Calculating the Modulus of Elasticity from a Stress-Strain Curve

In summary, The relationship "E = stress/strain" only applies to the linear portion of the stress-strain curve for steel. If the structure is loaded beyond this linear portion, it will deform plastically and not return to its original length. Young's modulus of elasticity is represented by tan(alpha) where alpha is the slope of the tangent line at the origin. A function E_t=sigma/eps can also be used to calculate the tangent modulus, which becomes dependent on total strain.
  • #1
kasse
384
1
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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  • #2
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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  • #3
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.
 

1. What is the Modulus of Elasticity?

The Modulus of Elasticity, also known as Young's Modulus, is a measure of a material's stiffness or resistance to elastic deformation.

2. How is the Modulus of Elasticity calculated?

The Modulus of Elasticity is calculated by dividing the stress applied to a material by the strain experienced by the material. This is typically represented by the equation E = σ/ε, where E is the Modulus of Elasticity, σ is stress, and ε is strain.

3. What units is the Modulus of Elasticity measured in?

The Modulus of Elasticity is typically measured in units of pressure, such as pounds per square inch (psi) or pascals (Pa). It can also be measured in units of force per unit area, such as newtons per square meter (N/m²).

4. How does temperature affect the Modulus of Elasticity?

Temperature can have a significant effect on the Modulus of Elasticity. In general, as temperature increases, the Modulus of Elasticity decreases, making the material less stiff and more prone to deformation.

5. What is the significance of the Modulus of Elasticity in materials science?

The Modulus of Elasticity is an important property in materials science as it provides information about a material's ability to withstand stress and deformation. It is used in engineering and design to select appropriate materials for specific applications and to ensure the safety and structural integrity of structures and components.

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