I think Hall Petch Impirical Relationship holds good for lower temperatures, up to or lower than 0.4 times melting point temperature. But at higher temperature, smaller grain size makes material weaker.

Please rectify the misunderstandings, if any.

Harshal hi,

Hall-Petch is valid for deformations caused by dislocation slip and the grain size effect comes from the dislocation pileups. Since superplasticity is dominated by  grain boundary sliding as the main deformation mechanism Hall-Petch would not work.

So you can think as;

A sufficiently high temperature is needed to make grain boundary sliding (GBS) possible, or to reduce the strength of the grain boundary, which is around 0.4TH(ratio of T to melting temperature). In addition, you need to have enough deformation (GBS) options to avoid or delay void nucleation. And finally, time is necessary to slide the grains over each other. 

Hi Harshal,

Above answers are correct, however, there is one more important thing. 

It is correct that the superplasticity is induced by the grain boundaries sliding. However, the effect is also observed in the ambient temperature. when the grain size reach critical value (nanometer sized), further decrease in it's size leads to increased plasticity. Why? Because the grains are so small, that phenomena leading to the deformation occur mainly at the grain boundaires, not within the grains. That is why further increasing of the grain boundaries number leads to increase in plasticity.

But, as I mentioned, this is true for nanometer-sized grains. That is why, superplasticity is observed mainly in the alloys deformed with SPD methods (ECAP and so on).

All the best, 

Bartek

Bartek's answer is correct and I would like to add further comments to his answer. Atomic-level events like diffusion and activation energy, crystal defects like stacking fault  and others seem to make contributions to the observation of the so-called inverse Hall-Petch relationship. The attached papers give a glimpse into the postulations made by researchers to explain Inverse Hall-Petch relationship and the lack of an universal explanation for this phenomenon as yet. Perhaps quantum mechanics approach holds the key.

Dear all

I agree with Prof. Malur answer, quantum mechanics can hold the key.

There is a new work that tries to combine both the Hall-Petch and its inverse in one model through presenting a multiscale model that enables description of both the Hall-Petch relation and its inverse in one equation without the need of prior knowledge of the grain size distribution, for more details, please see the following link:

https://www.researchgate.net/publication/324507369_A_new_multiscale_model_to_describe_a_modified_Hall-Petch_relation_at_different_scales_for_Nano_and_micro_materials

Hi Mr. Kulkarni,

Superplasticity is achieved in metals at higher temperature (roughly around 0.4-0.5 times melting temperature). At this high temperature, diffusion in the form of grain boundary sliding (GBS) contrbitues majorly along with dislocation slip.

1) Diffusion is a slow process compared to dislocation slip.So, if lower strain rate is prescribed, diffusion can sort of accomodate with the strain rate and high ducitility (even superplasticity) is achieved.

2) For smaller grain sizes,we get more and more grain boundary. So, grain boundary sliding is more favorable and thus increase ductility.

In contrast, classical Hall-Petch relationship is only true for low temperature deformation mechanism by dislocation movement where grain boundary acts as an energy barrier to dislocation movement. That energy barrier has to be overcome by peach-koehler force acting between accumulating dislocations. Thus, with larger grain size more and more dislocations can pile up and help moving the dislocations past the grain boundary. This in turn requires lower flow stress required to maintain the dislocation movement.

Hope this helps and will be happy to have further discussion on this topic.

Hello All,

My opinion: As far as I understand the H-P relation holds good for cases in which grain boundaries are stronger than the grains. Above certain temperature (a critical value, material dependent)

known as equi-cohesive temperature, there is transition of the relative strengths of grain and grain boundaries. Above equi-cohesive temperature, grains tends to be stronger than grain boundaries and therefore accomodation of deformation through grain boundaries (gb sliding) can be observed. Similar behaviour is observed in case of nanocrystalline materials strength as a function of nano-grain size. Here too, the gb accommodates the applied deformation.