Analytical Solutions of a Symmetrical Dynamic Crack Model of Bridging Fibers in Unidirectional Composites

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References

[1] D. B. Marshall, B. N. Cox and A. G. Evens, “The Mechanics of Matrix Cracking in Brittle-Matrix Fiber Composites,” Acta Metallurgical, Vol. 33, No. 11, 1985, pp. 2013-2021. doi:10.1016/0001-6160(85)90124-5

[2] B. Budiansky, J. W. Hutchinson and A. G. Evens, “Matrix Fracture in Fiber-Reinforced Ceramics,” Journal of the Mechanics and Physics of Solids. Vol. 34, No. 2, 1986, pp. 167-189. doi:10.1016/0022-5096(86)90035-9

[3] M. Ji and H. Ishikawa, “Analysis of an Internal Central Crack with Bridging Fibers in a Finite Orthotropic Plate,” International Journal of Engineering Science, Vol. 35, No. 4, 1997, pp. 549-560.

[4] D. B. Marshall and B. N. Cox, “Tensile Fracture of Brittle Matrix Composites: Influence of Fiber Strength,” Acta Metallurgica, Vol. 35, No. 11, 1987, pp. 2607-2619.
doi:10.1016/0001-6160(87)90260-4

[5] Z.-M. Wang, “Mechanics and Structural Mechanics of Composite Materials,” Publisher of Machinery Industry, Beijing, 1991, (in Chinese).

[6] G.-L. Shen, “Mechanics of Composite Materials,” Tsinghua University Press, Beijing, 1996, (in Chinese).

[7] C. W. Woo and Y. H. Wang, “Analysis of an Internal Crack in a Fine Anisotropic Plate,” International Journal of Fracture, Vol. 62, No. 2, 1993, pp. 203-208.
doi:10.1016/0955-7997(93)90038-M

[8] J. C. Lee, “Analysis of Fiber Bridged Crack near a Free Surface in Ceramic Matrix Composites,” Engineering Fracture Mechanics, Vol. 37, No. 2, 1990, pp. 209-219.
doi:10.1016/0013-7944(90)90344-G

[9] W. T. Tsai and I. R. Dharani, “Non Self-Similar Fiber Fracture in Unidirectional Composites,” Engineering Fracture Mechanics, Vol. 44, No. 1, 1993, pp. 43-49.
doi:10.1016/0013-7944(93)90080-C

[10] W. N. Liu, “Stress ahead of the Tip of a Finite-Width Center-Crack in Fiber-Reinforced Composite Specimens: Subjected to Non-Linearly Distributed Bridging Stresses,” International Journal of Fracture, Vol. 70, No. 1, 1994, pp. 31-35. doi:10.1016/0013-7944(94)90092-2

[11] K. Liao and K. Reifsnider, “A Tensile Strength Model for Unidirectional Fiber-reinforced Brittle Matrix Composite,” International Journal of Fracture, Vol. 106, No. 1, 2000, pp. 95-115. doi:10.1016/S1359-835X(02)00143-4

[12] V. Tamuzs, S. Tarasovs and U. Vilks, “Progressive Delamination and Fibre Bridging Modeling in Double Cantilever Beam Composite Specimens,” Engineering Fracture Mechanics, Vol. 68, No. 5, 2001, pp. 513-525.
doi:10.1016/S0013-7944(00)00131-4

[13] A. Piva and E. Viola, “Crack Propagation in An Orthotropic Media,” Engineering Fracture Mechanics, Vol. 29, No. 5, 1988, pp. 535-547.
doi:10.1016/0013-7944(88)90179-8

[14] J. De and B. Patra, “Elastodynimic Crack Problems in An Orthotrpic Medium through Complex Variable Approach,” Engineering Fracture Mechanics, Vol. 41, No. 5, 1998, pp. 895-909.

