Area Calculations to find Jc energy Parmeter (simple maths)

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SUMMARY

The discussion focuses on calculating the Jc energy parameter using area calculations from load-displacement plots. The user initially calculated the area of a triangle and three sections of a plot but obtained a negative value for the blue shaded region. After receiving feedback, the user revised their approach by splitting the diagram into four triangles and one rectangle, ultimately achieving a positive area and successfully solving the problem.

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  • Understanding of load-displacement plots
  • Knowledge of basic geometry, specifically area calculations for triangles and rectangles
  • Familiarity with the concept of Jc energy parameter in material science
  • Ability to interpret graphical data in engineering contexts
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  • Explore load-displacement behavior in materials under stress
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Students and professionals in materials science, mechanical engineering, and structural analysis who are involved in calculating energy parameters and interpreting load-displacement data.

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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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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?
 
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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