以原子尺度模擬探討奈米壓印之尺寸效應

Abstract

奈米尺度下的材料力學往往會表現出與巨觀不同的現象。奈米壓印試驗是一很好分析奈米尺度下材料力學的方法。本論文使用分子動力方法（MD）模擬單晶金、單晶鋁及單晶鎳在奈米尺度的壓印試驗並探討其中尺寸效應的現象。 尺寸效應現象是一在微小尺度的材料中常常被觀察到的現象。微小的材料尺寸在受壓後會被觀察到一隨壓印子尺寸遞增而硬度遞減的現象，形成此種現象的原因一般認為是幾何必要差排所影響（Nix & Gao, 1998）。應用幾何必要差排所推導的應變梯度塑性理論可以很有效的解釋微米尺度中的尺寸效應現象，但隨著壓印子的尺寸變小，在進入奈米的尺寸中時，應變梯度塑性理論的預測會出現與實驗量測觀察不吻合之情形，因此如何有效的利用幾何必要差排於奈米尺度中的尺寸效應現象是一個極為重要的課題。 本論文利用分子動力模擬半徑25奈米以下的球形壓印子壓印單晶金、單晶鋁及單晶鎳金屬試體。使用EAM勢能（potential）來描述此三種FCC立方晶體，並應用滑動向量（slip vector）、應變梯度（strain gradient）及模擬所擷取的幾何必要差排來探討奈米尺度下的尺寸效應現象。 在本論文中首先針對不同的金屬：單晶金及單晶鋁進行較小尺寸壓印子的模擬，用以比較不同金屬在奈米尺度中的尺寸效應現象。模擬所得的結果可以觀察到在10奈米以下的尺度可以觀察到尺寸效應的現象，且金與鋁所產生的差排結構會有相當不同的現象。金所產生的差排會聚在一半球體中；鋁則會觀察到大片滑動差排往四處擴散。 接著本論文針對單晶鎳進行較大尺寸的模擬，從模擬結果中觀察到相當不同的尺寸效應，在半徑5奈米至25奈米壓印子中可以觀察到三種不同的尺寸效應現象。使用滑動向量與幾何必要差排分析，均會發現兩種方法在三種階段中均呈現三種不同的趨勢，因此可以得知在奈米尺度下的尺寸效應，壓印子尺寸會對差排形成的結構有相當大的影響，有效的應用尺寸參數即可對奈米尺度中的尺寸效應現象有良好的解釋。

The Indentation size effect (ISE) is a phenomenon usually observed from the relation between indentation hardness and penetrated depth in micro and nano scale (Nix and Gao, 1998). In general, this phenomenon can be modeled by the theory based on geometrically necessary dislocations (GNDs) within the plastic zone underneath the contact area which was caused by indentor. However, previous studies have discussed this effect merely on the micro-indentation but the phenomenon at the nano scale. And the theory about the nano scale has not been established as accurately as about the micro scale. Thus, how these thin film materials act at nano scale need to be observed and discussed. In this thesis, the computer simulation to process a nanoindentation test with spherical indentor has been used to study the nanoindentation size effect (NISE) in nickel material. The theory of geometry necessarily dislocation was also examined by comparing with the results from molecular simulation. A static version of classical molecular dynamics has been used to study the nanohardness and dislocation activities during the process of nanoindentation. For metals, the interatomic potential was described by the embedded atom method (EAM). With regards to EAM, the interatomic potential contains not only the pair potential between two atoms but also the embedded energy induced by the local density of electrons surrounding the atoms of interest. To simulate indentation process, first of all, a purely repulsive force relationship between spherical indenter and thin films was implemented to model the indentation process instead of modeling the indentor by atoms directly. Secondly, the mean contact pressure, obtained by dividing the indenter load by the projected contact area, characterizes the material strength beneath the indenter. Third, the GNDs calculated from the simulation systems, combined slip vector method and bond angle distribution method to extract the GNDs from the dislocations information of simulation models. The indentation simulation model consists of a thin film specimen and an indenter. The specimens were composed of face-centered cubic (FCC) crystalline Ni atoms with a size of 1000 A×1000 A×200 A. These models contained over 40 million atoms. From the simulation results, it is observed that the hardness is decreased when indenter size increased, which means the ISE phenomenon is possible to observe in the nano scale. In order to examine the ISE phenomenon in the nano scale, we extract the GNDs from the simulation results. It is observed that the GNDs are declined with the indenter radius. This result imply that the GNDs is still affect the hardness in the nano scale and it is reasonable to use the GNDs theory to interpret the ISE phenomenon. The simulation of nanoindentation on single crystal Ni to observe the ISE phenomenon is succeed to observe the ISE phenomenon in the nano scale. The hardness of material has been decreasing with the increasing of the size of spherical indentor. However, the theory model of Nix and Gao will overestimated the hardness because of the effective plastic zone range is larger than the volume confined by the volume of idealized radius. A new scale of plastic zone is proposed in this paper to successfully explain the GND model from the results of atomistic simulation.