Grain boundary strengthening theory is valid for monolithic poly-crystalline materials where reducing grain size results in high yield strength. Is this theory valid for all dimensions particularly for bigger one?
I want to know how two different ceramic composite of same material with two different particle sizes will behave for a particular load.
The Hall-Petch relationship tells you as you decrease size the a certain limit then the strength increases. Below that size then cracks are similar in dimension to the size of the particle and (Griffith) crack propagation cannot occur . Its much more complex than this. See slides 19 onwards in:
October 2nd, 2013 The PSD, zeta potential, and rheology of ceramic materials and ceramic slurries/suspensions
https://www.brainshark.com/malvern/vu?pi=97328853&text=M021507
and for corollary information see:
October 6th, 2016 Controlling powder bulk density by optimizing particle size and shape distribution
https://www.brainshark.com/malvern/vu?pi=271602698&b=1&tx=120486&c1=22
There are two different aspects. One is grain size another one is sample size.
There is a classical equation in materials science called Hall Petch equation which shows finer the size greater will be the strength, due to presence of more number of grain boundaries that deflect the propagating crack and enhances strength. This is valid for all dimensions. For example say for glass (amorphous solid), as there is no grain boundary the crack propagates once generated and the whole body cracks. But with increasing the sample size, the probability of longer crack increases (Fracture mechanics, Griffith crack), Hence bigger the sample size lower will be the strength. So for same size of the test sample, lower grain size will give higher strength.
But this theory is not valid at high temperatures. The grain boundaries act as the source of impurity / defect concentration and chances of formation of any liquid is at grain boundary. Hence they act as the sliding plane for deformation and reduces strength at high temperature. There is a specific temperature for each system for this to occur, which is termed as equi-viscous temperature.
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