Abstract
The possibility of using a unified mathematical model, based on the theory of Markov chains, to describe the distribution of the conditional fatigue limit at a fixed number of loading cycles and the residual strength of a specimen after cyclic loading is demonstrated. Numerical examples are presented.
Similar content being viewed by others
References
Yu. Paramonov, M. Kleinhof, and A. Paramonova, “Markov model of connection between the distribution of static strength and fatigue life of a fibrous composite,” Mech. Compos. Mater., 42, No. 5, 431–442 (2006).
J. Andersons, I. Grušeckis, and J. Korsgaard, “The effect of overloads on the residual strength and life of laminated GRP,” Mech. Compos. Mater., 35, No. 6, 461–464 (1999).
M. S. Found and M. Quaresimin, “Two-stage fatigue loading of woven carbon fibre reinforced laminates,” Fatigue Fract. Eng. Mater. Struct., 26, 17–26 (2003).
A. M. Freudenthal and E. J. Gumbel, “Physical and statistical aspects of fatigue,” Adv. Appl. Mech. Vol. IV, Academic Press, New York (1956).
V. V. Bolotin, Statistical Methods in Structural Mechanics [in Russian], GSM, Moscow (1961).
J. Kemeny and J. Snell, Finite Markov Chains [Russian translation], Nauka, Moscow (1970).
A. Yu. Paramonova, M. A. Kleinhof, and Yu. M. Paramonov, “Binomial version of Markov model of fatigue life of composite with two reasons for failure,” Aviation, 8, No. 2, 15–20 (2004).
Yu. M. Paramonov, M. A. Kleinhof, and A. Yu. Paramonova, “A probabilistic model of the fatigue life of composite materials for fatigue-curve approximations,” Mech. Compos. Mater., 38, No. 6, 485–492 (2002).
M. Kleinhof, Yu. Paramonov, and A. Paramonova, “Regression model based on Markov chain theory for composite fatigue curve approximation,” Acta Commentat. Univ. Tartuensis Math., 8, 143–153 (2004).
Yu. M. Paramonov, M. A. Kleinhof, and A. Yu. Paramonova, “Estimating the parameters of fatigue curve of a composite material,” Mech. Compos. Mater., 41, No. 1, 77–86 (2005).
V. Tamuzs, J. Andersons, K. Aniskevich, J. Jansons, and J. Korsgaard, “Creep and damage accumulation in orthotropic composites under cyclic loading,” Mech. Compos. Mater., 34, No. 4, 321–330 (1998).
Author information
Authors and Affiliations
Additional information
__________
Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 559–568, July–August, 2008.
Rights and permissions
About this article
Cite this article
Paramonov, Y., Andersons, J., Kleinhofs, M. et al. Markov model for analyzing the residual static strength of a fiber-reinforced composite. Mech Compos Mater 44, 389–396 (2008). https://doi.org/10.1007/s11029-008-9031-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11029-008-9031-z