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Young's Modulus of Elasticity Problems  
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#1
Apr2213, 04:02 PM

P: 94

1. The problem statement, all variables and given/known data
Calculate Young's Modulus of Elasticity for the three materials using the graphs only. Stress (N/m2) Strain 70 0.06 100 0.11 150 0.22 200 0.35 220 0.48 2. Relevant equations ε = Stress / Strain 3. The attempt at a solution I believed that to calculate Young's Modulus was a case of stress over strain but surely it should give the same value throughout the elastic region to be a constant. The stress and strain results provided must be correct as they were already provided. 70 / 0.06 = 1166.66 100 / 0.11 = 909.09 150 / 0.22 = 681.82 200 / 0.35 = 571.43 220 / 0.48 = 458.33 So my main question is why are these so different, am i applying an incorrect formulae. Please note i was only using the formulae because i wanted to check i was getting it right and wasn't sure how to use the graphs to obtain the value. How do a derive the youngs modulus from a StressStrain graph? Please help as i only have 1 more day before this is due in. Many thanks, Joe 


#2
Apr2213, 04:33 PM

P: 3,246

Not my field but I found this which suggests the curve isn't allways straight...
Presumably the Youngs modulus normally quoted is the slope at the bottom left in the elastic region. Perhaps wait for other suggestions. 


#3
Apr2213, 04:41 PM

P: 3,246

Do you know what the material is? What units for strain?..
I ask because a youngs modulus of 1000 N/m^{2} seems quite low.. For example this page quotes that of rubber as 0.01 * 10^{9} to 0.1 * 10^{9} N/m^{2} http://www.engineeringtoolbox.com/yo...lusd_417.html 


#4
Apr2213, 05:13 PM

P: 94

Young's Modulus of Elasticity Problems 
That is the lowest values that were pregiven, the other 2 materials are
Stress Strain E 50000000 0.00128 39062500000 100000000 0.0016 62500000000 150000000 0.00187 80213903743 200000000 0.00213 93896713615 250000000 0.00227 1.10132E+11 300000000 0.00253 1.18577E+11 350000000 0.00339 1.03245E+11 375000000 0.00427 87822014052 400000000 0.00707 56577086280 Stress Strain E 100000000 0.00109 91743119266 200000000 0.00145 1.37931E+11 300000000 0.00182 1.64835E+11 400000000 0.00215 1.86047E+11 470000000 0.00236 1.99153E+11 460000000 0.00273 1.68498E+11 460000000 0.00291 1.58076E+11 500000000 0.00318 1.57233E+11 550000000 0.00382 1.43979E+11 600000000 0.00436 1.37615E+11 The idea of the assignment is to calculate the modulus of E and then research into what materials they could be. I'm going to presume the one i have already given would be something such as glass, which would explain why its so different. I'm meant to calculate the E from the graphs that i have anyway, how do i go about this? I thought modulus was meant to be a consistant number across the whole elastic region so why does it change?? Thanks 


#5
Apr2213, 06:34 PM

Emeritus
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Thanks
PF Gold
P: 6,727

Not every material has a perfectly elastic region in its stressstrain curve.



#6
Apr2213, 06:37 PM

P: 94

So what value would i use for the elasticity since there so different, would i have to take an average?



#7
Apr2213, 09:32 PM

Mentor
P: 5,375

Show us what the stressstrain graphs look like. (Strain = abscissa, Strain = ordinate). Seeing the graphs by eyeball should tell a lot.
Chet 


#8
Apr2213, 11:44 PM

Emeritus
Sci Advisor
HW Helper
Thanks
PF Gold
P: 6,727

strain = abscissa, stress = ordinate



#9
Apr2313, 02:24 AM

P: 94

http://imageshack.us/f/194/materialx.jpg/ http://imageshack.us/f/38/materialy.jpg http://imageshack.us/f/209/materialz.jpg There are the three stressstrain graphs 


#11
Apr2313, 07:04 AM

Mentor
P: 5,375

These plots that you have shown so far are already very revealing. 


