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系統識別號 U0026-0408201411375400
論文名稱(中文) 複合材料與多項材料楔形填充之裂縫及缺角應力分析
論文名稱(英文) Estimation of the stress intensity factors of cracks and notches in anisotropic, multi-material and inclusion material
校院名稱 成功大學
系所名稱(中) 土木工程學系
系所名稱(英) Department of Civil Engineering
學年度 102
學期 2
出版年 103
研究生(中文) 邱乾艷
研究生(英文) Chien-Yen Chiu
學號 n68961018
學位類別 博士
語文別 英文
論文頁數 117頁
口試委員 口試委員-徐德修
口試委員-施明祥
口試委員-林宜清
口試委員-鍾興陽
指導教授-朱聖浩
中文關鍵字 數位影像相關法  缺角  裂縫  有限元素  複合材料  填縫缺角 
英文關鍵字 Crack  Notch  Inclusion  Composite  Multi-material  Stress intensity factors  Digital-image-correlation experiment  H-integral  Least-squares method  Finite element method 
學科別分類
中文摘要 裂縫及缺角存在於許多工程構件中,且因材料性質與幾何形狀的不連續,大部分破裂都將發生於此處,大型構造物如:鋼構樑柱接頭、構件電銲處、航太材料、船舶殼體及汽車鈑金等,小型構件如:電子構裝、半導體封裝材料及太陽能板等。文獻中已有探究許多均質裂紋及均質缺角,相對少的文獻提出方法可將由異向彈性/複合材料/多項材料所構成之缺角來討論缺角周圍的位移與應力分佈。本文依據Stroh理論分析缺角周圍的位移與應力分佈,並將所得之變位值配合H積分和最小二乘法來計算缺角及裂縫的應力集中係數,利用影像相關性的實驗來取得試體表面的變位資料,使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。本文使用上述方法對於異向彈性/兩種複合材料/多項材料所構成之缺角及裂縫進行量測與模擬,得到的結果誤差也在可容許的範圍內。本論文發展優點為(1)試驗步驟及實驗儀器簡單、可行性及準確度高,且實驗裝置不需昂貴的設備。(2)可任意量測缺角變位,不需考慮邊界條件。(3)分析缺角應力集中係數時,不需使用非常靠近裂縫尖端之變位值。此方法對於從事缺角及裂縫的應力集中分析相關研究主題之人員,提供了非常簡便且適用範圍非常廣泛之分析工具。
英文摘要 Cracks and notches often occur in engineered objects, and failures can then initiate from these critical regions due to the resulting discontinuities in geometry and material properties. This can occur with large items, such a the beam-column joints of steel structures, welding members, and in aerospace, vessel and automobile components, as well as smaller items, such as those found in electronic packaging, semiconductor packaging and solar panels. While there are many studies that examine problems related to homogenous cracks and notches, relatively few consider the stress intensity factors (SIFs) of cracks and notches in anisotropic, multi-material and inclusion problems. This study thus estimated the notch-tip and crack-tip coordinates, as well as the SIFs, using image-correlation experiments with the least-squares method. In this approach the complex displacement functions are deduced into a least-squares form, and then displacement fields from the image-correlation experiments are substituted into the least-squares equation to obtain the SIFs. The results of the experiments are compared using H-integral and finite element analyses, and this reveals that the SIFs obtained using the proposed method are acceptably accurate. The major advantage of this approach is that it is easy, simple and systematic, and the experimental data required for it do not need to include that near the notch tip or specimen boundaries. In addition, it is not necessary to smooth the experimental data, since the least-squares method can average the deviations in this. The proposed method thus provides a very simple and convenient tool for researchers to obtain the SIFs of notch and crack problems.
