本論文針對奈米壓痕試驗的分析方法進行材料性質之量測研究，主要內容有三個主題。第一主題為利用接觸力學對圓球型壓頭的分析結果，針對角錐形壓頭尖端接近圓球外型主導部份的實驗結果，進行分析以求取四種不同性質塊材的彈性模數、降伏強度等機械性質。相較於一般常用的方法，利用圓球外型主導部份的實驗結果進行分析，有應力較小、材料內部結構受應力改變的影響也較小的優點。以本研究所提方法分析所得的機械性質，與傳統單軸拉伸試驗所得的值相比較差異不大，證明本研究利用奈米壓痕試驗配合接觸變形理論，提供了求取奈米尺度下材料機械性質的分析方法之可靠性。

　　第二個主題為分析覆膜材料的奈米壓痕試驗。本論文提出一漸近函數，將施加於覆膜材料的負載表示為施加於底材與薄膜之虛擬負載分別乘上個別權重函數的總和。而施加於底材與薄膜之虛擬負載皆可以用適當的冪次值，表示為各自的壓深冪次函數。關於底材的部分，可以由未覆膜的底材來進行試驗，直接得到負載與卸載過程的冪次函數。藉由覆膜試片的實驗數據來進行迴歸分析，以決定薄膜本質部分的參數。透過這套方法的分析，可以將薄膜本身負載與卸載過程的冪次函數，從覆膜試片的實驗數據中分離出來，進而計算出薄膜本身的硬度與彈性模數。這部分用於計算機械性質的接觸面積，係由量測壓痕殘餘形貌而得；以此接觸面積與常用之卸載斜率法進行比較，兩者差異不大。經由本研究所提的方法，一個大負載、大壓深的壓痕試驗數據，便可以提供整個範圍裡複合機械性質的變化，而不需要進行多個不同負載設定的壓痕試驗。

　　本論文的第三個主題為研究硬脆材料在進行奈米壓痕試驗時所表現出來的時依行為。本論文提出以滑塊、彈簧與兩個阻尼適當聯接的修正Voigt理論模型，來描述硬脆材料在進行奈米壓痕試驗時的塑性、彈性以及黏性行為。透過不同加載條件下的理論解與實際實驗的結果進行迴歸分析，模型中的滑塊、彈簧與阻尼等元件之係數便可以決定。結果顯示硬脆材料在進行壓痕實驗時，負載變化速率越大會使壓深產生越顯著的遲滯現象。本論文根據模型所提出硬脆材料卸載斜率的表示式不只與彈性係數有關，材料的黏性係數藉由壓深的一、二階時變率對卸載斜率發生影響；這個表示式在極小加載速率（穩態）的情況下，會與一般常用之O&P法完全一致。針對等加載速率的壓痕實驗，本研究提供了無加載速率（穩態）限制的分析模型。

　　除了等負、卸載率的加載方式外，本論文也進行以正弦函數震盪方式施加負載的奈米壓痕試驗。實驗結果顯示，運用高頻震盪方式的壓痕試驗能有效避開環境飄移等雜訊的影響。承受震盪負載時，壓深會呈現較負載相位落後（Phase lag）但同頻率的週期變化。無論是實驗或是由模型解得的結果，都顯示在震盪條件下的壓深對時間的變化並非一正弦函數；只有在震盪振幅極小的情況下，壓深對時間的變化才趨近正弦函數。基於壓深為正弦函數的假設，常用於動態壓痕實驗之連續剛性法的分析方法並不適用於大振幅的震盪情況。因此本論文根據模型提出由震盪試驗的實驗結果，分析出硬脆材料彈、黏性係數與負載振幅、頻率、壓深時變率、相位落後之間的表示式；該式在振幅極小的情況下，與連續剛性法所用儲存模數、損失模數的方程式一致。針對震盪加載條件的壓痕實驗，本研究提供了無振幅限制的分析模型。

　The load-depth (P-h) relationships matching the experimental results of the nanoindentation tests exhibited at the subregions of small and large depths are obtained respectively. The relationships associated with these two subregions are then linked by the hyperbolic logarithm function to attain single expression that is applied in the evaluation of the specimen’s elastic recovery ability shown in the unloading process. A new method is developed in the present study to evaluate the Young’s modulus and the yield strength of either a ductile or brittle material though the uses of the appropriate P-h relationships developed in the load and unloading processes. The results of the Young’s modulus and the yield strength by the present method are compared with that obtained from the conventional material tests for a lump material. The scatterings of the experimental data shown in the loading and unloading processes are also interpreted by different causes.

　The indentation depth generally expressed as a function of the indentation load can theoretically be converted into the indentation load expressed as a function of the indentation depth. This principle is applied in the present study. The indentation load applied to a specimen with a coating film can be expressed as the sum of the pseudo loads arising in the coating film and in the silicon substrate, timing their individual weighting function in the exponential form. The pseudo load in either the coating film or the substrate is further expressed as a power function of the indention depth using an appropriate value as the exponent. The exponent value for the substrate material is directly determined by the regressions of the experimental results for either the loading or the unloading process. Through the regression of the experimental results, the pseudo load-displacement profiles for the coating film can be obtained for both the loading and unloading processes. The full load-depth profile for the coating film is thus made available and used in the evaluations of the hardness and the reduced modulus of the coating film. The real contact areas are here obtained by scanning the profiles of the indentation cavities. The contact areas obtained from direct measurements are quite close to those predicted by the commonly-used theory. The load-depth profile of one composite response with a high load can provide the mechanical properties varying with a wide range of indentation depths.

　Through a special arrangement in the indentation test conditions, the lagging behavior exhibited in the block responsible for the plastic deformation is found to be very different from that shown in the spring responsible for the elastic deformation. A modified Voigt model is thus proposed by considering each of these two devices in parallel with their individual dashpot. Based on this model, the indentation depth solutions in response to the load conditions set for the loading, dwelling, and unloading processes are obtained. These solutions can be applied to determine four coefficients of these four devices in this modified Voigt model by a good fitting with the experimental results. These coefficients are then applied to study the lagging behavior due to the difference in the rise time. A new expression is derived for the parameters that is useful to investigate the effect of differing the rise time on the parameter of a hard material. Good agreement with the experimental data reveals that the modified Voigt solid model is suitable for the indentation behavior exhibited in the hard materials. The values of predicted in the present expression show good agreement with the experimental results. The expression can be used as the formula for evaluating the reduced modulus if the rise time is sufficiently long. The solution can be further applied to attain the material properties in conjunction with the experimental results of depth in response to an oscillating indentation load condition. The most significant advantage of the present model compared to CSM is free from the restriction on a small amplitude of the oscillating load in the indentation test, but is still able to obtain the same results. The phase lag between the indentation load and the indentation depth is almost linearly proportional to the frequency of the oscillating load. The effect of changing the oscillating load amplitude on the final mean indentation depth is quite small.

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