Knowing About the Modulus of Rigidity

The Modulus of Rigidity – G – (Shear Modulus) is the elasticity coefficient for a shearing force. It is defined as follows:

“the shear stress to the displacement ratio per unit the sample length (i.e. shear strain)”

Slope of the stress-strain curve that is obtained during tensile testing on a sample of the material can be used while calculating the modulus of rigidity.

The pascal is the SI unit derived from shear modulus, but it is usually expressed in gigapascals or thousands of pounds per square inch. M1 L-1 T-2 is its dimensional form. The shear modulus is always greater than zero.

What is the modulus of rigidity?

If a body has a distinct shape and size, it is said to be rigid. The solid bodies we see around us are not completely rigid. When applied with an external force, they can be compressed, stretched, and bent.

Objects deform when an external force is applied. Some objects have a tendency to revert to their original shapes. Stress is the internal force that acts per unit area of the body to return it to its original shape. Strain is defined as the ratio of the change in any dimension produced in the body to the original dimension.

The Modulus of Elasticity is a relationship that has been established between stress and strain. Within the elastic limit, it is defined as the ratio of stress to strain.

Unit

Nm-2 is the SI unit rigidity, and its dimensions are [ML-1T-2].

The three types of strain correspond to three types of modulus of elasticity (Longitudinal, Volumetric, and Shear).

Characteristics of Modulus of Rigidity

• The modulus of rigidity is a material property that remains constant at a given temperature.
• The shear modulus of a material is unaffected by its geometry.
• The modulus of rigidity decreases as temperature rises.
• A high modulus of rigidity value indicates that the material will retain its shape and a large force will be required to deform it, whereas a low shear modulus value indicates that the material is soft or flexible.
• Fluids (Liquids and Gases) have the lowest rigidity modulus (0) and begin to flow with a small amount of shear force applied.
• Diamond has the highest shear modulus value (478 GPa).
• Shear Strength is the maximum shear stress that a material can withstand without fracture or failure.

Modulus of Rigidity of Steel

Steel has a modulus of rigidity of around 79 GPa or 11,460 ksi. Steel has one of the highest values among commercially available metals due to this value.

The importance of modulus of rigidity in material selection is determined by the application of the item. If the material must hold or brace a component, choose a modulus of rigidity with a high safety factor. If the material is used as a covering or accessory rather than the primary load-bearing member, the modulus of rigidity may be closer to the theoretical maximum force.

Steel strength typically ranges from 36ksi to 50ksi. 

Higher strength alloys may be specified depending on the application. As strength grows, so does the cost. As a result, solving for the minimum shear modulus reduces costs and allows users to select the most cost-effective and effective alloy.

It is also critical to consider steel formation and material orientation. The grain direction of a plate, for example, is the result of a mill’s rolling process, which stretches the metallurgical structure. The bending ability of a material varies with and against the grain.

Isotropic and Anisotropic Materials

Some materials are shear isotropic, which means that the deformation in response to a force is the same regardless of orientation. Other materials are anisotropic, meaning they respond to stress or strain differently depending on their orientation. Anisotropic materials are much more prone to shear along one axis than the other. 

Consider the behaviour of a block of wood and how it may respond to a force applied parallel to the wood grain versus a force applied perpendicular to the grain.The orientation of the force with respect to the crystal lattice determines how easily the crystal shears.

Effect of Temperature and Pressure

As one might expect, the response of a material to an applied force varies with temperature and pressure. Shear modulus typically decreases with increasing temperature in metals. With increasing pressure, rigidity decreases.

Conclusion

Modulus of Rigidity – G – is the elasticity coefficient for a shearing force. It is defined as follows: “the shear stress-to-displacement ratio per unit sample length”. The slope of a stress-strain curve obtained during tensile testing on a sample of the material may be used to calculate the modulus of rigidity. The modulus of rigidity is a material property that remains constant at a given temperature. The shear modulus of a material is unaffected by its geometry. The importance of modulus of rigidity in material selection is determined by the application of the item. If the material is used as a covering or accessory rather than the primary load-bearing member, the modulus of rigidity may be closer to the theoretical maximum force.