0
Research Papers

A Probabilistic Design Method for Fatigue Life of Metallic Component

[+] Author and Article Information
Danial Faghihi

Institute for Computational Engineering
and Sciences,
The University of Texas at Austin,
Austin, TX 78712
e-mail: danial@ices.utexas.edu

Subhasis Sarkar, Mehdi Naderi, Nagaraja Iyyer

Technical Data Analysis, Inc.,
Falls Church, VA 22042

Jon E. Rankin, Lloyd Hackel

Curtiss-Wright,
MIC-Laser Peening Division,
Livermore, CA 94551

1Corresponding author.

Manuscript received July 17, 2017; final manuscript received November 2, 2017; published online December 12, 2017. Assoc. Editor: Alba Sofi.

ASME J. Risk Uncertainty Part B 4(3), 031005 (Dec 12, 2017) (11 pages) Paper No: RISK-17-1079; doi: 10.1115/1.4038372 History: Received July 17, 2017; Revised November 02, 2017

In the present study, a general probabilistic design framework is developed for cyclic fatigue life prediction of metallic hardware using methods that address uncertainty in experimental data and computational model. The methodology involves: (i) fatigue test data conducted on coupons of Ti6Al4V material, (ii) continuum damage mechanics (CDM) based material constitutive models to simulate cyclic fatigue behavior of material, (iii) variance-based global sensitivity analysis, (iv) Bayesian framework for model calibration and uncertainty quantification, and (v) computational life prediction and probabilistic design decision making under uncertainty. The outcomes of computational analyses using the experimental data prove the feasibility of the probabilistic design methods for model calibration in the presence of incomplete and noisy data. Moreover, using probabilistic design methods results in assessment of reliability of fatigue life predicted by computational models.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Oden, T. , Moser, R. , and Ghattas, O. , 2010, “ Computer Predictions With Quantified Uncertainty—Part I,” SIAM News, 43(9), pp. 1–3.
Oden, T. , Moser, R. , and Ghattas, O. , 2010, “ Computer Predictions With Quantified Uncertainty—Part II,” SIAM News, 43(10), pp. 1–4.
Lemaitre, J. , and Desmorat, R. , 2005, Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures, Springer Science & Business Media, Berlin.
Lemaitre, J. , 2012, A Course on Damage Mechanics, Springer Science & Business Media, Berlin.
Mashayekhi, M. , Taghipour, A. , Askari, A. , and Farzin, M. , 2013, “ Continuum Damage Mechanics Application in Low-Cycle Thermal Fatigue,” Int. J. Damage Mech., 22(2), pp. 285–300. [CrossRef]
Yu, T. , 2016, “ Continuum Damage Mechanics Models and their Applications to Composite Components of Aero-Engines,” Ph.D. thesis, University of Nottingham, Nottingham, UK.
McDowell, D. , and Dunne, F. , 2010, “ Microstructure-Sensitive Computational Modeling of Fatigue Crack Formation,” Int. J. Fatigue, 32(9), pp. 1521–1542. [CrossRef]
Dingreville, R. , Battaile, C. C. , Brewer, L. N. , Holm, E. A. , and Boyce, B. L. , 2010, “ The Effect of Microstructural Representation on Simulations of Microplastic Ratcheting,” Int. J. Plasticity, 26(5), pp. 617–633. [CrossRef]
Bolotin, V. , and Belousov, I. , 2001, “ Early Fatigue Crack Growth as the Damage Accumulation Process,” Probab. Eng. Mech., 16(4), pp. 279–287. [CrossRef]
Lardner, R. , 1967, “ A Theory of Random Fatigue,” J. Mech. Phys. Solids, 15(3), pp. 205–221. [CrossRef]
Birnbaum, Z. , and Saunders, S. C. , 1958, “ A Statistical Model for Life-Length of Materials,” J. Am. Stat. Assoc., 53(281), pp. 151–160. [CrossRef]
Ortiz, K. , and Kiremidjian, A. S. , 1988, “ Stochastic Modeling of Fatigue Crack Growth,” Eng. Fract. Mech., 29(3), pp. 317–334. [CrossRef]
Yang, J. , Salivar, G. , and Annis, C. , 1983, “ Statistical Modeling of Fatigue-Crack Growth in a Nickel-Base Superalloy,” Eng. Fract. Mech., 18(2), pp. 257–270. [CrossRef]
Shen, H. , Lin, J. , and Mu, E. , 2000, “ Probabilistic Model on Stochastic Fatigue Damage,” Int. J. Fatigue, 22(7), pp. 569–572. [CrossRef]
Correia, J. , Apetre, N. , Arcari, A. , De Jesus, A. , Muñiz-Calvente, M. , Calçada, R. , Berto, F. , and Fernández-Canteli, A. , 2017, “ Generalized Probabilistic Model Allowing for Various Fatigue Damage Variables,” Int. J. Fatigue, 100(Part 1), pp. 187–194. [CrossRef]