[15] K. B. Broberg, “The Propagation of a Brittle Crack,” Arkiv for Fysik, Vol. 18, No. 2, 1960, pp. 159-192.
doi:10.1016/0022-5096(60)90006-5

[16] Y. W. Craggs, “The Growth of a Disk-Shaped Crack,” International Journal of Engineering Science, Vol. 4, No. 2, 1966, pp. 113-124. doi:10.1016/0013-7944(80)90086-7

[17] J. G. Goree and R. S. Gross, “Analysis of a Unidirectional Composite Containing Broken Fibers and Matrix Damage,” Engineering Fracture Mechanics, Vol. 33, No. 3, 1979, 2001, pp. 55-578.
doi:10.1016/0020-7225(66)90019-X

[18] G. P. Cherepanov and E. F. Afanasov, “Some Dynamic Problems of the Theory of Elasticity—A Review,” International Journal of Engineering Science, Vol. 12, No. 8, 1974, 665-690. doi:10.1016/0020-7225(74)90043-3

[19] G. P. Charepanov, “Mechanics of Brittle Fracture,” Nauka, Moscow City, 1973.

[20] C. Atkinson, “The Propagation of a Brittle Crack in Anistropic Material,” International Journal of Engineering Science, Vol. 3, No. 1, 1965, pp. 77-91.
doi:10.1016/0020-7225(65)90018-2

[21] N.-C. Lü, X.-G. Li, Y.-H. Cheng and J. Cheng, “Fracture Dynamics Problem on Mode I Semi-Infinite Crack,” Archive of Applied Mechanics, Vol. 81, No. 9, 2011, pp. 1181-1193 doi:10.1016/j.amc.2011.04.028

[22] N. C, Lü, Y. H. Cheng. X. G. Li and J. Cheng, “Dynamic Propagation Problem of Mode Ⅰ Semi-Infinite Crack Subjected to Superimpose Loads,” Fatigue & Fracture of Engineering Materials & Structures. Vol. 33, No. 3, 2010, pp. 141-148.

[23] N. C. Lü, Y. H. Cheng, X. G. Li and J. Cheng, “An Asymmetrical Dynamic Model for Bridging Fiber Pull-Out of Unidirectional Composite Materials,” Meccanica, Vol. 47, No. 5, 2012, pp. 1247-1260.
doi:10.1016/j.tafmec.2012.05.007

[24] N. I. Muskhlishvili, “Singular Integral Equations,” Nauka, Moscow City, 1968.

[25] N. I. Muskhlishvili, “Some Fundamental Problems in the Mathematical Theory of Elasticity,” Nauka, Moscow City, 1966.

[26] F. D. Gakhov, “Boundary-Value Problems,” Fitzmatigiz, Moscow City, 1963.

[27] R. F. Hoskins, “Generalized Functions,” Horwood, Ellis, 1979.

[28] X. S Wang, “Singular Functions and Their Applications in Mechanics,” Scientific Press, Beijing, 1993 (in Chinese).

[29] G. C. Sih, “Mechanics of Fracture 4. Elastodynamics Crack Problems,” Noordhoff, Leyden, 1977.

[30] R. P. Kanwal and D. L. Sharma, “Singularity Methods for Eastostatics,” Journal of Elasticity, Vol. 6, No. 4, 1976, pp. 405-418.

[31] Editorial Group of Mathematics Handbook, “Mathematical Handbook,” Advanced Education Press, Beijing, 2002 (in Chinese).

[32] Teaching Office of Mathematics of Tongji University, “Advanced Mathematics,” Advanced Education Press, Beijing, 1994 (in Chinese).

[33] K. C. Wu, “Dynamic Crack Growth in Anisotropic Material,” International Journal of Fracture, Vol. 106, No. 1, 2000, pp. 1-12. doi:10.1016/S0022-5096(00)00012-0

[34] X.-G. Li, Y.-H. Cheng, N.-C. Lü, G.-D. Hao and J. Cheng, “A Dynamic Asymmetrical Crack Model of Bridging Fiber Pull-Out in Uniderectional Composite Materials,” Journal of Mechanical Science and Technoogy, Vol. 25, No. 9, 2011, pp. 2297-2309.
doi:10.1016/j.ymssp.2011.07.013

[35] N. C, Lü, Y. H. Cheng. H. L. Si and J. Cheng, “Dynamics of Asymmetrical Crack Propagation in Composite Materials,” Theoretical and Applied Fracture Mechanics, Vol. 47, No. 3, 2007, pp. 260-273.
doi:10.1016/j.tafmec.2007.01.004

[36] N. C. Lü, Y. H. Cheng and J. Cheng, “Mode I Crack Tips Propagating at Different Speeds under Differential Surface Tractions,” Theoretical and Applied Fracture Mechanics, Vol. 46, No. 3, 2006, pp. 262-275.

