[Spm] RE: Elastic modulus (Michal Wozniak) Spm Digest, Vol 49, Issue 3

[Barthel, Etienne]

Michal wrote:
Is the reduced elastic modulus (combined elastic modulus of probe and sample)
1/Ered = (1-vt^2)/Et + (1-vs^2)/Es   (1)
or
1/Ered = 3/4((1-vt^2)/Et + (1-vs^2)/Es))   (2)
where Ered - reduced elastic modulus, Et - Young's modulus of tip, Es -
Young's modulus of sample, vt - Poisson's ratio of tip,   vs - Poisson's
ratio of sample ?

Hi Michal,
Strictly speaking, the combined reduced modulus is Eq 1, without the 3/4. Then the Hertzian force is P=4/3 Ered a^3/R. When you deal exclusively with spheres, it is tempting to lump the 4/3 factor with Ered (see eg Maugis 1992). Then one gets Eq 2 and the force is P=Ered a^3/R (see eg table 2 in Butt 2005).
Best,
Etienne

P.S.: if you are also interested in adhesion, you may want to have a look at this recent review
http://hal.archives-ouvertes.fr/hal-00256886/fr/
or
http://www.iop.org/EJ/abstract/0022-3727/41/16/163001/

Dr Etienne Barthel
CNRS/Saint-Gobain
Surface du Verre et Interfaces
BP 135 
F-93303 Aubervilliers Cedex
France
 
tél: 33 1 48 39 55 57 fax: 33 1 48 39 55 62
 
www.saint-gobain-recherche.com/svi/en