本文是以有限元素分析模型模擬Berkovich奈米壓痕試驗，討論壓痕深度與應變硬化率對材料硬度量測所造成的誤差以及改變薄模彈性模數與降伏強度對壓痕臨界深度的影響。首先建立有限元素Berkovich奈米壓痕試驗模型，經由數值模擬所得的負載位移關係曲線與文獻中的實驗數據比對，驗證有限元素模型以及分析方法的正確性。本文探討在軟膜硬底和硬膜軟底兩種不同組合下壓痕深度對於薄膜機械性質的影響，發現當薄膜受到底層影響時，硬度值的誤差隨著底層材料塑性區域越大影響越大。數值結果顯示應變硬化率越大則量測得的硬度越大;觀察在同樣的壓痕深度下所產生的塑性應變量，應變硬化率大的材料塑性應變量比較小，顯示由於材料抵抗塑性變形能力佳，所以硬度大。經由改變薄膜的降伏強度與彈性模數，本文找出不同材料參數的臨界深度，結果顯示當薄膜的降伏強度與彈性模數越大，臨界深度越小。

參考文獻
1.郭正次, “奈米結構材料科學,” 全華出版社, 2004.
2.K. L. Johnson, “Contact Mechanics,” Cambridge University Press , 1985.
3. A. M. Korsunsky, M. R. Mcgurk, S. J. Bull, T. F. Page, “On the hardeness of coated systems,” Surface and Coating Technology, Vol. 99, pp. 171-183, 1998.
4. D. Lebouvier, P. Gilormini and E. Felder, “A kinematic solution for plane-strain indentation of a bilayer.” J. Phys. D: Appl. Phys. Vol. 18 , pp. 199-210, 1985.
5. D. Lebouvier, P. Gilormini and E. Felder, “A kinematic model for plastic indentation of a bilayer,” Thin Solid Films, Vol. 172, pp. 227-239, 1989.
6.I. N. Sneddon, “The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile,” International Journal of Engineering Science, Vol. 3, pp. 47, 1965.
7. M. Doerner, W. D. Nix, “A method for interpreting the data from depth-sensing indentation instruments,” Journal of Materials Research, Vol. 1, pp. 601-609, 1986.
8.R. B. King, “Elastic analysis of some punch problems for a layered medium,” International Journal of Solids Structures, Vol. 23, No. 12, pp. 1657-1664, 1987.
9.A. K. Bhattacharya, W. D. Nix, “Analysis of elastic and plastic deformation associated with indentation testing of thin films on substrates,” International Journal of Solids and Structures, Vol. 24, pp. 1287-1298, 1988.
10.W. C. Oliver, G. M. Pharr, “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments,” Journal of Materials Research, Vol. 7, No. 6, June 1992.
11.H. F. Wang, H. Bangert, “Three-dimensional finite element simulation of Vickers indentation on coated substrates,” Materials Science and Engineering, A, Vol. 163 , pp. 43, 1993.
12.X. Cai, H. Bangert, “Hardness measurements of thin films-determining the critical ratio of depth to thickness using FEM,” Thin Solid Films, Vol. 264, pp. 59-71, 1995.
13.M. Lichinchi, C. Lenardi, J. Haupt, R. Vitali, “Simulation of Berkovich nanoindentation experiments on thin films using finite element method,” Thin Solid Films, Vol. 312, pp. 240-248, 1998.
14.H. Pelletier, J. Keier, A. Cornet, P. Mille, “Limits of using bilinear stress-strain curve for finite element modeling of nanoindentation response on bulk materials,” Thin Solid Films, Vol. 379, pp.147-155, 2000.
15.R. Saha, W. D. Nix, “Soft films on hard substrates nanoindentation of tungsten films on sapphire substrates,” Materials Science and Engineering, A, Vol. 319-321, pp. 898-901, 2001.
16.R. Saha, W. D. Nix, “Effects of the substrates on the determination of thin film mechanical properties by nanoindentation,” Acta Materialia, Vol. 50, pp. 23-38, 2002.
17.J. D. Bressan, A. Tramontin, C. Rosa, “Modeling of nanoindentation of bulk and thin film by finite element method,” Wear, Vol. 258, pp.115-122, 2005.
18.S. W. Youn, C. G. Kang, “FEA study on nanodeformation behaviors of amorphous silicon and borosilicate considering tip geometry for pit array fabrication,” Materials Science and Engineering, A, Vol. 390, pp 233-239, 2005.
19 許志義, “薄膜壓痕試驗之有限元素分析,” 碩士論文, 國立暨南大學, 2004.
20.陳卓然, ”潛盾隧道襯砌環片螺栓對於環片錯位之影響初步探討,” 中華顧問工程司 地工部, 2006.
21.張瑞慶, “奈米壓痕技術與應用,” 聖約翰科技大學
22.W. F. Chen, D. J. Han, “Plasticity for Structural Engineering, ” Springer Verlag, 1988.
23.徐秉業、劉信聲, “應用彈塑性力學,” 凡異出版社, 1997.
24.W. Prager and P. G. Hodge Jr., “Theory of Perfectly Plastic Solids,□Wiley, New York, 1951.
25.A. Mendelson, “Plasticity：Theory and Application,□Macmillan, New York, 1968.
26.R. D. Cook, D. S. Malkus, M. E. Plesha, R. J. Witt, “Concepts and Application of Finite Element Analysis,” Wiley, New York, 2002.
27.李輝煌, “ANSYS 工程分析：基礎與觀念,□高立圖書有限公司, 2005.
28.N. Yu, A. A. Polycarpou, T. F. Conry, “Tip-radius effect in finite element modeling of sub-50 nm shallow nanoindentation,” Thin Solid Films, Vol. 450, pp. 295-303, 2004.
29.N. Panich, Y. Sun, “Effect of penetration depth on indentation response of soft coatings on hard substrates: a finite element analysis,” Surface and Coatings Technology, Vol. 182, pp. 342-350, 2004.
30.林宗億, “混合型破裂韌度的預測,” 碩士論文, 國立清華大學, 2006.
31.ANSYS theory reference. 000656. Seventh Edition. SAS IP, Inc.1994.