Finding Avg. True Stress for Annealed Copper

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SUMMARY

The discussion centers on calculating the average true stress for annealed copper using a true stress curve. The true stress in the unstrained condition is established at 12,000 psi, while the true stress in the strained condition is determined to be 72,000 psi, derived from a strain of 0.916 using the equation strain = ln(l/l_o). To find the average true stress, the user seeks a method to calculate the area under the curve between these two points, rather than simply averaging the two values.

PREREQUISITES
  • Understanding of true stress and strain concepts
  • Familiarity with logarithmic functions and their applications in material science
  • Knowledge of stress-strain curves and their interpretation
  • Basic calculus principles, specifically area under the curve calculations
NEXT STEPS
  • Research methods for calculating the area under a curve using numerical integration techniques
  • Learn about the trapezoidal rule for approximating the area under a stress-strain curve
  • Explore advanced material properties of annealed copper and its stress-strain behavior
  • Investigate software tools for stress analysis, such as MATLAB or Python libraries for numerical methods
USEFUL FOR

Material scientists, mechanical engineers, and students studying material mechanics who need to understand stress-strain relationships in metals, particularly in the context of annealed copper.

Jason03
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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...
 
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How would I find the area under the curve when I only have two points?
 

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