property of a material in torsion

1. MECHANICAL PROPERTIES
IN TORSION

2. In solid mechanics, torsion is the
twisting of an object due to an
applied torque.

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

4.  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

5. On the full sized parts such as
* Shafts,
* Axles,
* Twist drills and
Which are subjected to torsional loading in
service…..

6.  Testing brittle materials (tool steels)
 High temperature twist test (evaluate
forgeability of materials)

7. No, the torsion test has not been
standardized the same extend as the
tension test and it is rarely required
in materials specifications

9. 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

10. 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.

11.  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)

12.  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

13. But is the polar moment of inertia of
the area with respect to the axis of the
bar. Thus,
Where τ = shear stress, Pa
MT = torsional moment, Nm
r = radial distance measured
from centre of bar, m
J = polar moment of inertia, m4

14.  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
applied only for a
linear relationship.
Where D1 = Outside diameter of tube
D2 = Inside diameter of tube

15. 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

16. 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,

17.  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.

18.  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.

19.  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.

20.  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.

21.  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.

22.  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.

23.  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