Zhu, S.-P. , Huang, H.-Z. , Peng, W. , Wang, H.-K. , and Mahadevan, S. , 2016, “ Probabilistic Physics of Failure-Based Framework for Fatigue Life Prediction of Aircraft Gas Turbine Discs Under Uncertainty,” Reliab. Eng. Syst. Saf., 146, pp. 1–12. [CrossRef]
Zhu, S.-P. , Huang, H.-Z. , Li, Y. , Liu, Y. , and Yang, Y. , 2015, “ Probabilistic Modeling of Damage Accumulation for Time-Dependent Fatigue Reliability Analysis of Railway Axle Steels,” Proc. Inst. Mech. Eng., Part F, 229(1), pp. 23–33. [CrossRef]
Naderi, M. , Hoseini, S. , and Khonsari, M. , 2013, “ Probabilistic Simulation of Fatigue Damage and Life Scatter of Metallic Components,” Int. J. Plasticity, 43, pp. 101–115. [CrossRef]
Bahloul, A. , Ahmed, A. B. , Mhala, M. , and Bouraoui, C. , 2016, “ Probabilistic Approach for Predicting Fatigue Life Improvement of Cracked Structure Repaired by High Interference Fit Bushing,” Int. J. Adv. Manuf. Technol., 91(5–8), pp. 2161–2173.
Zhu, S. P. , Foletti, S. , and Beretta, S. , 2017, “ Probabilistic Framework for Multiaxial LCF Assessment Under Material Variability,” Int. J. Fatigue, 103, pp. 371–385.
Kwon, K. , Frangopol, D. M. , and Soliman, M. , 2011, “ Probabilistic Fatigue Life Estimation of Steel Bridges by Using a Bilinear S–N Approach,” J. Bridge Eng., 17(1), pp. 58–70. [CrossRef]
Zhu, S.-P. , Huang, H.-Z. , Smith, R. , Ontiveros, V. , He, L.-P. , and Modarres, M. , 2013, “ Bayesian Framework for Probabilistic Low Cycle Fatigue Life Prediction and Uncertainty Modeling of Aircraft Turbine Disk Alloys,” Probab. Eng. Mech., 34, pp. 114–122. [CrossRef]
Zhu, S.-P. , Huang, H.-Z. , Ontiveros, V. , He, L.-P. , and Modarres, M. , 2012, “ Probabilistic Low Cycle Fatigue Life Prediction Using an Energy-Based Damage Parameter and Accounting for Model Uncertainty,” Int. J. Damage Mech., 21(8), pp. 1128–1153. [CrossRef]
Babuska, I. , Sawlan, Z. , Scavino, M. , Szabó, B. , and Tempone, R. , 2016, “ Bayesian Inference and Model Comparison for Metallic Fatigue Data,” Comput. Methods Appl. Mech. Eng., 304, pp. 171–196. [CrossRef]
Lemaitre, J. , Sermage, J. , and Desmorat, R. , 1999, “ A Two Scale Damage Concept Applied to Fatigue,” Int. J. Fracture, 97(1–4), pp. 67–81. [CrossRef]
Eshelby, J. D. , 1957, “ The Determination of the Elastic Field of an Ellipsoidal Inclusion, Related Problems,” Proc. R. Soc. London, Ser. A, 241(1226), pp. 376–396. [CrossRef]
Kroner, E. , 1961, “ On the Plastic Deformation of Polycrystals,” Acta Metall., 9(2), pp. 155–161. [CrossRef]
Prudencio, E. E. , Bauman, P. T. , Williams, S. , Faghihi, D. , Ravi-Chandar, K. , and Oden, J. T. , 2013, “ A Dynamic Data Driven Application System for Real-Time Monitoring of Stochastic Damage,” Proc. Comput. Sci., 18, pp. 2056–2065. [CrossRef]
Prudencio, E. E. , Bauman, P. T. , Faghihi, D. , Ravi-Chandar, K. , and Oden, J. T. , 2014, “ A Computational Framework for Dynamic Data-Driven Material Damage Control, Based on Bayesian Inference and Model Selection,” Int. J. Numer. Methods Eng., 102(3–4), pp. 379–403.
Prudencio, E. , Bauman, P. , Williams, S. , Faghihi, D. , Ravi-Chandar, K. , and Oden, J. , 2014, “ Real-Time Inference of Stochastic Damage in Composite Materials,” Compos. Part B: Eng., 67, pp. 209–219. [CrossRef]
Saltelli, A. , Ratto, M. , Andres, T. , Campolongo, F. , Cariboni, J. , Gatelli, D. , Saisana, M. , and Tarantola, S. , 2008, Global Sensitivity Analysis: The Primer, Wiley, Hoboken, NJ.
Cukier, R. I. , Fortuin, C. M. , Shuler, K. E. , Petschek, A. G. , and Schaibly, J. H. , 1973, “ Study of the Sensitivity of Coupled Reaction Systems to Uncertainties in Rate Coefficients—I: Theory,” J. Chem. Phys., 59(8), pp. 3873–3878. [CrossRef]
Sobol', I. M. , 1990, “ Sensitivity Estimates for Nonlinear Mathematical Models,” Mat. Model., 2, pp. 112–118.
Sobol', I. M. , 1993, “ Sensitivity Analysis for Non-Linear Mathematical Models,” Math. Model. Comput. Exp., 1, pp. 407–414.
Homma, T. , and Saltelli, A. , 1996, “ Importance Measures in Global Sensitivity Analysis of Nonlinear Models,” Reliab. Eng. Syst. Saf., 52(1), pp. 1–17. [CrossRef]
