By hardness do you mean the Young's modulus, or the slope of the stress-strain curve in the plastic regime? The latter is known as work hardening and is described in detail in many textbooks. Basically, the more dislocations you have in a crystal the harder it is to move them because they block each other.
I mean Vickers and Knoop hardness, By increasing the load if hardness increases it mean that the crystal having more dislocations.
[A]First a few lines about hardness and the systems to measure it:
There are five systems (Vickers, Brinell, Rockwell, Knoop, Scleroscope ) of measuring the hardness in terms of Mohs scale from Hardness Number 1 (softest-Talc) to 10(hardest-Diamond). The Vickers test ( in HV or DPH units). is easiest to use because the calculations are independent of the size of the indenter and the indenter can be used for all materials irrespective of hardness. IT CALCULATES THE CRYSTAL’S ABILITY TO RESIST PLASTIC DEFORMATION from a standard source by the load over the surface area of the indentation and not the area normal to the force, and is therefore not a pressure.The hardness also refers to as crystal’s ability to resist abrasion or scratching. The square based pyramidal diamond indenter is generally used as Vickers hardness tester because it have high resistance to self-deformation. Loads of various magnitudes are applied to a flat surface. The HV number(kgf/mm²) is determined by the relation:
HV=F/A=1.8544F/d^2
where F(kgf ) is force applied, d(mm) is the distance from the indentation to the edge of the specimen and A(mm^2) is surface area of resulting indentation.
*Vickers hardness values are reported as aaaHVyy/zz. For example 440HV30/10 or15 or 20 convey:
aaa- 440 the hardness number; HV - Vickers hardness scale ;30 - load in kgf;
20 - loading time 10 s to 15 s or 20 seec.
HV values for some crystals are :Diamond(1000); CaF2(185); MNA[2-Methyl-4- nitroaniline(13).
[B]Mechanism :
The hardness is largely related to type of the crystal structures[7types of crystals having 14 Bravais lattices and two different types of packing of layers ABAB-- and ABCA-- ](6 parameters of a crystal :a,b,c; α,β,γ){ % of voids or empty spaces } and their particle size which varies on the surface and in their bulk[ in depth penetration]. When the load is increased, the applied stress increases. The planes/ layers slip past one and other ,i.e are dislocated to different extents.
*Vickers hardness numbers are generally independent of the test force( will come out the same for 500 gf and 50 kgf), as long as the force is at least 200 gf.
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