The trend followed the hall petch relationship with hardness linearly proportional to the inverse of square root of grain size.
Grain boundary strengthening ceramics.
Another major concern is to maintain an adequate grain boundary cohesive strength relative to the flow stress to mitigate cavitation or grain boundary cracking during large strain deformation.
It is based on the observation that grain boundaries are insurmountable borders for dislocations and that the number of dislocations within a grain have an effect on how stress builds up in the adjacent grain which will eventually activate.
Grain boundary strengthening or hall petch strengthening is a method of strengthening materials by changing their average crystallite grain size.
1 as the critical stress intensity klcsb required to propagate a crack along a grain boundary.
The orowan petch relation is a famous model to describe the strength of polycrystalline ceramics covering a wide range of grain sizes.
A few years ago nrl was the first to show that if you decrease the grain size of ceramics to tens of nanometers the hardness and strength increase james wollmershauser a materials research engineer in nrl s materials science and technology division says in a recent nrl news release.
Vickers hardness was measured and grain boundary strengthening observed showing hardness increase from 18 2 gpa up to 22 5 gpa as the grain sizes decreased from 60 3 to 10 1 nm.
At 0 d there is precipitate and solid solution strengthening with particulates strengthening structure at 1 d there is work forest hardening with line dislocations as the hardening mechanism and at 2 d there is grain boundary strengthening with surface energy of granular interfaces providing strength improvement.