Question

The ratio of stress and strain, called modulus of elasticity, is found to be a characteristic of the material. Experimental observation shows that for a given material, the magnitude of the strain produced is same whether the stress is tensile or compressive. The ratio of tensile (or compressive) stress (σ) to the longitudinal strain (ε) is defined as Young's modulus and is denoted by the symbol Y. Y = Stress (σ)/Strain (ε) = (F/A)/(ΔL/L) = F × L/(A × ΔL) Since strain is a dimensionless quantity, the unit of Young's modulus is the same as that of stress i.e., N m-2 or Pascal (Pa)

Assertion: On elastic bodies, though we apply force and experience elongation, it is a general practice to plot stress versus strain instead of plotting force versus elongation graph. Reason: Stress versus strain plotting makes the graph independent of the geometry of the sample body and reflects only the material property.

Draw stress and strain curve. Explain the various region or points that are necessary to understand this graph (i) Proportional Limit (ii) Elastic Limit (iii) Yield Point (iv) Ultimate Stress Point (v) Fracture or Breaking Point.

The graph shown below shows qualitatively the relation between the stress and the strain as the deformation gradually increases. Within Hooke's limit for a certain region stress and strain relation is linear. Beyond that up to a certain value of strain the body is still elastic and if deforming forces are removed the body recovers its original shape.