specimen,comment on any reason for discrepancy, comment on any instrumental/experimental errors, and area of application.
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