Abstract
An elastic analysis of an internal central crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane was performed. A dynamic model of bridging fiber pull-out of composite materials was presented. Resultingly the fiber failure is governed by maximum tensile stress, the fiber breaks and hence the crack extension should occur in self-similar fashion. By the methods of complex functions, the problem studied can be transformed into the dynamic model to the Reimann-Hilbert mixed boundary value problem, and a straightforward and easy analytical solution is presented. Analytical study on the crack propagation subjected to a ladder load and an instantaneous pulse loading is obtained respectively for orthotropic anisotropic body. By utilizing the solution, the concrete solutions of this model are attained by ways of superposition.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Marshall D B, Cox B N, Evens A G. The mechanics of matrix cracking in brittle-matrix fiber composites[J].Acta matallurgica, 1985,33(10):2013–2021.
Budiansky B, Hutchinson J W, Evens A G. Matrix fracture in fiber-reinforced ceramics[J].J Mech Phys Solids, 1986,34(2):167–189.
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[J].Internal J Fracture, 1994,70(4):L31-L35.
Woo C W, Wang Y H. Analysis of an internal crack in a fine anisotropic plate[J].Internat J Fracture, 1993,62(2):203–208.
Lee J C. Analysis of fiber bridged crack near a free surface in ceramic matrix composites[J].Engrg Fracture Mech, 1990,37(2):209–219.
Tsai W T, Dharani I R. Non self-similar fiber fracture in unidirectional composites[J].Engrg Fracture Mech, 1993,44(1):43–49.
Ji M, Ishikawa H. Analysis of an internal central crack with bridging fibers in a finite orthotropic plate[J].Internat J Engrg Sci, 1997,35(4):549–560.
Piva A, Viola E. Crack propagation in an orthotropic medium[J].Engrg Fracture Mech, 1988,32 (4):535–547.
De J, Patra B. Elastodynamic crack problems in an orthotropic medium through complex variable approach[J].Engrg Fracture Mech, 1986,31(6):895–909.
Goree J G, Gross R S. Analysis of an unidirectional composite containing broken fibers and matrix damage[J].Engrg Fracture Mech, 1979,13(5):563–578.
Goree J G, Dharnt L R, Jones W F. Crack growth and fracture of continuous fiber metal matrix composites: analysis and experiments[J].Metal Matrix Composites: Testing, Analysis, and Failure Modes, ASTM STP, 1989,1032(2):251–269.
Cherepanov G P, Afanasov E F. Some dynamic problems of the theory of elasticity—a review[J].Internal J Engrg Sci, 1974,12(5):665–690.
LÜ Nian-chun. Study of some problems on fracture dynamics of composite materials[D]. Ph D Harbin: Harbin Institute of Technology, 2002,60–70. (in Chinese)
CHENG Jin. Elastodynamics problems on some orthotropic anisotropic bodies[J].J Harbin Institute of Technology, Special Engineering Mechanics, 1985(Suppl):8–21. (in Chinese)
Hoskins R F.Generalized Functions[M]. New York: Ellis Horwood, 1979,19–125.
Muskhelishvili N I.Some Fundamental Problems in the Mathematical Theory of Elasticity[M]. Moscow: Nauka, 1968,8–120.
Gahov F D.Boundary-Value Problems[M]. Moscow: Fitzmatigiz, 1963,71–169.
Teaching Office of Mathematics of Tongji University.Advanced Mathematics[M]. Vol 1. Beijing: Higher Education Publishing House, 1994,167–172. (in Chinese)
Author information
Authors and Affiliations
Additional information
(Communicated by WANG Biao)
Biographies: LÜ Nian-chun (1965≈)
Rights and permissions
About this article
Cite this article
Nian-chun, L., Yun-hong, C., Hong-min, X. et al. Dynamic crack models on problem of bridging fiber pull-out of composite materials. Appl Math Mech 25, 1194–1202 (2004). https://doi.org/10.1007/BF02439872
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02439872