本文依據Stroh理論計算複合材料缺角周圍的位移與應力分佈，並利用H積分和最小二乘法來計算複合材料V型缺角的應力集中係數。本文利用影像相關性的實驗來取得試體表面的變位資料，用最小二乘法分析得到的應力集中係數，由實驗得到的實際應力集中係數再與H積分法和有限元素分析模擬的資料所得到的進行比較。之後繼續使用相同方法對於兩種材料的介面進行量測與模擬，得到的結果誤差也在可容許的範圍內。另外也觀察環境微振對於影像相關性實驗的影響，結果顯示振動導致分析結果離散程度增加。本文最後對於壓電材料做了一些基本的研究以及建立二維有限元素的程式。

This study developed the theoretical formulations based on the Stroh’s complex function approach to evaluate the displacement and stress fields. The least-squares formulation and the H-integral were used to obtain the notch SIFs of a shape V-notch anisotropic material. The displacements from image-correlation experiments were then introduced into the least-squares formulation to solve the notch SIFs and compared with the SIFs calculated from the H-integral and finite element method. The single composite material and the bi-material problems are considered with the same methods. The effects of environmental vibrations and man-made vibrations for the image correlation system were also investigated. The results show that the vibrations increase the standard deviations of the SIFs from the experiment. The preliminary study in piezoelectric materials was also performed, and the two-dimensional finite element model has been generated.

[1] McNeill SR, Peters WH, Sutton MA, Estimation of stress intensity factor by digital image correlation, Engineering Fracture Mechanics 1987; 28:101-112.
[2] D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, Digital speckle-displacement measurement using a complex spectrum method, Applied Optics 1993;32:1839-1849.
[3] M. Mahinfalah, L. Zackery, Photoelastic determination of mixed mode stress intensity factors for sharp reentrant corners, Engineering Fracture Mechanics 1995;52:639-645.
[4] Della-Ventura D, Smith RNL, Some applications of singular fields in the solution of crack problems. International Journal for Numerical Methods in Engineering 1998;42:927-942.
[5] Tong W., Detection of plastic deformation patterns in a binary aluminum alloy. Experimental Mechanics 1997; 37:452-459.
[6] Machida K., Study of stress-analyzing system by speckle photography, JSME International Journal Series A-Solid Mechanics and Material Engineering 2000;43,343-350.
[7] Potti PKG, Rao BN, Srivastava VK, Fracture strength of composite laminates containing surface notches. Advanced Composite Materials 2001;10:29-37.
[8] Niu LS, Shi HJ, Robin C, Pluvinage G, Elastic and elastic-plastic fields on circular rings containing a v-notch under inclined loads. Engineering Fracture Mechanics 2001;68: 949-962.
[9] Kondo T, Kobayashi M, Sekine H, Strain gage method for determining stress intensities of sharp-notched strips. Experimental Mechanics 2001;41:1-7.
[10] Mattoni MA., Zok FW. A method for determining the stress intensity factor of a single edge-notched tensile specimen. International Journal of Fracture 2003;119:376-392.
[11] Kumagai S, Shindo Y. Experimental and analytical evaluation of the notched tensile fracture of CFRP-woven laminates at low temperatures. Journal of Composite Materials 2004; 38:1151-1164.
[12] Park T.S., Baek D.C., Lee S.B., An experimental technique for the strain measurement of small structures using pattern recognition. Sensors and Actuators A: Physical 2004; 115:15-22.
[13] Diaz FV, Armas AF, Kaufmann GH, Galizzi GE, Fatigue damage accumulation around a notch using a digital image measurement system. Experimental Mechanics 2004;44:241-246.
[14] El-Hajjar R, Haj-Ali R. Mode-I fracture toughness testing of thick section FRP composites using the ESE(T) specimen. Engineering Fracture Mechanics 2005;72:631-643.
[15] Sun Y.F., John H.L. Pang, Experimental and numerical investigations of near-crack-tip deformation in a solder alloy. Acta Materialia 2008;56:537-548.
[16] Mason W.P., Physical Acoustics-Principles and Methods Vol. 1(part A). Academic Press, New York: 1964.
[17] Allik H., Hughes T.J.R., Finite element method for piezoelectric vibration. International Journal of Numerical Methods in Engineering 1970;2:151-157.
[18] Park S.B., Sun C.T., Effect of electric field on fracture of piezoelectric ceramics. International Journal of Fracture 1995;70:203-216.