論文目次 ABSTRACT i
摘要 ii
誌謝 iii
Contents iv
List of Figures vii
List of Tables xi
Nomenclature xiii
Chapter 1 Introduction 1
1.1 Background 1
1.2 Objectives and Scope of research 2
1.3 Organization of Dissertation 3
Chapter 2 Literature Review 5
2.1 Research correlated with determination of SIFs, crack-tip coordinates and crack angle in composite materials 5
2.2 Research correlated with determination of V-notch SIFs in multi-material anisotropic wedges by digital correlation experiments 7
2.3 Research correlated with determination of stress intensity factors for multi-material junctions 10
Chapter 3 Details of the image-correlation experiment 13
3.1 Introduction 13
3.2 Theory of image correlation method 14
3.3 Optical system 18
3.4 The procedures of the image correlation program CCD82 19
3.5 Summary 21
Chapter 4 Determination of notch SIFs, crack-tip coordinates and crack angle in composite
materials 24
4.1 Introduction 24
4.2 Displacements near the crack tip 24
4.3 Least-squares method to find KI and KII 27
4.4 Linear search and Powell methods to find crack-tip coordinates and angle b 28
4.5 Validations using the finite element method 30
4.5.1 Studing the accuracy of the crack-tip coordinates and angle b using equation (4.15) 31
4.5.2 Studing the accuracy of the SIFs using equation (4.17) 33
4.6 Validations using image correlation experiments 34
4.7 Conclusion 35
Chapter 5 Calculation of V-notch SIFs in multi-material notches 46
5.1 Introduction 46
5.2 Displacement and stress fields of notches 46
5.3 Definition of Notch SIFs 50
5.4 Evaluation of g using the H-integral 52
5.5 Evaluation of g using the least-squares method 54
5.6 Illustration of experiments 55
5.7 Results and comparisons 57
5.8 Conclusions 59
Chapter 6 Determination of stress intensity factors for multi-material junctions 66
6.1 Introduction 66
6.2 Displacement and stress fields of multi-material junctions 67
6.3 Junction-tip SIFs 70
6.4 Least-squares method to find inclusion tip coordinates and g 72
6.5 H-integral to find g using finite element results 74
6.6 Numerical validations 76
6.7 Validation using image correlation experiments 79
6.8 Conclusions 82
Chapter 7 Error and limitations study of generalized plane-strain least-squares method 90
7.1 Introduction 90
7.2 3D J-integral and least-squares method 92
7.3 Numerical examples 93
7.3.1 A plate with a central horizontal crack (case 1) 93
7.3.2 A plate with a central slant crack (case 2) 94
7.3.3 Finite Element results and discussions 94
Chapter 8 Conclusions and Recommendations 100
8.1 Conclusions 100
8.2 Recommendations for Further Research 102
References 104
參考文獻 [1] Akiniwa, Y., Fujii, T., Kimura, H. and Tanaka, K., Evaluation of fibre bridging stress of short fatigue cracks in scs-6/ti-15-3 composite, Fatigue and Fracture of Engineering Materials and Structures, Vol.30, No.3, pp.258-266, 2007.
[2] Ali, S. M., Rahmatollah G. and Marco A., Finite element evaluation of stress intensity factors in curved non-planar cracks in FGMs, Mechanics Research Communications, Vol.38, No.1, pp.17-23, 2011.
[3] Bakker, A., Three-dimensional constraint effects on stress intensity distributions in plate geometries with through-thickness cracks, Fatigue & Fracture of Engineering Materials & Structures, Vol.15, No.11, pp.1051-1069, 1992.
[4] Banks-Sills, L. and Ishbir, C., A conservative integral for bimaterial notches subjected to thermal stresses, International Journal for Numerical Methods in Engineering, Vol.60, No.6, pp.1075-1102, 2004.
[5] Becker, T. H., Mostafavi, M., Tait, R. B. and Marrow, T. J., An approach to calculate the J-integral by digital image correlation displacement field measurement, Fatigue & Fracture of Engineering Materials & Structures, Vol.35, No.10, pp.971-984, 2012.
[6] Bradshaw, R.D. and Gutierrez, S.E., Characterization of fatigue crack initiation and growth in hybrid aluminium-graphite fibre composite laminates using image analysis, Fatigue and Fracture of Engineering Materials and Structures, Vol.30, No.8, pp.766-781, 2007.
[7] Bruck, H.A., McNeill, S.R., Sutton, M.A. and Peters, W.H., Digital image correlation using Newton-Raphson method of partial differential correlation, Experimental Mechanics, Vol.29, No.3, pp.261-267, 1989.
