A cylindrical specimen of a hypothetical metal alloy is stressed in compression. If its original and final diameters are 19.636 and 19.661 mm, respectively, and its final length is 75.9 mm, calculate its original length if the deformation is totally elastic. The elastic and shear moduli for this alloy are 108 GPa and 37.1 GPa, respectively.

The original length of the specimen is found to be 76.093 mm.

Explanation:

From the conservation of mass principal, we know that the volume of the specimen must remain constant. Therefore, comparing the volumes of both initial and final state as state 1 and state 2:

Initial Volume = Final Volume

πd1²L1/4 = πd2²L2/4

d1²L1 = d2²L2

L1 = d2²L2/d1²

where,

d1 = initial diameter = 19.636 mm

d2 = final diameter = 19.661 mm

L1 = Initial Length = Original Length = ?

L2 = Final Length = 75.9 mm

Therefore, using values:

L1 = (19.661 mm) ² (75.9 mm) / (19.636 mm) ²

L1 = 76.093 mm