Poisson’s Ratio

A cuboid shaped rubber is pulled by a force F longitudinally. Can you guess what would happen?

As force is applied longitudinally, thus the rubber’s initial length will increase, width and the thickness will decrease.The length of the rubber rises by dL, while the width decreases by dB. 

What is “Strain”?

Strain is defined as the variation in length, width, and other dimensions of an item or form divided by its original dimension.

What is “Poisson’s Effect”?

When a material is stretched in one dimension, it will compress in the opposite direction of the force exerted, and vice versa. The Poisson’s ratio may be used to calculate this. For example, when a rubber band is stretched, it thins out.

What are the “Poisson’s Ratio Values” for Different Materials?

The value of Poisson’s ratio varies with each material, and it is determined by how a material reacts to compression and pulling forces.

Poisson’ s ratio lies in the range of negative 1 to positive 0.5. In most materials that we would encounter in day to day life, the ratio would be in the range of 0 to 0.5.

What are some examples of Poisson’s Ratio Values for different types of materials?

A soft material like Rubber has a Poisson’s ratio of around 0.4999, on the other hand a hard object like gold has the value between 0.42 – 0.44. Clay, Copper and Aluminium have Poisson’s ratio near about 0.30-0.35. Cast iron has a 0.21-0.26 ratio. Super hard materials like concrete have a further low ratio of 0.1-.0.2 . 

Some Important points about Poisson’s Ratio

• The value of the poisson’s ratio is both a scalar and a dimensionless unitless number.
• It has a positive value for tensile deformation and a negative value for compressive deformation.
• There will be no change in the diameter or breadth of an item when the Poisson’s Ratio approaches zero (0).

What does it mean by Poisson’s Ratio for a Material:

The Poisson’s Ratio is the ratio of a material’s transverse contraction to its longitudinal extension strain in the direction of the stretching force. The stress or strain might be created by the body exerting force on the material. For compressive deformation, the Poisson’s ratio is negative, but for tensile deformation, the Poisson’s ratio is positive. The positive strain is in the transverse direction, according to the negative Poisson’s ratio. For the most part, the Poisson’s Ratio is in the range of 0 to 0.5.

Plastics have a Poisson’s Ratio that ranges from 0 to 0.5. When the Ratio is zero, there is no deduction in size or, to put it another way, no laterally contraction occurs when the material is elongated, but the density does. When the diameter of the material drops throughout the elongation process or when the material is elastomeric, a value of point five implies that the volume of the item will not change.

Poisson’s Ratio is usually not negative for most common materials, since most common materials get compressed in the cross direction when stretched. Most materials resist changes in volume, as defined by the bulk modulus K or sometimes known as B, more than changes in form, as determined by the shear modulus G. The shape distortion also helps in realignment of the interatomic connections.

Poisson’s Ratio: Bending

The Poisson’s Ratio governs the curvature of a bar or plate in the direction perpendicular to the bending. In the instance of bending a rubber, the anticlastic curvature is plainly visible.

Poisson’s Ratio: Anisotropy

The physical characteristics of anisotropic solids, such as honeycombs, single crystals, and various fibrous composites, are affected by the direction in which they are stretched or bent, including the Poisson’s ratio and Elastic Moduli. Because of the huge magnitude of these anisotropic materials, the Poisson’s ratio might be positive or negative.

Poisson’s Ratio: Viscoelastic Materials

The Poisson’s Ratio of the viscoelastic material is affected by the circumstances of the transient test, such as creep and stress relaxation. If the deformation is sinusoidal, the Poisson’s Ratio is also affected by the frequency and phase angle. When it comes to viscoelastic solids, the transverse strain is usually out of phase with the longitudinal strain.

Poisson’s Ratio: Phase Transformations 

The Poisson’s Ratio of a material can be significantly affected by phase change. The bulk modulus softens the greatest near a phase transition, although the shear modulus has no effect. With the proximity of the phase change, the Poisson’s Ratio drops and can even become negative. As a result, it’s critical to investigate the impact of phase change on a material’s Poisson’s ratio.

Poisson’s Ratio; Stress Waves

The Poisson’s ratio of the various materials influences the speed of propagation and reflection of stress waves. From a geographical standpoint, the compression to shear wave ratio is critical since it aids in determining the composition of a rock deep below the earth. The Poisson’s ratio affects the wave speed ratio as well. The Poisson’s Ratio has an impact on the stress distribution near fractures as well as the stress decay.

Relation between Poisson Effect and Poisson’s Ratio

The Poisson effect is measured using Poisson’s Ratio. The Poisson effect is a phenomenon in which material expands in a direction that is perpendicular to the compression direction. Isotropic, orthotropic, and other materials have various Poisson effects. The Poisson’s Ratio is widely used in pressurised pipe flow, structural geology, and other fields.

The Poisson Ratio aids in determining a material’s qualities. Those that do not contract are brittle, whereas those that do contract are ductile. The Poisson ratio also informs us that materials with a high Poisson ratio may be drawn more easily than those with a low Poisson ratio.

Examples of Poisson’s Ratio

Poisson’s Ratio is used extensively in engineering, from house design to rocket development. The capacity to predict how materials will behave under stress helps us to choose the right material for the job.

Poisson’s Ratio, for example, is widely used to identify building materials such as flat plates that will be bent. The greater the Poisson’s Ratio value, the more stiff the plate will be and the more stress it will be able to withstand.

Conclusion 

The Poisson effect is a phenomenon in which material expands in a direction that is perpendicular to the compression direction. Poisson’s Ratio is used extensively in engineering, from house design to rocket development. It is an important part of the application of physics in real life scenarios.