Young’s Modulus

Young’s modulus is a mechanical property of substances that gives information about their stiffness in solid form. Young’s modulus describes the link between an object’s strain (proportional deformation) and the stress applied to it (which can be thought of as the force applied to the object per unit area of the object). The Young modulus is named after Thomas Young, a British polymath and physician. It’s vital to remember that when a solid substance is subjected to a modest amount of weight, it undergoes some elastic deformation. It’s also worth noting that solid-state elastic deformation is reversible.

Young’s Modulus

Young’s Modulus (also known as Elastic Modulus or Tensile Modulus) is a mechanical property of linear elastic solids such as rods, wires, and other similar objects. Other quantities, such as Bulk modulus and shear modulus, can be used to determine a material’s elastic properties, but Young’s Modulus is the most widely utilised. This is because it provides information about a material’s tensile elasticity (ability to deform along an axis).

When a specific load is applied to a solid object, it deforms. When the pressure is removed from an elastic object, the body returns to its previous shape. Beyond a small degree of distortion, many materials are not linear and elastic. Only linear elastic material has a constant Young’s modulus.

Formula for calculating Young’s modulus.

The formula for calculating young’s modulus is given as:

E= σ/e
where, is the stress and is the strain.

Now, stress is given as: σ=F/A where, F is the force and A is the area.

And strain is given as: ε=ΔL/L where, L is the change in length and L is the initial length.

Substituting the values of stress and strain in the formula for young’s modulus, we get:

E=F/A /ΔLL

    =FL/AΔL

Young’s modulus factors:

The Young’s modulus is used to calculate how much a material will deform when subjected to a given load.

Another thing to remember is that the lower the Young’s Modulus of a material, the more deformation the body will suffer, and in the case of clay and wood, this deformation might vary within a single sample. A clay sample deforms unevenly, but a steel bar deforms evenly.

Types of deformation:

• Permanent Deformation – Irreversible permanent deformation, also known as plastic deformation. It’s a type of deformation that persists long after applied forces have been removed.

• Temporary Deformation – This type of reversible deformation is also known as elastic deformation. It’s a type of deformation that vanishes when applied forces are removed.

Yield strength of material:

When forces are applied to a material, it undergoes elastic deformation followed by plastic deformation. The yield strength of a material determines when it transitions from an elastic to a plastic condition. Crystalline and amorphous materials have various plastic deformation mechanisms. Deformation in crystalline materials is performed through a process called slip, which involves the movement of dislocations. Deformation occurs in amorphous materials due to the sliding of atoms and ions without any directionality.

Plasticity:

It is a property of materials that prevents them from returning to their previous dimensions once deforming forces have been removed. Inelastic strain occurs in this material. Permanent deformity is the result in this scenario.

Elasticity:

It is the property of a material that allows it to deform under the impact of a load yet return to its original dimensions after the load is removed. The term “totally elastic body” refers to a body that comes back to its original state after removing the stress from it.

Ductility:

It is the quality of a material that allows it to be pulled out lengthwise to a smaller cross-sectional area when tensile stress is applied. It can also be defined as a material quality that allows a substance to be pulled out in the shape of wire.

Brittleness:

It refers to the inability of a material to be pulled out in the shape of wire. There is no considerable distortion when the collapse occurs.

Isotropic and Anisotropic material:

The Young’s modulus of a material is frequently affected by its orientation. Isotropic materials have the same mechanical characteristics in all directions. Pure metals and ceramics are two examples. Working a material or adding impurities can result in grain structures that cause directional mechanical characteristics. Depending on whether force is applied parallel to the grain or perpendicular to it, these anisotropic materials may have substantially varied Young’s modulus values. Wood, reinforced concrete, and carbon fibre are all examples of anisotropic materials.

Conclusion

Only in the range where the stress is proportional to the strain and the material returns to its original dimensions when the external force is withdrawn is Young’s modulus useful. As the tension on the material increases, it may either flow, causing irreversible distortion, or shatter.

The formula for calculating young’s modulus is given as:

E=σ/e
where, σ is the stress and is the strain.