Area Calculations to find Jc energy Parmeter (simple maths)

In summary, the conversation is about a problem involving calculating the area of a blue shaded region on a load-displacement plot. The attempt at a solution involves finding the area of different shapes and subtracting them to obtain the blue shaded region. The problem is that the calculated value is negative, but after further discussion, it is determined that the "largest triangle" is not actually a triangle and the problem is solved.
  • #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 shouldn't be a negative value, I can't see the problem in my method. Can any1 see what I am doing wrong?

Any Help is appreciated
Thanks
 
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  • #2
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
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!
 

1. What is the formula for calculating Jc energy parameter?

The formula for Jc energy parameter is Jc = A/Δx, where Jc is the parameter, A is the area of the sample, and Δx is the change in distance between voltage measurements.

2. How do I determine the area of the sample for Jc energy parameter calculation?

The area of the sample can be determined by measuring the length and width of the sample and multiplying them together.

3. Can Jc energy parameter be calculated with irregularly shaped samples?

Yes, Jc energy parameter can still be calculated with irregularly shaped samples. The area of the sample can be divided into smaller regular shapes and the Jc energy parameter can be calculated for each shape and then summed together.

4. What units are used for Jc energy parameter?

Jc energy parameter is typically measured in joules per meter squared (J/m^2).

5. How is Jc energy parameter used in scientific research?

Jc energy parameter is used to determine the critical current density of a material, which is an important parameter in superconductor research. It is also used to compare the performance of different superconducting materials and to study the effects of temperature and magnetic fields on superconductivity.

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