Calculating the Modulus of Elasticity from a Stress-Strain Curve

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SUMMARY

The modulus of elasticity (E) for materials such as steel can be accurately determined from a stress-strain curve by focusing on the linear portion of the graph. The relationship E = stress/strain is valid only within this linear region. Beyond this point, materials exhibit plastic deformation, and the modulus becomes a function of total strain. Specifically, Young's modulus is defined as the slope of the tangent line at the origin of the stress-strain curve, referred to as the tangent modulus.

PREREQUISITES
  • Understanding of stress-strain relationships in materials
  • Familiarity with Young's modulus and its significance
  • Knowledge of linear versus plastic deformation in materials
  • Ability to interpret stress-strain curves
NEXT STEPS
  • Study the derivation of Young's modulus from stress-strain curves
  • Learn about plastic deformation and its implications in material science
  • Explore the concept of tangent modulus and its calculation
  • Investigate different materials' stress-strain behaviors beyond the linear region
USEFUL FOR

Materials scientists, structural engineers, and students studying mechanical properties of materials will benefit from this discussion on calculating the modulus of elasticity from stress-strain curves.

kasse
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I've got a computer plot showing relations between stress and strain for steel. But how can I find the modulus of elasticity (E) from the graph? Isn't it so that E=(stress/strain)? The thing is that I get very different answers when I compute E in this way for various points on the graph.
 
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See http://www.uoregon.edu/~struct/courseware/461/461_lectures/461_lecture24/461_lecture24.html

The simple relation "E = stress/strain" only applies to the linear first part of the curve, i.e. the straight line through the origin on the plots.

If you load a structure so the stress and strain are larger than the linear part of the curve, the material deforms plastically and when you remove the load it will not return to its original length.
 
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Strictly speaking, Young's modulus of elasticity is tan(alpha), where alpha is the slope of the tangent line to the stress-strain curve at origin. If you define a function E_t=sigma/eps along the curve, you get the "tangent modulus, which as you noted, becomes function of total strain.
 

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