Question

Question: Figure 12-55 shows the stress–strain curve for a material. The scale of the stress axis is set by,s = 300 in units of${\mathbf{10}}^{\mathbf{6}}\mathit{N}\mathbf{/}{\mathit{m}}^{\mathbf{2}}$. (a) What is the Young’s modulus? And (b) What is the approximate yield strength for this material?

Figure:

Short answer

Answer:

1. The Young’s modulus for the material is$7.5\times {10}^{10}\frac{N}{m^2}$
2. The approximate yield strength is $2.9\times {10}^8\frac{N}{m^2}$.

Step-by-step solution

Determine the given quantities 

The stress-strain curve for a material is given for which scale is s =300 in units of 10⁶ N/m²

Determine the concept of force, tension and torque

Young’s modulus is the ratio of stress to strain. The stress is force per unit area. The strain is defined as change in length per unit original length.

Using the formula for Young’s modulus, find the Young’s modulus of the material.

Consider the formula is:

$E=\frac{stress}{strain}$

(a) Determine the values of Young’s modulus

The given plot is the plot of stress against strain. The slope of the plot will give us the ratio of stress against strain. It is equal to Young’s modulus. Therefore,

$$\begin{gathered} E=\frac{stress}{strain} \\ =slopeofthestress-straincurve \end{gathered}$$

From the given graph, the slope is equal to$7.5\times {10}^{10}N/m^2$ .

Therefore, the Young’s modulus is equal to$7.5\times {10}^{10}N/m^2$

(b) Determine the approximate yield strength of material

As the range of curve is linearly extends up to$2.9\times {10}^{8}N/m^2$.

Therefore,the approximate yield strength is$2.9\times {10}^{8}N/m^2$