Beginner's question on Stress-strain curve

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Discussion Overview

The discussion revolves around the behavior of the stress-strain curve, particularly the decrease in slope after the yield point. Participants explore concepts related to engineering versus true stress-strain curves, the implications of necking, and the forces at play during deformation.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions why the slope of the stress-strain curve decreases after yielding, suggesting a need for clarification on the relationship between strain-hardening and stress requirements.
  • Another participant explains the difference between engineering and true stress-strain curves, noting that the engineering curve assumes constant area, which leads to a perceived dip in stress during necking.
  • A follow-up post seeks clarification on the timing of necking and its relation to the yield point, questioning whether the area decreases significantly at the yield point.
  • Some participants propose that beyond the yield point, less force is required to deform the material due to weaker inter-molecular forces, contributing to the decrease in slope.
  • There is mention of a bend in the true stress-true strain curve, which some participants assert still occurs despite the use of instantaneous cross-sectional area.

Areas of Agreement / Disagreement

Participants express differing views on the mechanics of the stress-strain curve, particularly regarding the effects of necking and the interpretation of true versus engineering stress-strain curves. The discussion remains unresolved, with multiple competing explanations presented.

Contextual Notes

There are limitations in the assumptions made about area constancy and the timing of necking, which may affect interpretations of the stress-strain behavior. The discussion highlights the complexity of material behavior beyond the yield point.

kelvin490
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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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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.
 
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?
 
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.
 
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.
 

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