RE: I need help understanding what to do.?

Question

I have a graph that plots data from materials testing. I am a summer intern an my supervisor gave me the job to process and enter the information in an experimental data base. We have a metal bar that is placed in a device that rotates the bar while applying a certain stress to it. I dont run the machine I just look at the reports so the info I have is what they give me. the Y axis represents the stress applied. the x-axis represents the revolutions. the points are where the material broke at the given stress. so my points are (3498000,90) (6271600,85) (21939300, 80) (62070100,75) (87358800,70). just to be sure I am clear 3498000 is how many revolutions it took for the material to break at 90 KSI. So i need to find out approximately what stress would break the material @ 10,000,000 revolutions and 100,000,000 revolutions.

Answer 1

interpolate and extrapolate.

at 10,000,000 revolutions, (interpolate)
[(80-85)/(21939300-6271600)]=
[(x-85)/(10,000,000-6271600)]
-5/15667700 = (x-85)/3728400
x-85 = -1.189836415
x = 83.81016359

at 100,000,000 revolutions, (extrapolate)
[70-75)/(87358800-62070100)]=
[(x-70)/(100,000,000-87358800)
-5/25288700 = (x-70)/12641200
x-70 = -2.499377192
x = 67.50062281

Answer 2

The best method for extrapolating is divided differences. Start by setting up two columns x (revolutions) and y (ksi):

x.....................y
3498000.......90
6271600.......85
21939300......80
62070100......75
87358800......70

Then you start making more columns by subtracting y values then dividing by x values. The next column would look like this:
(85-90)/(6271600-3498000) = -5/2773600
(80-85)/(21939300-6271600) = -5/15667700
etc

The second column will have only 4 entries.

Continue this process making another column, only this time you subtract values from the previous column divided by every other x-value, thusly:

(-5/15667700 - -5/2773600)/(21939300 - 3498000) = 8.044895915*10^-14

Continue this process until you have a column with only one entry. Once you get to that point, you take the first entry in each column and multiply by x-values thusly:

3498000 + (-5/2773600)(x-6271600) + 8.044895915*10^-14(x-6271600)(x-21939300) + ....

What you will have is a 4th degree equation (n data points define an n-1 degree equation) and you can plug in 10000000 and 100000000 to find the extrapolated ksi values.

It isn't pretty, but I can send you an excel sheet that has all the numbers and formulas on it.

I used the same process when I worked for the Dept. of Transportation here, calculating compacted soil and asphalt densities.

Answer 3

You have plotted this data. Decide what approximate shape the data represents. You then want to approximate the equation that represents that shape. Then once you have that equation, you can plug in a new value of x to estimate the corresponding value of y.

Begin by saying the shape is linear. You will use Linear Regression to calculate the best fitting straight line to those points. EXCEL has a way to do this in TOOLS, DATA ANALYSIS, REGRESSION.

If your points are clearly non-linear, the problem gets a little harder.

Answer 4

My analysis is based on pure logic, and has little to do with any hardcore metalurgy theory.
The distance between the points (6.2 mil, 85) and (21. mil, 80) is about 15 mil revolutions., the mid point is about (13.7 mil, 82.5) so I surmise that 10mil should break at approximatly 81.25 psi.
100,000,000 mil will probally breakdown between 65 and 60 psi psi based on the fact that 21mil broke at 80, then 40 more mil revolutions broke at 75, 20 more mil revolutions broke at 70, so I would expect 10 more mil to break at 65 wich puts us at about 97mil, and 5 mil more revolutions will put us at about 103 mil revolutions and 60 psi.