What is Elasticity, and Elastic Limit?

          In this article we are going to learn about, what is elasticity, and what is elastic limit. These terms keeps a vital role in the study of subject strength of materials. Understanding about Stress and Strain is feasible when one must have the knowledge of these terms. Let's discuss about them one by one below.

What is Elasticity?

          When an external force is applied on a body the body tends to undergo some deformation. If the body returns back to its original shape and size (which means the deformation disappears completely) on the removal of the load, the body is known as Elastic Body. The property by virtue of which any material regains its original shape and size when load acting on it is completely removed is called Elasticity.

Elasticity: The property of a material by virtue of which it returns back to its original position (i.e., shape and size) after the removal of external force or load, is called Elasticity.

What is Elastic limit?

          A body will regain its previous shape and size only when the deformation caused by the external force, is within a certain limit. Thus there is a limiting value of force up to and within which, the deformation caused completely disappears on the removal of the external force. The value of stress corresponding to this limiting force is known as the elastic limit of the material. Elastomers like Rubber have the highest Elastic limit. The behavior can be explained by Hook's Law.

Elastic Limit: It is defined as the value of stress up to and within which the material regains its original position (i.e., shape and size) on the removal of external force.

          If the value of external force is so large that the stress exceeds the elastic limit, then the body will not completely regains its original position. The body loses its property of elasticity to some extent. And if the external force acting on the body is removed, in this condition the body will not return to its original shape and size and there will be  residual deformation within the material. 

Credits: Slideshare.net

                Scribd.com

TYPES OF STRESSES

Stresses are two types they are

               1. Normal stresses, and 

               2. Shear stresses

          Normal stress is the stress which acts in a way perpendicular to he area. It is represented by 'σ' (SIGMA). Normal stress is further divided into Tensile stress and Compressive stress.

Let us discuss each of them briefly

1. Tensile stress:

          The stress induced in a body, when subjected to two equal and opposite pull forces as shown fig., as a result of which there is an increase in length, is known as Tensile stress. The ratio of increase in length to the initial (or) original length is known as Tensile strain. The tensile stress acts normal to the area and it pulls on the area. 

              Let P = Pull force acting on the body,

                     A = Cross-sectional area of the body, 

                     L = Original length of the body, 

                   dL = Change in length 

                    σ  = Stress induced in the body, and 

                     e = Strain 

          Below fig., shows a bar subjected to a tensile force 'P' at its ends. Consider a cross section x-x which divides the bar into two parts. The part left to the section x-x, will be in equilibrium if Tensile force (P)=Resisting force (R). Similarly the part which is right to the cross section x-x, will be in equilibrium if P= Resisting force. This resisting force per unit area is known as Tensile stress or Intensity of stress.

2. Compressive stress: The stress induced in a body, when it is subjected to two equal and opposite push forces as shown in fig., as a result of which there is a decrease in length of the body, is known as Compressive Stress. The ratio of decrease in length to the initial (or) original length is known as Compressive strain. The compressive stress acts normal to the area and it pushes on the area. 

  

3. Shear stress: The stress induced in a body, when it is subjected to two equal and opposite push forces which are acting tangentially across the resisting section as shown in fig., as a result of which the body tends to shear off across the section, is known as Shear Stress. The corresponding strain is known as Shear strain. The shear stress which acts tangential to the area. Which is represented by 'τ' (Tau).

Credits: Mechanical engineers

                Slideshare.net

                Civilengineering.blog

STRAIN

          When a body is subjected to some external force, we observe some change in dimension of the body. The ratio of change in dimension to the original dimension of the body is known as "Strain". Strain is Dimensionless quantity.

           Strain is classified into:

                    1. Tensile strain

                    2. Compressive strain

                    3. Volumetric strain

                    4. Shear strain

          If there is some increase in length of a body due to some external force, then the ratio of increase in length to the original length of the body is known as Tensile strain. But if there is some decrease in length of the body, then the ratio of decrease in length to the original length of the body is called as Compressive strain.

          The ratio of change in volume to the original volume of the body is called Volumetric strain.

          The strain produced by the shear stress is known as Shear strain.

Credits: Mechanical engineers

STRESS

          Consider some external force acting on a body, the force of resistance per unit area offered by a body against deformation is known as Stress. This external force which is acting on body is called the Load (or) Force. When the load is applied on the body while the stress is induced in the material of the body. The loaded body remains in equilibrium when the resistance offered by the body against deformation and the applied load are equal. 

Stress is denoted by a letter "σ" (SIGMA)

Mathematically stress is written as σ = P/A

          Where σ = Stress (or  Intensity of stress)

                       P = External force (or) Load

                       A = Cross sectional area.

Units of Stress:

          Units of stress depends upon two factors, they are units of Load and Units of area. 

In MKS units, the force is expressed in kgf and area in square meters, so stress units are kgf/m^2.
In SI units, the force is expressed in Newtons and area in meter squares, hence units of stress becomes N/m^2.

SIMPLE STRESSES AND STRAINS

INTRODUCTION:

          When an external force acts on a body, the body tends to undergo some deformation. The body resists the deformation due to cohesion between the molecules. The resistance by which the body tends to oppose the deformation is termed as "Strength of Materials". The resistance that the material offered within certain limit is proportional to the deformation of the material by the external force. Also within this limit resistance is equal to the deformation. But beyond the elastic limit, the resistance offered by the material is less than the applied load. In this case, the deformation increases until the failure takes place.

          Within the elastic stage, the resisting force equals to the external force. This resisting force per unit area is called Stress (or) Intensity of Stress. 

Credits: All mechanical engineers

               wikipedia

               Slideshare.net