Plotting and Calculations

After a tensile test is performed, the output data is a computer file consisting of numerical values in three columns. Sample raw data files for select experiments can be accessed by clicking on the link to the left. A portion of a typical file is shown below.

Time		Force		Strain
0.500000        -0.019673       0.000254
0.750000        0.016394        0.000218
1.000000        0.009836        0.000145
1.250000        -0.016394       -0.000036
1.500000        -0.009836       0.000182
1.750000        0.003279        0.000073
2.000000        0.022952        0.000109
2.250000        -0.003279       -0.000073
2.500000        0.009836        0.000073
2.750000        0.026230        0.000182
3.000000        0.039346        0.000327
3.250000        0.039346        0.000073
3.500000        0.052461        -0.000109
3.750000        0.049182        0.000254
4.000000        0.085249        0.000290
4.250000        0.108201        0.000109
4.500000        0.108201        0.000073
4.750000        0.114758        0.000036
5.000000        0.144268        0.000290
5.250000        0.163940        0.000327

The first column contains the time at which the sample data in that row was measured. The second column contains the tensile force applied by the machine in kilo-pounds. The third column contains the strain. For the lab report associated with the tensile test, you are required to process this data using some computer plotting application (such as Matlab or Mathematica) to plot the stress versus strain curve. Remember that the applied load and not the stress is provided in the data file.

Such a plot generated using Matlab for the test data is shown in Figure 13. The different regions that were described earlier can now be identified on this figure. You are required to find and label the following from this plot:

1. Young's modulus,
2. Yield strength,
3. Ultimate strength,
4. Fracture strength.

Figure 13: The stress-strain plot from data

Exercise: Find and label Young's Modulus, the yield strength, the ultimate strength, and the fracture strength on the above plot.

Check your answers.

The Young's modulus is the slope of the initial linear region of the stress-strain curve. The Ultimate strength is the maximum Y coordinate of the curve. The fracture strength is the value of the stress at the farthest point from the Y-axis.

Some materials have a sharp yield point i.e., they behave elastically up to a certain point and then the stress-strain curve flattens abruptly. For such behavior the yield point is the point where the curve flattens. It is very common for materials to have a gradual transition from linear elastic to plastic yielding behavior. In such materials a standard procedure to determine the yield point has been developed. This procedure is described below.

Figure 14: Yield strength determination

To measure the yield strength, first draw a zoom of the curve near the initial linear portion containing a little of the yield region as shown in Figure 14. Note that the zoom can be done using the computer program, by resetting the axis to contain the origin and a point close to the end of the linear region. After printing this figure, you can draw a line parallel to the initial linear portion, and where this line intersects the curve is the yield point. The Y coordinate of this point is the yield strength.