#12
Apr2313, 07:35 AM

P: 94

Thankyou, my initial task was to calculate the CSA which i did at 0.00002m2. I was pregiven Load and Extension data for 2 materials and given StressStrain data for the third. I was tasked to calculate the stressstrain data for all three and then plot the relevant graphs.
Material X TEST DATA FOR X LOAD..EXT...CSA.........Stress (F/A)..Strain........Orig Length E (Stress / strain) 1000..0.48...0.00002....50000000.....0.00128............375...390625000 00 2000..0.6....0.00002.....100000000...0.0016..............375...62500000 000 3000..0.7....0.00002.....150000000...0.001866667......375...80357142857 4000..0.8....0.00002.....200000000...0.002133333......375...93750000000 5000..0.85..0.00002......250000000..0.002266667......375....1.10294E+11 6000..0.95..0.00002.....300000000..0.002533333.......375....1.18421E+11 7000..1.27..0.00002.....350000000..0.003386667.......375....1.03346E+11 7500..1.6....0.00002.....375000000..0.004266667.......375....8789062500 0 8000..2.65..0.00002.....400000000..0.007066667........375....5660377358 5 8500..5.5...0.00002......425000000..0.014666667.......375....2897727272 7 8300..7......0.00002......415000000..0.018666667.......375....222321428 57 8000..7.9....0.00002.....400000000..0.021066667.......375.....189873417 72 7000..8.7....0.00002.....350000000..0.0232...............375.....150862 06897 6100..9.1....0.00002.....305000000..0.024266667......375......125686813 19 Material Y TEST DATA FOR Y LOAD...EXT...CSA......... Stress.........Strain..........Orig Length....E (Stress / strain 2000....0.6...0.00002.....100000000..0.001090909.......550...9166666666 7 4000....0.8...0.00002.....200000000..0.001454545.......550....1.375E+11 6000...1......0.00002.....300000000..0.001818182.......550...1.65E+11 8000...1.18..0.00002.....400000000..0.002145455.......550....1.86441E+1 1 9400....1.3...0.00002.....470000000..0.002363636.......550...1.98846E+1 1 9200...1.5...0.00002.....460000000..0.002727273.......550...1.68667E+11 9200...1.6...0.00002.....460000000..0.002909091.......550....1.58125E+1 1 10000.1.75..0.00002.....500000000..0.003181818.......550....1.57143E+11 11000.2.1...0.00002.....550000000..0.003818182.......550...1.44048E+11 12000.2.4...0.00002.....600000000..0.004363636.......550...1.375E+11 14000.5.....0.00002.....700000000..0.009090909.......550....77000000000 12000.7.2..0.00002.....600000000..0.013090909......550....45833333333 10000.7.25.0.00002.....500000000..0.013181818.......550...37931034483 8000...7.27..0.00002.....400000000..0.013218182.......550....3026134800 6 For Material Z only the StressStrain data was given already TEST DATA FOR Z Stress...Strain.......CSA................................E (Stress / strain) 70...... 0.06..........0.00002........................... 1166.666667 100.... 0.11 ..........0.00002...........................909.0909091 150.... 0.22 ..........0.00002..........................681.8181818 200.... 0.35 ..........0.00002..........................571.4285714 220.... 0.48..........0.00002...........................458.3333333 You have asked for 0,0 data but i was not given any data close to that amount. Should i still include this on the graphs and just start the line from thin air essentially. Is my use of formulae correct. Should i change the scale data on my graphs? 


#13
Apr2313, 08:33 AM

Mentor
P: 5,375

The point 0,0 is known to be an exact point on your graph. If there is no applied stress, then there is no strain, and vice versa. I asked for the results on a loglog plot because it will increase the resolution in the region of small strains where the stressstrain behavior is expected to be linear. On a loglog plot, the linear stressstrain region should have a slope of 45 degrees (assuming equal spacing of the decades in the horizontal and vertical axes). If you are using a graphics package, just change the scales from arithmetic to logarithmic. And if you are switching to log scales, make sure you omit the point 0,0.
Chet 


#14
Apr2313, 08:43 AM

P: 94

So your suggesting the graph starts in mid air? I'm not sure what you mean but i'm confident i have to use arithmetic graphs and not log. Do i just use the gradient to determine Young's Modulus? So Change in Y axis / Change in X axis?
I have very little time left to get this done, i need to get a value and find the material. Thanks, Joe 


#15
Apr2313, 08:59 AM

Mentor
P: 5,375

If you don't want to use log scales, then you need to zoom in on the data at small strains and stresses. To do this, omit the data points that are well beyond the linear region, and, by doing so, expand the scales on both axes. Then you will get a better eyeball view of what is happening at small strains. Chet 


#16
Apr2313, 09:15 AM

Mentor
P: 5,375

I plotted up your data for two of the cases, and, in both cases, the data is offset along the strain axis. Otherwise, the data is pretty linear in the region of small strains, and you should be able to get a pretty accurate determination of the Young's modulus. I don't know why your data is offset along the strain axis.
Chet 


#17
Apr2313, 09:20 AM

P: 94

Thankyou, all the Load and extension data was provided. The area i believe to be correct and i'm confident my calculations are correct so any idea what to do now?



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