[8] Carpinteri, A. and Paggi, M., Analytical study of the singularities arising at multi-material interfaces in 2D linear elastic problems, Engineering Fracture Mechanics, Vol.74, No.1-2, pp.57-74, 2007.
[9] Carpinteri, A. and Paggi, M., Influence of the intermediate material on the singular stress field in tri-material junctions, Materials Science, Vol.42, No.1, pp.95-101, 2006.
[10] Carpinteri, A., Paggi, M., and Pugno, N., Numerical evaluation of generalized stress-intensity factors in multi-layered composites, International Journal of Solids and Structures, Vol.43, No.3-4, pp.627-641, 2006.
[11] Chen, J.T. and Wang, W.C., Experimental analysis of an arbitrarily inclined semi-infinite crack terminated at the bimaterial interface, Experimental Mechanics, Vol.36, No.1, pp.7-16, 1996.

[12] Chen, M.C. and Sze, K.Y., A novel hybrid finite element analysis of bimaterial wedge problems, Engineering Fracture Mechanics, Vol.68, No.13, pp.1463-1476, 2001.
[13] Chu, T.C, Ranson, W.F., Sutton, M.A. and Peters, W.H., Applications of digital-image-correlation techniques to experimental mechanics, Experimental Mechanics, Vol.25, No.3, pp.232-244, 1985.
[14] Ergun, E., Tasgetiren, S. and Topcu, M., Determination of SIF for patched crack in aluminum plates by the combined finite element and genetic algorithm approach, Fatigue and Fracture of Engineering Materials and Structures, Vol.31, No.11, pp.929-936, 2008.
[15] Guo, L.C., Wu, L.Z. and Ma L., The interface crack problem under a concentrated load for a functionally graded coating-substrate composite system, Composite Structures, Vol.63, No.3-4, pp.397-406, 2004.
[16] Hemann, J.H., Achenbach, J.D. and Fang, S.J., Dynamic photoelastic study of stress-wave propagation through an inclusion, Experimental Mechanics, Vol.16, No.8, pp.291-299, 1976.
[17] Henshell, R.D. and Shaw, K., Crack tip finite elements are unnecessary, International Journal for Numerical Methods in Engineering, Vol.9, No.3, pp.495-507, 1975.
[18] Heyder, M., Kolk, K. and Kuhn, G., Numerical and experimental investigations of the influence of corner singularities on 3D fatigue crack propagation, Engineering Fracture Mechanics, Vol.72, No.13, pp.2095-2105, 2005.
[19] Hwu, C., and Kuo, T.L., A unified definition for stress intensity factors of interface corners and cracks, International Journal of Solids and Structures, Vol.44, No.18-19, pp.6340-6359, 2007.
[20] Jackson, J. H., Kobayashi, A. S. and Atluri, S. N., A three dimensional numerical investigation of the T∗ integral along a curved crack front, Computer Modeling in Engineering & Sciences, Vol.6, No.1, pp.17-30, 2004.
[21] Jhao, B.J., Evaluation of notch stress intensity factors in composite and piezoelectric materials, pp.33-46, 2009.
[22] Ju, S.H. and Liu, S.H., Determining stress intensity factors of composites using crack opening displacement, Composite Structures, Vol.81, No.4, pp.614-621, 2007.
[23] Ju, S.H. and Rowlands, R.E., Thermoelastic determination of crack-tip coordinates in composites, International Journal of Solids and Structures, Vol.44, No.14-15, pp.4845-4859, 2007.
[24] Ju, S.H. and Rowlands, R.E., Thermoelastic determination of KI and KII in an orthotropic graphite/epoxy composite, Journal of Composite Materials, Vol.37, No.22, pp.2011-2025, 2003.
[25] Ju, S.H., Calculation of notch H-integrals using image correlation experiments, Experimental Mechanics, Vol.50, No.4, pp.517-525, 2010.
[26] Ju, S.H., Chiu, C.Y. and Jhao, B.J., Determination of SIFs, crack tip coordinates and crack angle of anisotropic materials, Fatigue and Fracture of Engineering Materials and Structures, Vol.33, No.1, pp.43-53, 2010b.
