Re: On the relationship between hardness and yield strength

"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

.

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