Elastic Modulus and Hardness


Schematic of Hooke's Law

Two mechanical properties, elastic modulus and hardness, can be determined by nanoindentation.

The elastic modulus (E), often referred to as Young’s modulus, is the ratio of stress (σ) to strain (ε) when deformation is totally elastic. In the elastic region, stress and strain are proportional through Hooke’s Law: σ = Eε

The elastic modulus is an intrinsic property of a material. At a fundamental level, E is a measure of the bond strength between atoms. The greater the modulus, the stiffer the material and the smaller the strain. An elastic response is non-permanent, so when an applied load is released, the sample returns to its original shape.

Hardness (H) is a measure of a material’s resistance to deformation by surface indentation. The plastic deformation is caused by the motion of dislocations in the atomic structure of a material. The yield strength of a material may be changed by inhibiting dislocation motion through imperfections, alloys or grain boundaries.

Material hardness can be increased by different means, including interstitial or substitutional hardening, where atoms are either added between or substituted in the atomic lattice:

Interstitial and substitutional hardness

 Interstitial and substitutional hardening

Microhardness testing and nanoindentation are standard methods of determining hardness. Nanoindentation has the added benefit of also providing elastic modulus.


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