[27] Ju, S.H., Chiu, C.Y. and Jhao, B.J., Determination of V-notch SIFs in multi-material anisotropic wedges by digital correlation experiments, International Journal of Solids and Structures, Vol.47, No.7-8, pp.894-900, 2010a.
[28] Ju, S.H., Chung, H.Y. and Jhao, B.J., Experimental calculation of mixed-mode notch stress intensity factors for anisotropic materials, Engineering Fracture Mechanics, Vol.76, No.14, pp.2260-2271, 2009.
[29] Ju, S.H., Development a nonlinear finite element program with rigid link and contact element, Report of NSC in R.O.C., NSC-86-2213-E-006-063, pp.66-81, 1997.
[30] Ju, S.H., Liu, S.H. and Liu, K.W., Measurement of stress intensity factors by digital camera, International Journal of Solids and Structures, Vol.43, No.5, pp.1009-1022, 2006.
[31] Ju, S.H., Simulating stress intensity factors for anisotropic materials by the least squares method, International Journal of Fracture, Vol.81, No.3, pp.283-297, 1996.
[32] Ju, S.H., Simulating three-dimensional stress intensity factors by the least-squares method, International Journal for Numerical Method in Engineering, Vol.43, pp.1437-1451, 1998.
[33] Khalil, S.A., Sun, C.T. and Hwang, W.C., Application of a hybrid finite element method to determine stress intensity factors in unidirectional composites, International Journal of Fracture, Vol.31, No.1, pp.37-51, 1986.
[34] Kim, J.H. and Paulino, G.H., Mixed-mode J-integral formulation and implementationusing graded elements for fracture analysis of nonhomogeneous orthotropic materials, Mechanics of Materials, Vol.35, pp.107-128, 2003.
[35] Kitey, R. and Tippur, H.V., Dynamic crack growth past a stiff inclusion: optical investigation of inclusion eccentricity and inclusion-matrix adhesion strength, Experimental Mechanics, Vol.48, No.1, pp.37-53, 2008.
[36] Labossiere, P.E.W. and Dunn, M.L., Stress intensities at interface corners in anisotropic bimaterials, Engineering Fracture Mechanics, Vol.62, No.6, pp.555-575, 1999.
[37] Lekhnitskii, S.G., Theory of elasticity of an anisotropic body, Holden-Day, San Francisco, 1963.
[38] Li, Y.T. and Song, M., Method to calculate stress intensity factor of v-notch in bimaterials, Acta Mechanica Solida Sinica, Vol.21, No.4, pp.337-346, 2008.
[39] Liu, X.Y., Xiao, Q.Z. and Karihaloo, B.L., XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials, International Journal for Numerical Methods in Engineering, Vol.59, No.8, pp.1103-1118, 2004.
[40] Lopez-Crespo, P., Shterenlikht, A., Patterson, E. A., Withers, P. J. and Yates, J. R., The stress intensity of mixed mode cracks determined by digital image correlation, Journal of Strain Analysis for Engineering Design, Vol.43, No.8, pp769-780, 2008.
[41] Lopez-Crespo, P., Shterenlikht, A., Yates, J. R., Patterson, E. A. andWithers, P. J., Some experimental observations on crack closure and crack tip plasticity, Fatigue and Fracture of Engineering Materials and Structures, Vol.32, No.5, pp.418-429, 2009.
[42] Lu, H. and Chiang, F.P., Photoelastic study of interfacial fracture of bimaterial, Optics and Lasers in Engineering, Vol.14, No.3, pp.217-234, 1991.
[43] Marsavina, L. and Sadowskia, T., Kinked crack at a bi-material ceramic interface: Numerical determination of fracture parameters, Computational materials science, Vol.44, No.3, pp.941-950, 2009.
[44] Marsavina, L. and Sadowskia, T., Stress intensity factors for an interface kinked crack in a bi-material plate loaded normal to the interface, International Journal of Fracture, Vol.145, No.3, pp.237-243, 2007.
[45] McNeill, S.R., Peters, W.H. and Sutton, M.A., Estimation of stress intensity factor by digital image correlation, Engineering Fracture Mechanics, Vol.28, No.1, pp.101-112, 1987.
