Question about solid's response to stress

[kelvin490]

I have a question about how the solid respond to stress at different stages. In textbooks the slope of typical stress-strain curve decreases after a point called yield point. Why is it so? Why less stress is required to further increase the strain compared to that before yielding?

 

[Studiot]

This question can be approached from several different directions or points of view so please tell us which angle you are particularly interested in.

Meanwhile here is an overview.

First it should be noted that the behaviour you describe only applies to certain solids, called ductile solids. These are mainly metals, especially the iron and steel we commonly use. It does not apply to brittle materials, rubber or plastics.

The application of direct stress also applies or induces shear stress within the material.
The yield point is where this induced shear stress is greater than the material can support at within some parts of the material. As a result the material flows plastically under this stress, redistributing the load to other parts of the material that have not yet yielded (=reached this limit). We see this as a reduction in the constant of proportionality of the stress-strain curve (please note carefully which axis is which).
Another viewpoint is that this process causes changes to the crystal matrix, accounting for the 'permanent set' since the molecules have moved about.

go well

 

[kelvin490]

Thank you very much for your reply.

Both viewpoints are interesting. I wonder for a poly-crystal metal, is the load mainly beared by the un-yielded parts of the specimen? If yes, can we say that the reduction of the slope of the stress-strain curve is in fact due to less material bearing the load?(so that the specimen elongates faster)

Another interesting thing is, if the whole metal sample is a single crystal, what would happen? Will the stress-strain curve looks the same? Because if it yields the whole sample yields.

 

[sliced cheese]

As I understand it, the reduction in slope of the stress-strain curve is, in fact due to a small area bearing the stress. Per unit area, even after the yield, it does take more force to induce the same amount of strain. However, due to the area the force is applied to being smaller, the material yields faster.

 

[Studiot]

As I understand it, the reduction in slope of the stress-strain curve is, in fact due to a small area bearing the stress. Per unit area, even after the yield, it does take more force to induce the same amount of strain. However, due to the area the force is applied to being smaller, the material yields faster.

Agreed.
The OP refers to the 'engineering stress strain curve'.
The true stress strain curve shows a contiued increase, albeit at a lower slope.

Of course the induced shear and resultant plastic flow is how the necking occurs.

 

[kelvin490]

Thanks to both. But even before yield the area is keep on decreasing (we have the "poison ratio"), but we still have a fairly strictly line in curve, meaning the slope does not change obviously. The significant change in slope only occur at the yield point, but we cannot observe large sudden decrease in the cross section area (this only occurs in "necking"). I wonder whether the area effect is so large.

 

[SteamKing]

It's Poisson ratio, not 'poison'.

 

[kelvin490]

It's Poisson ratio, not 'poison'.

Ops, typing mistake. Thanks, man.