Dear Sir,

I feel that the fine grained material will offer more resistance to crack propagation, as grain boundaries work as resistances in the path of the crack, however if the grain size is too small the material will exhibit brittle fracture characteristics and will have lower fracture toughness values. The grain size is related to the yield strength by Hall-Petch equation but the same eqaution is not applicable for very course grain and very fine grained materials. ( pl refer pages 397 and 361 of  the book Materials science by Callister)

Sir,

I am not working on fracture behaviour of materials.

However, It would be really difficult to comment about the fracture toughness unless we have the data related to the problems viz. type of materials, elements, alloys, any precipiate at the grain boundary (grain interior and grain boundary strength changes with the temperature as in case of creep) ,temperature etc).

If the material is alloy and precipitation phenomena is occuring, then, it will impact the Phase precipitation differently in case of coarse grained and fine grain materials

In case of fine grain materials there will huge number of high energetic grain boundary area and can assist in large number density of phase precipiatation at the grain boundary which may lead to early failure. Thus, lower fracture toughness.

Whereas in case of coarse grain material chance of brittle phase precipitation at the grain boundary is lesser which reduces the early failure of materials and may increase the fracture toughness.

In brief, generally the fracture toughness of fine grain metallic material is higher than its coarse grained counter, but it may not be always true for every materials

The answer is simple - Most of the metallic materials, the crack nucleation occurs at stress concentrations either pre-existing or in-situ generated. Since slip occurs easily before fracture unlike brittle materials, the dislocations start piling up at the grain boundaries thus building up the stress concentration there. Since given the same conditions as you stated, coarse grains will have larger pile-up formation for the stresses to  build up - hence easier for crack initiation. The crystal has a choice - to nucleate a crack or slip in the next grain, to relieve the stresses. If the slip is unfavourable then crack initiation occurs there by reducing the fracture toughness.  Hene, in general, fracture strength of a fine grain is higher than the coarse grain material, given all other factors the same. As you reduce the grain size - the fracture toughness as well as slip resistance both increase. If the grain size is too small the dislocation loop itself becomes unstable and hence initiation of slip becomes so difficult in relation to fracture stress. Hence in the nano case the fracture occurs - the competition is, of course, the grain boundary sliding vs crack initiation in the grain or along the grain boundary.. The relative energetics determine which takes place preferentially.  Hope this helps.

Perfect answer from Dr. Sadananda....is there a limit for the grain size from where this change in slip behaviour occurs.

Jalaji - you can determine the minimum grain size for a given material. One can image a dislocation loop and see if the dislocation loop can remain stable without collapsing due to the line tension against the forces of lattice friction Another way is to calculate the stress to nucleate a Frank-Reed loop and compare that to the Griffith crack nucleation of that size. The Implication is it is easier to crack than slip. They all provide some kind of estimation for the nano-grain size that can be sustained.

Thank you sir.

Dear Jalaj and all

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