[46] Meda, G., Messner, T.W., Sinclair, G.B. and Solecki, J.S., Path-independent H integrals for three-dimensional fracture mechanics, International Journal of Fracture, Vol.94, No.3, pp.217-234, 1998.
[47] Meguid, S.A. and Tan, M.A., Photoelastic analysis of the singular stress field in a bimaterial wedge, Experimental Mechanics, Vol.40, No.1, pp.68-74, 2000.
[48] Mukherjee, S., Jayaram, V. and Biswas, S.K., Validation of stresses and stress intensity factor in a notched bilayer system under four point bending, as determined by the solution of the Navier’s equation, International Journal of Mechanical Sciences, Vol.48, No.11, pp1287-1294, 2006.
[49] Noselli, G., Dal Corso, F. and Bigoni, D., The stress intensity near a stiffener disclosed by photoelasticity, International Journal of Fracture, Vol.166, No.1-2, pp.91-103, 2010.
[50] Omer, N. and Yosibash, Z., On the path independency of the point-wise J integral in three-dimensions, International Journal of Fracture, Vol.136, pp.1-36, 2005.
[51] Ozer, H., Duarte, C. A. and Al-Qadi I. L., Formulation and implementation of a high-order 3-D domain integral method for the extraction of energy release rates, Computational Mechanics, Vol.49, No.4, pp.459-476, 2012.
[52] Paggi, M. and Carpinteri, A., On the stress-singularities at multi-material interfaces and related analogies with fluid dynamics and diffusion, Applied Mechanics Reviews, Vol.61, No.2, pp.1-22, 2008.
[53] Ping, X.C., Chen M.C. and Xie J.L., Singular stress analyses of V-notched anisotropic plates based on a novel finite element method, Engineering Fracture Mechanics, Vol.75, No.13, pp.3819-3838, 2008.
[54] Pook, L. P., A 50-year retrospective review of three-imensional effects at cracks and sharp notches, Fatigue & Fracture of Engineering Materials & Structures, Vol.36, pp.699-723, 2013.
[55] Pook, L. P., A note on corner point singularities, International Journal of Fracture, Vol.53, pp.R3-R8, 1992.
[56] Powell, M. J. D., An efficient method for finding the minimum of a function of several variables without calculating derivatives, The Computer Journal, Vol.7, No.2, pp.155-162, 1964.
[57] Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vettenling, W.T., Numerical Recipes The Art of Scientific Computing, Cambridge University Press, New York, 1986.
[58] Raiser, G. and Clifton, R.J., High-strain rate deformation and damage in ceramic materials, Journal of Engineering Materials and Technology-Transactions of the ASME, Vol.115, No.3, pp.292-299, 1993.
[59] Rethore, J., Gravouil, A., Morestin, F. and Combescure, A., Estimation of mixed-mode stress intensity factors using digital image correlation and an interaction integral, International Journal of Fracture, Vol.132, No.1, pp.65-79, 2005.
[60] Rethore, J., Roux, S. and Hild, F., Optimal and noise-robust extraction of Fracture Mechanics parameters from kinematic measurements, Engineering Fracture Mechanics, Vol.78, No.9, pp.1827-1845, 2011.
[61] Rhee, J. and Rowlands, R.E., Moire-numerical hybrid analysis of cracks in orthotropic media, Experimental Mechanics, Vol.42, No.3, pp.311-317, 2002.

[62] Rice, J.R., A path independent integral and approximate analysis of strain concentration by notches and cracks, Journal of Applied Mechanics, Vol.35, No.2, pp.379-386, 1968.
[63] Roux, S. and Hild, F., Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches, International Journal of Fracture, Vol.140, No.1-4, pp.141-157, 2006.
[64] Sabelkin, V., Mall, S. and Avram, J.B., Fatigue crack growth analysis of stiffened cracked panel repaired with bonded composite patch, Engineering Fracture Mechanics, Vol.73, No.11 , pp.1553-1567, 2006.
[65] Savalia, P.C. and Tippur, H.V., A study of crack-inclusion interactions and matrix-inclusion debonding using Moire interferometry and finite element method, Experimental Mechanics, Vol.47, No.4, pp.533-547, 2007.
[66] Seif, M.A. and Dasari, N.B., Effect of combined loading on cracks in graphite/epoxy composites, Composite Structures, Vol.52, No.3, pp.539-544, 2001.
