220.127.116.11 Comparison of DMT, JKR and Maugis models
To compare the foregoing models we introduce the normalized radius of the contact area , force and penetration depth :
In Table 1 are collected major assumptions and restrictions of every theory while in Table 2 – corresponding normalized equations .
|Hertz||No surface forces||Not applied to small loads in the presence of surface forces|
|DMT||Long-range surface forces act only outside the contact area. Model geometry is as in the Hertz model||Contact area can be decreased due to the limited geometry. Applied only to small|
|JKR||Short-range surface forces act only within the contact area||Force magnitude can be decreased due to surface forces.Applied only to large|
|Maugis||Tip-sample interface is modeled as a ring.||The solution is analytical but equations are parametric. Applied to all values.|
Table 1. Comparison of quantitative adhesion models.
Table 2. Normalized equations of quantitative adhesion models.
Fig. 1 shows plots of normalized force vs. normalized penetration depth for DMT, JKR and Maugis models at different . As can be seen, at small the Maugis model approaches the DMT model while at large – the JKR model.
Fig. 1. Plot of the force vs. the penetration depth for the DMT, JKR and Maugis models
for the different values.
- Several theoretical models of adhesion having different ranges of application are proposed. The most accurate one is the Maugis model.
- Handbook of Micro/Nanotribology / Ed. by Bhushan Bharat. - 2d ed. - Boca Raton etc.: CRC press, 1999. – 859 p.