Introduction
Torsion test is very important test to know the resistance of material of a material when it is subject to torsion. Resistance of torsion can be denoted by shear modulus which is derived from performing torsion test and creating a graph of angle of twist vs torsion. By measuring the slope of the graph shear modulus is evaluated. Another property of material, Young’s modulus, can also be determined from the value of shear modulus if value of Poisson’s ratio is known. In this lab experiment two metals were used to determine their mechanical properties. The objective of this lab experiment was to determine material characteristics of cylindrical bars under torsion.
Methods
At first work length and diameter of each sample were measured. Then the specimen was installed in the chunks and it was made sure that the work section of the specimen coincided with the free surface of each chuck. Coarse angular displacement, torque meter, fine scale, and the counter were zeroed. Torque was applied to the sample by twisting it in angular steps of 1° (fine scale).
Magnitude of the torque was recorded and the angle reading from the radian meter was measured until the yield point was observed. Then the angle increments were gradually increased until failure. This process was repeated for all samples.
Experimental Results
In this section experimental data were tabulated and graph was drawn based on these data.
Following graph for Torsion vs Angle of Twist has was generated based on the experimental data.
Following graph for Torsion vs Angle of Twist has was generated based on the experimental data.
Discussion
Alluminium Sample:
Yield point is that point where the graph changes its linearity i.e. at Torque (T) 9.8 N-m.
Formula of shear stress and shear strain are:
Shear stress = τ = T.r/J, where r is radius and J is polar moment of inertia = 0.5 πr^4
Shear strain =γ = rφ/L, where L is length of sample and φ is angle of twist
So, Shear stress at yield point = 9800 / 0.5 π (3.32^3) = 170.4 N/mm2
Shear strain at yield point = 3.32 x 0.175 /72.9 = 0.008
So, value of G from curve = (ΔT/Δφ) (L/J) = [(7800-6900)/ (0.14-0.122)] (72.9/0.5 π (3.32^4) =
19099.6 N/mm2 = 19.1 GPa
Typical value of G for aluminium = 26 GPa
% difference = (26 - 19.1)/26 = 0.265 or 26.5%
E (Young’s Modulus) = 2G (1+υ) = 2x19.1 (1+0.3) = 49.66 GPa
Typical value of E for brass = 69 GPa
% difference = (69 – 49.66)/69 = 0.29 or 29 %
Brass Sample:
Yield point is that point where the graph changes its linearity i.e. at Torque (T) 15.2 N-m.
Formula of shear stress and shear strain are:
So, Shear stress at yield point = 15200 / 0.5 π (3.23^3) = 287.2 N/mm2
Shear strain at yield point = 3.23 x 0.157 /74.5 = 0.0068
So, value of G from curve = (ΔT/Δφ) (L/J) = [(8400-6600)/ (0.07-0.052)] (74.5/0.5 π (3.23^4) = 43.57 GPa
Typical value of G for brass = 37 GPa
% difference = (43.57 – 37)/ 37 = 0.178 or 17.8%.
E (Young’s Modulus) = 2G (1+υ) = 2x37 (1+0.33) = 98.42 GPa
Typical value of E for brass = 102 GPa
% difference = (102 – 98.42)/ 102 = 0.035 or 3.5%.
For both samples, crack is expected to occur at outer most fiber of the sample i.e. where value of r is maximum. As per formula of shear stress, it can be said that maximum shear stress i.e. crack will occur at outer surface of the sample where “r” is maximum.
It has been found out that there were deviation of value of G and E, found out based on experimental data, from the typical value. Possible sources of error might be presence of impurities in the sample causing change of properties of the sample; error occurred during taking measurement etc. However, shape of the graphs were found as desired.
Conclusions
The lab experiment was carried out safely. The values of shear modulus and young’s modulus of brass sample were almost similar to the typical values. Though there is significant difference i.e. 30% deviation between the values of shear modulus as well as Young’s modulus calculated from the experimental data and typical values for the aluminium sample. The experiment can be improved by eliminating possible sources of errors discussed in previous section. However, by performing this experiment, material characteristics of cylindrical bars under torsion were known and it can be concluded that goal of this lab experiment was met.
