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A Model for the Failure Process of Semicrystalline Polymer Materials under Static Fatigue

Published online by Cambridge University Press:  27 July 2009

Howard M. Taylor
Affiliation:
Department of Mathematical SciencesUniversity of Delaware Newark, Delaware 19716

Extract

A semicrystalline polymer fiber is a composite material consisting of difficult-to-deform crystals joined by more easily deformed and more easily broken amorphous materials. The failure process begins at the atomic level in the amorphous regions where random thermal fluctuations cause, at some time, a molecule to slip relative to other molecules or to rupture at one of its atomic bonds. The frequency of such random events is greatly enhanced by small increases in stress. As molecules slip or rupture, neighboring molecules become overloaded, thus increasing their failure rates. Such molecule failures accumulate locally and give rise to growing microcracks, although the exact kinetic mechanisms are not well understood. These growing minute cracks are the irreversible changes in the microstructure of the material that ultimately lead to macroscopic failure of the fiber.

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Articles
Copyright
Copyright © Cambridge University Press 1987

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References

Argon, A. S. (1972). Fracture of composites. In Treatise on Material Science and Technology, 1, 79114, Herman, H. (ed.). Academic Press, New York.Google Scholar
Argon, A. S. (1974). Statistical aspects of fracture. In Composite Materials, 1, 154190, Brotman, L. J. (ed). Academic Press, New York.Google Scholar
Bauer, M. A. (1982). The reliability of series-parallel load sharing systems that contain flaws. Ph.D. Thesis, Cornell University.Google Scholar
Borges, W. de S. (1983). On the limiting distribution of the failure time in fibrous composite materials. Adv. Appl. Prob. 15: 331348.CrossRefGoogle Scholar
Coleman, B. D. (1957). Time dependence of mechanical breakdown in bundles of fibers: I. Constant total load. J. of Applied Physics 28; 10581064.CrossRefGoogle Scholar
Daniels, H. E. (1945). The statistical theory of the strength of bundles of threads: I. Proc. Roy. Soc. (Ser. A) 183: 404435.Google Scholar
Dobrodumov, A. V. and El'yashevich, A. M. (1973). Simulation of brittle fraction of polymers by a network model in the Monte Carlo method. Soviet Physics–Solid State 15: 12591260.Google Scholar
Feigin, P. D. and Yashchin, E. (1982). Extreme value properties of the explosion time distribution in a pure birth process. J. Appl. Probability 19: 500509.CrossRefGoogle Scholar
Gotlib, Yu. Ya., El'yashevich, A. M., and Svetlov, Yu. E. (1973). Effect of microcracks on the local stress distribution in polymers and their deformation properties: Network model. Soviet Physics– Solid State 14: 26722677.Google Scholar
Gotlib, Yu. Ya., Dobrodumov, A. V., El'yashevich, A. M., and Svetlov, Yu. E. (1973). Cooperative kinetics of the fracture of solid polymers: Focus mechanism. Soviet Physics–Solid State 15: 555559.Google Scholar
Gucer, D. E. and Gurland, J. (1962). Comparison of the statistics of two fracture modes. J. Mech. Phys. Solids 10: 365373.CrossRefGoogle Scholar
Harlow, D. G. (1977). Probabilistic models for the tensile strength of composite materials. Ph.D. Thesis, Cornell University.Google Scholar
Harlow, D. G. and Phoenix, S. L. (1978a). The chain-of-bundles probability model for the strength of fibrous materials: 1. Analysis and conjectures. J. Composite Mater. 12: 195214.CrossRefGoogle Scholar
Harlow, D. G. and Phoenix, S. L. (1978b). The chain-of-bundles probability model for the strength of fibrous materials: II. A numerical study of convergence. J. Composite Mater. 12: 314334.CrossRefGoogle Scholar
Harlow, D. G. and Phoenix, S. L. (1979). Bounds on the probability of failure of composite materials. Int. J. Fracture 15: 321336.CrossRefGoogle Scholar
