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View Full Version : Why graph curves after yield point in stress-strain graph.


Yusf
Aug 17, 2015, 11:05 AM
I understand these things:
Stress is the internal force that neighbouring particles exert on one another.

Strain is a measure of deformation of an object. Strain equals extension÷original length.

Are they right?

And also I don't get why strain reduces after the yield point. My point is, if an excess of force is being applied after yield point, how is the material providing the extra opposite force?

Hope I am clear about the question. Someone please make me clear about the answer too.

ebaines
Aug 17, 2015, 11:37 AM
Your definitions are OK. But the premise behind this question is incorrect:


I don't get why strain reduces after the yield point. My point is, if an excess of force is being applied after yield point, how is the material providing the extra opposite force?

Once enough stress has been applied for the material to reach its yield point, the strain increases at a higher rate (i.e., the slope of the stress-strain curve decreases), because less additional force is required per unit of additional strain. Given:

\sigma = E \epsilon

where \sigma = stress, \epsilon = strain, and E = Young's Modulus, you can see that as E decreases past the yield point then increasing strain requires smaller amounts of additional stress..

kreysiz
Aug 18, 2015, 12:00 AM
The graph curves after the yield point because, it no longer follows the Hooke's Law after the yield point.
Hooke's Law states that " stress is directly proportional to strain".

Yusf
Aug 18, 2015, 09:33 AM
no I don't understand.

The graph curves (stress on y axis and attain on x axis) meaning that the gradient has decreased. So a smaller change in stress occurs over a larger change in stress. So rate of change of stress decreases, that what I understand.

And will it be right to say that a smaller stress is required to make a higher strain, so the graph curves down. (after the yield point)

ebaines
Aug 18, 2015, 10:08 AM
So a smaller change in stress occurs over a larger change in stress.

I think you mean: "So a smaller change in stress occurs over a larger change in strain."


So rate of change of stress decreases, that what I understand.

Correct. As noted previosuly, the material gets a bit weaker, so the value for Young's Modulus "E" decreases, and the slope of the stress-strain curve decreases.


And will it be right to say that a smaller stress is required to make a higher strain, so the graph curves down. (after the yield point)

For many materials that's indeed what happens. After the yield point the slope decreases, but is still positve. But as the material is stretched more and more it reaches a point of ultimate tensile stress, where the slope becomes negative. At this point the material starts to neck down, and less stress is needed to make it continue stretching. Finally you reach the fracture point.

Yusf
Aug 18, 2015, 03:15 PM
Fully understood! Thanks!