Markov model of fatigue of a composite material with the poisson process of defect initiation

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• 作者：Yu. Paramonov (1) yuri.paramonov@gmail.com
  R. Chatys (2)
  J. Andersons (2)
  M. Kleinhofs (1)
• 关键词：fatigue &#8211 ; Markov chains &#8211 ; composite
• 刊名：Mechanics of Composite Materials
• 出版年：2012
• 出版时间：May 2012
• 年：2012
• 卷：48
• 期：2
• 页码：217-228
• 全文大小：498.3 KB
• 参考文献：1. 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).
  2. 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).
  3. M. A. Kleinhof, Yu. M. Paramonov, and A. Yu. Paramonova, “Regression model based on Markov chain theory for composite fatigue curve approximation,” Acta Comment. Univ. Tart., No. 8, 143-153 (2004).
  4. 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).
  5. A. Yu. Paramonova, M. A. Kleinhof, and Yu. M. Paramonov, “Markov models of composite degradation in fatigue test,” in: Longevity, Aging and Degradation Models in Reliability, Univ. Publ. Ltd, St. Petersburg, 1 (2004), pp. 217-234.
  6. Yu. M. Paramonov, M. A. Kleinhof, and A. Yu. 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).
  7. Yu. M. Paramonov, J. Andersons, M. A. Kleinhofs, and A. Yu. Paramonova, “Markov model for analyzing the residual static strength of a fiber-reinforced composite,” Mech. Compos. Mater., 44, No. 4, 389-396 (2008).
  8. V. P. Tamuzh and V. D. Protasov (eds.), Fracture of Structures of Composite Materials [in Russian], Zinatne, Riga (1986).
  9. F. G. Pascual and W. Q. Meeker, “Estimating fatigue curves with the random fatigue-limit model,” Technometrics, 41, 277-302 (1999).
  10. B. Harris (ed.), Fatigue in Composites, Woodhead Publ. Ltd, Cambridge, England (2003).
  11. T. P. Philippidis and V. A. Passipoularidis, “Residual strength after fatigue in composites: Theory vs. experiment,” Inter. J. Fatigue, 29, 2104-2116 (2007).
  12. Yu. M. Paramonov, Methods of Mathematical Statistics in Problems on the Estimation and Maintenance of Fatigue Life of Aircraft Structures [in Russian], RIIGA, Riga (1992).
  13. J. G. Kemeny and J. L. Snell, Finite Markov Chains, Van Nostrand, Princeton, New Jersey (1966).
  14. M. M. Shokrieh and F. A. Taheri-Behrooz, “Unified fatigue life model based on energy method,” Compos. Struct., 75, 444-450 (2006).
  15. OPTIMAT BLADES, Reliable Optimal Use of Materials for Wind Turbine Rotor Blades, Contract No. ENK6- CT-2001-00552. Available from (2001-2006): <http://www.ecn.nl/optimat/>.
  16. T. P. Philippidis, T. T. Assimakopoulou, V. A. Passipoularidis, and A. E. Antoniou, Static and Fatigue Tests on ISO Standard 卤45_ Coupons, OB_TG2_R020_UP, August 2004. Available from: <http://www.kcwmc.nl/optimatblades/Publications>.
  17. T. P. Philippidis, T. T. Assimakopoulou, A. E. Antoniou, and V. A. Passipoularidis, Residual Strength Tests on ISO Standard 卤45_ Coupons, OB_TG5_R008_UP, July 2005. Available from: <http://www.kcwmc.nl/optimatblades/Publications>.
  18. T. P. Philippidis, T. T. Assimakopoulou, A. E. Antoniou, and V. A. Passipoularidis, Residual Strength Tests on ISO Standard 卤45 Coupons, Main Test Phase II, OB_TG2_R037_UP, June 2006. Available from: <http://www.kc-wmc.nl/optimatblades/Publications>.
• 作者单位：1. Aviation Institute, Riga Technical University, Riga, LV 1019 Latvia2. Institute of Polymer Mechanics, University of Latvia, Riga, LV 1006 Latvia
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Chemistry
  Characterization and Evaluation Materials
  Ceramics,Glass,Composites,Natural Materials
  Mechanics
  Structural Mechanics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-8922

文摘

As a development of the model where only one weak microvolume (WMV) and only a pulsating cyclic loading are considered, in the current version of the model, we take into account the presence of several weak sites where fatigue damage can accumulate and a loading with an arbitrary (but positive) stress ratio. The Poisson process of initiation of WMVs is considered, whose rate depends on the size of a specimen. The cumulative distribution function (cdf) of the fatigue life of every individual WMV is calculated using the Markov model of fatigue. For the case where this function is approximated by a lognormal distribution, a formula for calculating the cdf of fatigue life of the specimen (modeled as a chain of WMVs) is obtained. Only a pulsating cyclic loading was considered in the previous version of the model. Now, using the modified energy method, a loading cycle with an arbitrary stress ratio is “transformed” into an equivalent cycle with some other stress ratio. In such a way, the entire probabilistic fatigue diagram for any stress ratio with a positive cycle stress can be obtained. Numerical examples are presented.