Harlow, D. G. and Phoenix, S. L. (1981a). Probability distributions for the strength of composite materials: 1. Two level bounds. Int. J. Fracture 17: 347372.CrossRefGoogle Scholar
Harlow, D. G. and Phoenix, S. L. (1981b). Probability distributions for the strength of composite materials: II. A convergent sequence of tight bounds. Int. J. Fracture 17: 601630.CrossRefGoogle Scholar
Harlow, D. G. and Phoenix, S. L. (1982). Probability distributions for the strength of fibrous materials: I. Two level failure and edge effects. Adv. Appl. Prob. 14: 6894.CrossRefGoogle Scholar
Hedgepeth, J. M. and Van, Dyke P. (1967). Local stress concentrations in imperfect filamentary materials. J. Composite Mater. 1: 294309.CrossRefGoogle Scholar
Kelley, R. P. (1978). Further examination and a local load-sharing extension of Coleman's time to failure model for fiber bundles. Ph.D. Thesis, Cornell University.Google Scholar
Marsden, J. E. (1973). Basic Complex Analysis, W. H. Freeman, San Francisco.Google Scholar
Phoenix, S. L. (1983), Statistical modeling of the time and temperature dependent failure of fibrous composites. Proceedings of the Ninth U.S. National Congress of Applied Mechanics, The American Society of Mechanical Engineers.Google Scholar
Phoenix, S. L. and Tierney, L.-J. (1983). A statistical model for the time dependent failure of unidirectional composite materials under local elastic load sharing among fibers. Engineering Fracture Mechanics 18: 193215.CrossRefGoogle Scholar
Pitt, R. E. and Phoenix, S. L. (1981). On modeling the statistical strength of yarns and cables under localized load sharing among fibers. Textile Research J. 51: 408425.CrossRefGoogle Scholar
Pitt, R. E. and Phoenix, S. L. (1982). Probability distributions for the strength of composite materials: III. The effect of fiber arrangement. International J. of Fracture 20: 291311.CrossRefGoogle Scholar
Rosen, B. W. (1964). Tensile failure of fibrous composites. AIAA J. 2: 19851991.CrossRefGoogle Scholar
Rosenstock, H. B. and Newell, G. F. (1953). J. Chem. Physics 21: 16.Google Scholar
Scop, P. M. and Argon, A. S. (1969). Statistical theory of strength of laminated composites: II. J. Composite Mater. 3: 3047.CrossRefGoogle Scholar
Smith, R. L. (1982). The asymptotic distribution of the strength of a series-parallel system with equal load sharing. Ann. Probability 10: 137171.CrossRefGoogle Scholar
Smith, R. L. (1984). A model for chopped fiber composites. (preprint.)Google Scholar
Taylor, H. M. and Karlin, S. (1984). Introduction to Stochastic Modeling, Academic Press, New York.Google Scholar
Termonia, Y., Meakin, P. and Smith, P. (1985). Theoretical study of the influence of the molecular weight on the maximum tensile strength of polymer fibers. Macromolecules.CrossRefGoogle Scholar
Tierney, L.-J. (1980). Limit theorems for the failure time of bundles of fibers under unequal load sharing. Ph.D. Thesis, Cornell University.Google Scholar
Tierney, L.-J. (1982). Asymptotic bounds on the time to fatigue failure of bundles of fibers under load sharing. Adv. Appl. Probability 14: 95121.CrossRefGoogle Scholar
Tierney, L.-J. (1984). A probability model for the time to fatigue failure of a fibrous composite with local load sharing. Stoch. Processes and Their Applic. 18: 114.Google Scholar
Yashchin, E. (1981). Modeling and analyzing breakdown phenomena in thin film insulators–a stochastic approach. Doctoral Dissertation, Technion, Haifa, Israel.Google Scholar
Young, R. J. (1983), Introduction to Polymers, Chapman and Hall, New York.Google Scholar
Zhurkov, S.N. (1965). Kinetic concept of the strength of solids. International J. of Fracture Mechanics 1: 311323.CrossRefGoogle Scholar
Zweben, C. (1968). Tensile failure of fiber composites. AIAA J. 6: 23252331.CrossRefGoogle Scholar
Zweben, C. and Rosen, B. W. (1970). A statistical theory of material strength with application to composite materials. J. Mech. Phys. Solids 18: 189206.CrossRefGoogle Scholar