以原子尺度模擬探討幾何必要差排與奈米壓痕尺寸效應

Abstract

壓痕試驗為微觀及奈米尺度中最為普遍之材料強度檢測方式，當壓痕深度小至微米尺度時，硬度會隨著壓痕深度降低而升高，這種現象稱之為「壓痕尺寸效應」，Nix and Gao以幾何必要差排理論成功的解釋在微米尺度壓痕試驗的尺寸效應，但是在將其理論應用至奈米尺度時，硬度的預測則有高估的情形。近年來，許多研究紛紛針對此現象提出不同的看法，嘗試利用其他變數修正並解釋壓痕尺寸效應在奈米尺度下的行為。本研究將提出一在原子尺度模擬下量測差排密度的方法，並利用Taylor dislocation theory將其與原子尺度模擬下直接量測之硬度相對照，並利用原子尺度模擬探討相關機制與奈米壓痕尺寸效應。 本研究以半徑20 Å至60 Å的球形壓痕探針檢測FCC單晶鎳、單晶銅、單晶金之奈米薄膜。模擬結果顯示利用本研究所提出之方法量測之幾何必要差排密度在模型大小設置足夠的情況下表現良好。本研究發現利用各尺寸之球型壓痕探針所得到之幾何差排密度遠小於Swadener等人之理論模型，此結果與Feng等人所提出的結果一致。利用幾何必要差排密度所推導得到的硬度與原子尺度模擬下量測的硬度相差不遠，而原子尺度模擬下量測的硬度亦與壓痕探針之半徑開根號成反比，成功驗證奈米尺度下應變梯度塑性理論與幾何必要差排密度尺寸效應。

Indentation experiment is one of the most useful method to probe the strength of materials that are manufactured at micro or nano scales. When indentation depth decrease to micro meters, the hardness increase as the indentation depth decrease. It is known as the indentation size effect. Nix and Gao present a theoretical model to explain the indentation size effect in microindentation. However, it overestimate the hardness in nanoindentation. For years, many studies tried to explain and modify Nix and Gao model for nanoindentation with free parameters. In this study, a method is presented to measure the dislocation density directly in atomistic simulation, and using the Taylor dislocation theory to compare with the hardness from atomistic simulation. Atomistic simulation were conducted to elucidate the relationship between size effect and the geometrically necessary dislocation density. In this study, spherical indenters with their radius from 20Å to 60Å was exploited to examine the FCC single crystal thin film of nickel, copper and gold. Indentation experiments methods of measuring dislocation density and hardness also works well in atomistic simulation. Geometrically necessary dislocation density measuring by our method works well in simulation if the size of the model is large enough to ignore the boundary effects. In present work, diverse radius of spherical indenter indicated that the geometry necessary dislocation density is much smaller than the theory proposed by Swadener et al., which is in agreement of the findings of Feng[1]. Hardness derived by dislocation density is close to the hardness directly computed from atomistic simulation. Hardness directly from simulation is inversely proportion to the square root of indenter radius which is agreed with the theory of strain gradient plasticity. It can be concluded that the strain gradient plasticity of size effect and geometric necessary dislocation density were valid at atomistic scale.