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Chapter 10
Torsion Tests
Subjects of interest
• Introduction/Objectives • Mechanical properties in torsion • Torsional stresses for large plastic strains • Type of torsion failures • Torsion test vs.Tension test • Hot torsion testing
Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Objectives
• This chapter provides fundamental knowledge of torsion test and significant parameters such as torque, modulus of rupture in torsion and angle of rotation will be highlighted. • Different types of torsion failures will be evaluated and differentiated from tension failures.
Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Introduction
• Torsion test is not widely accepted as much as tensile test. • Torsion tests are made on materials to determine such properties as the modulus of elasticity in shear, the torsion yield strength and the modulus of rupture. • Often used for testing brittle materials and can be tested in full-sized parts, i.e., shafts, axles and twist drills which are subjected to torsional loading in service.
Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Introduction
Examples: • Driveshaft is subjected to torsion in service. www.caradvice.com
GKN driveline
Bar shaft
Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Torsion-testing equipment
Torsion-testing equipment consists of 1) A twisting head, with a chuck for gripping the specimen and for applying the twisting moment to the specimen. 2) A weight head, which grips the other end of the specimen and measures the twisting moment of torque. www.echoscaninc.com
Specimen used A circular cross section specimen is normally used since in the elastic range, shear stress varies linearly from a value zero at the centre of the bar to a maximum value at the surface. Note: Thin-walled tubular specimen is frequently used.
Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Determination of torsion test
• Applying twisting moment to the specimen and measure the torque. • Determination is made of the angular displacement (or degree of rotation) of a point near one end of the test section of the specimen with respect to a point on the same longitudinal element at the opposite end (using Troptometer). • The shear strain γ is given by
Where
γ = tan φ =
rθ L
Eq.1
θ is the angle of twist or degree of
rotation, radian L is the test length of the specimen.
Torque-degree of rotation diagram
Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Mechanical properties in torsion
• 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) Where τ = shear stress, Pa MT = torsional moment, Nm r =0 r o r = radial distance measured Eq.2 from centre of bar, m 2 J = polar moment of inertia, m4 ∫ r dA is the polar moment But of inertia of the area with respect to the axis of the bar. Thus,
MT = ∫
r =a
τrdA =
τ
∫
a
r 2 dA
MTr M T = , or τ = r J
Eq.3
τJ
Suranaree University of Technology
Torsion of a solid bar
Tapany Udomphol
May-Aug 2007
Shear stress
• The maximum shear stress at the surface of the bar is
τ max =
M T D / 2 16 M T = 4 πD / 32 πD 3
Eq.4
• For a tubular specimen, the shear stress on the outer surface is
16M T D1 τ= π ( D14 − D24 )
Where D1 = Outside diameter of tube D2 = Inside diameter of tube
Eq.5
Note: Eq.4 and Eq.5 is applied only for a linear relationship. Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Elastic properties and yield strength
• The elastic properties in torsion can be obtained by using the torque at the proportional limit (~ 0.04 rad.m-1) where the shear stress is calculated corresponding to the twisting moment from Eq.4 or Eq.5. • The torsional elastic...
Torsion Tests
Subjects of interest
• Introduction/Objectives • Mechanical properties in torsion • Torsional stresses for large plastic strains • Type of torsion failures • Torsion test vs.Tension test • Hot torsion testing
Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Objectives
• This chapter provides fundamental knowledge of torsion test and significant parameters such as torque, modulus of rupture in torsion and angle of rotation will be highlighted. • Different types of torsion failures will be evaluated and differentiated from tension failures.
Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Introduction
• Torsion test is not widely accepted as much as tensile test. • Torsion tests are made on materials to determine such properties as the modulus of elasticity in shear, the torsion yield strength and the modulus of rupture. • Often used for testing brittle materials and can be tested in full-sized parts, i.e., shafts, axles and twist drills which are subjected to torsional loading in service.
Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Introduction
Examples: • Driveshaft is subjected to torsion in service. www.caradvice.com
GKN driveline
Bar shaft
Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Torsion-testing equipment
Torsion-testing equipment consists of 1) A twisting head, with a chuck for gripping the specimen and for applying the twisting moment to the specimen. 2) A weight head, which grips the other end of the specimen and measures the twisting moment of torque. www.echoscaninc.com
Specimen used A circular cross section specimen is normally used since in the elastic range, shear stress varies linearly from a value zero at the centre of the bar to a maximum value at the surface. Note: Thin-walled tubular specimen is frequently used.
Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Determination of torsion test
• Applying twisting moment to the specimen and measure the torque. • Determination is made of the angular displacement (or degree of rotation) of a point near one end of the test section of the specimen with respect to a point on the same longitudinal element at the opposite end (using Troptometer). • The shear strain γ is given by
Where
γ = tan φ =
rθ L
Eq.1
θ is the angle of twist or degree of
rotation, radian L is the test length of the specimen.
Torque-degree of rotation diagram
Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Mechanical properties in torsion
• 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) Where τ = shear stress, Pa MT = torsional moment, Nm r =0 r o r = radial distance measured Eq.2 from centre of bar, m 2 J = polar moment of inertia, m4 ∫ r dA is the polar moment But of inertia of the area with respect to the axis of the bar. Thus,
MT = ∫
r =a
τrdA =
τ
∫
a
r 2 dA
MTr M T = , or τ = r J
Eq.3
τJ
Suranaree University of Technology
Torsion of a solid bar
Tapany Udomphol
May-Aug 2007
Shear stress
• The maximum shear stress at the surface of the bar is
τ max =
M T D / 2 16 M T = 4 πD / 32 πD 3
Eq.4
• For a tubular specimen, the shear stress on the outer surface is
16M T D1 τ= π ( D14 − D24 )
Where D1 = Outside diameter of tube D2 = Inside diameter of tube
Eq.5
Note: Eq.4 and Eq.5 is applied only for a linear relationship. Suranaree University of Technology
Tapany Udomphol
May-Aug 2007
Elastic properties and yield strength
• The elastic properties in torsion can be obtained by using the torque at the proportional limit (~ 0.04 rad.m-1) where the shear stress is calculated corresponding to the twisting moment from Eq.4 or Eq.5. • The torsional elastic...
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