Instead of a general consideration of the fractal dimension (D) and the topothesy (G*) as two invariants in the fractal analysis of surface asperities, these two roughness parameters in the present study are varied by changing the mean separation (d*) of two contact surfaces. The relationship between the fractal dimension and the mean separation is found first. By equating the structure functions developed in two different ways, the relationship among the scaling coefficient in the power spectrum function, the fractal dimension, and topothesy of asperity heights can be established. The variation of topothesy can be determined when the fractal dimension and the scaling coefficient have been obtained from the experimental results of the number of contact spots and the power spectrum function at different mean separations. A numerical scheme is developed in this study to determine the convergent values of fractal dimension and topothesy corresponding to a given mean separation. The theoretical results of the contact spot number predicted by the present model show good agreement with the reported experimental results. Both the fractal dimension and the topothesy are elevated by increasing the mean separation. Significant differences in the contact load or the total contact area are shown between the models of constant D and G* and variable D and G* as the mean separation is reduced to smaller values.
Most statistical contact analyses assume that asperity height distributions (g(z*)) follow a Gaussian distribution. However, engineered surfaces are frequently non-Gaussian with the type dependent on the material and surface state being evaluated. When two rough surfaces experience contact deformations, the original topography of the surfaces varies with different loads, and the deformed topography of the surfaces after unloading and elastic recovery is quite different from surface contacts under a constant load. A theoretical method is proposed in the present study to discuss the variations of the topography of the surfaces for two contact conditions. The first kind of topography is obtained during the contact of two surfaces under a normal load. The second kind of topography is obtained from a rough contact surface after elastic recovery. The profile of the probability density function is quite sharp and has a large peak value if it is obtained from the surface contacts under a normal load. The profile of the probability density function defined for the contact surface after elastic recovery is quite close to the profile before experiencing contact deformations if the plasticity index is a small value. However, the probability density function for the contact surface after elastic recovery is closer to that shown in the contacts under a normal load if a large initial plasticity index is assumed. How skewness (Sk) and kurtosis (Kt), which are the parameters in the probability density function, are affected by a change in the dimensionless contact load, the initial skewness (the initial kurtosis is fixed in this study) or the initial plasticity index of the rough surface is also discussed on the basis of the topography models mentioned above. The behavior of the contact parameters exhibited in the model of the invariant probability density function is different from the behavior exhibited in the present model.
Nanoindentation tests in which oscillating loads were applied to specimens were carried out to study the work (Wf) required for a coating film to delaminate from its substrate. A sharp increase in the indentation depth occurred during coating film delamination. A theoretical model was developed for the present study to evaluate the difference between the work in the load-depth profiles obtained with and without delamination. Arranging that the maximum load was reached at the end of the loading process allowed us to obtain an approximately constant value for the indentation depth propagation rate during in one cycle. This allowed a determination of the number of oscillating cycles and, thus, the work required by assuming that there was no delamination during this delamination period. The depth propagation rates and the work required for coating film delamination were investigated by varying Pmax, Pmean, P0, and frequency (f). The depth propagation rates were slightly increased by increasing the Pmax value but were significantly lowered by increasing the frequency (f). The effects due to the changes in Pmean and P0 on the depth propagation rate were insignificant. The Wf value was slightly lowered by increasing the Pmax value but was significantly increased by increasing the oscillating load frequency (f). The effects of varying P0 and Pmean on the Wf value were found to be small. The Wf values showed an exponential drop when the depth propagation rate was increased; they were asymptotic to a constant value when the depth propagation rate was sufficiently high. Coating film delamination produced a sharp increase in the indentation depth even in the case of a very small load increase. The oscillating load-depth cycles appearing after delamination allowed us to establish the film-substrate contact behavior occurring during the loading/unloading process of one oscillating cycle.
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