×

Asymmetrical dynamic fracture model of bridging fiber pull-out of unidirectional composite materials. (English) Zbl 1427.74156

Summary: An elastic analysis of an internal crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane is studied, and asymmetrical dynamic fracture model of bridging fiber pull-out of unidirectional composite materials is presented for analyzing the distributions of stress and displacement with the internal asymmetrical crack under the loading conditions of an applied non-homogenous stress and the traction forces on crack faces yielded by the bridging fiber pull-out model. Thus the fiber failure is ascertained by maximum tensile stress, the fiber ruptures and hence the crack propagation should also appear in the modality of self-similarity. The formulation involves the development of a Riemann-Hilbert problem. Analytical solution of an asymmetrical propagation crack of unidirectional composite materials under the conditions of two increasing loads given is obtained, respectively. In terms of correlative material properties, the variable rule of dynamic stress intensity factor was depicted very well. After those analytical solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be gained.

MSC:

74R10 Brittle fracture
74E30 Composite and mixture properties
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
74H35 Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Marshall, D.B., Cox, B.N., Evans, A.G.: The mechanics of matrix cracking in brittle-matrix fiber composites. Acta Metall. 33, 2013–2021 (1985)
[2] Budiansky, B., Hutchinson, J.W., Evens, A.G.: Matrix fracture in fiber-reinforced ceramics. J. Mech. Phys. Solids 34, 167–189 (1986) · Zbl 0575.73106
[3] Ji, M., Ishikawa, H.: Analysis of an internal central crack with bridging fibers in a finite orthotropic plate. Int. J. Eng. Sci. 35, 549–560 (1997) · Zbl 0912.73038
[4] Marshall, D.B., Cox, B.N.: Tensile fracture of brittle matrix composites: influence of fiber strength. Acta Metall. 35, 2607–2619 (1987)
[5] Woo, C.W., Wang, Y.H.: Analysis of an internal crack in a fine anisotropic plate. Int. J. Fract. 62, 203–208 (1993)
[6] Lee, J.C.: Analysis of fiber bridged crack near a free surface in ceramic matrix composites. Eng. Fract. Mech. 37, 209–219 (1990)
[7] Tsai, W.T., Dharani, I.R.: Non self-similar fiber fracture in unidirectional composites. Eng. Fract. Mech. 44, 43–49 (1993)
[8] Liu, W.N.: Stress ahead of the tip of a finite-width center-crack in fiber-reinforced composite specimens: subjected to non-linearly distributed bridging stresses. Int. J. Fract. 70(4), L31–L35 (1994)
[9] Liao, K., Reifsnider, K.: A tensile strength model for unidirectional fiber-reinforced brittle matrix composite. Int. J. Fract. 106, 95–115 (2000)
[10] Tamuzs, V., Tarasovs, S., Vilks, U.: Progressive delamination and fibre bridging modeling in double cantilever beam composite specimens. Eng. Fract. Mech. 68(5), 513–525 (2001)
[11] Piva, A., Viola, E.: Crack propagation in an orthotropic media. Eng. Fract. Mech. 29, 535–547 (1988)
[12] De, J., Patra, B.: Elastodynamic crack problems in an orthotropic medium through complex variable approach. Eng. Fract. Mech. 41, 895–909 (1998)
[13] Cheng, J.: Problems on elastodynamics of some orthotropic anisotropic bodies. J. Harbin. Inst. Tech. Eng. Mech, Special, 8–21 (1985) (in Chinese)
[14] Lü, N.C., Cheng, J.: Models of crack dynamics of bridge in composite materials. Eng. Mech. 17(6), 117–120 (2000) (in Chinese)
[15] Lü, N.C., Cheng, J.: A model of crack dynamics problem on composite material. Chin. Q. Mech. 23(4), 504–508 (2002) (in Chinese)
