Scope:

ASTM E143 is used to calculate the shear modulus, which determines whether a structural material complies with torsion (torsion is the twisting of an object due to an applied torque). Shear modulus is used in the design of rotating shafts and helical compression springs.

This test is for materials that follow linear elastic stress-strain behavior. The structural material must follow Hooke’s law, which means that the angle of twist should be proportional to the applied torque. 

For materials that follow nonlinear elastic stress-strain behavior, the value of tangent or chord shear modulus can be used to calculate the discontinuity between stress and strain. However, this is outside the scope of this ASTM E143 standard. 

Elastic properties such as Young’s modulus and Poisson’s ratio are not usually determined and are generally not specified in the material’s specification.

Test Procedure:

The dimensions of the test specimen are measured as per ASTM E143. The cylindrical or the tubular test specimen is aligned and loaded on the fixture that holds the specimen. An external torque is applied to the specimen, which twists the gauge length (the part of the specimen which changes during the test.) 

The applied torque and the corresponding changes in the angle of twist are mapped out on a stress-strain curve. The appropriate slope is then calculated from the shear stress-strain curve. The slope could be derived under conditions of either increasing or decreasing torque.

Video 01: Mechanical properties of solids – shear stress and shear strain

Specimen size:

• Specimens should be chosen from good, clean material. Slight imperfections near the surface, which would have a negligible effect in determining Young’s modulus, cause significant errors in the shear modulus.  

• The test specimen used in ASTM E143 testing should be either circular, cylindrical, or tubular. In the case of solid cylinders, the specimen should be straight and of uniform diameter for a length equal to the gauge length plus two to four diameters. Tubes should be straight and of uniform diameter and wall thickness for a length equal to the gauge length plus at least four outside diameters. The gauge length should be at least four times the diameter.

Data:

The following data is calculated in ASTM E143:

Shear modulus for the circular specimen is calculated by:

G=TL/Jθ

G = shear modulus of the specimen, 

T = torque, 

L = gauge length, 

J = polar moment of inertia of the section about its center, and 

θ = angle of twist, in radians. 

For a solid cylinder:

D = diameter. 

For a tube:

D₀ = outside diameter, and 

D_i = inside diameter. 

Conclusion:

ASTM E143 is used to calculate the shear modulus, which determines whether a structural material complies with torsion (torsion is the twisting of an object due to an applied torque).