要利用統計或碎形理論研究光滑平面或光滑曲面對粗糙平面的接觸行為之前，必須先分析單一粗糙峰的變形行為。傳統單一粗糙峰之接觸力學模型皆是建立於不考慮分子間作用力的情況；然而在微觀尺度之下，以往在巨觀尺度忽略的分子間作用力諸如靜電力、凡得瓦爾力或黏著力(Adhesion force)在如此小的尺度之下，卻佔有極重要的地位，因此使用接觸力學模型來分析微觀尺度下單一粗糙峰變形行為並不適當。本文以分子動力學模擬(MD Simulation)來觀察微觀尺度下銅膜及鑽石膜之單一粗糙峰變形行為，並假設粗糙峰為半圓球形。銅之粗糙峰模型由曲率半徑 的半圓球及底材共126341顆銅原子組成；鑽石之粗糙峰模型由曲率半徑 的半圓球以44173顆碳原子組成。上平板是由碳原子組成的鑽石平面，尺寸為 及 24.18nm×24.18nm×0.62nm及15.26nm×15.26nm×0.62nm，分別由73984顆及29584顆碳原子組成。為了增加模擬的效率，本文以平行運算原子分散法配合分子動力學進行模擬。
　　模擬為絕熱狀態，溫度保持為300K，模擬過程為鑽石上平板下壓半圓球至預設干涉量後再進行滑動。由分子動力學模擬結果可得銅及鑽石半圓球在微觀尺度下接觸負載及接觸面積對干涉量的關係式和滑動摩擦力及摩擦係數。模擬結果顯示光滑平面對半圓球粗糙峰滑動之間的滑動摩擦力表現出振盪現象，而且非金屬材料鑽石半圓球的振盪現象比金屬材料銅半圓球劇烈。在相同的負載速度下，接觸負載、接觸面積、摩擦力及摩擦係數皆會隨著干涉量愈大而增加。在相同負載速度及干涉量下，隨著滑動速度的加快，摩擦力及摩擦係數都有上升的趨勢，這說明了摩擦力和滑動速度有關。
　　利用分子動力學模擬得到微觀尺度下單一粗糙峰之變形行為再配合實驗得到的碎形及統計參數值，並假設粗糙平面上粗糙峰為高斯機率分佈。則碎形理論是利用上述結果再對尺寸分佈函數(size distribution function)n(a)作積分，統計理論對高度分佈函數g(z)作積分，即可得到利用碎形及統計理論將銅膜及鑽石膜單一粗糙峰變形行為擴展至光滑平面及曲面對粗糙平面的接觸行為。結果顯示分子動力學模擬所得之接觸負載比傳統接觸模型計算所得要大，而分子動力學模擬所得之接觸面積比全塑性接觸模型計算所得小，這是由於分子間作用力造成的。而不論是由統計或碎形理論所得之接觸負載、接觸面積，其值都相當接近，但與實驗所得之值有一定的差距。根據分子動力學模擬與全塑性接觸模型比較結果，可知利用分子動力學模擬在微觀尺度下之接觸行為是比較合適的。

Before analysing the microcontact behavior between a rigid smooth flat plane and a rigid smooth semisphere in contact with a deformable rough flat plane by using the statistic or fractal theory, the deformed behavior about the single asperity must be established. The interaction effect between the molecules like adhesion force or Van der Waals’ force which could be neglected under the macroscopic scale will have a significant effect when under the microscopic scale. Because the traditional contact theory do not take the molecular interaction effect into account, use the traditional contact theory to analyse the microcontact behavior about the single asperity is unsuitable. Molecular dynamics(MD) simulation was carried out to investigate the microcontact behavior of the single copper and diamond asperity, assumed that the single asperity was semisphere. The single copper asperity composed of the radius of 6.2nm copper semisphere and the copper substrate, was comprised by 126341 copper atoms, the radius of 4.8nm single diamond semisphere was comprised by 44173 carbon atoms. The upper flat diamond plane was comprised by 73984 and 29584 carbon diamonds respectively. For increasing the simulation efficiency, the parallel algorithms atom decomposition (AD) method combined with MD was adopted.

During the simulation, the adiabatic thermal condition was imposed, and the starting temperature was 300K. The upper flat diamond plane indented to the copper and diamond semisphere initially, and then it slipped through the copper and diamond semisphere. The dependence of the contact load and contact area on the interference (δ) and the dynamic frictional force and coefficient can be determined by MD simulation. From the simulation results, the dynamic frictional force had a oscillated behavior when flat diamond plane slipped through the semisphere, and furthermore the oscillated behavior was stronger when flat diamond plane slipped through the nonmetal material diamond semisphere. The contact load、contact area、dynamic frictional force and dynamic frictional coefficient would get growing as the interference(δ) increased under the same loading velocity. Besides, the dynamic frictional force and dynamic frictional coefficient would get growing as the sliding velocity increased under the same loading velocity and interference(δ), it showed that the dynamic frictional force and dynamic frictional coefficient was related to the sliding velocity.

By Combined the single asperity deformed behavior obtained by MD simulation and the fractal and statistic parameters obtained by Atomic Force Microscope(AFM), also assumed that the rough surface satisfied Gaussian distribution, the fractal theory was integrated with the size distribution function n(a), the statistic theory was integrated with the Gaussian distribution function, we could get the microcontact behavior between a rigid smooth flat plane and rigid smooth semisphere to deformable rough flat plane. The results revealed that the contact load obtained by MD simulation was greater than the contact load obtained by traditional contact theory, and the contact area obtained by MD simulation was smaller than the contact area obtained by traditional contact theory, it was due to the molecular interaction effect. It got the near contact load and contact area whether employed the fractal theory or statistic theory, but far smaller than the results obtained by the experiment. Finally, it could be showed that used MD simulation was more suitable than used traditional contact theory to investigate the microcontact behavior.

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