本論文的主題為研究類鑽碳(Diamond-like carbon)分別鍍在SKH51、AL6061兩種底材上硬度的過渡行為分析。在奈米壓痕過程中，我們考慮了包含壓痕器與薄膜接觸、薄膜彎曲、薄膜與底材接觸這三種現象，對複合硬度(Composite hardness)從薄膜硬度逐漸趨近底材硬度的行為探討，並使用方程式去描述壓痕發生的過程。首先，壓痕深度可以表示成壓痕負載的函數，這個函數包含了薄膜與底材各自的負載係數(Loading coefficient)、卸載係數(Unloading coefficient)以及薄膜彎曲的等效剛性(Equivalent stiffness of the film deflection)。而藉由此函數，便可以對覆膜材料的壓痕實驗數據做準確的擬合(fitting)。我們以Sakai所提出的奈米壓痕模型為基礎，藉由一連串公式的推導，可以預測在不同壓痕器傾斜角度(Indenter inclined angle)對一塊材做壓痕實驗的負載係數、卸載係數的理論值；另一方面將提出的覆膜材料奈米壓痕模型，套用到不同負載條件下，由實驗得到的覆膜材料壓深負載圖，便可得到覆膜材料底材的負載係數以及卸載係數。在兩種不同的模型中，觀察到負載係數以及卸載係數的趨勢有極高相似性。利用負載及卸載係數將兩個模型做結合，得到在不同的壓痕深度時，對應到的覆膜材料界面虛擬壓痕器傾斜角度(Virtual indenter inclined angle)。最後與MTS所得到的底材硬度權重比做比較發現，兩種覆膜材料其相同虛擬壓痕器傾斜角度所對應到底材權重比非常吻合。證實虛擬壓痕器傾斜角度的確與覆膜材料硬度過渡性質有極大的關聯性。

The transitional hardness behavior of the two composite materials (DLC/SKH51,DLC/AL) is the topic in this study. Using the Nanoindentation concept of M. Sakai, and combine some basic Nanoindentation formulas, we can get two new equations. If the true hardness, reduce modulus are known, the loading and unloading coefficient, which vary with the incline angle of indenter can be got by these two equation. A model considering the deformation of a composite material, including the contact between film and indenter, film inflection, the contact between interface and substrate, was proposed. The indentation depth was expressed as a function of indentation load, which is relate to the loading and unloading coefficients of film, substrate and the film deflection stiffness. Good agreement revealed between the P-h results of two composite materials and the proposed equation of this composite materials model if properly choosing the parameter. There is a very similar trend between the loading/unloading coefficient of bulk in the different incline angle of indenter and the loading/unloading coefficient of substrate of composite materials in the different nondimensional depth. From this relationship, we can get the virtual indenter angle in interface if the nondimensional depth is known. Using MTS-Nano-indenter-XP system, the hardness weighting factor of substrate in different nondimsional depth can be available. Finally, we find the same hardness weighting factor of substrate in different composite materials always correspond to the same virtual indenter angle. So, the virtual indenter angle must play a critical role in the transitional hardness behavior of the two composite materials in this study.

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