本研究利用分子動力學模擬建立一套由球形奈米壓痕負載－深度曲線反演材料單軸壓縮力學性質之方法。首先，藉由原子von Mises等效應力分布辨識壓痕作用下之有效影響區域，並根據橫向與深度方向之影響範圍建立有效影響體積。進一步將壓入深度與有效影響深度之比值定義為等效應變，並對奈米壓痕卸載之負載－深度曲線進行積分以取得應變能；將應變能除以有效影響體積得到應變能密度，再對等效應變微分求得等效應力，以建立奈米壓痕之等效應力－應變曲線。為驗證所提出方法之適用性，本研究分別探討不同壓頭半徑、薄膜厚度及晶格方向之影響，並與相對應晶格方向之單軸壓縮模擬結果進行比較。
結果顯示，在本研究所探討之條件範圍內，壓頭半徑與薄膜厚度的改變對轉換所得之等效楊氏模數影響有限，而不同晶格方向則會使有效影響區域及轉換後之力學行為產生差異。進一步引入無因次等效應變校正係數後，Ag[001]、Ag[011]與Ag[111]三種晶格方向之等效楊氏模數皆可與相應之單軸壓縮結果相近。綜合而言，本研究所建立之轉換方法能反映不同模擬條件與晶格方向下的力學差異，並可作為由奈米壓痕行為評估材料單軸彈性行為之方法。

This study uses molecular dynamics simulations to develop a method for deriving uniaxial compressive mechanical properties from spherical nanoindentation load–depth curves. The indentation-affected region is identified from the atomic von Mises stress distribution, and an effective volume is determined from its lateral and depthwise extents. Equivalent strain is defined using the indentation depth and effective influence depth, while the unloading load–depth curve is integrated to obtain strain energy. The strain energy density is then calculated and differentiated with respect to the equivalent strain to obtain the equivalent stress–strain response. The effects of indenter radius, film thickness, and crystallographic orientation are evaluated by comparison with corresponding uniaxial compression simulations.
The results show that indenter radius and film thickness have limited influence on the converted equivalent Young’s modulus, whereas crystallographic orientation produces more noticeable differences. After introducing a dimensionless equivalent-strain correction factor, the equivalent Young’s moduli of Ag[001], Ag[011], and Ag[111] agree closely with the corresponding uniaxial compression results. These results demonstrate the feasibility of the proposed method for evaluating uniaxial elastic behavior from nanoindentation responses.

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