以原子尺度模擬探討幾何必要差排與壓痕探針之尺寸效應

Abstract

奈米壓痕為微觀及奈米尺度中最為普遍之材料強度檢測法。其力學性質隨量測尺度變化而有所改變，與一般連體材料並不相同，被稱之為壓痕尺寸效應。Nix and Gao以幾何必要差排密度補足應變之幾何不相容，提出應變梯度塑性理論解釋尺寸效應。對於微小奈米尺度實驗有技術上之困難性，以原子尺度模擬探討尺寸效應與幾何必要差排密度為重要之可行之策。 本研究使用半徑20A至100A球形壓痕探針及角錐形壓痕探針檢測FCC單晶鎳之奈米薄膜。由原子模擬資訊直接計算硬度，分別與壓痕探針半徑平方根及壓痕深度平方根成反比，成果吻合於應變梯度塑性理論。 為計算幾何必要差排密度，以理論模型之等效塑性區進行擷取差排，各尺寸球形壓痕探針及角錐形壓痕探針所計算出之幾何必要差排密度分別與Swadener等人及Nix&Gao之理論模型相吻合。本研究之硬度與幾何必要差排密度皆符合理論推導，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。

Nanoindentaiton is the most useful test method to probe the strength of materials that are manufactured at micro or nano scales. Unlike the continuum behavior, the mechanical properties exhibit a strong dependency with characteristic length scale, which is also referring to the nanoindentation size effect. Nix and Gao proposed the strain gradient plasticity theory to interpret the size effect by introducing a geometrically necessary dislocation density to overcome the strain incompatibility. Atomistic simulations were conducted to elucidate the relationship between size effect and the geometrically necessary dislocation density in this study. In this study, spherical indenters with their radius from 20A to 100A and Berkovich indenter were exploited to examine the FCC single crystal thin firm of Nickel. Hardness was directly obtained from the atomistic simulation that hardness is inversely proportion to the square root of indenter radius and indentation depth respectively. The findings agree with the well-known strain gradient theory. In order to calculate the geometry necessary dislocation density, an equivalent plastic zone size was chose to meet the theoretic requirement. In present work, diverse radius of spherical indenter and Berkovich indenter indicated that the geometry necessary dislocation density showed a great agreement with the theory proposed by Swadener et al and Nix&Gao respectively. The hardness and geometric necessary dislocation density extracted directly from atomistic simulation were both agreed with the theory. It can be concluded that the strain gradient plasticity of size effect and geometric necessary dislocation density were valid at atomistic scale.