Elastic behaviour of solids
* When a force acts on a body, it accelerates in the direction of the net force.
* When a set of equal and opposite forces acts on a body, there is no net force on the body but it gets deformed, changing its size or shape or both.
* The deformation of the body changes the inter molecular separation, and gives rise to inter-molecular forces.
* In some materials, when deforming forces are removed, the inter-molecular forces try to restore the body to its original shape and size. Materials such as these are called elastic and this property of a body is called elasticity.
* Some materials display little or no tendency to return to their original size and shape even when deforming forces are removed. Such materials are called plastic and this property is called plasticity.
* Deforming forces may change the length, volume or shape of a body on which they act.
Stress strain and Hooke’s law
* Stress is the sum total of restoring intermolecular forces per unit area within a deformed body. It is measured as the external deforming force per unit area.
* Strain is defined as the fractional deformation produced in the body by external deforming forces.
* Longitudinal stress is equal to the deforming force per unit area.
* Longitudinal strain is the ratio of change in length to its original length.
* Bulk or volume stress is equal to the change in pressure. Bulk or volume strain is the ratio of change in volume to the original volume.
* Shear or tangential stress is equal to tangential deforming force per unit area. Shear strainis the angle through which the dimension perpendicular to the faces under the action of deforming forces rotates.
* Hooke’s law states that for small values of strain, stress is directly proportional to strain.
* All materials do not follow Hooke’s law.
Stress strain curve
* Stress strain curve is a straight line for low values of strain, and Hooke’s law is obeyed.
* Beyond the elastic limit, a material cannot regain its original size on removal of the load.
* Materials that fracture at small values of strain are brittle and those that fracture at higher values of strain are ductile.
Elastic modulus-young modulus
* The ratio of stress to strain in the straight line on the stress strain curve is called modulus of elasticity.
* Young’s modulus is the ratio of longitudinal stress to longitudinal strain.
* Different materials have different values of young’s modulus.
* The higher young’s modulus, the more elastic the material.
Shear and bulk modulus
* When a pair of equal and opposite forces is applied tangentially to opposite end faces of a body, the shape of the body is distorted.
* The ratio of shear stress to shear strain for a material is the shear modulus or the modulus of rigidity.
* When deforming forces are perpendicular to a body’s surface at each point, the volume of the body changes.
* Bulk modulus is the ratio of bulk stress to bulk strain.
* Compressibility is the reciprocal of bulk modulus.
Applications of elastic behaviour of materials
* The theory of elasticity is used to design safe and stable manmade structures.
* Cranes used to lift loads use ropes that are designed so that the stress due to the maximum load does not exceed the breaking stress.
* Load bearing bridges and buildings are constructed using beams supported on pillars.
* Beams and pillars are designed to remain stable and safe within the range of the maximum load they are designed to carry.
* The maximum height of a mountain on the earth can also be estimated using the Theory of Elasticity.