[16] Lü, N.C., Cheng, J., Cheng, Y.H.: Models of fracture dynamics of bridging fiber pull-out of composite materials. Mech. Res. Commun. 32(1), 1–14 (2005) · Zbl 1090.74018
[17] Lü, N.-C., Cheng, Y.-H., Xu, H.-M., Cheng, J., Tang, L.-Q.: Dynamic crack models on problems of bridging fiber pull-out of composite materials. Appl. Math. Mech. 25(10), 1194–1202 (2004) · Zbl 1147.74383
[18] Jiang, M.-Z., Lü, N.-C., Cheng, J.: A fracture dynamics model of bridging fiber pull-out of composite materials. J. Harbin Inst. Tech. 37(3), 423–426 (2005) (in Chinese)
[19] Sih, G.C.: Some elastodynamics problems of cracks. Int. J. Fract. 1(1), 51–68 (1968)
[20] Broberg, K.B.: The propagation of a brittle crack. Ark. Fys. 18, 159–192 (1960)
[21] Atkinson, C.: The propagation of a brittle crack in anisotropic material. Int. J. Eng. Sci. 3, 77–91 (1965) · Zbl 0135.43403
[22] Lü, N.-C., Cheng, Y.-H., Cheng, J.: An asymmetrical self-similar dynamic crack model of bridging fiber pull-out in unidirectional composite materials. Int. J. Comput. Methods Eng. Sci. Mech. 9(3), 171–179 (2008) · Zbl 1136.74038
[23] Lü, N.C., Cheng, Y.H., Cheng, J.: Mode I crack tips propagating at different speeds under differential surface tractions. Theor. Appl. Fract. Mech. 46(3), 262–275 (2006)
[24] Craggs, Y.W.: The growth of a disk-shaped crack. Int. J. Eng. Sci. 4, 113–124 (1966) · Zbl 0139.20001
[25] Goree, J.G., Gross, R.S.: Analysis of a unidirectional composite containing broken fibers and matrix damage. Eng. Fract. Mech. 33, 563–578 (1979)
[26] Goree, J.G., Dharnt, L.R., Jones, W.F.: Crack growth and fracture of continuous fiber metal matrix composites: analysis and experiments. In: Metal Matrix Composites: Testing, Analysis, and Failure Modes. STP, vol. 1032, pp. 251–269. ASTM, Philadelphia (1989)
[27] Charepanov, G.P., Afanasov, E.F.: Some dynamic problems of the theory of elasticity–A review. Int. J. Eng. Sci. 12, 665–690 (1970) · Zbl 0296.73012
[28] Charepanov, G.P.: Mechanics of Brittle Fracture, pp. 732–792. Nauka, Moscow (1973)
[29] Erigen, A.C., Suhubi, E.S.: Linear Theory. Elastodynamics, vol. 2. Academic Press, New York (1975)
[30] Muskhlishvili, N.I.: Singular Integral Equations. Nauka, Moscow (1968)
[31] Muskhlishvili, N.I.: Some Fundamental Problems in the Mathematical Theory of Elasticity. Nauka, Moscow (1966)
[32] Gakhov, F.D.: Boundary-Value Problems. Fizmatgiz, Moscow (1963) · Zbl 0141.08001
[33] Hoskins, R.F.: Generalized Functions. Ellis Horwood, Chichester (1979) · Zbl 0425.46025
[34] Wang, X.S.: Singular Functions and Their Applications in Mechanics, pp. 3–45. Scientific Press, Beijing (1993) (in Chinese)
[35] Sih, G.C.: Elastodynamics Crack Problems. Mechanics of Fracture, vol. 4, pp. 213–247. Noordhoff, Leyden (1977)
[36] Kanwal, R.P., Sharma, D.L.: Singularity methods for elastostatics. J. Elast. 6(4), 405–418 (1976) · Zbl 0352.73026
[37] Lü, N.C., Cheng, Y.H., Si, H.L., Cheng, J.: Dynamics of asymmetrical crack propagation in composite materials. Theor. Appl. Fract. Mech. 47(3), 260–273 (2007)
[38] Shen, G.-L.: Mechanics of Composite Materials. Tsinghua University Press, Beijing (1996) (in Chinese)
[39] Editorial group of mathematics handbook: Mathematics Handbook, pp. 244–300. Advanced Education Press, Beijing (2002) (in Chinese)
[40] Teaching office of mathematics of Tongji University: Advanced Mathematics, vol. 1, pp. 167–172. Advanced Education Press, Beijing (1994) (in Chinese)
[41] Wu, K.C.: Dynamic crack growth in anisotropic material. Int. J. Fract. 106(1), 1–12 (2000)
