On the relationship between hardness and yield strength

For many materials, there is a relationship between hardness and yield strength, it seems that the hardness is three times of yield strength. I'm wondering is there any theorical origin on this relationship?

Kelven Leo wrote:
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Just very, very roughly.
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A hardness indentation and yielding both needs dislocation movement.
Michael Dahms

Does hardness shows any relationship with % Elongations also (for a particular composition)? I wanted to know if someone wants to plot a curve between hardness and other meachanical properties (such as % Elongation, YS,UTS) is it possible?
mrigendra
Michael Dahms wrote:
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Yes, anyone can plot one property aginst another, so it is possible to plot hardness vs "whatever you like". Many people have done this from time to time.
An excellent example of intelligent cross plotting of data of materials is by Prof. M. F. Ashby... "Materials Selection in Mechanical Design"
You can buy it at Amazon.com or go to a good technical library and look at his dozens of examples of intelligent cross plotting of materials properties.
If you are afraid of taking the time to do the work.... maybe you can find it already done in standard reference works.
mrigendra wrote:
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Then, who can tell what hardness mean? That is, what is the physical meaning of hardness? Is hardness a index of materials against (plastic) deformation? Unlike the yield strength, the elastic modulus which are the fundmental properties of materials, hardness is only the "surface" property of materials. The question is how to relate hardness with those fundmental properties?

Kelven Leo wrote:
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"Hardness" is the result of an experiment....
There are many ways to measure "hardness" and it has long been known that there is not necessarily a relatinship between them.
Youngsters often demand that "Hardness" really be "SOMETHING".
Real reading in good books will often mitigate that illness.
Those who don't read will never be satisfied, confident that if they persist, they will eventually discover the "Truth".
Bye .......

"Is hardness a index of materials against (plastic) deformation?"
Yes, and different indentation hardness tests impose different penetration geometries so give different results.
"Unlike the yield strength, the elastic modulus which are the fundmental properties of materials,..... The question is how to relate hardness with those fundmental properties? "
There is no particular reason they should be closely related. Elastic modulii are based on extremely small, recoverable deformations while indentation hardnesses are based on non-recoverable macroscopic deformations. These are completely opposite ends of a deformaton spectrum.
Consider the effect of heat treatment on a carbon steel. The elastic modulii don't change very much but hardness can be changed tremendously.
Probably the most that can be said regarding the relationship between modulus and hardness is something like a material's maximum possible hardness is proportional to its shear modulus - unlike the minimum hardness which is probably bounded by zero.
There is no logical relationship between a crystalline material's bulk modulus and hardness; When a crystalline material "yields" under hydrostatic loading it does so by changing to a different crystalline structure - it ceases to exist.
Dave