Saltelli, A. , and Tarantola, S. , 2002, “ On the Relative Importance of Input Factors in Mathematical Models,” J. Am. Stat. Assoc., 97(459), pp. 702–709. [CrossRef]
Tarantola, A. , 2005, “ Inverse Problem Theory and Methods for Model Parameter Estimation,” 1st ed., SIAM, Philadelphia, PA.
Calvetti, D. , and Somersalo, E. , 2007, Introduction to Bayesian Scientific Computing: Ten Lectures on Subjective Computing, Springer, Berlin.
Farrell, K. , Oden, J. T. , and Faghihi, D. , 2015, “ A Bayesian Framework for Adaptive Selection, Calibration, and Validation of Coarse-Grained Models of Atomistic Systems,” J. Comput. Phys., 295, pp. 189–208. [CrossRef]
Oden, J. T. , Babuska, I. , and Faghihi, D. , 2004, “ Predictive Computational Science: Computer Predictions in the Presence of Uncertainty,” Encyclopedia of Computational Mechanics, E. Stein, R. de Borst, and T. J. R. Hughes, eds., Wiley, NJ. [PubMed] [PubMed]
Farrell, K. , and Oden, J. T. , 2014, “ Calibration and Validation of Coarse-Grained Models of Atomic Systems: Application to Semiconductor Manufacturing,” Comput. Mech., 54(1), pp. 3–19. [CrossRef]
Kaipio, J. , and Somersalo, E. , 2006, Statistical and Computational Inverse Problems, Vol. 160, Springer Science & Business Media, Berlin.
Allahverdizadeh, N. , Manes, A. , and Giglio, M. , 2012, “ Identification of Damage Parameters for Ti-6al-4v Titanium Alloy Using Continuum Damage Mechanics,” Materialwiss. Werkstofftech., 43(5), pp. 435–440. [CrossRef]
Hammer, J. T. , 2012, “ Plastic Deformation and Ductile Fracture of Ti-6Al-4V Under Various Loading Conditions,” Ph.D. thesis, The Ohio State University, Columbus, OH. http://www.tc.faa.gov/its/worldpac/techrpt/tctt14-2.pdf
Yatnalkar, R. S. , 2010, “ Experimental Investigation of Plastic Deformation of Ti-6Al-4V Under Various Loading Conditions,” Ph.D. thesis, The Ohio State University, Columbus, OH. https://etd.ohiolink.edu/rws_etd/document/get/osu1282067894/inline
Zherebtsov, S. , Salishchev, G. , Galeyev, R. , and Maekawa, K. , 2005, “ Mechanical Properties of Ti–6Al–4V Titanium Alloy With Submicrocrystalline Structure Produced by Severe Plastic Deformation,” Mater. Trans., 46(9), pp. 2020–2025. [CrossRef]
Saltelli, A. , 2002, “ Making Best Use of Model Evaluations to Compute Sensitivity Indices,” Comput. Phys. Commun., 145(2), pp. 280–297. [CrossRef]
Saltelli, A. , Annoni, P. , Azzini, I. , Campolongo, F. , Ratto, M. , and Tarantola, S. , 2010, “ Variance Based Sensitivity Analysis of Model Output. Design and Estimator for the Total Sensitivity Index,” Comput. Phys. Commun., 181(2), pp. 259–270. [CrossRef]
Helton, J. C. , and Davis, F. J. , 2003, “ Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses of Complex Systems,” Reliab. Eng. Syst. Saf., 81(1), pp. 23–69. [CrossRef]
McKay, M. D. , Beckman, R. J. , and Conover, W. J. , 1979, “ Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code,” Technometrics, 21(2), pp. 239–245.
Prudencio, E. , and Schulz, K. , 2012, “ The Parallel c++ Statistical Library ‘Queso’: Quantification of Uncertainty for Estimation, Simulation and Optimization,” Euro-Par 2011: Parallel Processing Workshops (Lecture Notes in Computer Science), Vol. 7155, M. Alexander , P. D'Ambra , A. Belloum , G. Bosilca , M. Cannataro , M. Danelutto , B. Martino , M. Gerndt , E. Jeannot , R. Namyst , J. Roman , S. Scott , J. Traff , G. Vallée , and J. Weidendorfer , eds., Springer, Berlin, pp. 398–407. [CrossRef]
Prudencio, E. , and Cheung, S. H. , 2012, “ Parallel Adaptive Multilevel Sampling Algorithms for the Bayesian Analysis of Mathematical Models,” Int. J. Uncertainty Quantif., 2(3), pp. 215–237.
Lagarias, J. C. , Reeds, J. A. , Wright, M. H. , and Wright, P. E. , 1998, “ Convergence Properties of the Nelder–Mead Simplex Method in Low Dimensions,” SIAM J. Optim., 9(1), pp. 112–147. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Computational model as a black-box (input–output). The underlying physics of the fatigue damage model is hidden in order to develop a general uncertainty treatment process.

