[Spm] Elastic modulus

[Igor Sokolov]

Dear Michal,

The term "reduced Young's modulus" refers  frequently to E/(1-vt^2). This is
to avoid a lengthy and sometime complicated measurements of the Poisson's
ratio (which is, in addition, does not change substantially for different
materials). From that point of view, the first formula (1/Ered = (1-vt^2)/Et
+ (1-vs^2)/Es) makes more sense because it can be directly extrapolated to
the above "reduced Young's modulus" definition. However, the second
expression 3/4((1-vt^2)/Et + (1-vs^2)/Es)) does naturally occur in classical
Hertzian/Sneddon formulas. But I am not sure if it makes sense to define it
as 1/Ered. Of course, it would still be just a definition, which does not
change the physics as soon as one remembers how to use it in formulas.

 

I  hope a mechanical engineer could answer your question in more detail. I
would be glad to see that. I remember from my graduate times that there was
even a definition of "reduced elastic modulus" that does not have direct
relation to the reduced Young's modulus, which is you are presumably asking.

 

Best regards,

Igor

 

_____________________________________

 Igor Sokolov, Ph.D.

 Director of NanoBio Laboratory (NABLAB), Clarkson University,

 Professor,

 Department of Physics,

 Department of Chemistry and Biomolecular Science,

 Clarkson University, 

 NY Center for Advanced Material Processing (CAMP)

 Potsdam, NY 13699

 

Phone:    315-268-2375

Fax:        315-268-6610

email:      isokolov at clarkson.edu

Web:       http://www.clarkson.edu/~isokolov

               http://www.clarkson.edu/~nablab 

_____________________________________

 

From: Michal Wozniak [mailto:micwoz at gmail.com] 
Sent: Tuesday, August 05, 2008 8:35 PM
To: Spm at spmlist.di.com
Subject: [Spm] Elastic modulus

 

Dear SPMers 
   Some time ago I study contact mechanics SPM tip probe and sample. To be
honest, I am a little confused, lets me explain why. I found many papers
where it is equation for reduced elastic modulus (combine elastic modulus on
probe and sample). In about 50% of papers 
equation looks like this
1/Ered = (1-vt^2)/Et + (1-vs^2)/Es 
[e.g.      D.M. Ebenstein et al., Nanotoday 1(2006) 26] 
but in other 50% of papers looks like
1/Ered = 3/4((1-vt^2)/Et + (1-vs^2)/Es))
[e.g.   H.J. Butt et al., Surf. Sci. Report 59 (2005) 1, R.W. Carpick et
al., J. Colloid Interf. Sci. 211 (1999) 395]
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. 
So the difference between equations is factor 3/4
Could someone explain me this, please. 

Than you in advance for your kind help

Michal 

-- 
Michal J. WOZNIAK Ph.D.
Scanning Probe Microscopy
Polymeric Biomaterials Group
Biomaterials Center
National Institute for Materials Science
1-1 Namiki, Tsukuba, Ibaraki 3050044
Japan 

Phone: +81 29 851 33 54 (ext. 8699) 
Phone: +81 29 851 33 54 (ext. 8774) 
Fax: +81 29 860 4714

WOZNIAK.Michaljerzy at nims.go.jp
micwoz at gmail.com

http://www.nims.go.jp/eng/index.html

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