Beginner's question on Stress-strain curve

[kelvin490]

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.

 

[streeters]

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.

 

[kelvin490]

Thank you for your reply but I still want to have some points clarified.

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?

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?

 

[shushu97]

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.

 

[shushu97]

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.