An Energy-Based Prognostic Framework to Predict Fatigue Damage Evolution in Composites



Juan Chiach ́ıo Manuel Chiach ́ıo Abhinav Saxena Guillermo Rus Kai Goebel


In this work, a prognostics framework to predict the evolution of damage in fiber-reinforced composites materials un- der fatigue loads is proposed. The assessment of internal damage thresholds is a challenge for fatigue prognostics in composites due to inherent uncertainties, existence of multiple damage modes, and their complex interactions. Our framework considers predicting the balance of release strain energies from competing damage modes to establish a reference threshold for prognostics. The approach is demonstrated on data collected from a run-to-failure tension-tension fatigue experiment measuring the evolution of fatigue damage in carbon-fiber-reinforced polymer (CFRP) cross-ply laminates. Results are presented for the prediction of expected degradation by micro-cracks for a given panel with the associated uncertainty estimates.

How to Cite

Chiach ́ıo . J., Chiach ́ıo M. ., Saxena, A. ., Rus, G., & Goebel, K. . (2013). An Energy-Based Prognostic Framework to Predict Fatigue Damage Evolution in Composites. Annual Conference of the PHM Society, 5(1).
Abstract 139 | PDF Downloads 60



Fatigue Prognosis, RUL prediction, Physics based prognostics, composites

Aboudi, J., Lee, S., & Herakovich, C. (1988). Three- dimensional analysis of laminates with cross cracks. ASME, Transactions, Journal of Applied Mechanics, 55, 389–397.
Arulampalam, M. S., Maskell, S., Gordon, N., & Clapp, T. (2002). A tutorial on particle filters for online nonlinear/non-gaussian bayesian tracking. Signal Processing, IEEE Transactions on, 50(2), 174–188.
Beaumont, P., Dimant, R., & Shercliff, H. (2006). Failure processes in composite materials: getting physical. Journal of Materials Science, 41(20), 6526–6546.
Bogdanoff, J., & Kozin, F. (1985). Probabilistic models of comulative damage. John Wiley & Sons.
Cappe ́,O.,Godsill,S.J.,&Moulines,E. (2007). An overview of existing methods and recent advances in sequential Monte Carlo. Proceedings of the IEEE, 95(5), 899–924.
Chiachio, J., Chiachio, M., & Rus, G. (2011). An inverse- problem based stochastic approach to model the cumulative damage evolution of composites. Procedia Engineering, 14(0), 1557 - 1563.
Daigle, M., & Goebel, K. (2010). A model-based prognostics approach applied to pneumatic valves. International Journal of the PHM Society, 2(8), 16.
Daigle, M., & Goebel, K. (2011). Multiple damage progression paths in model-based prognostics. In Aerospace conference, 2011 IEEE (pp. 1–10).
Daigle, M. J., & Goebel, K. (2013). Model-based prognostics with concurrent damage progression processes. Systems, Man, and Cybernetics: Systems, IEEE Transactions on, 43(3), 535-546.
Doucet, A., De Freitas, N., & Gordon, N. (2001). Sequential Monte Carlo methods in practice. Springer Verlag.
Ganesan, R. (2000). A data-driven stochastic approach to model and analyze test data on fatigue response. Com- puters & Structures, 76(4), 517–531.
Hashin, Z. (1985). Analysis of cracked laminates: a variational approach. Mechanics of Materials, 4(2), 121– 136.
Hosoi, A., Takamura, K., Sato, N., & Kawada, H. (2011). Quantitative evaluation of fatigue damage growth in cfrp laminates that changes due to applied stress level. International Journal of Fatigue, 33(6), 781–787.
Jamison, R. (1985). The role of microdamage in tensile failure of graphite/epoxy laminates. Composites Science and Technology, 24(2), 83–99.
Jamison, R. D., Schulte, K., Reifsnider, K. L., & Stinch- comb, W. W. (1984). Characterization and analysis of damage mechanisms in tension-tension fatigue of graphite/epoxy laminates. Effects of defects in composite materials, ASTM STP, 836, 21–55.
Kantas, N., Doucet, A., Singh, S. S., & Maciejowski, J. M. (2009). An overview of sequential monte carlo methods for parameter estimation in general state- space models. In 15th IFAC Symposium on System Identification (Vol. 15).
Larrosa, C., & Chang, F. (2012). Real time in-situ damage classification, quantification and diagnosis for composite structures. In Proceedings of the 19th International Congress on Sound and Vibration (Vol. 15).
Lee, J., Allen, D., & Harris, C. (1989). Internal state variable approach for predicting stiffness reductions in fibrous laminated composites with matrix cracks. Journal of Composite Materials, 23(12), 1273–1291.
Lee, J., & Hong, C. (1993). Refined two-dimensional analysis of cross-ply laminates with transverse cracks based on the assumed crack opening deformation. Composites Science and Technology, 46(2), 157–166.
Lin, Y., & Yang, J. (1983). On statistical moments of fatigue crack propagation. Engineering Fracture Mechanics, 18(2), 243–256.
Liu, J., & West, M. (2001). Combined parameter and state estimation in simulation-based filtering. In A. Doucet, N. Freitas, & N. Gordon (Eds.), Sequential monte carlo methods in practice (p. 197-223). Springer New York.
Nairn, J., & Hu, S. (1992). The initiation and growth of delaminations induced by matrix microcracks in laminated composites. International Journal of Fracture, 57(1), 1–24.
Paris, P., Gomez, M., & Anderson, W. (1961). A rational analytic theory of fatigue. The Trend in Engineering, 13, 9–14.
Patwardhan, S. C., Narasimhan, S., Jagadeesan, P., Gopaluni, B., & Shah, S. L. (2012). Nonlinear bayesian state estimation: A review of recent developments. Control Engineering Practice, 20(10), 933 - 953.
Reifsnider, K., & Talug, A. (1980). Analysis of fatigue damage in composite laminates. International Journal of Fatigue, 2(1), 3 - 11.
Rowatt, J., & Spanos, P. (1998). Markov chain models for life prediction of composite laminates. Structural Safety, 20, 117–135.
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., et al. (2008). Global sensitivity analysis: the primer. Wiley-Interscience.
Saxena, A., Celaya, J., Saha, B., Saha, B., & Goebel, K. (2010). Metrics for offline evaluation of prognostic performance. International Journal of the PHM Society, 1(1), 20.
Saxena, A., Goebel, K., Larrosa, C., Janapati, V., Roy, S., & Chang, F. (2011). Accelerated aging experiments for prognostics of damage growth in composites materials. In The 8th International Workshop on Structural Health Monitoring, F.-K. Chang, editor. (Vol. 15).
Storvik, G. (2002). Particle filters for state-space models with the presence of unknown static parameters. Signal Processing, IEEE Transactions on, 50(2), 281–289.
Talreja, R. (2008). Damage and fatigue in composites – A personal account. Composites Science and Technology, 68, 2585–2591.
Talreja, R., & Singh, C. V. (2012). Damage and failure of composite materials. Cambridge University Press.
Wei, B.-S., Johnson, S., & Haj-Ali, R. (2010). A stochastic fatigue damage method for composite materials based on Markov chains and infrared thermography. International Journal of Fatigue, 32(2), 350–360.
Wu, W., & Ni, C. (2004). Probabilistic models of fatigue crack propagation and their experimental verification. Probabilistic Engineering Mechanics, 19(3), 247–257.
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