Grahic Jump Location
Fig. 2

The proposed framework of uncertainty treatment in computational model and observational data. First, the computational fatigue damage model is subjected to sensitivity analysis to determine significant input parameters of the model. Next, using experimental data, the important parameters of model are calibrated. Utilizing statistical inverse methods (Bayesian approach) for model calibration results in encapsulating all the uncertainties due to fatigue test data and inadequacy of the fatigue damage model into the probability distribution function of the model parameters. Finally, the statistically calibrated model is used to make prediction or design decision with quantified uncertainty.

Grahic Jump Location
Fig. 3

Scatterplots illustrating a qualitative sensitivity analysis for the fatigue damage using 1000 Monte Carlo samples of the parameter space

Grahic Jump Location
Fig. 4

Scatterplots illustrating a qualitative sensitivity analysis for the fatigue damage using 1000 Monte Carlo samples of the parameter space

Grahic Jump Location
Fig. 5

Total effect sensitivity index computed using 1000 Monte Carlo samples

Grahic Jump Location
Fig. 6

Comparison between the KDEs of the number of cycles before failure resulting from fatigue damage model for the cases when (S, s) and (E, ν) considered as single (deterministic) values. Results obtained from 2000 Monte Carlo samples of the parameter space according to the distributions are presented in Table 1.

Grahic Jump Location
Fig. 7

(a) Airfoil coupon of Ti6Al4V designed to generate fatigue test data used to calibrate lifetime predictions. (b) Fatigue test coupon instrumented for strain measurements on fatigue rig.

Grahic Jump Location
Fig. 8

Stress analysis of fatigue test coupon including notch agrees with the 35 ksi loading and predicts 99 ksi load in the notch

Grahic Jump Location
Fig. 9

Calibrated material parameters of the fatigue damage model. Posterior marginal density estimation of (a) damage denominator S and (b) damage exponent s.

Grahic Jump Location
Fig. 10

Model prediction of fatigue strength of material (S–N diagram) with R = 0.1: mean values and 95% confidence interval

Grahic Jump Location
Fig. 11

Probability density of the failure cycles under maximum stress of 100 ksi and R = 0.1 applied load and compressive residual plastic strain of 0.193. Results obtained from 100 Monte Carlo samples of posterior distributions of random parameters.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Articles from Part A: Civil Engineering
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In