How Do You Calculate Elastic Modulus and Strengths from a Stress-Strain Curve?

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SUMMARY

This discussion focuses on calculating elastic modulus, yield strength, tensile strength, and elongation from stress-strain curves. The elastic modulus is determined using the formula E = stress/strain, specifically from the linear region of the curve, typically measured from 0 to 0.02 strain for materials like aluminum. Yield and tensile strengths can be identified from the curve, while uniform and total elongation require understanding the original and final lengths of the material. The 2% rule is highlighted as a method for estimating Young's modulus in non-linear materials like aluminum.

PREREQUISITES
  • Understanding of stress-strain curves
  • Knowledge of Young’s modulus and its calculation
  • Familiarity with yield strength and tensile strength concepts
  • Basic grasp of engineering strain definitions
NEXT STEPS
  • Research the calculation of yield strength from stress-strain curves
  • Study the differences between uniform and total elongation
  • Learn about the application of the 2% rule for estimating Young's modulus in materials
  • Explore the characteristics of stress-strain curves for different materials, such as steel and aluminum
USEFUL FOR

Materials engineers, mechanical engineers, and students studying material properties will benefit from this discussion, particularly those involved in analyzing stress-strain behaviors and material strength calculations.

Name:riley
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Hello I'm having trouble wrapping my head around finding things from stress strain curvesI need to find:
Elastic modulus (Young’s modulus)
•Yield strength
•Tensile strength
•Uniform and total elongation (ductility)
upload_2014-10-14_20-26-54.png


elastic modulus I think is 1240/0.02 = 62000

but I'm unsure of how to find the others.

Thank you to anyone who helps out.
 
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No, that is not the Youngs modulus.

Can you define any of the terms in your own words? i.e. do you know what you are looking for?
 
Thank you for your response

I am OK with yield and tensile strength it turns out.

I know what the elongation is and understand the formula Lf - Lo/Lo I just don't understand where to get the lengths from in the curve, I believe the strain is the elongation of the material but don't know where to get the original an final lengths from. Either from uniform at the 0.2% point or the total elongation.

The elastic modulus is the measure of the elasticity of the material, I know that is measured form 0 to 0.02 ( the 2% rule) of the strain as this is the beginning of the plastic region. As E= stress/strain I thought but it seems that's not the case.

I hope these explanations are satisfactory, I understand why you asked for them I guess I should have showed more of an effort to find the answers.
 
Last edited:
Name:riley said:
Thank you for your response

I am OK with yield and tensile strength it turns out.

I know what the elongation is and understand the formula Lf - Lo/Lo I just don't understand where to get the lengths from in the curve, I believe the strain is the elongation of the material but don't know where to get the original an final lengths from. Either from uniform at the 0.2% point or the total elongation.

You need to review the definition of 'engineering strain':

http://www.engineeringtoolbox.com/stress-strain-d_950.html

Scroll down until your reach the section titled 'Strain'.

The elastic modulus is the measure of the elasticity of the material, I know that is measured form 0 to 0.02 ( the 2% rule) of the strain as this is the beginning of the plastic region. As E= stress/strain I thought but it seems that's not the case.

This rule only applies to materials for which there is no region where Hooke's law applies, i.e., the stress is not a linear function of the strain anywhere on the stress-strain curve. Steel, for example, has a well-defined region where the stress-strain curve is linear; aluminum does not, and therefore the 2% rule is used to estimate Young's modulus for aluminum and aluminum alloys.
 

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