The question is very large so here is a quick global answer..

During straining of a metal, plastic deformation manifests as dislocation are produced and form specific structures conforming to the microstructure. Grain boundaries are usually considered as obstacles to dislocation motion (because they separate regions with different crystallographic orientations and/or because they are more disordered that the center of grains) and dislocations tend to pile-up at grain boundaries. Process like transmission of dislocations through the boundary or activation of new sources in the neighboring grain due to local state of stress exist but they usually require an increase in the applied stress to occur more easily. That being said, you should understand that the more grain boundaries are present in you metal (i.e. the grain size is reduced), the more barriers to dislocation motion and dislocation pile-ups there will be. Therefore, you will increase the strength and hardness of your material (the so-called grain size effect).

Thank you so much Julien Genée

I agreed with the answer from Julien Genée.

and that being said, I think we can safely said that as the grain size decrease, the strain hardening rate would decrease and vice versa. assuming the grain size homogeneous.

I am very grateful to you Timothy Alexander Listyawan

To the excellent previous answers it can be added that one of the consequences of this barrier effect is the dependence of the yield stress on the grain size, a dependence that can be considered in terms of the Hall-Petch relationship.

I am very grateful to you Edgardo Santarelli

I support the answers from Julien Genée , Edgardo Santarelli and Timothy Alexander Listyawan

I am very grateful to you Oluwasegun Samuel Odebiyi

Dear Osamah

In addition to what Julien Genee said, one should realize that grain boundaries between grains are dislocation zones-constrained of free movements, unlike the dislocations in the grains, i.e., regions of dense dislocations that were formed as a result of the crystallization of the grains. Therefore, the more grain boundaries present in a microstructure, by reducing the grain size by the strain hardening, the more barriers will exist for the free movement of dislocations in the grains.

I am very grateful to you Khaled J. Habib

The commonly[1] observed (near micron size) grain-boundary strengthening or Hall–Petch strengthening[1,2] (HPS mode) is limited[2,3] by the size of dislocations, etc.

In nanosize scale strengthening issues become not so monotonic (as in HPS case-mode), but more complex[4], when grain boundaries start to slide[2-4], rotate[5], etc. ('inverse' Hall–Petch effect[6]).

1. The Hall-Petch effect as a manifestation of the general size effect https://arxiv.org/pdf/1507.01223.pdf

2. In grain-boundary strengthening, the grain boundaries act as pinning points impeding further dislocation propagation. Since the lattice structure of adjacent grains differs in orientation, it requires more energy for a dislocation to change directions and move into the adjacent grain. The grain boundary is also much more disordered than inside the grain, which also prevents the dislocations from moving in a continuous slip plane. Impeding this dislocation movement will hinder the onset of plasticity and hence increase the yield strength of the material: Grain boundary strengthening https://en.wikipedia.org/wiki/Grain_boundary_strengthening

3. Nanostructured Metals and Alloys https://www.sciencedirect.com/topics/engineering/hall-petch-relationship

4. Effect of soluble particles on microstructural evolution during directional recrystallization https://www.sciencedirect.com/science/article/abs/pii/S1359645420301191

5. Grain Rotation in Plastic Deformation https://www.researchgate.net/publication/334717827_Grain_Rotation_in_Plastic_Deformation

6. What is behind the inverse Hall–Petch effect in nanocrystalline materials? https://www.sciencedirect.com/science/article/abs/pii/S1359645407001590

I am very grateful to you Ioannis Samaras

I am very grateful to you Ioannis Samaras

Effective barriers to movement of dislocations/line defects hence increase the effective stress to cause plastic deformation leading to enhance strength mostly with reduced ductility

Correctly mentioned above that GB are the cites of the dislocations and within the grain, dislocation can move easily within the grain but GB CREATE THE hurdle for the dislocation to move. So any mechanism in which grain size is reduced improves the strength as, during the process, dislocation piled up at the GBs. and the grain in which dislocation can move freely, the size of the grains reduced. Restriction of the movement of the dislocation strengthens the material.

During Strain hardening or work hardening process, grain boundaries block the continued movement of dislocations in the metal. As more dislocations become blocked, the metal becomes more difficult to deform. This blockage of dislocations made the material stronger.

Hello, Mr. Osamah Ihsan Ali.

Hall-Petch equation doesn't define the effect of grain size on work hardening itself because the work hardening is defined by the derivative of the stress-strain curve at the plastic regime (dσ/dε). Besides, it is a empirical equation, so, it doesn't consider the micro mechanisms of work hardening.

So, the right answer would be: it depends! And it depends mainly on the deformation mechanism of the metals.

In metastable metals which deform by transformation reaction-induced plasticity (TRIP), the bigger the grain size, the higher the work hardening.

In metals at high temperature, deformation occurs by boundary sliding and rotation and boundaries act as source and sink of vacancies, so boundaries decrease the work hardening (try to study about superplastic alloys, which has very small and homogeneous grain size).

In metals which deforms by twinning, the texture of grains is more important than boundaries, but big grains uses to help twinning, so, it increases work hardening.

The pile-up model a kind of explain work hardening of fcc metals deformed by dislocation slip. But it does not sufice, I think. It is well know nowadays that boundaries enforce more than one slip system to be activated and also act as dislocation source, so the smaller the grain, the bigger the work hardening. When you have nanosize grains, there is a deviation because a large volume of the material is filled with boundaries. But the trend is still the same. The theories that I know which explain work hardening due dislocation slip were develop by:

G. I. Taylor¹ (much earlier than Hall and Petch);

A. Seeger²

D. Kuhlmann-Wilsdorf³

The grain size probably influences the work hardening in the begining of plastic deformation (stage I and II of shear stress-strain curve). The microstructure becomes very fragmented at high strains and boundaries do not determine the work hardening anymore.

So, I hope my coments improve your knowledge on this issue.

some sources:

¹ TAYLOR, G. I. Theory of work-hardening curve. Proc. Roy. Soc., v. 145, p. 362-388, 1934.

²A. Seeger, in Work Hardening, TMS-AIME Conf., Vol. 46, 1966, p. 27

³ D. Kuhlmann--Wilsdorf, Met. Trans. 11A (1985) 2091

Well as everybody explained, the GBs can act as an obstacle to dislocation motions, generated under the loading condition resulting in stress accumulation/ concentration at the GBs resulting in high strength, generally referred to as GB-strengthening/hardening mechanism. As explain in terms of Hall-Petch strengthening. However, it is pertinent to mention here that after the certain grain size, the Hall-Petch equation fails and strength will reduce instead of increasing, which is refereed to as GB-softening. So based on the specific application, one has to make a compromise between the grain size and achieved strength.

Higher the number of grain boundaries ... higher would be the stacking faults ... also known as dislocations ... thus interlocking ... deformed planes ... staking faults ... all need strains to stabilise themselves ... thus higher is the strain hardening effect