[67] Semenski, D. and Jecic, S., Experimental caustics analysis in fracture mechanics of anisotropic materials, Experimental Mechanics, Vol. 39, No.3, pp.177-183, 1999.
[68] Shang, L.Y., Zhang, Z.L. and Skallerud, B., Evaluation of fracture mechanics parameters for free edges in multi-layered structures with weak singularities, International Journal of Solids and Structures, Vol.46, No.5, pp.1134-1148, 2009.
[69] Shih, C. F., Moran, B. and Nakamura, T., Energy release rate along a three-dimensional crack front in a thermally stressed body, International Journal of Fracture, Vol.30, No.2, pp.79-102, 1986.
[70] Shimamoto, A., Nam J., Oguchi T. and Azakami T., Effect of crack closure by shrinkage of embedded shape-memory tini fiber epoxy composite under mixed-mode loading, International Journal of Materials and Product Technology, Suppl.1, pp.263-268, 2001.
[71] Shin, K.C., Kim, W.S. and Lee, J.J., Application of stress intensity to design of anisotropic/isotropic bi-materials with a wedge, International Journal of Solids and Structures, Vol.44, No.24, pp7748-7766, 2007.
[72] Shukla, A., Chalivendra, V.B., Parameswaran, V. and Lee, K.H., Photoelastic investigation of interfacial fracture between orthotropic and isotropic materials, Optics and Lasers in Engineering, Vol.40, No.4, pp.307-324, 2003.
[73] Sinclair, G.B., Stress singularities in classical elasticity-I: Removal, interpretation, and analysis, Applied Mechanics Review, Vol.57, No.4, pp.251-297, 2004a.
[74] Sinclair, G.B., Stress singularities in classical elasticity-II: Asymptotic identification, Applied Mechanics Review, Vol.57, No.5, pp.385-439, 2004b.
[75] Song, C., Analysis of singular stress fields at multi‐material corners under thermal loading, International Journal for Numerical Methods in Engineering, Vol.65, No.5, pp.620-652, 2005.
[76] Stroh, A.N., Steady state problems in anisotropic elasticity, Journal of Mathematics and Physics, Vol.41, No.2, pp.77-103, 1962.
[77] Ting, T.C.T., Anisotropic Elasticity: Theory and Application, Oxford University Press, New York, 1996.
[78] Ting, T.C.T., Barnett-Lothe tensors and their associated tensors for monoclinic materials with the symmetry plane at x3=0, Journal of Elasticity, Vol.27, No.2, pp.143-165, 1992.
[79] Wang, Q., Noda, N.A., Honda, M.A. and Chen, M., Variation of stress intensity factor along the front of a 3D rectangular crack by using a singular integral equation method, International Journal of Fracture, Vol.108, No.2, pp.119-131, 2001.
[80] Williams, M.L., Stress singularities resulting from variousboundary onditions in angular corners of plates in extension, Journal of Applied Mechanics, Transactions ASME, Vol.19, No.4, pp.526–528, 1962.
[81] Wu, K.C. and Chang, F.T., Near-tip field in a notched body with dislocations and body forces, Journal of Applied Mechanics-Transactions of the ASME, Vol.60, No.4, pp.936-941, 1993.
[82] Xua, J.Q., Liu, Y.H. and Wang, X.G., Numerical methods for the determination of multiple stress singularities and related stress intensity coefficients, Engineering Fracture Mechanics, Vol.63, No.6, pp.775–790, 1999.
[83] Yao, X.F., Chen, J.D. and Jin G.C., Arakawa K. and Takahashi K., Caustic analysis of stress singularities in orthotropic composite materials with mode-i crack, Composites Science and Technology, Vol.64, No.7-8, pp.917-924, 2004.
[84] Yoneyama, S., Ogawa, T. and Kobayashi, Y., Evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods, Engineering Fracture Mechanics, Vol.74 ,No.9, pp.1399-1412, 2007.
[85] Yosibash, Z., Numerical analysis on singular solutions of the Poisson equation in two-dimensions, Computational Mechanics, Vol.20 ,No.4, pp.320-330, 1997.
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