Mechanical Properties Of Matter-I

Elastic Behaviour of Solids and the Concept of Stress and Strain Elasticity It is the property of a body by virtue of which it tends to regain its original size and shape after the applied force is removed.Examples of elastic materials − quartz fibre, phosphor bronze PlasticityIt is the inability of a body in regaining its original status on the removal of the deforming forces.Examples of plastic materials − bakelite, plastic StressThe restoring force or experienced by a unit area is called stress. S.I unit = Nm−2 Types of Stress Normal StressWhen the elastic restoring force or deforming force acts perpendicular to the area, the stress is called normal stress. Normal stress can be sub-divided into the following categories: Tensile StressWhen there is an increase in the length or the extension of the body in the direction of the force applied, the stress set up is called tensile stressHere,l = Original lengthΔl = Increase in length Compressive Stress When there is a decrease in the length or the compression of the body due to the force applied, the stress set up is called compressive stress.Here,l = Original lengthΔl = Increase in length Tangential or Shearing StressWhen the elastic restoring force or deforming force acts parallel to the surface area, the stress is calledtangential stress. StrainRatio of change in configuration to the original configurationStrain = It is a dimensionless quantity. Types of Strain Longitudinal Strain  Longitudinal Strain = Volumetric Strain Volumetric Strain =  Shearing StrainAn angle (in radian) through which a plane perpendicular to the fixed surface of the cubical body gets turned under the effect of a tangential force. Shearing Strain  Hooke's Law For small deformations, stress and strain are proportional to each otherStress α strainStress = k × strainWhere, k is the proportionality constant, and is known as the modulus of elasticity Stress-strain curve for brittle materials:  Note:When the material does not regain its original dimension, it is said to have a permanent set, and the deformation is said to be plastic deformation. Stress-strain curve for elastomers:They do not obey Hooke’s law, and always return to their original shape. Elastic Moduli Modulus of elasticity − According to Hooke’s law, within elastic limit,Stress ∝ StrainStress = E × Strain= E = constantWhere, E is known as modulus of elasticity Types of modulus of elasticity Young’s Modulus of Elasticity (Y)Y = Y = ∴ Y = Where,F - Force appliedr - Radius of the wirel - Original lengthΔl - Change in lengthUnit → Nm−2 or Pascal (denoted by Pa) Bulk modulus of elasticity (B)B = B = If P is the increase in pressure applied on the spherical body, thenP = F/a∴ B =  Where,F - Force applieda - Volume of the objectV - Original volumeΔV - Change in volumeUnit → Nm−2 or Pascal Compressibility (k) − Reciprocal of bulk modulus of elasticity (B) i.e.,k = 1/B Modulus of Rigidity or shear modulus of elasticity (G)G = Here, ∠HAH′ = θ = ∠GBG′ and HH′ = ΔLShearing strain = θ = Tangential stress = F/a∴ G = Where, F - Force applieda - Areal - Original lengthΔl - Change in lengthUnits → Nm−2 or Pascal Applications of Elastic Behaviour of Materials The metallic parts of the machinery are never subjected to a stress beyond elastic limit; otherwise they will get permanently deformed. The thickness of the metallic rope used in the crane in order to lift a given load is decided from the knowledge of elastic limit of the material of the rope and the factor of safety. The bridges are designed in such a way that they do not bend much or break under the load of heavy traffic, force of strongly blowing wind, and their own weights.he depressionδ produced at middle point in the bar is given by,Where,Y − Young’s modulusW − Load attached at its middle pointl − Length of the barb − Breadth of the bard − Depth supported horizontallyIn order to have smaller depression (δ), for a given load, l should be small while Y, b,and d should be large.