I want to know what are the best ways to increase the Young's modulus of any material and what are the maximum attainable values as known from experiments?
Well, it's quite possible to increase the mechanical properties of metal by doing heat treatment on it. The research paper will give you some idea on the effect of heat treatment on mechanical properties.
in case of polymer: make composite or try to do 99.99% of reaction;
for metals such as steel heat treatment and/or plastic deformation or/and (in case of Al alloys) 'aging' may improve Young modulus;
according to ceramics - make composite or add additional components to make bridges between grains, but ceramics usually has high modulus.
Thinking about your question, I see thousands of different materials from 4 basics sections: metals, polymers, composites, ceramics. All of them got differ enhancement mechanism/way/procedure and its impossible to give you 1 answer. Please let me know what kind of material (type/name/chemical composition) you are interested in?
You can improve properties by SPD as suggested by Mr. Braj. Well in terms of commercial solution you have to modify the process parameters such as temperature, strain, strain rate and heat treatment parameters to acheive finer grain size which will increase the properties as per hall petch relation
Actually I'm interested in aluminum alloys, I want to know what are the highest reachable values of Young's modulus of any of them and by what mechanism?
Fro soil materials it can be very different, because it is not homogenous material and E very depends on density, soil natural conditions and loading according to which the soil will be tested.
There are many subject according to Al alloys. The first is the E may differ because of measurement method. With the increase of tension during the measurement modulus decreases. It means that for higher tension E will smaller. E may be different if measurement is static or dynamic.
According to purity of alumina: higher purify = lower E.
According to alloy composition: usually, alloying elements with higher E will cause higher Young Modulus of alloy. BUT IT IS GENERALLY - not always, because total effect depends on distribution of the alloy component in the structure. For instance: the impact of component contained in the solid solution is weaker than that of the same active ingredient present as a separate phase in alloy. Usually Cu+Ni+Si will increase E (about 20% will affect on E 14 - 20 GPa more). Magnessium content will decrease E (ca. 30% Mg may decrease to ca. 55GPa).
According to plastic deformation: depending on purify of Al, deformation will decrease E but for higher tension E will be higher. Texture in aluminum alloys can also affect the elastic modulus.
According to all above: I was playing with alumina alloy 15 years ago, so what I wrote may be not the newest information, but believe will give you basics where you may start searching.
If you tell about the abstract material, then for this material there are a matrix of constants which define the material reaction on the applied load. For this material it is constant on the base of definition it has. But if you tell about the peace of metal which shows you some level of mechanical strain after you applied stress, then there are a lots of factors which can play a role (anisotropy, microstructure, texture, treatment, diluted elements distribution, and so on). The modulus of the system is not the modulus of its parts.
I hope that next time you will be able to ask the question preciesly. The answer on this question is no the Young modulus of the material can not be changed. But you can change the material chemical composition or material's state with subsequent cange in the properties.
Then you could take as an example a zirconium alloy.
At the beginning the stress-strain curve of the alloy is low.
But after the tube production, which include multiple heat treatments, various types of hot and cold extrusion the obtained texture will show at least two times more mechanical resistance to applied load. But the macro specimen is a complex system of small grains. And if you perform nanoindentaion the Young modulus will not change as it is the material charachteristic.
Nano-state is something other and it is very interesting, but it is not the equilibrium state which can go to the equilibrium in some moment in the future that you do can not plan with the degradation of properties. So it is not the best solution.
Doping introduces other elements inside the structure - so it is already another material - this will change the modulus.
I think this is related to the transfer of interactions at different scales and it's a complicated process until now it isn't well understood. Some of the mutiscale models are trying to figure out this and understand the relation between micro and macro levels and how the properties of molecular parts are transferred to macro levels.
I refer to Mr. Karan Prajapathi's answer to promote further discussion on the original question. He has attached a paper to support his statement that mechanical properties of nst 37-2 steel. I got interested in this paper as this one of the very few where Young's modulus values before and after heat treatment have been reported (see Table-3 in the paper). The values in N/mm2 are: before heat treatment-465.78, after annealing-562, after normalizing-534.85, after hardening-1235.31, after tempering-535.17. It is to be implied from the reported values that Young's modulus of this steel is strongly influenced by the heat treatment given. I took a closer look at the paper to find that the Young's modulus has been determined by calculating the slope of the stress-strain curve, which my experience is has not proved to be reliable, to say the least. There are better ways and one of them is the use of piezoelectric ultrasonic composite oscillator technique (PUCOT). Secondly the unit reported in this paper is N/mm2 which is the same as MPa. From this viewpoint the values of Young's modulus are far too low compared to a reference value 210 GPa for steel. Therefore any conclusions related to Young's modulus based on this paper would be questionable. I would appreciate further discussion on the original question which pertains to Young's modulus. My answer is meant to promote further discussion and NOT to question any person or research work referred to in this answer.
I have seen in polymer blends with the effect of stiffener CB the youngs modulus increase by 1.5 or more .But that is not the case of metals as the microlevel voids are much much less .However the arrangement and stress development direction have the say.