本論文針對統計理論之微接觸模型以及奈米壓痕試驗進行研究。利用原子力顯微鏡(Atomic Force Microscope，AFM)掃瞄表面形貌，可獲得表面形貌的高度資料，粗糙度的量測與分析，而計算出統計參數。並利用統計理論將中碳鋼S45C（1045）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，即可得到受粗糙度效應的接觸負載與接觸面積。結果顯示材料表面受到氧化作用，使得表層之機械性質改變。受到粗糙度效應的影響，結果顯示壓痕試驗所得負載與壓深也跟著受到影響，並且與統計理論之微接觸模型推測之值相當接近。
本論文所模擬之結果，發現中碳鋼粗糙峰的變形行為主要是由彈塑性行為和塑性行為所主導，彈性行為所貢獻的量是很小，這跟試件之機械性質以及表面形貌有關。且施加相同的負載時，粗糙度效應較大的試片其真實接觸面積較小，因此真實接觸壓力較大，這個現象跟以視壓力的觀點或是以巨觀的觀點是不同的。壓深小時，接觸力主要都是曲率半徑較小的粗糙峰所貢獻。壓深大時，接觸力轉變為曲率半徑較大的粗糙峰所貢獻。

The force-depth behavior of initial contact between a Berkovich indenter that is treated as a rigid sphere with radius of 300 nm and the S45C steel specimens prepared to have different surface characteristics was considered. The statistical evaluation of contact force and area was proposed in the basis of Fourier cosine series. The native oxide on the steel surface is observed and measured to have the hardness of 5.5 GPa and modulus of 300 GPa. The force-depth responses obtained by the proposed method revealed good agreement with the experimental results for all the prepared surface characteristics. The evaluated results of the deformation fraction and the contact pressure showed the fully plastic deformation exhibited in the initial contact. Through the proposed method, the dominant radii of summits were evaluated and demonstrated their relation to the indentation depth.

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