Chapter 9, Problem 37QAP

To determine

(a)

What is the yield strength if the following data are associated with an alloy of steel, plot a graph of stress versus strain for the alloy?

Strain (%)	Stress ( ${10}^{9}N/m^2$)	Strain (%)	Stress ( ${10}^{9}N/m^2$)
0	0	1	300
0.1	125	1.5	325
0.2	250	2	350
0.3	230	2.5	375
0.4	230	3	400
0.5	235	3.5	375
0.6	240	4	350
0.7	250	4.5	325
0.8	260	5	300
0.9	270

Answer to Problem 37QAP

The yield strength is the tensile stress at which the material becomes permanently deformed $=250\times {10}^{9}N/m^2$

Explanation of Solution

Calculation:

The graph is drawn and is given by

The yield strength is the tensile stress at which the material becomes permanently deformed $=250\times {10}^{9}N/m^2$

Conclusion:

The yield strength is the tensile stress at which the material becomes permanently deformed $=250\times {10}^{9}N/m^2$

To determine

(b)

The ultimate strength if the following data are associated with an alloy of steel, plot a graph of stress versus strain for the alloy?

Strain (%)	Stress ( ${10}^{9}N/m^2$)	Strain (%)	Stress ( ${10}^{9}N/m^2$)
0	0	1	300
0.1	125	1.5	325
0.2	250	2	350
0.3	230	2.5	375
0.4	230	3	400
0.5	235	3.5	375
0.6	240	4	350
0.7	250	4.5	325
0.8	260	5	300
0.9	270

Answer to Problem 37QAP

The ultimate strength is the maximum tensile stress the material can withstand $=400\times {10}^{9}N/m^2$

Explanation of Solution

Calculation:

The graph is drawn and is given by

The ultimate strength is the maximum tensile stress the material can withstand $=400\times {10}^{9}N/m^2$

Conclusion:

The ultimate strength is the maximum tensile stress the material can withstand $=400\times {10}^{9}N/m^2$

To determine

(c)

Young's modulus for the material if the following data are associated with an alloy of steel, plot a graph of stress versus strain for the alloy?

Strain (%)	Stress ( ${10}^{9}N/m^2$)	Strain (%)	Stress ( ${10}^{9}N/m^2$)
0	0	1	300
0.1	125	1.5	325
0.2	250	2	350
0.3	230	2.5	375
0.4	230	3	400
0.5	235	3.5	375
0.6	240	4	350
0.7	250	4.5	325
0.8	260	5	300
0.9	270

Answer to Problem 37QAP

The Young's modulus is the slope of the initial linear region $=125000\times {10}^{9}N/m^2$

Explanation of Solution

Given info:

Formula used:

Calculation:

The graph is drawn and is given by

The Young's modulus is the slope of the initial linear region $=125000\times {10}^{9}N/m^2$

Conclusion:

The Young's modulus is the slope of the initial linear region $=125000\times {10}^{9}N/m^2$