MECHANICAL PROPERTIES IN TORSION

In solid mechanics, torsion is the twisting of an object due

to an applied torque.

The TORSION TEST has not met with the wide acceptance and the USE that have been given

by the TENSION TEST

It is useful in many engineering applications and also in “theoretical studies of plastic flow”

Torsion test are made on materials to determine such properties as the * Modulus of elasticity in shear* Torsional yield strength * Modulus of rupture

On the full sized parts such as* Shafts, * Axles,* Twist drills and

Which are subjected to torsional loading in service…..

Testing brittle materials (tool steels) High temperature twist test

(evaluate forgeability of materials)

No, the torsion test has not been standardized the same extend as

the tension test and it is rarely required in materials specifications

Consists of• Twisting head with chuck (one end)• Weighing head (other end) –

measures the twisting moment or torque

• Troptometer (twisting measuring device) – measures the deformation of the specimen

Determination is made of the angular displacement of a point near one

end of the test section of the specimen wrt a point on the same

longitudinal element at the opposite end.

Generally circular cross section, since this represents the simplest geometry for the calculation of the stress

Since, in the elastic range the shear stress varies linearly from value zero at the centre of the bar to maximum vaule at the surface, it is frequently desirable to test a thin walled tubular specimen (this results in a nearly uniform shear stress over the cross section of the specimen)

Consider a cylindrical bar subjected to a torsional moment at one end.

• The twisting moment is resisted by shear stresses set up in the cross section of the bar. (zero at centre, max at surface)

Equating the twisting moment to the internal resisting moment

Multiply with r/r

Torsion of a solid bar

But is the polar moment of inertia of the area with respect to the axis of the bar. Thus,

Where τ = shear stress, PaMT = torsional moment, Nmr = radial distance measuredfrom centre of bar, mJ = polar moment of inertia, m4

Since the shear stress is a maximum at the surface of the bar, for a solid cylindrical specimen where J=πD^4 ∕ 32

The maximum shear stress at the surface of the bar is

For a tubular specimen, the shear stress on the outer surface is

Where D1 = Outside diameter of tubeD2 = Inside diameter of tube

applied only for a linear relationship.

The troptometer is used to determine the angle of twist θ, usually expressed in radians, if L is the length of the specimen, from the fig, it will be seen that the shear strain is given by

During a torque test, measurement are made of the twisting moment Mт & the angle of twist θ

A torque twist diagram is usually obtained as shown in fig,

The elastic properties in torsion may be obtained by using the torque at the proportional limit or torque at some offset angle of twist (frequently 0.04 rad/m)

Tubular specimen is usually required for a precision measurements of torsional elastic limit or yield strength.

Because of the stress gradient across the diameter of the solid bar, the surface fibers are restrained from yielding by theless highly stressed inner fibres.

Thus, the first onset of yielding is generally not readily apparent with the instruments ordinarily used for measuring the angle of twist.

The use of a thin-walled tubular specimen minimizes this effect because the stress gradient is practically eliminated.

Care should be taken, however, that the wall thickness is not reduced too greatly, or the specimen will fail by buckling rather than torsion.

Experience has shown that for determinations of the shearing yield strength and modulus of elasticity the ratio of the length of the reduced test section to the outside diameter should be about 10 and the diameter-thickness ratio should be about 8 to 10.

Once the torsional yield strength has been exceeded the shear-stress distribution from the center to the surface of the specimen is no longer linear and the equation

does not strictly apply.

However, an ultimate torsional shearing strength or modulus of rupture, is frequently determined by substituting the maximum measured torque into these equations.

The result obtained by this procedure overestimate the ultimate shear stress.

Although the procedure just described results in considerable error, for the purpose of comparing and selecting materials it is generally sufficient accurate.

For the determination of the modulus of rupture with the tubular specimens, the ratio of gage length to diameter should be about 0.5 and the diameter-thickness ratio about 10 to 12.

Within the elastic range the shear stress can be considered proportional to the shear strain.

The constant proportionality G is the modulus of elasticity in shear or the modulus of rigidity.

Substituting equations

into equation Gives an expression for the shear modulus in terms of the geometry of the specimen, the torque and the angle of twist