平行化分子動力模擬應用於奈米壓痕試驗

Application of Parallel Molecular Dynamics Simulation to Nano-Indentation Tests

林敬淶(Chen-Lai Lim)

指導教授 ： 郭昌宏

國立暨南國際大學/科技學院/土木工程學系/碩士(2009年)

https://doi.org/10.6837/NCNU.2009.00230

摘要

本研究係利用平行化分子動力模擬探討不同的試體尺寸、壓痕深度與探針尖端半徑對於單晶銅奈米壓痕試驗結果之影響。分析方法是假設探針為剛體，並將X和Y方向邊界設定為週期邊界條件。各原子初始速度是以高斯亂數產生器建立，並利用Morse勢能函數計算銅-銅與碳-銅原子之間的作用力。時間積分演算法選用五階Gear預測修正演算法，計算各時間步之原子的位移、速度和加速度。藉由模擬所得之加載-卸載曲線和Oliver-Pharr壓痕理論，計算材料硬度和楊氏係數。數值分析結果顯示，系統的溫度易受模型邊界的影響，模擬的試體尺寸越小,系統溫度在壓痕過程中持續上升的幅度越高。當模型尺寸小於45.6x45.6x12.3nm3，系統必須在整個壓痕的過程中，每隔一定時間進行溫度修正，而當模型尺寸大於45.6x45.6x12.3nm3，僅需在初始平衡的階段中作溫度修正。此外，本研究分別以錐角為60°的圓錐形探針和Berkovich探針探討不同壓痕深度與探針尖端半徑對硬度與楊氏係數的影響。分析結果顯示，試體平面尺寸與厚度不足皆會影響硬度與楊氏係數的量測。一般而言，當壓痕深度超過試體厚度10%時，基底效應對量測結果的影響愈趨明顯。

關鍵字

Morse勢能 ； 平行化分子動力模擬 ； 奈米壓痕 ； 單晶銅 ； 探針尖端半徑

並列摘要

In this study, a parallel molecular dynamics simulation is applied to investigate the effects of sample size, indentation depth and the radius of indenter tip on the nanoindentation measurement of monocrystalline copper. The indenter is assumed rigid and the periodic boundary conditions are set along the X and Y-directions of the model. The initial velocity for each atom is assigned by using the Gaussian random generator, and the Morse potential is used to model the interaction forces between the Cu - Cu atoms and C - Cu atoms. The Gear’s fifth predictor-corrector algorithm is used to calculate the displacement, velocity and acceleration for the atoms at each time step. The hardness and Young’s modulus are calculated by using the simulated loading-unloading curve during the indentation process and the Oliver-Pharr theory. Numerical results show that the system temperature can be raised during the simulation by the boundaries of the model. For the smaller size of the model, the temperature increments appear higher during the nano-indentation test. The results show that, for the size of the model smaller than 45.6x45.6x12.3nm3, a readjustment of the system temperature is needed for a certain time steps while the adjustment is only needed in the initial equilibrium when the size of the model is greater than 45.6x45.6x12.3nm3. In addition, a cone indenter with 60 degree angle and a Berkovich indenter are employed to study the effect of indentation depth and radius of indenter tip on the hardness and Young’s modulus. The results show that both planar size and thickness could affect the measurement of hardness and Young’s modulus. In general, the substrate effect becomes more evident as the indentation depth is over 10% of sample thickness.

並列關鍵字

Morse potential ； parallel molecular dynamics simulation ； nano-indentation ； monocrystalline copper ； radius of indenter tip

參考文獻

1. Fischer-Cripps, A. C., “Nanoindentation 2nd. Ed.”, Springer, (2002)

2. Oliver, W. C., Pharr, G. M., “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments”, J. Mater. Res., 7 (1992) 1564-1583

3. Bhattacharya, A. K., Nix, W. D., “Analysis of elastic and plastic deformation associated with indentation testing of thin films on substrates”, Int. J. Solids Structures, 24 (1998) 1287-1298

4. Shih, C. W., Yang, M., Li, J. C. M., “Effect of tip radius on nanoindentation”, J. Mater. Res., 6 (1991) 2623-2628

5. Cai, X., Bangert, H., “Hardness measurements of thin films-determining the critical ratio of depth to thickness using FEM”, Thin Solid Films, 264 (1995) 59-71