CBSE Class 11: Mechanical Properties of Solids

The mechanical properties of solids elaborate on their characteristics, such as their resistance to deformation and their strength. Strength is the ability of an object to withstand the applied stress, to what extent can it bear the stress. Resistance to deformation is how resistant any object is to a change of shape. If the resistance to deformation is less, the object can easily change its shape, and vice versa.
 

• Elastic properties of solids
• Tension and stress
• Hooke's law
• Shear modulus of stiffness, bulk modulus, and Young's modulus
• Poisson's Ratio and Elasticity

Deforming Force: A force that produces a change in the configuration of the object upon applying it is called a deforming force.

Elasticity :  Elasticity is an object's ability to return to its initial configuration following the removal of a deforming force.

Elastic Limit : The elastic limit is the maximum deforming force at which the body fully returns to its previous shape if the deforming force is withdrawn; at this point, increasing the deforming force causes the body to permanently lose its elasticity.

Perfectly elastic bodies : Perfectly elastic bodies are those that instantly and totally return to their initial configuration upon the absence of the deforming force. such as phosphor bronze, quartz, etc. Perfectly plastic bodies include putty, paraffin, wax, and other materials that do not even partially return to their previous shape when the deforming force is removed.

Stress : In a deformed body, stress is the internal restorative force per unit area.Its dimensional formula is [M¹ L^–1 T^–2] and its unit is N/m2, or Pascal. A tensor quantity is stress.
There are two kinds of stress.

(i) Typical Stress: The stress is referred to as normal stress if the deforming force is applied to the area normally.Tensile tension is the type of stress that occurs when there is an increase in length.Compression stress is the type of stress that occurs when there is a reduction in length

(2) Tangential Stress: Tangential stress is the type of stress that results from applying a tangential deforming force.

Strain: The fractional modification in arrangement is referred to as a strain.It is a dimensionless quantity with no unit. The configuration modification indicates that there are three different forms of strain. 

(1) Longitudinal strain  
(2) Volumetric strain 
(3) Shearing strain is the angular displacement of the plane perpendicular to the fixed surface.
Hooke’s Law: The stress and strain are proportionate within the elastic limit.

                              E * Strain = Stress

where E is the body's material's modulus of elasticity.

Types of Modulus of Elasticity:

1. Young’s Modulus of Elasticity : Within the elastic limit, it is defined as the ratio of normal stress to longitudinal strain.Its unit is N/m2 or Pascal, and its dimensional formula is [].

                              y = longitudinal strain / normal stress.

2. Bulk Modulus of Elasticity: Within the elastic limit, it is defined as the normal stress to volumetric strain ratio.

                                 K= = Δp V / Δ V
where, Δp = Change in pressure.
Its unit is N/m2, or Pascal and its dimensional formula is [M-1T-2 ].
3. Modulus of Rigidity (η): It is defined as the ratio of tangential stress to the shearing strain, within the elastic limit.

                                        η = Tangential stress / Shearing strain
Its urut is N/m2 or Pascal and its dimensional formula is [ML-1T-2 ].

Compressibility : The reciprocal of a material's bulk modulus of elasticity is its compressibility. C = 1 / k is the compressibility. Its CGS unit is dyne-1 cm2, and its SI unit is N-1m2. Rubber is less elastic than steel. Gases are the least elastic, while solids are the most elastic. The modulus of stiffness is zero for liquids. Only solid materials have a modulus of stiffness (η) and Young's modulus (Y).

Limit of Elasticity : The maximum value of deforming force for which elasticity is present in the body is called its limit of elasticity.
Breaking Stress: The minimum value of stress required to break a wire, is called breaking stress. Breaking stress is fixed for a material but breaking force varies with area of cross-section of the wire.

elastic relaxation Time : Elastic relaxation time is the amount of time that passes until the deforming force is removed and the configuration returns to its initial state.Phosphor bronze and quartz have very little time to do this.

Elastic Reaction:  The elastic aftereffect refers to the momentary lag in the elastic body's return to its initial configuration following the cessation of the deforming force.

Elastic Fatigue: Elastic fatigue is the characteristic of an elastic body that causes it to behave less elastically when subjected to repeated, alternating deforming forces.

Ductile Materials: Ductile materials, such as copper, silver, iron, aluminum, etc., exhibit a wide plastic range that extends beyond the elastic limit. Sheets and springs are made of ductile materials. brittle substances Brittle materials are those, such as glass, cast iron, etc., that exhibit very little plastic range beyond the elastic limit.

Elastomers: Elastomers are materials, such as rubber, the elastic tissue of the aorta, the main blood conduit that comes from the heart, etc., for which the strain created is substantially greater than the stress applied, within the limit of elasticity. There is no plastic range for elastomers.

Elastic Potential Energy in a Stretched Wire: The work done in stretching a wire is stored in the form of the potential energy of the wire.

                                 Potential energy U = Average force * Increase in length

Elastic potential energy per unit volume

U = * Stress * Strain

U=Young’s modulus) * (Strain)2

Elastic potential energy of a stretched spring = kx2

where k is the force constant of the spring and x is the change in length.

Thermal Stress: Thermal stress is the result of changing the temperature of a rod that is fixed at both ends.
                                             Thermal stress =  = yαΔθ
where, α = coefficient of linear expansion of the material of the rod.When temperature of a gas enclosed in a vessel is changed, the thermal stress produced is equal to change in pressure (Δp) of the gas.

Thermal stress = Δ p = Ky Δ θ

where, K = bulk modulus of elasticity and
            γ = coefficient of cubical expansion of the gas.
                   Interatomic force constant
            K = Yro
where ro = interatomic distance.

Poisson’s Ratio: When a deforming force is applied at the free end of a suspended wire of length 1 and radius R, its length increases by dl but its radius decreases by dR. Now two types of strains are produced by a single force.

Longitudinal strain = ΔUl
Poisson’s Ratio (σ): The theoretical value of Poisson’s ratio lies between -1 and 0.5. Its practical value lies between 0 and 0.5

FAQ

Q. What are the mechanical properties of solids?

Ans. Mechanical properties refer to the characteristics of solids that describe their response to applied forces or loads. These properties include elasticity, plasticity, strength, hardness, toughness, ductility, and brittleness.

Q. What is elasticity?

Ans. Elasticity is the ability of a solid material to deform reversibly under the influence of an applied force and return to its original shape and size after the force is removed. It is characterized by Young's modulus, which quantifies the stiffness of a material.

Q. What is plasticity?

Ans. Plasticity is the ability of a solid material to undergo permanent deformation without rupturing when subjected to an applied force beyond its elastic limit. Plastic deformation involves the rearrangement of atomic or molecular structure within the material.

Q. What is strength?

Ans. Strength refers to the ability of a solid material to withstand an applied force without failure or deformation. It is often characterized by parameters such as tensile strength, compressive strength, shear strength, and yield strength.