[42] Kalthof, J.F., Beinart, J., Winkler, S.: Measurements of dynamic stress intensity factors for fastrunning and arresting cracks in double-cantilever-beam specimens. In: Fast Fracture and Crack Arrest. STP, vol. 627, pp. 161–176. ASTM, Philadelphia (1977)
[43] Kobayashi, A.S.: Dynamic fracture analysis by dynamic finite element method, generation and prediction analyses. In: Nonlinear and Dynamic Fracture Mechanics. AMD, vol. 35, pp. 19–36. ASME, New York (1979)
[44] Ravi-Chandar, K., Knauss, W.G.: An experimental investigation into dynamic fracture: Part 1, crack initiation and arrest. Int. J. Fract. 25(41), 247–262 (1984)
[45] Ravi-Chandar, K., Knauss, W.G.: An experimental investigation into dynamic fracture: Part 2, microstructural aspects. Int. J. Fract. 26(11), 65–80 (1984)
[46] Ravi-Chandar, K., Knauss, W.G.: An experimental investigation into dynamic fracture: Part 3, on steady-state crack propagation and crack branching. Int. J. Fract. 26(2), 141–152 (1984)
[47] Ravi-Chandar, K., Knauss, W.G.: An experimental investigation into dynamic fracture: Part 4, on the interaction of stress waves with propagation cracks. Int. J. Fract. 26(3), 189–200 (1984)
[48] Sneddon, N.I.: Fourier Transform. McGraw-Hill, New York (1951)
[49] Muskhelishvili, N.I.: Some Basic Problems from the Mathematical Theory of Elasticity. Groningen-Holland, Noordhoff (1953) · Zbl 0052.41402
[50] Galin, L.A.: Contact Problems in Elasticity Theory. GITTL, Moscow (1953)
[51] Lü, N.C., Cheng, Y.H., Li, X.G., Cheng, J.: Dynamic propagation problem of mode I semi-infinite crack subjected to superimpose loads. Fatigue Fract. Eng. Mater. Struct. 33(3), 141–148 (2010)
[52] Wang, Y.H., Cheung, Y.K., Woo, C.W.: Anti-plane shear problem for an edge crack in a finite orthotropic plate. Eng. Fract. Mech. 42(6), 971–976 (1992)
[53] Lü, N.-C., Cheng, Y.-H., Li, X.-G., Cheng, J.: Dynamic propagation problems concerning the surfaces of asymmetrical mode III crack subjected to moving loads. Appl. Math. Mech. 29(10), 1279–1290 (2008) · Zbl 1165.74039
[54] Lü, N.C., Cheng, Y.H., Wang, Y.T., Cheng, J.: Dynamic fracture of orthotropic solids under anti-plane shear loading. Mech. Adv. Mat. Struct. 17(3), 215–224 (2010)
[55] Wang, Y.-S., Wang, D.: Transient motion of an interface dislocation and self-similar propagation of an interface crack: anti-plane motion. Eng. Fract. Mech. 55(5), 717–725 (1996)
[56] Wu, K.-C.: Transient motion of an interfacial line force or dislocation in an anisotropic elastic material. Int. J. Solids Struct. 40(8), 1811–1823 (2003) · Zbl 1041.74040
[57] Atkinson, C.: On the dynamic stress and displacement field associated with a crack propagating across the interface between two media. Int. J. Eng. Sci. 13(5), 491–506 (1975) · Zbl 0282.73063
[58] Lü, N.-C., Yang, D.-N., Cheng, Y.-H., Cheng, J.: Asymmetrical dynamic propagation problems on mode III interface crack. Appl. Math. Mech. 28(4), 501–510 (2007) · Zbl 1231.74381
[59] Lü, N.-C., Cheng, J., Tian, X.-B., Cheng, Y.-H.: Dynamic propagation problem on dugdale model of mode III interface crack. Appl. Math. Mech. 26(9), 1212–1221 (2005) · Zbl 1144.74369
[60] Lü, N.-C., Cheng, Y.-H., Cheng, J.: Dynamic propagation problems concerning asymmetrical mode III interface crack. Int. J. Comput. Methods Eng. Sci. Mech. 9(4), 246–253 (2008) · Zbl 1151.74406
[61] Lü, N.C., Cheng, Y.H., Li, X.G., Cheng, J.: Asymmetrical dynamic propagation problems concerning mode III interface crack. Compos. Interfaces 17(1), 37–48 (2010)
[62] Lü, N.-C., Cheng, J., Cheng, Y.-H.: Self-similar solutions of fracture dynamics problems on axially symmetry. Appl. Math. Mech. 22(12), 1429–1435 (2001) · Zbl 1035.74050
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.