Question

Figure shows stress-strain curve for a given material. What are (a) Young’s Modulus and (b) approximate yield strength for this material?

Answer 1

First of all, we have to understand the meaning of Young’s Modulus.Young’s Modulus of a substance is defined as the elasticity of a substance, in some way. It is the amount of stress that acts on a substance having some strain. Then, we have to understand the yield strength of the material and hence find the answer to the given question.

Complete step by step answer:
Young’s Modulus also known as the modulus of elasticity is referred to as the mechanical property which indicates the tensile strength of a substance. It is the amount of strain that a material possesses to the stress exerted on the same amount of the material. The SI unit of Young’s Modulus is $\dfrac{N}{{{m^2}}}$. So, in order to find the Young’s Modulus, the formula required is,
${\text{Young's Modulus}} = \dfrac{{{\text{Stress}}}}{{{\text{Strain}}}}$

(a) In the given graph, let us consider the point A we get,
$\text{Young’s Modulus} = \dfrac{{150 \times {{10}^6}}}{{0.002}} \\\ \therefore \text{Young’s Modulus} = 7.5 \times {10^{10}}{\text{ }}\dfrac{N}{{{m^2}}}$

(b) Yield strength of a material is defined as the stress level till which the material starts to deform plastically is known as yield strength. The yield point is the point on the curve on which it gradually starts to decrease.In the given graph, point B is the yield point.
$\text{Yield strength} =300 \times {10^6}{\text{ }}\dfrac{N}{{{m^2}}} \\\ \therefore \text{Yield strength} = 3 \times {10^8}{\text{ }}\dfrac{N}{{{m^2}}}$
So, the yield strength is $3 \times {10^8}{\text{ }}\dfrac{N}{{{m^2}}}$.

Note: It must be noted that at plastic deformation the structure or shape of the substance does not deform totally or permanently, it just temporarily deforms. It is often difficult to determine the exact point where yielding begins so we consider an approximate value. This is where the stress to give a certain amount of strain is used to define the yield strength.