4.0 Theory and Equations
Torsion tests involve applying a twisting moment (torque) to a specimen to measure value of shear stress and strain. The main property derived is the Modulus of Rigidity (G).
When a specimen is subjected to Torque (T), it twists by an angle (θ). This creates maximum shear stress at the outer surface.
Torsion Testing Setup Schematic
Mechanics Solver (Hover to animate)
1. Shear Stress (Elastic)
2. Shear Strain
3. Modulus of Rigidity
4. Stress Distribution
τ increases with Radius (r)
5.0 Torsion Protocol
1. Measure the diameter and the length of the test specimen.
2. Draw a straight line using pencil lead on the specimen length in order to observe the effect of twisting. Fix both ends of the specimen into the specimen holder.
3. Mount the specimen between the loading device and the torque measuring unit. Make sure that the shifting specimen holder of the load is in the mid position.
4. Make sure that the specimen is not initially loaded. Turn on the hand wheel clockwise to provide the applied load. Switch on the measurement amplifier and set it to zero. The read out values is the applied torque.
5. For the first rotation choose an increment of a quarter rotation (90°), for the second and third rotation of a half rotation (180°) and for the fourth to 8th rotation of one rotation (360°). For the 9th to specimen fracture, take the reading of the applied load and angle of twist for each 5 or 10 rotations.
Note: It is best to count the number of rotations and then later convert it to degrees when writing the report. Record the final torque reading of the specimen at failure and also measure the new diameter at the fracture point.
5.1 Safety Measures
1. Eye Protection
Wear safety glasses. Brittle materials like cast iron can shatter explosively.
2. Machine Guards
Ensure any safety guards are in place before starting the motor.
6.0 Result
1. The experimental data should be filled in the table as provided in the worksheet and complete the tables by using the appropriate equations (i.e. calculate the shear strain from experimental angle of twist and shear stress from applied torque).
2. Plot the graph:
- Torque (y-axis) vs angle of twist (x-axis)
- Shear stress (y axis) vs shear strain (x-axis)
3. Determine the experimental modulus of rigidity from the graph (i) (i.e. the slope of the line). Then, in conjunction with the modulus of elasticity from a reference value, calculate the Poisson`s ratio. Also, determine the yield shear stress, ultimate shear stress and fracture shear stress.
4. Sketch the fracture surface of the tested specimen.
Table 1: Specimen Dimensions
| Material | Overall Length L (mm) | Gauge Length Lg (mm) | Diameter d (mm) | Polar Moment J (mm⁴) |
|---|---|---|---|---|
| Mild Steel | ||||
| Cast Iron |
Table 2: Observation Data (Mild Steel)
| No | Torque (Nm) | Angle of Twist (°) | Angle (rad) | Shear Stress (MPa) | Shear Strain (x10⁻³) |
|---|
📷 Specimen Photo Documentation
Capture photos of your specimen before and after the torsion test.
1 Before Test
2 After Test (Fractured)
Table 6.0: Calculated Results
| Property | Symbol | Value | Unit |
|---|---|---|---|
| Modulus of Rigidity | G | GPa | |
| Max Shear Stress | τ_max | MPa |
7.0 Discussion
Virtual Torsion Lab
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Test Your Knowledge
1. What is the unit of Shear Stress?
2. Brittle materials in torsion typically fail at:
3. What is the recommended increment for the first rotation?
4. What must be measured at the fracture point after failure?
5. Why is a straight line drawn on the specimen?
📚 Resource Center
📋 Standards
- • ASTM E143 (Shear Modulus)
- • ISO 7800 (Wire Torsion)
- • BS 18 (Torsion Testing)
🔢 Key Formulas
- • τ = Tr/J (Shear Stress)
- • γ = rθ/L (Shear Strain)
- • G = τ/γ (Modulus of Rigidity)
- • J = πd⁴/32 (Polar Moment)
🎯 Key Concepts
- • Ductile: Fails at 45° (Tension)
- • Brittle: Fails at 90° (Shear)
- • Max stress at outer surface
- • Linear stress distribution
⚠️ Safety & Tips
- • Use safety shield always
- • Measure diameter accurately
- • Apply torque gradually
- • Record angle at each step
💡 Common Material Properties (Typical Values)
Mild Steel
G ≈ 80 GPa
Poisson's ratio ≈ 0.3
Aluminum
G ≈ 26 GPa
Poisson's ratio ≈ 0.33
Brass
G ≈ 40 GPa
Poisson's ratio ≈ 0.34