What is Hooke’s Law?
Stress and strain take completely different forms in, unlike situations. Normally, for tiny deformations, the stress and strain are proportional to each other, and this is referred to as Hooke’s Law. Steel displays linear-elastic behaviour in most engineering applications; Hooke's law is valid for it throughout its elastic span. For some other materials, such as aluminium, Hooke's law is only valid for a part of the elastic range.
Hooke’s Law Definition
“Hooke’s law defines that the strain of the substance is proportional to the applied stress within the elastic limit of that substance.”
When the elastic materials are stretched or compressed, the atoms and molecules disfigure until the force is applied, and when the force is removed, they return to their previous state.
Hooke’s law Formula
Mathematically, within the proportional limit of a material the Hooke’s law formula is expressed as follows-
σ = Eε
Where, in SI units
- σ is the stress; Pa
- E is the modulus of elasticity or Young’s modulus, Pa (Normally GPA)
- ε is the strain, dimensionless
Hooke’s Law Graph
The figure below shows the stress-strain curve for mild steel.
The material shows elastic behaviour up to the proportional limit, Beyond that the material loses elasticity and shows plasticity.
From the emergence to the proportional limit nearing yield strength, the straight line suggests that the material follows Hooke’s law. Beyond the elastic limit between proportional limit and yield strength, the material no longer has its elasticity and shows plasticity. The area under the curve from emergence to the proportional limit falls under the elastic span. The area under the curve from a proportional limit to the fracture point/rupture falls under the plastic span.
The material’s ultimate strength is described based on the maximum ordinate value given by the stress-strain curve (from emergence to rupture). The value gives the rupture strength at a point of rupture.
Hooke’s Law Applications
Hooke’s Law is used in all branches of science and engineering; For understanding the behaviour of elastic materials there is no replacement for Hooke's law. Following are some of the applications of Hooke’s Law:
- It is used as a fundamental principle behind the manometer, spring scale, and the balance wheel of the clock.
- Hooke’s law sets the foundation for seismology, acoustics and molecular mechanics.
Hooke’s Law Disadvantages
Even though Hooke’s law is used widely in Engineering, it’s not a universal principle. The law is not applicable as soon as the elastic limit of a material is surpassed. Usually, for solid particles, Hooke’s law provides precise results when the deformations are small. Numerous materials deviate from Hooke’s law even well before reaching the elastic limit. Following are some of the disadvantages of Hooke’s Law:
- Hooke’s law comes to an end when applied beyond the elastic limit of a material.
- Hooke’s law is correct just for solid bodies if the forces and deformations are small.
- Hooke’s law isn’t a universal principle and solely applies to the materials as long as they aren’t stretched well past their capacity.
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