1. Experiment # 2 Torsion Test

2. ■ Objectives:
1. To study the torsional stress-strain relationship and determine shear modulus
(G) and Poisson’s ratio (ν) .
2. To study qualitatively the relationship between torsional load and angle of twist for a full range of strains till failure.
3. To determine the mode of failure (ductile or brittle).

3. G: shear modulus of elasticity
Determining the G :
■ Hooke’s Law in shear:
Hooke's law is an approximation that states that the amount by which a material body is deformed (the strain) is linearly related to the force causing the deformation (the stress).
τ = G . γ
τ: shear stress
G: shear modulus of elasticity
■ Shear modulus (G) is the slope of the linear portion of the shear stress-strain of
a material.

4. Determining G : Shear stress J: polar moment of inertia
GJ: torsional rigidity
Angle of twist
Shear strain

5. shear stress-strain curve for a metallic material
Determining the G :
shear stress-strain curve for a metallic material

6. Determining Poisson's ratio :
■ Poisson ratio (Siméon Denis Poisson ( )) denoted by the  :
The elongation produced by an axial tensile force (P) in the direction of the
force (x axis) is accompanied by a contraction in any transverse direction (y
and z axis).
-Axial elongation and lateral contraction of a prismatic bar in tension: (a) bar before loading and (b) bar after loading
■ The relationship between E and G :

7. Modes of failure under torsion:
■ Ductile materials fail in shear when subjected to torsion. Specimens will break
along a plane perpendicular to its longitudinal axis.
■ Brittle materials are generally weak in tension than in shear. When subjected
to torsion a specimen tends to break along surfaces which are perpendicular
to the direction in which tension is maximum.

9. To Be Reported: Part 1: Study the T-φ curve
■ The torque and corresponding twist angle measured during the experiment will be given to you. Plot the T-φ curve from zero point to failure!
■ Qualitatively describe the behavior of this material as it responds to increasing applied torque. Pay special attention to the region above the yield where linear elastic theory no longer applies.

10. To Be Reported: Part 2: Figure G and υ out
■ In the first phase of the test while the material is behaving linearly the shear Torque and Angle of twist will be measured and they will be recorded in the computer.
■ You will be given the data in blue columns. The data in yellow column should be calculated.
■ Plot the stress-strain curve. Determine the G from the up to proportional limit part of the curve.
■ After looking up the value of modulus of elasticity in a reliable reference, calculate the Poisson's ratio.
■ Compare the obtained G and ν from the test with the authoritative tests as given in the text book and other resources. Compare and discuss about G and  value. T
(N.m)
Rotation
(deg.)

11. To Be Reported:
Part 3:
■ Describe and discuss the mode of failure (brittle or ductile) !

12. Thank you !
Question?