Beginner's question on Stress-strain curve

In summary, the slope of a typical stress-strain curve decreases after yielding due to the assumption of constant area in an engineering curve, resulting in a dip in the curve. However, in a true curve, the instantaneous cross-sectional area is used, so there is a continuous rise until failure. The decrease in slope after the yield point is due to weaker inter-molecular forces, and there is still a sudden bend in the true stress-true strain curve due to the area being almost the same as the initial area at the yield point.
  • #1
kelvin490
Gold Member
228
3


Why the slope of typical stress-strain curve decreases after yielding? If it is strain-hardening, why less stress is required to further increase the strain compared to that before yielding?

All replies are much welcome, thank you.
 
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  • #2
ok, you have to know the difference between engineering stress-strain curve and true stress-strain curve.

to begin with E = stress/strain, and stress = F/Area,

In engineering curve, you assume that the initial area is constant throughout the test, as this is easier than trying to measure it dynamically. This is not true of course, due to Poisson's ratio, but it is a time saver. As a consequence, when necking begins, despite the area getting significantly smaller, you assume its the same. so the stress is calculated to be smaller than it actually is. Hence the dip.

In a true curve, you don't get this dip but instead see the curve rise continuously until it fails (snaps/breaks/whatever). This is because the instantaneous cross-sectional area is used.
 
  • #3
Thank you for your reply but I still want to have some points clarified.


streeters said:
As a consequence, when necking begins, despite the area getting significantly smaller, you assume its the same. so the stress is calculated to be smaller than it actually is. Hence the dip.

I appreciate that when necking begins the area decreases significantly. However, necking mainly occurs in the latest part of loading, it seems that it is not occurs at the yield point. Then why the slope decreases a lot after yield point? Does the area also decrease significantly at the yield point so there is a sudden decrease in the slope?


streeters said:
In a true curve, you don't get this dip but instead see the curve rise continuously until it fails (snaps/breaks/whatever). This is because the instantaneous cross-sectional area is used.

I have checked for some book that for true stress-true strain curve there is still a sudden bend in the curve, why is it so?
 
  • #4
Beyond the yield point less force is needed to deform the material due to weaker inter-molecular forces.
The slope of the curve decreases.
The biggest difference between the engineering and true curve is after the ultimate tensile stress.
At yield point the area is almost the same as the initial area.
 
  • #5
Beyond the yield point less force is needed to deform the material due to weaker inter-molecular forces.
The slope of the curve decreases.
The biggest difference between the engineering and true curve is after the ultimate tensile stress.
At yield point the area is almost the same as the initial area.
 

1. What is a stress-strain curve?

A stress-strain curve is a graphical representation of the relationship between the amount of stress applied to a material and the resulting strain or deformation of the material. It is used to determine the mechanical properties and behavior of a material under different levels of stress.

2. How is a stress-strain curve measured?

A stress-strain curve is typically measured using a tensile test, where a sample of the material is subjected to gradually increasing levels of stress until it reaches its breaking point. The strain, or change in length, of the sample is recorded at each level of stress, and a graph is plotted to show the relationship between the two.

3. What information can be obtained from a stress-strain curve?

A stress-strain curve can provide information on the strength, stiffness, and ductility of a material. It can also show the material's yield point, ultimate tensile strength, and fracture point, which are important factors in determining its suitability for different applications.

4. How does the shape of a stress-strain curve differ for different materials?

The shape of a stress-strain curve can vary depending on the type of material being tested. For example, brittle materials like glass or ceramics have a steep curve with little to no plastic deformation, while ductile materials like metals have a more gradual curve with significant plastic deformation before reaching their breaking point.

5. How can a stress-strain curve be used to analyze the behavior of a material?

A stress-strain curve can be used to analyze the behavior of a material by identifying its elastic and plastic regions. The slope of the curve in the elastic region represents the material's stiffness or Young's modulus, while the area under the curve in the plastic region represents its ability to withstand deformation before breaking. This information can be used to select the most suitable material for a particular application.

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