Area Calculations to find Jc energy Parmeter (simple maths)

  • Thread starter 50Cent
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  • #1
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Homework Statement


I have been given the following load-displacement plots for the same specimin with two different crack lengths. The lines are identical up to a load od 750N

1zmi0zl.jpg


i need to calculate the area of the blue shaded region to obtain a value of Jc using a separate equation.

Homework Equations


Area of triangle = 0.5(b)(h)
Area of rectangle = (b)(h)

The Attempt at a Solution


I found the area of the largest triangle (tip at 1750)
Total Area = (0.5)(0.003)(1750)=2.625

Then split the lower half of the plot into 3 sections labeled 1,2&3. And calculated the areas
Area 1=(0.5)(0.0012)(750)=0.45
Area 2=(0.003-0.0012)(750)=1.35
Area 3=(0.5)(0.003-0.0012)(1740-750)=0.891

So Total Area - Area 1 -Area 2 - Area 3 = the blue shaded region
However i get a negative value,

Blue Shaded region = 2.625-0.45-1.35-0891 = -0.066

Just by looking at the picture, it shouldnt be a negative value, I cant see the problem in my method. Can any1 see what im doing wrong?

Any Help is appreciated
Thanks
 

Answers and Replies

  • #2
445
5
Part of your problem is I think the "largest triangle" is not actually a triangle. If (1.2,750) is a point on the line, then (3,a) yields 750 x 2.5 for a, which is not 1750. Can't you just use 10 as the base and 1.8 as the height for a triangle?
 
  • #3
33
0
Hi,

I tried it again by doing what you suggested and splitting the diagram further into 4 triangles and 1 rectangle. I got a positive area and solved the question :D

Thanks for your help!
 

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