A tension test was performed on a steel specimen having an original diameter of 12.5 mm and gauge length

of 50 mm. Using the data listed in the table, plot the stress–strain diagram, and determine approximately the
modulus of toughness. Use a scale of 20 mm-50 MPa and 20 mm = 0.05 mm/mm.

Load (kN)
0
11.1
31.9
37.8
40.9
43.6
53.4
62.3
64.5
62.3
58.8

Elongation (mm)
0
0.0175
0.0600
0.1020
0.1650
0.2490
1.0160
3.0480
6.3500
8.8900
11.9380

I know that I have to use the equations sigma=(P/A) and epsilon=(dL/L) to get the points for stress and strain... but how do I get the values for the equations? I tried to get the stress with the second values of the table:

sigma=(11.1e3 Pa)/(pi*(0.0175e3m)^2)
I get 11.54 and it is supposed to be 90.45 MPa. How do I do these?

sigma is in fact Pressure, which is force/area. you are given force, compute area from the diameter.

epsilon is change of length divided by length. You are given deltaL (elongation). L was given as 50mm.
Surely you can calculate delta L /L

For each data point given, calculate those two quantities (sigma, deltaL/L), and plot the graph

To calculate the stress and strain values using the given data, you need to use the following formulas:

Stress (σ) = Force (P) / Area (A)
Strain (ε) = Change in length (ΔL) / Original length (L)

In this case, the original diameter is given as 12.5 mm, so the original radius (r) is 6.25 mm (0.00625 m). The gauge length (L) is given as 50 mm (0.05 m).

To calculate the area (A), you need to use the formula for the area of a cylinder:

A = π * (radius)^2

Now let's calculate the stress and strain for the second set of values from the table.

Given:
Force (P) = 11.1 kN = 11,100 N
Change in length (ΔL) = 0.0175 mm = 0.0000175 m

First, calculate the area (A):

A = π * (0.00625 m)^2
A = 0.00012272 m^2

Next, calculate the stress (σ):

σ = 11,100 N / 0.00012272 m^2
σ = 90,515.81 Pa
Note: To convert Pa to MPa, divide by 1,000,000.
σ = 90.52 MPa (approximately)

Finally, calculate the strain (ε):

ε = 0.0000175 m / 0.05 m
ε = 0.00035 (approximately)

Now you can plot the stress-strain diagram using these values. Use the given scale of 20 mm-50 MPa and 20 mm = 0.05 mm/mm.

To calculate the stress and strain values, you need to use the given load and elongation measurements and apply the appropriate equations.

First, convert the given values into SI units. There are 1,000 mm in 1 meter, so the elongation values need to be divided by 1,000, and the load values in kN need to be multiplied by 1,000 to convert them to Newtons.

Load (N):
0
11,100
31,900
37,800
40,900
43,600
53,400
62,300
64,500
62,300
58,800

Elongation (m):
0
0.0175 / 1,000 = 0.0000175
0.0600 / 1,000 = 0.0000600
0.1020 / 1,000 = 0.0001020
0.1650 / 1,000 = 0.0001650
0.2490 / 1,000 = 0.0002490
1.0160 / 1,000 = 0.0010160
3.0480 / 1,000 = 0.0030480
6.3500 / 1,000 = 0.0063500
8.8900 / 1,000 = 0.0088900
11.9380 / 1,000 = 0.0119380

Now, let's calculate the stress (sigma) and strain (epsilon) values for each data point using the given equations:

For stress:
sigma = P / A
where P is the load and A is the cross-sectional area.

The original diameter is given as 12.5 mm, so the radius (r) is 12.5 mm / 2 = 6.25 mm = 0.00625 m.
The cross-sectional area (A) is given by A = pi * r^2 = pi * (0.00625)^2 = 0.0001227137 m^2.

For strain:
epsilon = delta L / L
where delta L is the elongation and L is the original gauge length (50 mm = 0.05 m).

Now we can calculate the stress and strain for each data point:

Load (N)
0
11,100
31,900
37,800
40,900
43,600
53,400
62,300
64,500
62,300
58,800

Elongation (m)
0
0.0000175
0.0000600
0.0001020
0.0001650
0.0002490
0.0010160
0.0030480
0.0063500
0.0088900
0.0119380

Stress (Pa)
0
(11,100) / (0.0001227137)
(31,900) / (0.0001227137)
(37,800) / (0.0001227137)
(40,900) / (0.0001227137)
(43,600) / (0.0001227137)
(53,400) / (0.0001227137)
(62,300) / (0.0001227137)
(64,500) / (0.0001227137)
(62,300) / (0.0001227137)
(58,800) / (0.0001227137)

Strain (mm/mm)
0
0.0000175 / 0.05
0.0000600 / 0.05
0.0001020 / 0.05
0.0001650 / 0.05
0.0002490 / 0.05
0.0010160 / 0.05
0.0030480 / 0.05
0.0063500 / 0.05
0.0088900 / 0.05
0.0119380 / 0.05

Now, you have the stress and strain values for each data point that you can use to plot the stress-strain diagram.