Mechanics of Deformable Bodies
Objective:
To study the behaviour of ductile and brittle materials subject to torsion
Equipment:
1. Torsion testing machine Tinius Olsen
2. Micrometer
3. Scale
Specimens:
Standard torsion test specimens of steel, aluminum or cast iron
Procedure:
1. Using the micrometer measure the diameter of specimen to the nearest 0.02 mm at
several points along the length of the specimen and record the average diameter.
2. Check the length of the torsion specimen (200.0 mm).
3. Mount specimen in the torsion testing machine. Set the load indicator dial zero.
4. Load and/or deformation increments will be as follows:
Steel 56.5 Nm (500 in-lb) in the linear range
45 in nonlinear range
Aluminum 33.9 Nm (300 in-lb) in the linear range
30 in the nonlinear range
Cast Iron 28.25 Nm (250 in-lb) in the linear range
5 in the nonlinear range
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5. Apply the load slowly by manually operating the machine. Take readings of torque (T)
and angle of twist () simultaneously, at the specified increments, without stopping the
machine, and carefully record these experimental data.
6. When the yield point (for ductile material) is approached (as noted by the increased
readings of angle of twist), the readings of the torque and angle of twist must be
obtained more frequently so the stress-strain diagram will be well defined in this
vicinity.
7. After the yield point (for ductile material) has been exceeded, apply the load until
failure occurs. Readings in this range are based on deformation increments.
8. For cast iron, the specimen should be loaded manually until failure occurs.
9. Examine the fracture surface, and the type of failure that occurred in each specimen.
Report:
Prepare your Lab report according to the general instructions provided in the document on
Structure & Format of Lab Reports. This is a formal report that should be written using a
word processor; the only hand writing allowed is for the sample calculations. Include the
following sections a
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Data Sheet – Torsion Test
Material Steel Aluminum Cast Iron
Type of specimen
Length
(mm)
Average Diameter
(mm)
Average Cross-sectional Area
(mm2
)
Proportional Limit in Shear
(MPa)
Yield Point or Yield Strength in
Shear at 0.001 Radians Offset
(MPa)
Modulus of Rigidity
(Shear Modulus) (GPa)
Ultimate Shearing Stress
(MPa)
Shearing Stress at Rupture
(MPa)
Modulus of Elasticity (Calculated
using = 0.30) (GPa)
4
Hints for filling in the data sheet
T = torque
J = polar moment of inertia
= shearing strain
ρ = radial distance measured from the axis of the cylindrical specimen (
0 Ro
)
Ro = outside radius of a cylindrical or tubular test piece
Ri = inside radius of a tubular test piece
L = distance between collars of the cylindrical specimen
= angle of twist (radians)
= shearing stress
G = modulus of rigidity (shear modulus)
Shearing strain
L
Within the proportionality limit,
J
T
G
L
G
For solid cross sections,
4
2
Ro
J
For tubular cross sections,
4 4
2
Ro Ri
J
Additional hints for filling in the data sheet
1. The proportional limit is to be obtained from the shear stress-shear strain curve (enlarged
graph). It is the stress at which the stress-shear strain curve ceases to be linear.
2. Yield strength in shear (see figure)
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3. Modulus of rigidity (shear modulus)
shear strain
shear stress G
It is the slope of the shear stress-shear stain curve below the proportional limit.
4. Ultimate shearing stress =
J
T Ro
max
(MPa)
(assuming the elastic torsion formula holds good up to rupture)
5. Shear stress at rupture =
J
Trupture Ro
(MPa)
(assuming the elastic torsion formula holds good up to rupture)
6. Modulus of elasticity
E = 2G (1 + )
= Poisson’s ratio
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