[37] A. S. Kobayashi, “Dynamic Fracture Analysis by Dynamic Finite Element Method. Generation and Prediction Analyses,” In: Nonlinear and Dynamic Fracture Mechanics, New York Publisher, New York, 1979, pp. 19-36.

[38] J. F. Kalthof, J. Beinert and S. Winkler, “Measurements of Dynamic Stress Intensity Factors for Fast Running and Arresting Cracks in Double-Cantilever-Beam Specimens,” In: Fast Fracture and Crack Arrest, PA Publisher, Philadelphia, 1977, pp. 161-176.

[39] K. Ravi-Chandar and W. G. Knauss, “An Experimental Investigation into Dynamic Fracture: Part 1, Crack Initiation and Arrest,” International Journal of Fracture, Vol. 25, No. 41, 1984, pp. 247-262,

[40] K. Ravi-Chandar and W. G. Knauss, “An Experimental Investigation into Dynamic Fracture: Part 2, Microstructural Aspects,” International Journal of Fracture, Vol. 18, No. 7, 1984, pp. 735-738.
doi:10.1016/0036-9748(84)90330-2

[41] K. Ravi-Chandar and W. G. Knauss, “An Experimental Investigation into Dynamic Fracture: Part 3, on Steady-State Crack Propagation and Crack Branching,” International Journal of Fracture, Vol. 26, No. 2, 1984, pp. 141-152.

[42] L. B. Freund, “Crack Propagation in an Elastic Solid Subjected to General Loading—I. Constant Rate of Extension,” Journal of the Mechanics and Physics of Solids, Vol. 20, No. 3, 1972, pp. 129-140.
doi:10.1016/0022-5096(72)90006-3

[43] N. I. Sneddon, “Fourier Transform,” McGraw-Hill, New York, 1951.

[44] N. I. Muskhelishvili, “Some Basic Problems of the Mathematical Theory of Elasticity,” Noordoff, Groningen, 1953.

[45] L. A. Galin, “Contact Problems in Elasticity Theory,” GITTL, Moscow City, 1953.

[46] N.-C. Lü, Y.-H. Cheng, X. G. Li and J. Cheng, “Fracture Dynamics Problem on Mode I Semi-Infinite Crack for Anisotropic Orthotropic Body,” Nonlinear Dynamics, Vol. 67, No. 4, 2012, pp. 2381-2396.

[47] N.-C. Lü, Y.-H. Cheng, Y.-T. Wang and J. Cheng, “Dynamic Extension Problems Concerning Asymmetrical Mode III Crack,” Applied Mathematical Modelling, Vol. 35, No. 5, 2011, pp. 2499-2507.
doi:10.1016/j.apm.2010.11.058

[48] N.-C. Lü, Y.-H. Cheng, Y.-T. Wang and J. Cheng, “Fracture Dynamics Problems of Orthotropic Solids under Anti-Plane Shear Loading,” Nonlinear Dynamics, Vol. 63, No. 4, 2011, pp. 793-806.

[49] N.-C. Lü, Y.-H. Cheng, X. G. Li and J. Cheng, “Asymmetrical Dynamic Propagation Problems Concerning Mode Ⅲ Interface Crack,” Composite Interfaces, Vol. 17, No. 1, 2010, pp. 37-48.

[50] N.-C. Lü, J. Cheng and Y.-H. Cheng, “Self-Similar Solutions of Fracture Dynamics Problems on Axially Symmetry,” Applied Mathematical and Mechanics, Vol. 22, No. 12, 2001, pp. 1429-1435.