[19] Beom H.G., Atluri S.N., Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media. International Journal of Fracture 1996;75:163-183.
[20] Ding H.J., Wang G.Q., Chen W.Q., A boundary integral formulation and 2D fundamental solutions for piezoelectric media. Computer methods in applied mechanics and engineering 1998; 158:65-80.
[21] Gao C.F., Fan W.X., A general solution for the plane problem in piezoelectric media with collinear cracks. International Journal of Engineering Science 1999; 37:347-363.
[22] Shindo Y., Watanabe K., Narita F., Electroelastic analysis of a piezoelectric ceramic strip with a central crack. International Journal of Engineering Science 2000; 38:1-19.
[23] Liu J.X., Wang X.Q., Interaction of a screw dislocation with a notch in a piezoelectric bi-material. Archive of Applied Mechanics 2004; 73:553-560.
[24] Chen M.C, Ping X.C., Xie H.M, Liu Z.W., Numerical and experimental analyses of singular electro-elastic fields around a V-shaped notch tip in piezoelectric materials. Engineering Fracture Mechanics 2008; 75:5029-5041.
[25] Peters W.H, Ranson W.F., Digital imaging techniques in experimental stress analysis. Optical Engineering 1982; 21:427-432.
[26] T.C. Chu, W.F. Ranson, M.A. Sutton and W.H. Peters, Applications of digital-image-correlation techniques to experimental mechanics. Experimental Mechanics 1985; 25:232-244.
[27] H.A. Bruck, S.R. McNeill, M.A. Sutton and W.H. Peters III, Digital image correlation using Newton-Raphson method of partial differential correction. Experimental Mechanics 1989; 29:261-268.
[28] Zili Sun, Jed S. Lyons, Stephen R. McNeill, Measuring Microscopic Deformations with Digital Image Correlation. Optics and Lasers in Engineering 1997;27:409-428.
[29] Williams M.L., Stress singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics 1952;74:526-528.
[30] Wu K.C., Chang F.T., Near-tip field in a notched body with dislocations and body forces. ASME Journal of Applied Mechanics 1993;60:936-941.
[31] Williams M.L., The stresses around a fault or crack in dissimilar media. Bulletin of the Seismological Society of America 1959;49:199-204.
[32] Hein V.L., Stress singularities in a two-material wedge. International Journal of Fracture Mechanics 1971;7:317-330.
[33] Paul E.W. Labossiere, Martin L. Dunn, Stress intensities at interface corners in anisotropic bimaterials. Engineering Fracture Mechanics 1999;62:555-575.
[34] Lekhnitskii SG., Theory of elasticity of an anisotropic body. Holden-Day, San Francisco; 1963.
[35] Ting TCT. Anisotropic elasticity: theory and application. Oxford University Press, New York; 1996.
[36] Moulson A.J., Herbert J.M., Electroceramics: materials, properties, applications. Chapman and Hall, London; 1990.
[37] Nye J.F., Physical properties of crystals: their representation by tensors and matrices. Oxford University Press, New York, 1957.
[38] Tzou H.S., Piezoelectric shells: distributed sensing and control of continua. Kluwer Academic Publishers, Boston, 1993.
[39] Press W.H., Flannery B.P., Teukolsky S.A., Vettenling W.T., Numerical recipes, the art of scientific computing. Cambridge University Press, New York; 1986.
[40] Sokolnikoff I.S., Mathematical theory of elasticity, 2nd ed, Mcgraw Hill; 1965.
[41] Ju S.H., Liu S.H., Determining stress intensity factors of composites using crack opening displacement. Composites Structures 2007; 81:614-621.
[42] Ju S.H., Development of a nonlinear finite element program with rigid link and contact element. Report of NSC in R.O.C., NSC-86-2213-E-006-063, 1997, This report and the source codes in an executable compressed file can be obtained from the Internet, at myweb.ncku.edu.tw/~juju.
[43] Liu S.H., Noncontact image-based measurement techniques and automatic programming using digital camera. Doctoral thesis, Department of Civil Engineering, National Cheng Kung University 2007, Taiwan (R.O.C.).
[44] Tu S.P., Application of image correlation to measure displacement. Master thesis, Department of Civil Engineering, National Cheng Kung University 2007, Taiwan (R.O.C.).
[45] 周卓明,壓電力學,全華科技圖書,台北市,2003.