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If a body has a definite shape and size, it is considered rigid. The solid bodies we observe in our environment aren’t perfectly rigid. When an external force is applied to these objects, they deform. However, some items tend to revert to their original shape.
Stress is the internal force acting per unit area of the body to return it to its former shape. It’s the proportion of any change in a body’s dimension to its original size.
Elastic constants are the sum of Young’s modulus, rigidity modulus and bulk modulus of an elastic solid. When a deforming force acts on a solid, it causes the solid’s original dimension to alter. In such instances, the relation between elastic constants can be used to determine the magnitude of deformation. There is no significant difference between Modulus of Rigidity and Shear Modulus.
There are three different forms of elasticity modulus, each corresponding to another type of strain (Longitudinal, Volumetric, and Shear)
Young’s Modulus
Bulk Modulus
Shear Modulus
What is the Shear Modulus (Modulus of Rigidity)?
The elasticity coefficient for a shearing force is called the modulus of rigidity. Experiments can be used to determine the slope of a stress-strain curve obtained during tensile tests on a material sample. The ratio between shear stress and shear strain is called shear modulus.
Units of Shear Modulus
The SI unit for stiffness or shear modulus is Pascal (Pa). It is, however, commonly presented in gigapascals (GPa). In the English system, its unit is thousand pounds per square inch (KSI). The dimensional form of shear modulus is M1L−1T−2.
When we apply shear force on an object, the linear dimensions of the thing remain the same, but the body’s shape deforms. Shear strain is the strain related to shear stress.
F/A = Shear Stress = Force Shearing/ Area which is Under Shear
Shear strain is defined as any gradient relative motion divided by its separation from a fixed layer.
Example: What would be the Modulus of rigidity if the tension on a body is 6 x 105
N/m² and the strain is 3 x 10-3?
Answer:
Stress = 6 x105 N/m².
Strain = 3 x 10-3
Shear Stress/ Shear Strain = Shear Modulus (G)
= 6 x105 N/m² / 3 x 10-3
Hence, Shear Modulus (G) = 2 x 108 N/m².
Materials that are both isotropic and anisotropic
When it concerns shear, certain elements are isotropic. In other words, the displacement is identical irrespective of the direction of the force. The orientation of anisotropic materials affects how they respond to strain or tension. When compared to isotropic materials, anisotropies are more vulnerable to flex in one direction.
Observe how a diamond reacts when pressure is applied to it. The ease with which the crystal bends is determined by the direction of the force in relation to the lattice structure. For example, consider the difference between a load exerted along the wood kernel against a load exerted perpendicular to the surface of a woodblock.
Temperature and Pressure Effects
Metals’ shear modulus normally decreases as temperature goes up. As the pressure increases, the stiffness decreases. Metals’ shear modulus changes linearly across a temperature and pressure range.
It’s more difficult to model behaviour outside of this range. Steinberg-Cochran-Guinan shear modulus model, the Mechanical Threshold Stress and the Nadal and LePoac shear modulus model are used to investigate the impact of heating rate on shear modulus.
Shear Modulus Values Table
Diamond, a complicated and rigid solid, has an extremely high shear modulus. The shear modulus of steel and the values of several samples at normal temperature are shown in this table. The shear modulus of soft, flexible substrates is frequently low. Alkaline earth and core metals have medium values. Transformation alloys and metals have a high market value.
It’s worth noticing that the values of Young’s modulus have a predictable tendency. The modulus of rigidity or linear ductility and toughness of a solid is measured by the Shear modulus. Young’s modulus and bulk modulus are flexibility moduli that are related by formulas and are derived from Hooke’s law.
Conclusion
The modulus of rigidity is a material attribute that remains constant at a given temperature for a particular material. The geometry of the material has no bearing on the shear modulus. The modulus of stiffness decreases as the temperature rises.
A high modulus of rigidity indicates that the material will hold its shape and that a substantial force will be required to distort it. In contrast, a low shear modulus means that the material is soft or flexible. Fluids (liquids and gases) have the lowest stiffness modulus (zero), and they begin to flow after shear tension is applied in a minimal amount.
The shear modulus of a diamond is the highest (478 GPa). Shear strength is the most outstanding shear stress value that a material can endure without fracture or failure.
