Tabor parameter

For nanoaerosol, e 1 because of the great rigidity. Several theoretical models of adhesion energy can be found in the literature. Two of the most well-known ones are JKR model and DMT model. These two models contradict each other because they represent two extremes in the Tabor parameter spectrum. JKR model is applied for soft material, large radius, compliant spheres, and large adhesion energy, and DMT model is for hard material, small radius, and low adhesion energy. Therefore, DMT model should be considered first for nanoaerosol thermal rebound analysis. 

There was some argument in the literature over the relative merits and demerits of the JKR and the DMT theories [23-26], but the controversy has now been satisfactorily resolved. A critical comparison of the JKR and DMT theories can be obtained from the literature [23-30]. According to Tabor [23], JKR theory is valid when the dimensionless parameter given by Eq. 25 exceeds a value of about five. 

The difference of the Chin-Gilman parameter for differing types of chemical bonding accounts for the Tabor constant not being three for non-metals. 

Vasic and deMan (1968) defined hardness (H) as the ratio of load to the area of the impression made by the penetrometer. This parameter was explained as the cone will sink into the fat until the stress exerted by the increasing contact surface of the cone is balanced by the hardness of the fat (deMan, 1983). Vasic and deMan (1968) defined fat hardness in a similar way to the Brinell hardness used in metallurgy (Tabor, 1948). The relationship between the applied force load (P), hardness (H), half cone angle (e), radius of the flat tip of the cone (r), penetration impression area (yl jmp) and depth id) for the cone in Figure 7.6 is given by Equation 2 (Vasic and deMan, 1968) ... 

Microhardness, therefore, appears to be an elastic-plastic rather elusive parameter (Marsh, 1964). Microhardness as a property is, in fact, a complex combination of other properties elastic modulus, yield strength and strain hardening capacity. One way to differentiate between the reversible and irreversible components of contact deformation is to measure the elastic recovery during unloading of the indenter (Stilwell Tabor, 1961). Extreme cases of depth recovery are best described by soft metals, where it is negligible, and fully elastic rubber, where it is complete. 

The differences between Pitts (P) and Fuoss-Onsager (F-O) are first, the above mentioned omission by F-O of the effect of asymmetric potential on the local velocities of the solvent near the ions second, the use of the more usual boundary conditions 5.2.28b by F-O compared to the P assumption that perturbations cease to be important at r = a. Pitts, Tabor and Daly, who have analysed in detail both treatments, concluded that the discrepancy due to the different boundary conditions is small but has the effect of reducing ionic interactions in the P treatment with respect to the F-O. This is confirmed by the analysis of data with both theories. Usually P requires a smaller value of the a parameter than F-O. The third discrepancy between the theoretical treatments is in the expression of Vj, in eqn. 5.2.5, for which F-O add a term which involves the effect of the asymmetry of the ionic atmosphere upon the central ion surrounded by such atmosphere. The last difference lies in the hydrodynamic approaches and the corresponding boundary conditions. P imposes the condition that the velocity of the smoothed... 

It is possible to test the validity of JKR analysis using Tabor s equation [Tabor, 1977 Johnson and Greenwoods, 1997], The dimensionless parameter /u. is expressed... 

The random roughness of surfaces can be modeled by a statistical distribution, as first shown by Johnson and later much expanded by others. Using such a statistical theory, Fuller and Tabor defined an adhesion parameter which was the asperity height divided by the maximum extension an asperity could withstand before adhesive fracture. This adhesion parameter increased with roughness and elastic modulus but decreased with work of adhesion and asperity... 

Depending upon these factors, the Intensity of contact which Is intimately related to friction, is defined. It has been pointed out by Bowden and Tabor that the area of real contact Is usually much smaller than the nominal area on account of the presence of surface roughness and that the determination of the real area is of fundamental Importance In tribology. This Is undoubtedly justified, considering the fact that the failure of adhesion occurs at the real area of contact. The real area has been regarded as the key parameter in the description of the intensity of contact. 

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