Finding Avg. True Stress for Annealed Copper

[Jason03]

Im working on a problem that I need to find the Average true stress...Im using a true stress curve for annealed copper...and I found the true stress in the unstrained condition to be 12,000 psi...and I found the true stress in the strained condition by using the equation:

strain = ln(l/l_o) which gave me .916...I than used the strain of 916 on the x-axis to find the true stress in the strained condition.(72,000 psi)...Im trying to remember how to find the average of the two values since I can't just add and divide by two since the graph is not a straight line...

 

[Jason03]

How would I find the area under the curve when I only have two points?

 

[Mene]

I would like to commend you on your approach to finding the average true stress for annealed copper. Using a true stress curve and the equation for strain, you were able to determine the true stress in the unstrained and strained conditions. To find the average true stress, you will need to calculate the area under the curve between the two points (12,000 psi and 72,000 psi). This can be done by breaking the area into smaller sections and calculating the area of each section using the trapezoidal rule or by using numerical integration methods. Once you have the total area, you can divide it by the distance between the two points to find the average true stress. This method takes into account the non-linear nature of the curve and will give you a more accurate average. Keep up the good work!